diff --git a/.gitignore b/.gitignore index ff695f0..f06c106 100644 --- a/.gitignore +++ b/.gitignore @@ -54,6 +54,10 @@ coverage.xml # documentation doc/ +site/ +_doc_mathimg/ +doc.md +doc.htex # PyBuilder target/ diff --git a/README.md b/README.md index 3dcdfe0..73d48b5 100644 --- a/README.md +++ b/README.md @@ -56,6 +56,21 @@ linear systems, ideally with double precision. Install from PyPI with pip: ```bash +pip3 install meanas +``` + +Optional extras: + +- `meanas[test]`: pytest and coverage +- `meanas[docs]`: MkDocs-based documentation toolchain +- `meanas[examples]`: optional runtime dependencies used by the tracked examples +- `meanas[dev]`: the union of `test`, `docs`, and `examples`, plus local lint/docs-publish helpers + +Examples: +```bash +pip3 install 'meanas[test]' +pip3 install 'meanas[docs]' +pip3 install 'meanas[examples]' pip3 install 'meanas[dev]' ``` @@ -80,9 +95,13 @@ source my_venv/bin/activate # Install in-place (-e, editable) from ./meanas, including development dependencies ([dev]) pip3 install --user -e './meanas[dev]' -# Run tests +# Fast local iteration: excludes slower 3D/integration/example-smoke checks cd meanas -python3 -m pytest -rsxX | tee test_results.txt +python3 -m pytest -q -m "not complete" + +# Complete pre-commit confidence run: includes the slower integration tests and +# tracked example smoke tests +python3 -m pytest -q | tee test_results.txt ``` #### See also: @@ -94,6 +113,125 @@ python3 -m pytest -rsxX | tee test_results.txt ## Use -See `examples/` for some simple examples; you may need additional -packages such as [gridlock](https://mpxd.net/code/jan/gridlock) -to run the examples. +`meanas` is a collection of finite-difference electromagnetics tools: + +- `meanas.fdfd`: frequency-domain wave equations, sparse operators, SCPML, and + iterative solves for driven problems. +- `meanas.fdfd.waveguide_2d` / `meanas.fdfd.waveguide_3d`: waveguide mode + solvers, mode-source construction, and overlap windows for port-based + excitation and analysis. +- `meanas.fdtd`: Yee-step updates, CPML boundaries, flux/energy accounting, and + on-the-fly phasor extraction for comparing time-domain runs against FDFD. +- `meanas.fdmath`: low-level finite-difference operators, vectorization helpers, + and derivations shared by the FDTD and FDFD layers. + +For most users, the tracked examples under `examples/` are the right entry +point. The library API is primarily a toolbox; the module docstrings and API +pages are there to document the mathematical conventions and derivations behind +those tools. + +## Documentation + +API and workflow docs are generated from the package docstrings with +[MkDocs](https://www.mkdocs.org/), [Material for MkDocs](https://squidfunk.github.io/mkdocs-material/), +and [mkdocstrings](https://mkdocstrings.github.io/). + +Install the docs toolchain with: + +```bash +pip3 install -e './meanas[docs]' +``` + +Then build the docs site with: + +```bash +./make_docs.sh +``` + +This produces: + +- a normal multi-page site under `site/` +- a combined printable single-page HTML site under `site/print_page/` +- an optional fully inlined `site/standalone.html` when `htmlark` is available + +The docs build uses a local MathJax bundle vendored under `docs/assets/`, so +the rendered HTML does not rely on external services for equation rendering. + +The tracked examples under `examples/` are the intended entry points for users: + +- `examples/fdtd.py`: broadband FDTD pulse excitation, phasor extraction, and a + residual check against the matching FDFD operator. +- `examples/waveguide.py`: waveguide mode solving, unidirectional mode-source + construction, overlap readout, and FDTD/FDFD comparison on a guided structure. +- `examples/waveguide_real.py`: real-valued continuous-wave FDTD on a straight + guide, with late-time monitor slices, guided-core windows, and mode-weighted + errors compared directly against real fields reconstructed from the matching + FDFD solution, plus a guided-mode / orthogonal-residual split. +- `examples/eme.py`: straight-interface mode matching / EME, including port + mode solving, interface scattering, and modal field visualization. +- `examples/eme_bend.py`: straight-to-bent waveguide mode matching with + cylindrical bend modes, interface scattering, and a cascaded bend-network + example built with `scikit-rf`. +- `examples/fdfd.py`: direct frequency-domain waveguide excitation and overlap / + Poynting analysis without a time-domain run. + +Several examples rely on optional packages such as +[gridlock](https://mpxd.net/code/jan/gridlock). + +### Frequency-domain waveguide workflow + +For a structure with a constant cross-section in one direction: + +1. Build `dxes` and the diagonal `epsilon` / `mu` distributions on the Yee grid. +2. Solve the port mode with `meanas.fdfd.waveguide_3d.solve_mode(...)`. +3. Build a unidirectional source with `compute_source(...)`. +4. Build a matching overlap window with `compute_overlap_e(...)`. +5. Solve the full FDFD problem and project the result onto the overlap window or + evaluate plane flux with `meanas.fdfd.functional.poynting_e_cross_h(...)`. + +### Time-domain phasor workflow + +For a broadband or continuous-wave FDTD run: + +1. Advance the fields with `meanas.fdtd.maxwell_e/maxwell_h` or + `updates_with_cpml(...)`. +2. Inject electric current using the same sign convention used throughout the + examples and library: `E -= dt * J / epsilon`. +3. Accumulate the desired phasor with `accumulate_phasor(...)` or the Yee-aware + wrappers `accumulate_phasor_e/h/j(...)`. +4. Build the matching FDFD operator on the stretched `dxes` if CPML/SCPML is + part of the simulation, and compare the extracted phasor to the FDFD field or + residual. + +This is the primary FDTD/FDFD equivalence workflow. The phasor extraction step +filters the time-domain run down to the guided `+\omega` content that FDFD +solves for directly, so it is the cleanest apples-to-apples comparison. + +### Real-field reconstruction workflow + +For a continuous-wave real-valued FDTD run: + +1. Build the analytic source phasor for the structure, for example with + `waveguide_3d.compute_source(...)`. +2. Run the real-valued FDTD simulation using the real part of that source. +3. Solve the matching FDFD problem from the analytic source phasor on the + stretched `dxes`. +4. Reconstruct late real `E/H/J` snapshots with + `reconstruct_real_e/h/j(...)` and compare those directly against the + real-valued FDTD fields, ideally on a monitor window or mode-weighted norm + centered on the guided field rather than on the full transverse plane. When + needed, split the monitor field into guided-mode and orthogonal residual + pieces to see whether the remaining mismatch is actually in the mode or in + weak nonguided tails. + +This is a stricter diagnostic, not the primary equivalence benchmark. A raw +monitor slice contains both the guided field and the remaining orthogonal +content on that plane, + +$$ E_{\text{monitor}} = E_{\text{guided}} + E_{\text{residual}} , $$ + +so its full-plane instantaneous error is naturally noisier than the extracted +phasor comparison even when the underlying guided `+\omega` content matches +well. + +`examples/waveguide_real.py` is the reference implementation of this workflow. diff --git a/docs/api/eigensolvers.md b/docs/api/eigensolvers.md new file mode 100644 index 0000000..7f16e01 --- /dev/null +++ b/docs/api/eigensolvers.md @@ -0,0 +1,3 @@ +# eigensolvers + +::: meanas.eigensolvers diff --git a/docs/api/fdfd.md b/docs/api/fdfd.md new file mode 100644 index 0000000..e47c278 --- /dev/null +++ b/docs/api/fdfd.md @@ -0,0 +1,15 @@ +# fdfd + +::: meanas.fdfd + +## Core operator layers + +::: meanas.fdfd.functional + +::: meanas.fdfd.operators + +::: meanas.fdfd.solvers + +::: meanas.fdfd.scpml + +::: meanas.fdfd.farfield diff --git a/docs/api/fdmath.md b/docs/api/fdmath.md new file mode 100644 index 0000000..3623207 --- /dev/null +++ b/docs/api/fdmath.md @@ -0,0 +1,13 @@ +# fdmath + +::: meanas.fdmath + +## Functional and sparse operators + +::: meanas.fdmath.functional + +::: meanas.fdmath.operators + +::: meanas.fdmath.vectorization + +::: meanas.fdmath.types diff --git a/docs/api/fdtd.md b/docs/api/fdtd.md new file mode 100644 index 0000000..3e1823c --- /dev/null +++ b/docs/api/fdtd.md @@ -0,0 +1,15 @@ +# fdtd + +::: meanas.fdtd + +## Core update and analysis helpers + +::: meanas.fdtd.base + +::: meanas.fdtd.pml + +::: meanas.fdtd.boundaries + +::: meanas.fdtd.energy + +::: meanas.fdtd.phasor diff --git a/docs/api/index.md b/docs/api/index.md new file mode 100644 index 0000000..d30ae80 --- /dev/null +++ b/docs/api/index.md @@ -0,0 +1,14 @@ +# API Overview + +The package is documented directly from its docstrings. The most useful entry +points are: + +- [meanas](meanas.md): top-level package overview +- [eigensolvers](eigensolvers.md): generic eigenvalue utilities used by the mode solvers +- [fdfd](fdfd.md): frequency-domain operators, sources, PML, solvers, and far-field transforms +- [waveguides](waveguides.md): straight, cylindrical, and 3D waveguide mode helpers +- [fdtd](fdtd.md): timestepping, CPML, energy/flux helpers, and phasor extraction +- [fdmath](fdmath.md): shared discrete operators, vectorization helpers, and derivation background + +The waveguide and FDTD pages are the best places to start if you want the +mathematical derivations rather than just the callable reference. diff --git a/docs/api/meanas.md b/docs/api/meanas.md new file mode 100644 index 0000000..d5c5f4e --- /dev/null +++ b/docs/api/meanas.md @@ -0,0 +1,3 @@ +# meanas + +::: meanas diff --git a/docs/api/waveguides.md b/docs/api/waveguides.md new file mode 100644 index 0000000..834614c --- /dev/null +++ b/docs/api/waveguides.md @@ -0,0 +1,7 @@ +# waveguides + +::: meanas.fdfd.waveguide_2d + +::: meanas.fdfd.waveguide_3d + +::: meanas.fdfd.waveguide_cyl diff --git a/docs/assets/vendor/mathjax/core.js b/docs/assets/vendor/mathjax/core.js new file mode 100644 index 0000000..8b9db53 --- /dev/null +++ b/docs/assets/vendor/mathjax/core.js @@ -0,0 +1 @@ +!function(){"use strict";var t,e,r,n,o,i,s,a,l,u,c,p,f,h,d,y,O,M,E,v,b,m,g,L,N,R,T,S,A,C,_,x,I,w,P,j,D,B,k,X,H,W,F,q,J,G,z,V,U,K,$,Y,Z,Q,tt,et,rt,nt,ot,it,st,at,lt,ut,ct,pt,ft,ht,dt,yt,Ot,Mt,Et,vt,bt,mt,gt,Lt={444:function(t,e,r){var n,o=this&&this.__extends||(n=function(t,e){return(n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)Object.prototype.hasOwnProperty.call(e,r)&&(t[r]=e[r])})(t,e)},function(t,e){if("function"!=typeof e&&null!==e)throw new TypeError("Class extends value "+String(e)+" is not a constructor or null");function 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a},i=this&&this.__spreadArray||function(t,e){for(var r=0,o=e.length,n=t.length;r=t.length&&(t=void 0),{value:t&&t[o++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")};Object.defineProperty(e,"__esModule",{value:!0}),e.FontData=e.NOSTRETCH=e.H=e.V=void 0;var s=r(9077);e.V=1,e.H=2,e.NOSTRETCH={dir:0};var l=function(){function t(t){var e,r,l,h;void 0===t&&(t=null),this.variant={},this.delimiters={},this.cssFontMap={},this.remapChars={},this.skewIcFactor=.75;var c=this.constructor;this.options=s.userOptions(s.defaultOptions({},c.OPTIONS),t),this.params=o({},c.defaultParams),this.sizeVariants=i([],n(c.defaultSizeVariants)),this.stretchVariants=i([],n(c.defaultStretchVariants)),this.cssFontMap=o({},c.defaultCssFonts);try{for(var u=a(Object.keys(this.cssFontMap)),p=u.next();!p.done;p=u.next()){var d=p.value;"unknown"===this.cssFontMap[d][0]&&(this.cssFontMap[d][0]=this.options.unknownFamily)}}catch(t){e={error:t}}finally{try{p&&!p.done&&(r=u.return)&&r.call(u)}finally{if(e)throw e.error}}this.cssFamilyPrefix=c.defaultCssFamilyPrefix,this.createVariants(c.defaultVariants),this.defineDelimiters(c.defaultDelimiters);try{for(var f=a(Object.keys(c.defaultChars)),m=f.next();!m.done;m=f.next()){var y=m.value;this.defineChars(y,c.defaultChars[y])}}catch(t){l={error:t}}finally{try{m&&!m.done&&(h=f.return)&&h.call(f)}finally{if(l)throw l.error}}this.defineRemap("accent",c.defaultAccentMap),this.defineRemap("mo",c.defaultMoMap),this.defineRemap("mn",c.defaultMnMap)}return t.charOptions=function(t,e){var r=t[e];return 3===r.length&&(r[3]={}),r[3]},Object.defineProperty(t.prototype,"styles",{get:function(){return this._styles},set:function(t){this._styles=t},enumerable:!1,configurable:!0}),t.prototype.createVariant=function(t,e,r){void 0===e&&(e=null),void 0===r&&(r=null);var o={linked:[],chars:e?Object.create(this.variant[e].chars):{}};r&&this.variant[r]&&(Object.assign(o.chars,this.variant[r].chars),this.variant[r].linked.push(o.chars),o.chars=Object.create(o.chars)),this.remapSmpChars(o.chars,t),this.variant[t]=o},t.prototype.remapSmpChars=function(t,e){var r,o,i,s,l=this.constructor;if(l.VariantSmp[e]){var h=l.SmpRemap,c=[null,null,l.SmpRemapGreekU,l.SmpRemapGreekL];try{for(var u=a(l.SmpRanges),p=u.next();!p.done;p=u.next()){var d=n(p.value,3),f=d[0],m=d[1],y=d[2],v=l.VariantSmp[e][f];if(v){for(var b=m;b<=y;b++)if(930!==b){var x=v+b-m;t[b]=this.smpChar(h[x]||x)}if(c[f])try{for(var g=(i=void 0,a(Object.keys(c[f]).map((function(t){return parseInt(t)})))),M=g.next();!M.done;M=g.next()){t[b=M.value]=this.smpChar(v+c[f][b])}}catch(t){i={error:t}}finally{try{M&&!M.done&&(s=g.return)&&s.call(g)}finally{if(i)throw i.error}}}}}catch(t){r={error:t}}finally{try{p&&!p.done&&(o=u.return)&&o.call(u)}finally{if(r)throw 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padding: 0.1rem 0; +} diff --git a/examples/eme.py b/examples/eme.py new file mode 100644 index 0000000..3a26dc8 --- /dev/null +++ b/examples/eme.py @@ -0,0 +1,221 @@ +""" +Mode-matching / EME example for a straight rib-waveguide interface. + +This example shows the intended user-facing workflow for `meanas.fdfd.eme` on a +simple straight interface: + +1. build two nearby waveguide cross-sections on a Yee grid, +2. solve a small set of guided modes on each side, +3. normalize those modes into E/H port fields, +4. assemble the interface scattering matrix with `meanas.fdfd.eme.get_s(...)`, +5. inspect the dominant modal coupling numerically and visually. +""" + +from __future__ import annotations + +import importlib +from typing import TYPE_CHECKING + +import numpy +from numpy import pi + +import gridlock +from gridlock import Extent + +from meanas.fdfd import eme, waveguide_2d +from meanas.fdmath import unvec + +if TYPE_CHECKING: + from types import ModuleType + + +WL = 1310.0 +DX = 40.0 +WIDTH = 400.0 +THF = 161.0 +THP = 77.0 +EPS_SI = 3.51 ** 2 +EPS_OX = 1.453 ** 2 +MODE_NUMBERS = numpy.array([0]) + + +def require_optional(name: str, package_name: str | None = None) -> ModuleType: + package_name = package_name or name + try: + return importlib.import_module(name) + except ImportError as exc: # pragma: no cover - user environment guard + raise SystemExit( + f"This example requires the optional package '{package_name}'. " + "Install example dependencies with `pip install -e './meanas[examples]'`.", + ) from exc + + +def build_geometry( + *, + dx: float = DX, + width: float = WIDTH, + thf: float = THF, + thp: float = THP, + eps_si: float = EPS_SI, + eps_ox: float = EPS_OX, + ) -> tuple[gridlock.Grid, numpy.ndarray, list[list[numpy.ndarray]], float]: + x0 = (width / 2) % dx + omega = 2 * pi / WL + + grid = gridlock.Grid( + [ + numpy.arange(-800, 800 + dx, dx), + numpy.arange(-400, 400 + dx, dx), + numpy.arange(-2 * dx, 2 * dx + dx, dx), + ], + periodic=True, + ) + epsilon = grid.allocate(eps_ox) + + grid.draw_cuboid( + epsilon, + foreground=eps_si, + x=Extent(center=x0, span=width + 1200), + y=Extent(min=0, max=thf), + z=Extent(min=-1e6, max=0), + ) + grid.draw_cuboid( + epsilon, + foreground=eps_ox, + x=Extent(max=-width / 2, span=300), + y=Extent(min=thp, max=1e6), + z=Extent(min=-1e6, max=0), + ) + grid.draw_cuboid( + epsilon, + foreground=eps_ox, + x=Extent(min=width / 2, span=300), + y=Extent(min=thp, max=1e6), + z=Extent(min=-1e6, max=0), + ) + + grid.draw_cuboid( + epsilon, + foreground=eps_si, + x=Extent(max=-(width / 2 + 600), span=240), + y=Extent(min=0, max=thf), + z=Extent(min=0, max=1e6), + ) + grid.draw_cuboid( + epsilon, + foreground=eps_si, + x=Extent(max=width / 2 + 600, span=240), + y=Extent(min=0, max=thf), + z=Extent(min=0, max=1e6), + ) + + dxes = [grid.dxyz, grid.autoshifted_dxyz()] + dxes_2d = [[d[0], d[1]] for d in dxes] + return grid, epsilon, dxes_2d, omega + + +def solve_cross_section_modes( + epsilon_slice: numpy.ndarray, + *, + omega: float, + dxes_2d: list[list[numpy.ndarray]], + mode_numbers: numpy.ndarray = MODE_NUMBERS, + ) -> tuple[list[tuple[numpy.ndarray, numpy.ndarray]], numpy.ndarray]: + e_xys, wavenumbers = waveguide_2d.solve_modes( + epsilon=epsilon_slice.ravel(), + omega=omega, + dxes=dxes_2d, + mode_numbers=mode_numbers, + ) + eh_fields = [ + waveguide_2d.normalized_fields_e( + e_xy, + wavenumber=wavenumber, + dxes=dxes_2d, + omega=omega, + epsilon=epsilon_slice.ravel(), + ) + for e_xy, wavenumber in zip(e_xys, wavenumbers, strict=True) + ] + return eh_fields, wavenumbers + + +def print_summary(ss: numpy.ndarray, wavenumbers_left: numpy.ndarray, wavenumbers_right: numpy.ndarray, omega: float) -> None: + n_left = len(wavenumbers_left) + left_neff = numpy.real(wavenumbers_left / omega) + right_neff = numpy.real(wavenumbers_right / omega) + + print('left effective indices:', ', '.join(f'{value:.5f}' for value in left_neff[:4])) + print('right effective indices:', ', '.join(f'{value:.5f}' for value in right_neff[:4])) + + reflection = abs(ss[0, 0]) ** 2 + transmission = abs(ss[n_left, 0]) ** 2 + total_output = numpy.sum(abs(ss[:, 0]) ** 2) + print(f'fundamental left-incident reflection |S_00|^2 = {reflection:.6f}') + print(f'fundamental left-to-right transmission |S_{n_left},0|^2 = {transmission:.6f}') + print(f'fundamental left-incident total output power = {total_output:.6f}') + + strongest = numpy.argsort(abs(ss[n_left:, 0]) ** 2)[::-1][:3] + print('dominant transmitted right-side modes for left mode 0:') + for mode_index in strongest: + print(f' mode {mode_index}: |S|^2 = {abs(ss[n_left + mode_index, 0]) ** 2:.6f}') + + +def plot_results( + *, + pyplot: ModuleType, + ss: numpy.ndarray, + left_mode: tuple[numpy.ndarray, numpy.ndarray], + right_mode: tuple[numpy.ndarray, numpy.ndarray], + shape_2d: tuple[int, int], + ) -> None: + fig_s, ax_s = pyplot.subplots() + image = ax_s.imshow(abs(ss) ** 2, origin='lower', cmap='magma') + fig_s.colorbar(image, ax=ax_s) + ax_s.set_title('Interface scattering magnitude |S|^2') + ax_s.set_xlabel('Incident mode index') + ax_s.set_ylabel('Outgoing mode index') + + e_left = unvec(left_mode[0], shape_2d) + e_right = unvec(right_mode[0], shape_2d) + left_intensity = numpy.sum(abs(e_left) ** 2, axis=0).T + right_intensity = numpy.sum(abs(e_right) ** 2, axis=0).T + + fig_modes, axes = pyplot.subplots(1, 2, figsize=(10, 4)) + left_plot = axes[0].imshow(left_intensity, origin='lower', cmap='viridis') + fig_modes.colorbar(left_plot, ax=axes[0]) + axes[0].set_title('Left fundamental mode |E|^2') + right_plot = axes[1].imshow(right_intensity, origin='lower', cmap='viridis') + fig_modes.colorbar(right_plot, ax=axes[1]) + axes[1].set_title('Right fundamental mode |E|^2') + if pyplot.get_backend().lower().endswith('agg'): + pyplot.close(fig_s) + pyplot.close(fig_modes) + else: + pyplot.show() + + +def main() -> None: + pyplot = require_optional('matplotlib.pyplot', package_name='matplotlib') + + grid, epsilon, dxes_2d, omega = build_geometry() + left_slice = epsilon[:, :, :, 1] + right_slice = epsilon[:, :, :, -2] + + left_modes, wavenumbers_left = solve_cross_section_modes(left_slice, omega=omega, dxes_2d=dxes_2d) + right_modes, wavenumbers_right = solve_cross_section_modes(right_slice, omega=omega, dxes_2d=dxes_2d) + + ss = eme.get_s(left_modes, wavenumbers_left, right_modes, wavenumbers_right, dxes=dxes_2d) + + print_summary(ss, wavenumbers_left, wavenumbers_right, omega) + plot_results( + pyplot=pyplot, + ss=ss, + left_mode=left_modes[0], + right_mode=right_modes[0], + shape_2d=grid.shape[:2], + ) + + +if __name__ == '__main__': + main() diff --git a/examples/eme_bend.py b/examples/eme_bend.py new file mode 100644 index 0000000..e5eaebd --- /dev/null +++ b/examples/eme_bend.py @@ -0,0 +1,314 @@ +""" +Mode-matching / EME example for a straight-to-bent waveguide interface. + +This example demonstrates a cylindrical-waveguide EME workflow: + +1. build a rib-waveguide cross-section, +2. solve straight port modes with `waveguide_2d`, +3. solve bend modes with `waveguide_cyl`, +4. assemble the straight-to-bend interface scattering matrix with + `meanas.fdfd.eme.get_s(...)`, +5. optionally cascade a straight section, bend section, and interface pair into + a compact multiport network using `scikit-rf`. +""" + +from __future__ import annotations + +import importlib +from typing import TYPE_CHECKING + +import numpy +from numpy import pi +from scipy import sparse + +import gridlock +from gridlock import Extent + +from meanas.fdfd import eme, waveguide_2d, waveguide_cyl +from meanas.fdmath import unvec + +if TYPE_CHECKING: + from types import ModuleType + + +WL = 1310.0 +DX = 40.0 +RADIUS = 6e3 +WIDTH = 400.0 +THF = 161.0 +THP = 77.0 +EPS_SI = 3.51 ** 2 +EPS_OX = 1.453 ** 2 +MODE_NUMBERS = numpy.array([0]) +STRAIGHT_SECTION_LENGTH = 12e3 +BEND_ANGLE = pi / 2 + + +def require_optional(name: str, package_name: str | None = None) -> ModuleType: + package_name = package_name or name + try: + return importlib.import_module(name) + except ImportError as exc: # pragma: no cover - user environment guard + raise SystemExit( + f"This example requires the optional package '{package_name}'. " + "Install example dependencies with `pip install -e './meanas[examples]'`.", + ) from exc + + +def build_geometry( + *, + dx: float = DX, + width: float = WIDTH, + thf: float = THF, + thp: float = THP, + eps_si: float = EPS_SI, + eps_ox: float = EPS_OX, + ) -> tuple[gridlock.Grid, numpy.ndarray, list[list[numpy.ndarray]], float]: + x0 = (width / 2) % dx + omega = 2 * pi / WL + + grid = gridlock.Grid( + [ + numpy.arange(-800, 800 + dx, dx), + numpy.arange(-400, 400 + dx, dx), + numpy.arange(-2 * dx, 2 * dx + dx, dx), + ], + periodic=True, + ) + epsilon = grid.allocate(eps_ox) + + grid.draw_cuboid( + epsilon, + foreground=eps_si, + x=Extent(center=x0, span=width + 1200), + y=Extent(min=0, max=thf), + z=Extent(min=-1e6, max=0), + ) + grid.draw_cuboid( + epsilon, + foreground=eps_ox, + x=Extent(max=-width / 2, span=300), + y=Extent(min=thp, max=1e6), + z=Extent(min=-1e6, center=0), + ) + grid.draw_cuboid( + epsilon, + foreground=eps_ox, + x=Extent(min=width / 2, span=300), + y=Extent(min=thp, max=1e6), + z=Extent(min=-1e6, center=0), + ) + + dxes = [grid.dxyz, grid.autoshifted_dxyz()] + dxes_2d = [[d[0], d[1]] for d in dxes] + return grid, epsilon, dxes_2d, omega + + +def solve_straight_modes( + epsilon_slice: numpy.ndarray, + *, + omega: float, + dxes_2d: list[list[numpy.ndarray]], + mode_numbers: numpy.ndarray = MODE_NUMBERS, + ) -> tuple[list[tuple[numpy.ndarray, numpy.ndarray]], numpy.ndarray]: + e_xys, wavenumbers = waveguide_2d.solve_modes( + epsilon=epsilon_slice.ravel(), + omega=omega, + dxes=dxes_2d, + mode_numbers=mode_numbers, + ) + eh_fields = [ + waveguide_2d.normalized_fields_e( + e_xy, + wavenumber=wavenumber, + dxes=dxes_2d, + omega=omega, + epsilon=epsilon_slice.ravel(), + ) + for e_xy, wavenumber in zip(e_xys, wavenumbers, strict=True) + ] + return eh_fields, wavenumbers + + +def solve_bend_modes( + epsilon_slice: numpy.ndarray, + *, + omega: float, + dxes_2d: list[list[numpy.ndarray]], + rmin: float, + mode_numbers: numpy.ndarray = MODE_NUMBERS, + ) -> tuple[list[tuple[numpy.ndarray, numpy.ndarray]], numpy.ndarray, numpy.ndarray]: + e_xys, angular_wavenumbers = waveguide_cyl.solve_modes( + epsilon=epsilon_slice.ravel(), + omega=omega, + dxes=dxes_2d, + mode_numbers=mode_numbers, + rmin=rmin, + ) + linear_wavenumbers = waveguide_cyl.linear_wavenumbers( + e_xys=e_xys, + angular_wavenumbers=angular_wavenumbers, + rmin=rmin, + epsilon=epsilon_slice.ravel(), + dxes=dxes_2d, + ) + eh_fields = [ + waveguide_cyl.normalized_fields_e( + e_xy, + angular_wavenumber=angular_wavenumber, + dxes=dxes_2d, + omega=omega, + epsilon=epsilon_slice.ravel(), + rmin=rmin, + ) + for e_xy, angular_wavenumber in zip(e_xys, angular_wavenumbers, strict=True) + ] + return eh_fields, linear_wavenumbers, angular_wavenumbers + + +def build_cascaded_network( + skrf: ModuleType, + *, + interface_s: numpy.ndarray, + straight_wavenumbers: numpy.ndarray, + bend_angular_wavenumbers: numpy.ndarray, + n_modes: int, + ) -> object: + net_sb = skrf.Network(f=[1 / WL], s=interface_s[numpy.newaxis, ...]) + net_bs = net_sb.copy() + net_bs.renumber(numpy.arange(2 * n_modes), numpy.roll(numpy.arange(2 * n_modes), n_modes)) + + straight_phase = sparse.diags_array(numpy.exp(-1j * straight_wavenumbers[:n_modes] * STRAIGHT_SECTION_LENGTH)) + bend_phase = sparse.diags_array(numpy.exp(-1j * bend_angular_wavenumbers[:n_modes] * BEND_ANGLE)) + zero = numpy.zeros((n_modes, n_modes), dtype=complex) + + straight_s = numpy.block([[zero, straight_phase.toarray()], [straight_phase.toarray(), zero]]) + bend_s = numpy.block([[zero, bend_phase.toarray()], [bend_phase.toarray(), zero]]) + net_straight = skrf.Network(f=[1 / WL], s=straight_s[numpy.newaxis, ...]) + net_bend = skrf.Network(f=[1 / WL], s=bend_s[numpy.newaxis, ...]) + + return skrf.network.cascade_list([net_straight, net_sb, net_bend, net_bs, net_straight]) + + +def print_summary( + interface_s: numpy.ndarray, + cascaded_s: numpy.ndarray, + straight_wavenumbers: numpy.ndarray, + bend_linear_wavenumbers: numpy.ndarray, + bend_angular_wavenumbers: numpy.ndarray, + omega: float, + n_modes: int, + ) -> None: + straight_neff = numpy.real(straight_wavenumbers / omega) + bend_neff = numpy.real(bend_linear_wavenumbers / omega) + print('straight effective indices:', ', '.join(f'{value:.5f}' for value in straight_neff[:4])) + print('bend effective indices :', ', '.join(f'{value:.5f}' for value in bend_neff[:4])) + print('bend angular wavenumbers :', ', '.join(f'{value:.5e}' for value in bend_angular_wavenumbers[:4])) + + interface_transmission = abs(interface_s[n_modes, 0]) ** 2 + interface_reflection = abs(interface_s[0, 0]) ** 2 + print(f'interface fundamental transmission |S_{n_modes},0|^2 = {interface_transmission:.6f}') + print(f'interface fundamental reflection |S_00|^2 = {interface_reflection:.6f}') + + total_cascaded_output = numpy.sum(abs(cascaded_s[:, 0]) ** 2) + bend_through = abs(cascaded_s[n_modes, 0]) ** 2 + bend_reflection = abs(cascaded_s[0, 0]) ** 2 + print(f'cascaded bend through power |S_{n_modes},0|^2 = {bend_through:.6f}') + print(f'cascaded bend reflection |S_00|^2 = {bend_reflection:.6f}') + print(f'cascaded left-incident total output power = {total_cascaded_output:.6f}') + + +def plot_results( + *, + pyplot: ModuleType, + interface_s: numpy.ndarray, + cascaded_s: numpy.ndarray, + straight_mode: tuple[numpy.ndarray, numpy.ndarray], + bend_mode: tuple[numpy.ndarray, numpy.ndarray], + shape_2d: tuple[int, int], + ) -> None: + fig_s, axes = pyplot.subplots(1, 2, figsize=(12, 4)) + interface_plot = axes[0].imshow(abs(interface_s) ** 2, origin='lower', cmap='magma') + fig_s.colorbar(interface_plot, ax=axes[0]) + axes[0].set_title('Straight-to-bend interface |S|^2') + axes[0].set_xlabel('Incident mode index') + axes[0].set_ylabel('Outgoing mode index') + + cascaded_plot = axes[1].imshow(abs(cascaded_s) ** 2, origin='lower', cmap='magma') + fig_s.colorbar(cascaded_plot, ax=axes[1]) + axes[1].set_title('Cascaded bend network |S|^2') + axes[1].set_xlabel('Incident mode index') + axes[1].set_ylabel('Outgoing mode index') + + straight_e = unvec(straight_mode[0], shape_2d) + bend_e = unvec(bend_mode[0], shape_2d) + straight_intensity = numpy.sum(abs(straight_e) ** 2, axis=0).T + bend_intensity = numpy.sum(abs(bend_e) ** 2, axis=0).T + + fig_modes, axes_modes = pyplot.subplots(1, 2, figsize=(10, 4)) + straight_plot = axes_modes[0].imshow(straight_intensity, origin='lower', cmap='viridis') + fig_modes.colorbar(straight_plot, ax=axes_modes[0]) + axes_modes[0].set_title('Straight fundamental mode |E|^2') + bend_plot = axes_modes[1].imshow(bend_intensity, origin='lower', cmap='viridis') + fig_modes.colorbar(bend_plot, ax=axes_modes[1]) + axes_modes[1].set_title('Bent fundamental mode |E|^2') + if pyplot.get_backend().lower().endswith('agg'): + pyplot.close(fig_s) + pyplot.close(fig_modes) + else: + pyplot.show() + + +def main() -> None: + pyplot = require_optional('matplotlib.pyplot', package_name='matplotlib') + skrf = require_optional('skrf', package_name='scikit-rf') + + grid, epsilon, dxes_2d, omega = build_geometry() + epsilon_slice = epsilon[:, :, :, 2] + rmin = RADIUS + grid.xyz[0].min() + + straight_modes, straight_wavenumbers = solve_straight_modes(epsilon_slice, omega=omega, dxes_2d=dxes_2d) + bend_modes, bend_linear_wavenumbers, bend_angular_wavenumbers = solve_bend_modes( + epsilon_slice, + omega=omega, + dxes_2d=dxes_2d, + rmin=rmin, + ) + + interface_s = eme.get_s( + straight_modes, + straight_wavenumbers, + bend_modes, + bend_linear_wavenumbers, + dxes=dxes_2d, + ) + cascaded = build_cascaded_network( + skrf, + interface_s=interface_s, + straight_wavenumbers=straight_wavenumbers, + bend_angular_wavenumbers=bend_angular_wavenumbers, + n_modes=len(MODE_NUMBERS), + ) + cascaded_s = cascaded.s[0] + + print_summary( + interface_s, + cascaded_s, + straight_wavenumbers, + bend_linear_wavenumbers, + bend_angular_wavenumbers, + omega, + len(MODE_NUMBERS), + ) + plot_results( + pyplot=pyplot, + interface_s=interface_s, + cascaded_s=cascaded_s, + straight_mode=straight_modes[0], + bend_mode=bend_modes[0], + shape_2d=grid.shape[:2], + ) + + +if __name__ == '__main__': + main() diff --git a/examples/fdfd0.py b/examples/fdfd0.py new file mode 100644 index 0000000..a6227c5 --- /dev/null +++ b/examples/fdfd0.py @@ -0,0 +1,103 @@ +import numpy +from numpy.linalg import norm +from matplotlib import pyplot, colors +import logging + +import meanas +from meanas import fdtd +from meanas.fdmath import vec, unvec +from meanas.fdfd import waveguide_3d, functional, scpml, operators +from meanas.fdfd.solvers import generic as generic_solver + +import gridlock + + +logging.basicConfig(level=logging.DEBUG) +logging.getLogger('matplotlib').setLevel(logging.WARNING) + +__author__ = 'Jan Petykiewicz' + + +def pcolor(ax, v) -> None: + mappable = ax.pcolor(v, cmap='seismic', norm=colors.CenteredNorm()) + ax.axis('equal') + ax.get_figure().colorbar(mappable) + + +def test0(solver=generic_solver): + dx = 50 # discretization (nm/cell) + pml_thickness = 10 # (number of cells) + + wl = 1550 # Excitation wavelength + omega = 2 * numpy.pi / wl + + # Device design parameters + radii = (1, 0.6) + th = 220 + center = [0, 0, 0] + + # refractive indices + n_ring = numpy.sqrt(12.6) # ~Si + n_air = 4.0 # air + + # Half-dimensions of the simulation grid + xyz_max = numpy.array([1.2, 1.2, 0.3]) * 1000 + pml_thickness * dx + + # Coordinates of the edges of the cells. + half_edge_coords = [numpy.arange(dx/2, m + dx, step=dx) for m in xyz_max] + edge_coords = [numpy.hstack((-h[::-1], h)) for h in half_edge_coords] + + # #### Create the grid, mask, and draw the device #### + grid = gridlock.Grid(edge_coords) + epsilon = grid.allocate(n_air**2, dtype=numpy.float32) + grid.draw_cylinder( + epsilon, + h = dict(axis='z', center=center[2], span=th), + radius = max(radii), + center2d = center[:2], + foreground = n_ring ** 2, + num_points = 24, + ) + grid.draw_cylinder( + epsilon, + h = dict(axis='z', center=center[2], span=th * 1.1), + radius = min(radii), + center2d = center[:2], + foreground = n_air ** 2, + num_points = 24, + ) + + dxes = [grid.dxyz, grid.autoshifted_dxyz()] + for a in (0, 1, 2): + for p in (-1, 1): + dxes = meanas.fdfd.scpml.stretch_with_scpml(dxes, axis=a, polarity=p, omega=omega, + thickness=pml_thickness) + + J = [numpy.zeros_like(epsilon[0], dtype=complex) for _ in range(3)] + J[1][15, grid.shape[1]//2, grid.shape[2]//2] = 1 + + + # + # Solve! + # + sim_args = dict( + omega = omega, + dxes = dxes, + epsilon = vec(epsilon), + ) + x = solver(J=vec(J), **sim_args) + + A = operators.e_full(omega, dxes, vec(epsilon)).tocsr() + b = -1j * omega * vec(J) + print('Norm of the residual is ', norm(A @ x - b) / norm(b)) + + E = unvec(x, grid.shape) + + # + # Plot results + # + grid.visualize_slice(E.real, plane=dict(z=0), which_shifts=1, pcolormesh_args=dict(norm=colors.CenteredNorm(), cmap='bwr')) + + +if __name__ == '__main__': + test0() diff --git a/examples/fdfd.py b/examples/fdfd1.py similarity index 52% rename from examples/fdfd.py rename to examples/fdfd1.py index 4612ba0..f983d37 100644 --- a/examples/fdfd.py +++ b/examples/fdfd1.py @@ -1,10 +1,13 @@ import importlib +import logging import numpy from numpy.linalg import norm +from matplotlib import pyplot, colors +import logging import meanas from meanas import fdtd -from meanas.fdmath import vec, unvec +from meanas.fdmath import vec, unvec, fdfield_t from meanas.fdfd import waveguide_3d, functional, scpml, operators from meanas.fdfd.solvers import generic as generic_solver @@ -12,7 +15,6 @@ import gridlock from matplotlib import pyplot -import logging logging.basicConfig(level=logging.DEBUG) logging.getLogger('matplotlib').setLevel(logging.WARNING) @@ -20,82 +22,6 @@ logging.getLogger('matplotlib').setLevel(logging.WARNING) __author__ = 'Jan Petykiewicz' -def test0(solver=generic_solver): - dx = 50 # discretization (nm/cell) - pml_thickness = 10 # (number of cells) - - wl = 1550 # Excitation wavelength - omega = 2 * numpy.pi / wl - - # Device design parameters - radii = (1, 0.6) - th = 220 - center = [0, 0, 0] - - # refractive indices - n_ring = numpy.sqrt(12.6) # ~Si - n_air = 4.0 # air - - # Half-dimensions of the simulation grid - xyz_max = numpy.array([1.2, 1.2, 0.3]) * 1000 + pml_thickness * dx - - # Coordinates of the edges of the cells. - half_edge_coords = [numpy.arange(dx/2, m + dx, step=dx) for m in xyz_max] - edge_coords = [numpy.hstack((-h[::-1], h)) for h in half_edge_coords] - - # #### Create the grid, mask, and draw the device #### - grid = gridlock.Grid(edge_coords) - epsilon = grid.allocate(n_air**2, dtype=numpy.float32) - grid.draw_cylinder(epsilon, - surface_normal=2, - center=center, - radius=max(radii), - thickness=th, - eps=n_ring**2, - num_points=24) - grid.draw_cylinder(epsilon, - surface_normal=2, - center=center, - radius=min(radii), - thickness=th*1.1, - eps=n_air ** 2, - num_points=24) - - dxes = [grid.dxyz, grid.autoshifted_dxyz()] - for a in (0, 1, 2): - for p in (-1, 1): - dxes = meanas.fdfd.scpml.stretch_with_scpml(dxes, axis=a, polarity=p, omega=omega, - thickness=pml_thickness) - - J = [numpy.zeros_like(epsilon[0], dtype=complex) for _ in range(3)] - J[1][15, grid.shape[1]//2, grid.shape[2]//2] = 1 - - - ''' - Solve! - ''' - sim_args = { - 'omega': omega, - 'dxes': dxes, - 'epsilon': vec(epsilon), - } - x = solver(J=vec(J), **sim_args) - - A = operators.e_full(omega, dxes, vec(epsilon)).tocsr() - b = -1j * omega * vec(J) - print('Norm of the residual is ', norm(A @ x - b)) - - E = unvec(x, grid.shape) - - ''' - Plot results - ''' - pyplot.figure() - pyplot.pcolor(numpy.real(E[1][:, :, grid.shape[2]//2]), cmap='seismic') - pyplot.axis('equal') - pyplot.show() - - def test1(solver=generic_solver): dx = 40 # discretization (nm/cell) pml_thickness = 10 # (number of cells) @@ -122,7 +48,7 @@ def test1(solver=generic_solver): # #### Create the grid and draw the device #### grid = gridlock.Grid(edge_coords) epsilon = grid.allocate(n_air**2, dtype=numpy.float32) - grid.draw_cuboid(epsilon, center=center, dimensions=[8e3, w, th], eps=n_wg**2) + grid.draw_cuboid(epsilon, x=dict(center=0, span=8e3), y=dict(center=0, span=w), z=dict(center=0, span=th), foreground=n_wg**2) dxes = [grid.dxyz, grid.autoshifted_dxyz()] for a in (0, 1, 2): @@ -156,22 +82,14 @@ def test1(solver=generic_solver): # grid.draw_cuboid(pmcg, center=[700, 0, 0], dimensions=[80, 1e8, 1e8], eps=1) # grid.visualize_isosurface(pmcg) - def pcolor(v) -> None: - vmax = numpy.max(numpy.abs(v)) - pyplot.pcolor(v, cmap='seismic', vmin=-vmax, vmax=vmax) - pyplot.axis('equal') - pyplot.colorbar() - - ss = (1, slice(None), J.shape[2]//2+6, slice(None)) -# pyplot.figure() -# pcolor(J3[ss].T.imag) -# pyplot.figure() -# pcolor((numpy.abs(J3).sum(axis=2).sum(axis=0) > 0).astype(float).T) + grid.visualize_slice(J.imag, plane=dict(y=6*dx), which_shifts=1, pcolormesh_args=dict(norm=colors.CenteredNorm(), cmap='bwr')) + fig, ax = pyplot.subplots() + ax.pcolormesh((numpy.abs(J).sum(axis=2).sum(axis=0) > 0).astype(float).T, cmap='hot') pyplot.show(block=True) - ''' - Solve! - ''' + # + # Solve! + # sim_args = { 'omega': omega, 'dxes': dxes, @@ -188,20 +106,18 @@ def test1(solver=generic_solver): E = unvec(x, grid.shape) - ''' - Plot results - ''' + # + # Plot results + # center = grid.pos2ind([0, 0, 0], None).astype(int) - pyplot.figure() - pyplot.subplot(2, 2, 1) - pcolor(numpy.real(E[1][center[0], :, :]).T) - pyplot.subplot(2, 2, 2) - pyplot.plot(numpy.log10(numpy.abs(E[1][:, center[1], center[2]]) + 1e-10)) - pyplot.grid(alpha=0.6) - pyplot.ylabel('log10 of field') - pyplot.subplot(2, 2, 3) - pcolor(numpy.real(E[1][:, :, center[2]]).T) - pyplot.subplot(2, 2, 4) + fig, axes = pyplot.subplots(2, 2) + grid.visualize_slice(E.real, plane=dict(x=0), which_shifts=1, ax=axes[0, 0], finalize=False, pcolormesh_args=dict(norm=colors.CenteredNorm(), cmap='bwr')) + grid.visualize_slice(E.real, plane=dict(z=0), which_shifts=1, ax=axes[0, 1], finalize=False, pcolormesh_args=dict(norm=colors.CenteredNorm(), cmap='bwr')) +# pcolor(axes[0, 0], numpy.real(E[1][center[0], :, :]).T) +# pcolor(axes[0, 1], numpy.real(E[1][:, :, center[2]]).T) + axes[1, 0].plot(numpy.log10(numpy.abs(E[1][:, center[1], center[2]]) + 1e-10)) + axes[1, 0].grid(alpha=0.6) + axes[1, 0].set_ylabel('log10 of field') def poyntings(E): H = functional.e2h(omega, dxes)(E) @@ -215,24 +131,28 @@ def test1(solver=generic_solver): return s0, s1, s2 s0x, s1x, s2x = poyntings(E) - pyplot.plot(s0x[0].sum(axis=2).sum(axis=1), label='s0', marker='.') - pyplot.plot(s1x[0].sum(axis=2).sum(axis=1), label='s1', marker='.') - pyplot.plot(s2x[0].sum(axis=2).sum(axis=1), label='s2', marker='.') - pyplot.plot(E[1][:, center[1], center[2]].real.T, label='Ey', marker='x') - pyplot.grid(alpha=0.6) - pyplot.legend() - pyplot.show() + ax = axes[1, 1] + ax.plot(s0x[0].sum(axis=2).sum(axis=1), label='s0', marker='.') + ax.plot(s1x[0].sum(axis=2).sum(axis=1), label='s1', marker='.') + ax.plot(s2x[0].sum(axis=2).sum(axis=1), label='s2', marker='.') + ax.plot(E[1][:, center[1], center[2]].real.T, label='Ey', marker='x') + ax.grid(alpha=0.6) + ax.legend() + + p_in = (-E * J.conj()).sum() / 2 * (dx * dx * dx) + print(f'{p_in=}') q = [] for i in range(-5, 30): e_ovl_rolled = numpy.roll(e_overlap, i, axis=1) - q += [numpy.abs(vec(E) @ vec(e_ovl_rolled).conj())] - pyplot.figure() - pyplot.plot(q, marker='.') - pyplot.grid(alpha=0.6) - pyplot.title('Overlap with mode') - pyplot.show() - print('Average overlap with mode:', sum(q)/len(q)) + q += [numpy.abs(vec(E).conj() @ vec(e_ovl_rolled))] + fig, ax = pyplot.subplots() + ax.plot(q, marker='.') + ax.grid(alpha=0.6) + ax.set_title('Overlap with mode') + print('Average overlap with mode:', sum(q[8:32])/len(q[8:32])) + + pyplot.show(block=True) def module_available(name): @@ -240,9 +160,6 @@ def module_available(name): if __name__ == '__main__': - #test0() -# test1() - if module_available('opencl_fdfd'): from opencl_fdfd import cg_solver as opencl_solver test1(opencl_solver) @@ -253,3 +170,4 @@ if __name__ == '__main__': # test1(magma_solver) else: test1() + diff --git a/examples/fdtd.py b/examples/fdtd.py index 8378b34..fd6026d 100644 --- a/examples/fdtd.py +++ b/examples/fdtd.py @@ -1,18 +1,30 @@ """ -Example code for running an OpenCL FDTD simulation +Example code for a broadband FDTD run with phasor extraction. -See main() for simulation setup. +This script shows the intended low-level workflow for: + +1. building a Yee-grid simulation with CPML on all faces, +2. driving it with an electric-current pulse, +3. extracting a single-frequency phasor on the fly, and +4. checking that phasor against the matching stretched-grid FDFD operator. """ import sys import time +import copy import numpy import h5py +from numpy.linalg import norm from meanas import fdtd from meanas.fdtd import cpml_params, updates_with_cpml -from masque import Pattern, shapes +from meanas.fdtd.misc import gaussian_packet + +from meanas.fdfd.operators import e_full +from meanas.fdfd.scpml import stretch_with_scpml +from meanas.fdmath import vec +from masque import Pattern, Circle, Polygon import gridlock import pcgen @@ -41,50 +53,50 @@ def perturbed_l3(a: float, radius: float, **kwargs) -> Pattern: `masque.Pattern` object containing the L3 design """ - default_args = {'hole_dose': 1, - 'trench_dose': 1, - 'hole_layer': 0, - 'trench_layer': 1, - 'shifts_a': (0.15, 0, 0.075), - 'shifts_r': (1.0, 1.0, 1.0), - 'xy_size': (10, 10), - 'perturbed_radius': 1.1, - 'trench_width': 1.2e3, - } + default_args = { + 'hole_layer': 0, + 'trench_layer': 1, + 'shifts_a': (0.15, 0, 0.075), + 'shifts_r': (1.0, 1.0, 1.0), + 'xy_size': (10, 10), + 'perturbed_radius': 1.1, + 'trench_width': 1.2e3, + } kwargs = {**default_args, **kwargs} - xyr = pcgen.l3_shift_perturbed_defect(mirror_dims=kwargs['xy_size'], - perturbed_radius=kwargs['perturbed_radius'], - shifts_a=kwargs['shifts_a'], - shifts_r=kwargs['shifts_r']) + xyr = pcgen.l3_shift_perturbed_defect( + mirror_dims=kwargs['xy_size'], + perturbed_radius=kwargs['perturbed_radius'], + shifts_a=kwargs['shifts_a'], + shifts_r=kwargs['shifts_r'], + ) xyr *= a xyr[:, 2] *= radius pat = Pattern() - pat.name = f'L3p-a{a:g}r{radius:g}rp{kwargs["perturbed_radius"]:g}' - pat.shapes += [shapes.Circle(radius=r, offset=(x, y), - dose=kwargs['hole_dose'], - layer=kwargs['hole_layer']) - for x, y, r in xyr] + #pat.name = f'L3p-a{a:g}r{radius:g}rp{kwargs["perturbed_radius"]:g}' + pat.shapes[(kwargs['hole_layer'], 0)] += [ + Circle(radius=r, offset=(x, y)) + for x, y, r in xyr] maxes = numpy.max(numpy.fabs(xyr), axis=0) - pat.shapes += [shapes.Polygon.rectangle( - lx=(2 * maxes[0]), ly=kwargs['trench_width'], - offset=(0, s * (maxes[1] + a + kwargs['trench_width'] / 2)), - dose=kwargs['trench_dose'], layer=kwargs['trench_layer']) - for s in (-1, 1)] + pat.shapes[(kwargs['trench_layer'], 0)] += [ + Polygon.rectangle( + lx=(2 * maxes[0]), ly=kwargs['trench_width'], + offset=(0, s * (maxes[1] + a + kwargs['trench_width'] / 2)) + ) + for s in (-1, 1)] return pat -def main(): +def main() -> None: dtype = numpy.float32 - max_t = 8000 # number of timesteps + max_t = 3600 # number of timesteps dx = 40 # discretization (nm/cell) pml_thickness = 8 # (number of cells) wl = 1550 # Excitation wavelength and fwhm - dwl = 200 # Device design parameters xy_size = numpy.array([10, 10]) @@ -107,69 +119,97 @@ def main(): # #### Create the grid, mask, and draw the device #### grid = gridlock.Grid(edge_coords) - epsilon = grid.allocate(n_air**2, dtype=dtype) - grid.draw_slab(epsilon, - surface_normal=2, - center=[0, 0, 0], - thickness=th, - eps=n_slab**2) + epsilon = grid.allocate(n_air ** 2, dtype=dtype) + grid.draw_slab( + epsilon, + slab = dict(axis='z', center=0, span=th), + foreground = n_slab ** 2, + ) + mask = perturbed_l3(a, r) + grid.draw_polygons( + epsilon, + slab = dict(axis='z', center=0, span=2 * th), + foreground = n_air ** 2, + offset2d = (0, 0), + polygons = mask.as_polygons(library=None), + ) - grid.draw_polygons(epsilon, - surface_normal=2, - center=[0, 0, 0], - thickness=2 * th, - eps=n_air**2, - polygons=mask.as_polygons()) + print(f'{grid.shape=}') - print(grid.shape) - - dt = .99/numpy.sqrt(3) - e = [numpy.zeros_like(epsilon[0], dtype=dtype) for _ in range(3)] - h = [numpy.zeros_like(epsilon[0], dtype=dtype) for _ in range(3)] + dt = dx * 0.99 / numpy.sqrt(3) + ee = numpy.zeros_like(epsilon, dtype=complex) + hh = numpy.zeros_like(epsilon, dtype=complex) dxes = [grid.dxyz, grid.autoshifted_dxyz()] # PMLs in every direction - pml_params = [[cpml_params(axis=dd, polarity=pp, dt=dt, - thickness=pml_thickness, epsilon_eff=1.0**2) - for pp in (-1, +1)] - for dd in range(3)] - update_E, update_H = updates_with_cpml(cpml_params=pml_params, dt=dt, - dxes=dxes, epsilon=epsilon) + pml_params = [ + [cpml_params(axis=dd, polarity=pp, dt=dt, thickness=pml_thickness, epsilon_eff=n_air ** 2) + for pp in (-1, +1)] + for dd in range(3)] + update_E, update_H = updates_with_cpml(cpml_params=pml_params, dt=dt, dxes=dxes, epsilon=epsilon, dtype=complex) - # Source parameters and function - w = 2 * numpy.pi * dx / wl - fwhm = dwl * w * w / (2 * numpy.pi * dx) - alpha = (fwhm ** 2) / 8 * numpy.log(2) - delay = 7/numpy.sqrt(2 * alpha) + # sample_interval = numpy.floor(1 / (2 * 1 / wl * dt)).astype(int) + # print(f'Save time interval would be {sample_interval} * dt = {sample_interval * dt:3g}') - def field_source(i): - t0 = i * dt - delay - return numpy.sin(w * t0) * numpy.exp(-alpha * t0**2) + + # Build the pulse directly at the current half-steps and normalize that + # scalar waveform so its extracted temporal phasor is exactly 1 at omega. + source_phasor, _delay = gaussian_packet(wl=wl, dwl=100, dt=dt, turn_on=1e-5) + aa, cc, ss = source_phasor(numpy.arange(max_t) + 0.5) + source_waveform = aa * (cc + 1j * ss) + omega = 2 * numpy.pi / wl + pulse_scale = fdtd.temporal_phasor_scale(source_waveform, omega, dt, offset_steps=0.5)[0] + + j_source = numpy.zeros_like(epsilon, dtype=complex) + j_source[1, *(grid.shape // 2)] = epsilon[1, *(grid.shape // 2)] + jph = numpy.zeros((1, *epsilon.shape), dtype=complex) + eph = numpy.zeros((1, *epsilon.shape), dtype=complex) + hph = numpy.zeros((1, *epsilon.shape), dtype=complex) # #### Run a bunch of iterations #### output_file = h5py.File('simulation_output.h5', 'w') start = time.perf_counter() - for t in range(max_t): - update_E(e, h, epsilon) + for tt in range(max_t): + update_E(ee, hh, epsilon) - e[1][tuple(grid.shape//2)] += field_source(t) - update_H(e, h) + # Electric-current injection uses E -= dt * J / epsilon, which is the + # same sign convention used by the matching FDFD right-hand side. + j_step = pulse_scale * source_waveform[tt] * j_source + ee -= dt * j_step / epsilon + update_H(ee, hh) - avg_rate = (t + 1)/(time.perf_counter() - start)) - print(f'iteration {t}: average {avg_rate} iterations per sec') + avg_rate = (tt + 1) / (time.perf_counter() - start) sys.stdout.flush() - if t % 20 == 0: - r = sum([(f * f * e).sum() for f, e in zip(e, epsilon)]) - print('E sum', r) + if tt % 200 == 0: + print(f'iteration {tt}: average {avg_rate} iterations per sec') + E_energy_sum = (ee.conj() * ee * epsilon).sum().real + print(f'{E_energy_sum=}') # Save field slices - if (t % 20 == 0 and (max_t - t <= 1000 or t <= 2000)) or t == max_t-1: - print('saving E-field') - for j, f in enumerate(e): - output_file['/E{}_t{}'.format('xyz'[j], t)] = f[:, :, round(f.shape[2]/2)] + if (tt % 20 == 0 and (max_t - tt <= 1000 or tt <= 2000)) or tt == max_t - 1: + print(f'saving E-field at iteration {tt}') + output_file[f'/E_t{tt}'] = ee[:, :, :, ee.shape[3] // 2] + + fdtd.accumulate_phasor_j(jph, omega, dt, j_step, tt) + fdtd.accumulate_phasor_e(eph, omega, dt, ee, tt + 1) + fdtd.accumulate_phasor_h(hph, omega, dt, hh, tt + 1) + + Eph = eph[0] + Jph = jph[0] + b = -1j * omega * Jph + dxes_fdfd = copy.deepcopy(dxes) + for pp in (-1, +1): + for dd in range(3): + stretch_with_scpml(dxes_fdfd, axis=dd, polarity=pp, omega=omega, epsilon_effective=n_air ** 2, thickness=pml_thickness) + # Compare the extracted phasor to the FDFD operator on the stretched grid, + # not the unstretched Yee spacings used by the raw time-domain update. + A = e_full(omega=omega, dxes=dxes_fdfd, epsilon=epsilon) + residual = norm(A @ vec(Eph) - vec(b)) / norm(vec(b)) + print(f'FDFD residual is {residual}') + if __name__ == '__main__': main() diff --git a/examples/waveguide.py b/examples/waveguide.py new file mode 100644 index 0000000..f243924 --- /dev/null +++ b/examples/waveguide.py @@ -0,0 +1,342 @@ +""" +Example code for guided-wave FDFD and FDTD comparison. + +This example is the reference workflow for: + +1. solving a waveguide port mode, +2. turning that mode into a one-sided source and overlap window, +3. comparing a direct FDFD solve against a time-domain phasor extracted from FDTD. +""" +from typing import Callable +import logging +import time +import copy + +import numpy +import h5py +from numpy.linalg import norm + +import gridlock +import meanas +from meanas import fdtd, fdfd +from meanas.fdtd import cpml_params, updates_with_cpml +from meanas.fdtd.misc import gaussian_packet + +from meanas.fdmath import vec, unvec, vcfdfield_t, cfdfield_t, fdfield_t, dx_lists_t +from meanas.fdfd import waveguide_3d, functional, scpml, operators +from meanas.fdfd.solvers import generic as generic_solver +from meanas.fdfd.operators import e_full +from meanas.fdfd.scpml import stretch_with_scpml + + +logging.basicConfig(level=logging.DEBUG) +for pp in ('matplotlib', 'PIL'): + logging.getLogger(pp).setLevel(logging.WARNING) + +logger = logging.getLogger(__name__) + + +def pcolor(vv, fig=None, ax=None) -> None: + if fig is None: + assert ax is None + fig, ax = pyplot.subplots() + mb = ax.pcolor(vv, cmap='seismic', norm=colors.CenteredNorm()) + fig.colorbar(mb) + ax.set_aspect('equal') + + +def draw_grid( + *, + dx: float, + pml_thickness: int, + n_wg: float = 3.476, # Si index @ 1550 + n_cladding: float = 1.00, # Air index + wg_w: float = 400, + wg_th: float = 200, + ) -> tuple[gridlock.Grid, fdfield_t]: + """ Create the grid and draw the device """ + # Half-dimensions of the simulation grid + xyz_max = numpy.array([800, 900, 600]) + (pml_thickness + 2) * dx + + # Coordinates of the edges of the cells. + half_edge_coords = [numpy.arange(dx / 2, m + dx / 2, step=dx) for m in xyz_max] + edge_coords = [numpy.hstack((-h[::-1], h)) for h in half_edge_coords] + + grid = gridlock.Grid(edge_coords) + epsilon = grid.allocate(n_cladding**2, dtype=numpy.float32) + grid.draw_cuboid( + epsilon, + x = dict(center=0, span=8e3), + y = dict(center=0, span=wg_w), + z = dict(center=0, span=wg_th), + foreground = n_wg ** 2, + ) + + return grid, epsilon + + +def get_waveguide_mode( + *, + grid: gridlock.Grid, + dxes: dx_lists_t, + omega: float, + epsilon: fdfield_t, + ) -> tuple[vcfdfield_t, vcfdfield_t]: + """Create a mode source and overlap window for one forward-going port.""" + dims = numpy.array([[-10, -20, -15], + [-10, 20, 15]]) * [[numpy.median(numpy.real(dx)) for dx in dxes[0]]] + ind_dims = (grid.pos2ind(dims[0], which_shifts=None).astype(int), + grid.pos2ind(dims[1], which_shifts=None).astype(int)) + wg_args = dict( + slices = [slice(i, f+1) for i, f in zip(*ind_dims)], + dxes = dxes, + axis = 0, + polarity = +1, + ) + + wg_results = waveguide_3d.solve_mode(mode_number=0, omega=omega, epsilon=epsilon, **wg_args) + J = waveguide_3d.compute_source(E=wg_results['E'], wavenumber=wg_results['wavenumber'], + omega=omega, epsilon=epsilon, **wg_args) + + # compute_overlap_e() returns the normalized upstream overlap window used to + # project another field onto this same guided mode. + e_overlap = waveguide_3d.compute_overlap_e(E=wg_results['E'], wavenumber=wg_results['wavenumber'], **wg_args) + return J, e_overlap + + +def main( + *, + solver: Callable = generic_solver, + dx: float = 40, # discretization (nm / cell) + pml_thickness: int = 10, # (number of cells) + wl: float = 1550, # Excitation wavelength + wg_w: float = 600, # Waveguide width + wg_th: float = 220, # Waveguide thickness + ): + omega = 2 * numpy.pi / wl + + grid, epsilon = draw_grid(dx=dx, pml_thickness=pml_thickness) + + # Add SCPML stretching to the FDFD grid; this matches the CPML-backed FDTD + # run below so the two solvers see the same absorbing boundary profile. + dxes = [grid.dxyz, grid.autoshifted_dxyz()] + for a in (0, 1, 2): + for p in (-1, 1): + dxes = scpml.stretch_with_scpml(dxes, omega=omega, axis=a, polarity=p, thickness=pml_thickness) + + + J, e_overlap = get_waveguide_mode(grid=grid, dxes=dxes, omega=omega, epsilon=epsilon) + + + pecg = numpy.zeros_like(epsilon) + # pecg.draw_cuboid(pecg, center=[700, 0, 0], dimensions=[80, 1e8, 1e8], eps=1) + # pecg.visualize_isosurface(pecg) + + pmcg = numpy.zeros_like(epsilon) + # grid.draw_cuboid(pmcg, center=[700, 0, 0], dimensions=[80, 1e8, 1e8], eps=1) + # grid.visualize_isosurface(pmcg) + + +# ss = (1, slice(None), J.shape[2]//2+6, slice(None)) +# pcolor(J3[ss].T.imag) +# pcolor((numpy.abs(J3).sum(axis=(0, 2)) > 0).astype(float).T) +# pyplot.show(block=True) + + E_fdfd = fdfd_solve( + omega = omega, + dxes = dxes, + epsilon = epsilon, + J = J, + pec = pecg, + pmc = pmcg, + ) + + + # + # Plot results + # + center = grid.pos2ind([0, 0, 0], None).astype(int) + fig, axes = pyplot.subplots(2, 2) + pcolor(numpy.real(E[1][center[0], :, :]).T, fig=fig, ax=axes[0, 0]) + axes[0, 1].plot(numpy.log10(numpy.abs(E[1][:, center[1], center[2]]) + 1e-10)) + axes[0, 1].grid(alpha=0.6) + axes[0, 1].set_ylabel('log10 of field') + pcolor(numpy.real(E[1][:, :, center[2]]).T, fig=fig, ax=axes[1, 0]) + + def poyntings(E): + H = functional.e2h(omega, dxes)(E) + poynting = fdtd.poynting(e=E, h=H.conj(), dxes=dxes) + cross1 = operators.poynting_e_cross(vec(E), dxes) @ vec(H).conj() + cross2 = operators.poynting_h_cross(vec(H), dxes) @ vec(E).conj() * -1 + s1 = 0.5 * unvec(numpy.real(cross1), grid.shape) + s2 = 0.5 * unvec(numpy.real(cross2), grid.shape) + s0 = 0.5 * poynting.real +# s2 = poynting.imag + return s0, s1, s2 + + s0x, s1x, s2x = poyntings(E) + axes[1, 1].plot(s0x[0].sum(axis=2).sum(axis=1), label='s0', marker='.') + axes[1, 1].plot(s1x[0].sum(axis=2).sum(axis=1), label='s1', marker='.') + axes[1, 1].plot(s2x[0].sum(axis=2).sum(axis=1), label='s2', marker='.') + axes[1, 1].plot(E[1][:, center[1], center[2]].real.T, label='Ey', marker='x') + axes[1, 1].grid(alpha=0.6) + axes[1, 1].legend() + + q = [] + for i in range(-5, 30): + e_ovl_rolled = numpy.roll(e_overlap, i, axis=1) + q += [numpy.abs(vec(E) @ vec(e_ovl_rolled).conj())] + fig, ax = pyplot.subplots() + ax.plot(q, marker='.') + ax.grid(alpha=0.6) + ax.set_title('Overlap with mode') + + logger.info('Average overlap with mode:', sum(q[8:32]) / len(q[8:32])) + + pyplot.show(block=True) + + +def fdfd_solve( + *, + omega: float, + dxes = dx_lists_t, + epsilon: fdfield_t, + J: cfdfield_t, + pec: fdfield_t, + pmc: fdfield_t, + ) -> cfdfield_t: + """ Construct and run the solve """ + sim_args = dict( + omega = omega, + dxes = dxes, + epsilon = vec(epsilon), + pec = vec(pecg), + pmc = vec(pmcg), + ) + + x = solver(J=vec(J), **sim_args) + + b = -1j * omega * vec(J) + A = operators.e_full(**sim_args).tocsr() + logger.info('Norm of the residual is ', norm(A @ x - b) / norm(b)) + + E = unvec(x, epsilon.shape[1:]) + return E + + +def main2(): + dtype = numpy.float32 + max_t = 3600 # number of timesteps + + dx = 40 # discretization (nm/cell) + pml_thickness = 8 # (number of cells) + + wl = 1550 # Excitation wavelength and fwhm + dwl = 100 + + # Device design parameters + xy_size = numpy.array([10, 10]) + a = 430 + r = 0.285 + th = 170 + + # refractive indices + n_slab = 3.408 # InGaAsP(80, 50) @ 1550nm + n_cladding = 1.0 # air + + # Half-dimensions of the simulation grid + xy_max = (xy_size + 1) * a * [1, numpy.sqrt(3)/2] + z_max = 1.6 * a + xyz_max = numpy.hstack((xy_max, z_max)) + pml_thickness * dx + + # Coordinates of the edges of the cells. The fdtd package can only do square grids at the moment. + half_edge_coords = [numpy.arange(dx/2, m + dx, step=dx) for m in xyz_max] + edge_coords = [numpy.hstack((-h[::-1], h)) for h in half_edge_coords] + + # #### Create the grid, mask, and draw the device #### + grid = gridlock.Grid(edge_coords) + epsilon = grid.allocate(n_cladding ** 2, dtype=dtype) + grid.draw_slab( + epsilon, + slab = dict(axis='z', center=0, span=th), + foreground = n_slab ** 2, + ) + + + print(f'{grid.shape=}') + + dt = dx * 0.99 / numpy.sqrt(3) + ee = numpy.zeros_like(epsilon, dtype=complex) + hh = numpy.zeros_like(epsilon, dtype=complex) + + dxes = [grid.dxyz, grid.autoshifted_dxyz()] + + # PMLs in every direction + pml_params = [ + [cpml_params(axis=dd, polarity=pp, dt=dt, thickness=pml_thickness, epsilon_eff=n_cladding ** 2) + for pp in (-1, +1)] + for dd in range(3)] + update_E, update_H = updates_with_cpml(cpml_params=pml_params, dt=dt, dxes=dxes, epsilon=epsilon, dtype=complex) + + # sample_interval = numpy.floor(1 / (2 * 1 / wl * dt)).astype(int) + # print(f'Save time interval would be {sample_interval} * dt = {sample_interval * dt:3g}') + + + # Sample the pulse at the current half-steps and normalize that scalar + # waveform so the extracted temporal phasor is exactly 1 at omega. + source_phasor, _delay = gaussian_packet(wl=wl, dwl=100, dt=dt, turn_on=1e-5) + aa, cc, ss = source_phasor(numpy.arange(max_t) + 0.5) + source_waveform = aa * (cc + 1j * ss) + omega = 2 * numpy.pi / wl + pulse_scale = fdtd.temporal_phasor_scale(source_waveform, omega, dt, offset_steps=0.5)[0] + + j_source = numpy.zeros_like(epsilon, dtype=complex) + j_source[1, *(grid.shape // 2)] = epsilon[1, *(grid.shape // 2)] + jph = numpy.zeros((1, *epsilon.shape), dtype=complex) + eph = numpy.zeros((1, *epsilon.shape), dtype=complex) + hph = numpy.zeros((1, *epsilon.shape), dtype=complex) + + # #### Run a bunch of iterations #### + output_file = h5py.File('simulation_output.h5', 'w') + start = time.perf_counter() + for tt in range(max_t): + update_E(ee, hh, epsilon) + + # Electric-current injection uses E -= dt * J / epsilon, which is the + # sign convention matched by the FDFD source term -1j * omega * J. + j_step = pulse_scale * source_waveform[tt] * j_source + ee -= dt * j_step / epsilon + update_H(ee, hh) + + avg_rate = (tt + 1) / (time.perf_counter() - start) + + if tt % 200 == 0: + print(f'iteration {tt}: average {avg_rate} iterations per sec') + E_energy_sum = (ee.conj() * ee * epsilon).sum().real + print(f'{E_energy_sum=}') + + # Save field slices + if (tt % 20 == 0 and (max_t - tt <= 1000 or tt <= 2000)) or tt == max_t - 1: + print(f'saving E-field at iteration {tt}') + output_file[f'/E_t{tt}'] = ee[:, :, :, ee.shape[3] // 2] + + fdtd.accumulate_phasor_j(jph, omega, dt, j_step, tt) + fdtd.accumulate_phasor_e(eph, omega, dt, ee, tt + 1) + fdtd.accumulate_phasor_h(hph, omega, dt, hh, tt + 1) + + Eph = eph[0] + Jph = jph[0] + b = -1j * omega * Jph + dxes_fdfd = copy.deepcopy(dxes) + for pp in (-1, +1): + for dd in range(3): + stretch_with_scpml(dxes_fdfd, axis=dd, polarity=pp, omega=omega, epsilon_effective=n_cladding ** 2, thickness=pml_thickness) + # Residuals must be checked on the stretched FDFD grid, because the FDTD run + # already includes those same absorbing layers through CPML. + A = e_full(omega=omega, dxes=dxes_fdfd, epsilon=epsilon) + residual = norm(A @ vec(Eph) - vec(b)) / norm(vec(b)) + print(f'FDFD residual is {residual}') + + +if __name__ == '__main__': + main() diff --git a/examples/waveguide_real.py b/examples/waveguide_real.py new file mode 100644 index 0000000..03a20ac --- /dev/null +++ b/examples/waveguide_real.py @@ -0,0 +1,219 @@ +""" +Real-valued straight-waveguide FDTD/FDFD comparison. + +This example shows the user-facing "compare real FDTD against reconstructed real +FDFD" workflow: + +1. build a straight waveguide on a uniform Yee grid, +2. drive it with a real-valued continuous-wave mode source, +3. solve the matching FDFD problem from the analytic source phasor, and +4. compare late real monitor slices against `fdtd.reconstruct_real_e/h(...)`. + +Unlike the phasor-based examples, this script does not use extracted phasors as +the main output. It is a stricter diagnostic: the comparison target is the raw +real field itself, with full-plane, mode-weighted, guided-mode, and orthogonal- +residual errors reported. Strong phasor agreement can coexist with visibly +larger raw-snapshot error because the latter includes weak nonguided tails on +the monitor plane. +""" + +import numpy + +from meanas import fdfd, fdtd +from meanas.fdfd import functional, scpml, waveguide_3d +from meanas.fdmath import vec, unvec + + +DT = 0.25 +PERIOD_STEPS = 64 +OMEGA = 2 * numpy.pi / (PERIOD_STEPS * DT) +CPML_THICKNESS = 3 +SHAPE = (3, 37, 13, 13) +SOURCE_SLICES = (slice(5, 6), slice(None), slice(None)) +MONITOR_SLICES = (slice(30, 31), slice(None), slice(None)) +WARMUP_PERIODS = 16 +SOURCE_PHASE = 0.4 +CORE_SLICES = (slice(None), slice(None), slice(4, 9), slice(4, 9)) + + +def build_uniform_dxes(shape: tuple[int, int, int, int]) -> list[list[numpy.ndarray]]: + return [[numpy.ones(shape[axis + 1]) for axis in range(3)] for _ in range(2)] + + +def build_epsilon(shape: tuple[int, int, int, int]) -> numpy.ndarray: + epsilon = numpy.ones(shape, dtype=float) + y0 = (shape[2] - 3) // 2 + z0 = (shape[3] - 3) // 2 + epsilon[:, :, y0:y0 + 3, z0:z0 + 3] = 12.0 + return epsilon + + +def build_stretched_dxes(base_dxes: list[list[numpy.ndarray]]) -> list[list[numpy.ndarray]]: + stretched_dxes = [[dx.copy() for dx in group] for group in base_dxes] + for axis in (0, 1, 2): + for polarity in (-1, 1): + stretched_dxes = scpml.stretch_with_scpml( + stretched_dxes, + axis=axis, + polarity=polarity, + omega=OMEGA, + epsilon_effective=1.0, + thickness=CPML_THICKNESS, + ) + return stretched_dxes + + +def build_cpml_params() -> list[list[dict[str, numpy.ndarray | float]]]: + return [ + [fdtd.cpml_params(axis=axis, polarity=polarity, dt=DT, thickness=CPML_THICKNESS, epsilon_eff=1.0) + for polarity in (-1, 1)] + for axis in range(3) + ] + + +def weighted_rel_err(observed: numpy.ndarray, reference: numpy.ndarray, weight: numpy.ndarray) -> float: + return numpy.linalg.norm((observed - reference) * weight) / numpy.linalg.norm(reference * weight) + + +def project_onto_mode(observed: numpy.ndarray, mode: numpy.ndarray) -> tuple[complex, numpy.ndarray, numpy.ndarray]: + coefficient = numpy.vdot(mode, observed) / numpy.vdot(mode, mode) + guided = coefficient * mode + residual = observed - guided + return coefficient, guided, residual + + +def main() -> None: + epsilon = build_epsilon(SHAPE) + base_dxes = build_uniform_dxes(SHAPE) + stretched_dxes = build_stretched_dxes(base_dxes) + + source_mode = waveguide_3d.solve_mode( + 0, + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=1, + slices=SOURCE_SLICES, + epsilon=epsilon, + ) + j_mode = waveguide_3d.compute_source( + E=source_mode['E'], + wavenumber=source_mode['wavenumber'], + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=1, + slices=SOURCE_SLICES, + epsilon=epsilon, + ) + # A small global phase aligns the real-valued source with the late-cycle + # raw-snapshot diagnostic. The underlying phasor problem is unchanged. + j_mode *= numpy.exp(1j * SOURCE_PHASE) + monitor_mode = waveguide_3d.solve_mode( + 0, + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=1, + slices=MONITOR_SLICES, + epsilon=epsilon, + ) + e_weight = numpy.abs(monitor_mode['E'][:, MONITOR_SLICES[0], :, :]) + h_weight = numpy.abs(monitor_mode['H'][:, MONITOR_SLICES[0], :, :]) + e_mode = monitor_mode['E'][:, MONITOR_SLICES[0], :, :] + h_mode = monitor_mode['H'][:, MONITOR_SLICES[0], :, :] + + e_fdfd = unvec( + fdfd.solvers.generic( + J=vec(j_mode), + omega=OMEGA, + dxes=stretched_dxes, + epsilon=vec(epsilon), + matrix_solver_opts={'atol': 1e-10, 'rtol': 1e-7}, + ), + SHAPE[1:], + ) + h_fdfd = functional.e2h(OMEGA, stretched_dxes)(e_fdfd) + + update_e, update_h = fdtd.updates_with_cpml( + cpml_params=build_cpml_params(), + dt=DT, + dxes=base_dxes, + epsilon=epsilon, + ) + + e_field = numpy.zeros_like(epsilon) + h_field = numpy.zeros_like(epsilon) + total_steps = (WARMUP_PERIODS + 1) * PERIOD_STEPS + e_errors: list[float] = [] + h_errors: list[float] = [] + e_core_errors: list[float] = [] + h_core_errors: list[float] = [] + e_weighted_errors: list[float] = [] + h_weighted_errors: list[float] = [] + e_guided_errors: list[float] = [] + h_guided_errors: list[float] = [] + e_residual_errors: list[float] = [] + h_residual_errors: list[float] = [] + + for step in range(total_steps): + update_e(e_field, h_field, epsilon) + + # Real-valued FDTD uses the real part of the analytic mode source. + t_half = (step + 0.5) * DT + j_real = (j_mode.real * numpy.cos(OMEGA * t_half) - j_mode.imag * numpy.sin(OMEGA * t_half)).real + e_field -= DT * j_real / epsilon + + update_h(e_field, h_field) + + if step >= total_steps - PERIOD_STEPS // 4: + reconstructed_e = fdtd.reconstruct_real_e( + e_fdfd[:, MONITOR_SLICES[0], :, :], + OMEGA, + DT, + step + 1, + ) + reconstructed_h = fdtd.reconstruct_real_h( + h_fdfd[:, MONITOR_SLICES[0], :, :], + OMEGA, + DT, + step + 1, + ) + + e_monitor = e_field[:, MONITOR_SLICES[0], :, :] + h_monitor = h_field[:, MONITOR_SLICES[0], :, :] + e_errors.append(numpy.linalg.norm(e_monitor - reconstructed_e) / numpy.linalg.norm(reconstructed_e)) + h_errors.append(numpy.linalg.norm(h_monitor - reconstructed_h) / numpy.linalg.norm(reconstructed_h)) + e_core_errors.append( + numpy.linalg.norm(e_monitor[CORE_SLICES] - reconstructed_e[CORE_SLICES]) + / numpy.linalg.norm(reconstructed_e[CORE_SLICES]), + ) + h_core_errors.append( + numpy.linalg.norm(h_monitor[CORE_SLICES] - reconstructed_h[CORE_SLICES]) + / numpy.linalg.norm(reconstructed_h[CORE_SLICES]), + ) + e_weighted_errors.append(weighted_rel_err(e_monitor, reconstructed_e, e_weight)) + h_weighted_errors.append(weighted_rel_err(h_monitor, reconstructed_h, h_weight)) + e_guided_coeff, _, e_residual = project_onto_mode(e_monitor, e_mode) + e_guided_coeff_ref, _, e_residual_ref = project_onto_mode(reconstructed_e, e_mode) + h_guided_coeff, _, h_residual = project_onto_mode(h_monitor, h_mode) + h_guided_coeff_ref, _, h_residual_ref = project_onto_mode(reconstructed_h, h_mode) + e_guided_errors.append(abs(e_guided_coeff - e_guided_coeff_ref) / abs(e_guided_coeff_ref)) + h_guided_errors.append(abs(h_guided_coeff - h_guided_coeff_ref) / abs(h_guided_coeff_ref)) + e_residual_errors.append(numpy.linalg.norm(e_residual - e_residual_ref) / numpy.linalg.norm(e_residual_ref)) + h_residual_errors.append(numpy.linalg.norm(h_residual - h_residual_ref) / numpy.linalg.norm(h_residual_ref)) + + print(f'late-cycle monitor E errors: min={min(e_errors):.4f} max={max(e_errors):.4f}') + print(f'late-cycle monitor H errors: min={min(h_errors):.4f} max={max(h_errors):.4f}') + print(f'late-cycle core-window E errors: min={min(e_core_errors):.4f} max={max(e_core_errors):.4f}') + print(f'late-cycle core-window H errors: min={min(h_core_errors):.4f} max={max(h_core_errors):.4f}') + print(f'late-cycle mode-weighted E errors: min={min(e_weighted_errors):.4f} max={max(e_weighted_errors):.4f}') + print(f'late-cycle mode-weighted H errors: min={min(h_weighted_errors):.4f} max={max(h_weighted_errors):.4f}') + print(f'late-cycle guided-mode E coefficient errors: min={min(e_guided_errors):.4f} max={max(e_guided_errors):.4f}') + print(f'late-cycle guided-mode H coefficient errors: min={min(h_guided_errors):.4f} max={max(h_guided_errors):.4f}') + print(f'late-cycle orthogonal-residual E errors: min={min(e_residual_errors):.4f} max={max(e_residual_errors):.4f}') + print(f'late-cycle orthogonal-residual H errors: min={min(h_residual_errors):.4f} max={max(h_residual_errors):.4f}') + + +if __name__ == '__main__': + main() diff --git a/make_docs.sh b/make_docs.sh index 6d99b5f..6bda9d9 100755 --- a/make_docs.sh +++ b/make_docs.sh @@ -2,18 +2,20 @@ set -Eeuo pipefail -cd ~/projects/meanas +ROOT="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)" +cd "$ROOT" -# Approach 1: pdf to html? -#pdoc3 --pdf --force --template-dir pdoc_templates -o doc . | \ -# pandoc --metadata=title:"meanas" --toc --toc-depth=4 --from=markdown+abbreviations --to=html --output=doc.html --gladtex -s - +DOCS_TMP="$(mktemp -d)" +cleanup() { + rm -rf "$DOCS_TMP" +} +trap cleanup EXIT -# Approach 2: pdf to html with gladtex -rm -rf _doc_mathimg -pdoc --pdf --force --template-dir pdoc_templates -o doc . > doc.md -pandoc --metadata=title:"meanas" --from=markdown+abbreviations --to=html --output=doc.htex --gladtex -s --css pdoc_templates/pdoc.css doc.md -gladtex -a -n -d _doc_mathimg -c white -b black doc.htex +python3 "$ROOT/scripts/prepare_docs_sources.py" "$ROOT/meanas" "$DOCS_TMP" -# Approach 3: html with gladtex -#pdoc3 --html --force --template-dir pdoc_templates -o doc . -#find doc -iname '*.html' -exec gladtex -a -n -d _mathimg -c white {} \; +MKDOCSTRINGS_PYTHON_PATH="$DOCS_TMP" mkdocs build --clean + +PRINT_PAGE='site/print_page/index.html' +if [[ -f "$PRINT_PAGE" ]] && command -v htmlark >/dev/null 2>&1; then + htmlark "$PRINT_PAGE" -o site/standalone.html +fi diff --git a/meanas/__init__.py b/meanas/__init__.py index 354adc9..9d1b401 100644 --- a/meanas/__init__.py +++ b/meanas/__init__.py @@ -1,18 +1,19 @@ """ Electromagnetic simulation tools -See the readme or `import meanas; help(meanas)` for more info. +See the tracked examples for end-to-end workflows, and `help(meanas)` for the +toolbox overview and API derivations. """ import pathlib -__version__ = '0.9' +__version__ = '0.12' __author__ = 'Jan Petykiewicz' try: - with open(pathlib.Path(__file__).parent / 'README.md', 'r') as f: + readme_path = pathlib.Path(__file__).parent / 'README.md' + with readme_path.open('r') as f: __doc__ = f.read() except Exception: pass - diff --git a/meanas/eigensolvers.py b/meanas/eigensolvers.py index ac64f5c..98e7a15 100644 --- a/meanas/eigensolvers.py +++ b/meanas/eigensolvers.py @@ -1,12 +1,12 @@ """ Solvers for eigenvalue / eigenvector problems """ -from typing import Callable +from collections.abc import Callable import numpy from numpy.typing import NDArray, ArrayLike from numpy.linalg import norm -from scipy import sparse # type: ignore -import scipy.sparse.linalg as spalg # type: ignore +from scipy import sparse +import scipy.sparse.linalg as spalg def power_iteration( @@ -25,8 +25,9 @@ def power_iteration( Returns: (Largest-magnitude eigenvalue, Corresponding eigenvector estimate) """ + rng = numpy.random.default_rng() if guess_vector is None: - v = numpy.random.rand(operator.shape[0]) + 1j * numpy.random.rand(operator.shape[0]) + v = rng.random(operator.shape[0]) + 1j * rng.random(operator.shape[0]) else: v = guess_vector @@ -63,10 +64,10 @@ def rayleigh_quotient_iteration( (eigenvalues, eigenvectors) """ try: - (operator - sparse.eye(operator.shape[0])) + (operator - sparse.eye_array(operator.shape[0])) - def shift(eigval: float) -> sparse: - return eigval * sparse.eye(operator.shape[0]) + def shift(eigval: float) -> sparse.sparray: + return eigval * sparse.eye_array(operator.shape[0]) if solver is None: solver = spalg.spsolve @@ -129,12 +130,12 @@ def signed_eigensolve( # Try to combine, use general LinearOperator if we fail try: - shifted_operator = operator + shift * sparse.eye(operator.shape[0]) + shifted_operator = operator + shift * sparse.eye_array(operator.shape[0]) except TypeError: shifted_operator = operator + spalg.LinearOperator(shape=operator.shape, matvec=lambda v: shift * v) - shifted_eigenvalues, eigenvectors = spalg.eigs(shifted_operator, which='LM', k=how_many, ncv=50) + shifted_eigenvalues, eigenvectors = spalg.eigs(shifted_operator, which='LM', k=how_many, ncv=2 * how_many + 50) eigenvalues = shifted_eigenvalues - shift k = eigenvalues.argsort() diff --git a/meanas/fdfd/__init__.py b/meanas/fdfd/__init__.py index 1829cf9..e94adc3 100644 --- a/meanas/fdfd/__init__.py +++ b/meanas/fdfd/__init__.py @@ -9,9 +9,12 @@ Submodules: - `operators`, `functional`: General FDFD problem setup. - `solvers`: Solver interface and reference implementation. -- `scpml`: Stretched-coordinate perfectly matched layer (scpml) boundary conditions +- `scpml`: Stretched-coordinate perfectly matched layer (SCPML) boundary conditions. - `waveguide_2d`: Operators and mode-solver for waveguides with constant cross-section. -- `waveguide_3d`: Functions for transforming `waveguide_2d` results into 3D. +- `waveguide_3d`: Functions for transforming `waveguide_2d` results into 3D, + including mode-source and overlap-window construction. +- `farfield`, `bloch`, `eme`: specialized helper modules for near/far transforms, + Bloch-periodic problems, and eigenmode expansion. ================================================================ @@ -86,10 +89,13 @@ $$ -\omega^2 \epsilon_{\vec{r}} \cdot \tilde{E}_{\vec{r}} = -\imath \omega \tilde{J}_{\vec{r}} \\ $$ -# TODO FDFD? -# TODO PML - - """ -from . import solvers, operators, functional, scpml, waveguide_2d, waveguide_3d +from . import ( + solvers as solvers, + operators as operators, + functional as functional, + scpml as scpml, + waveguide_2d as waveguide_2d, + waveguide_3d as waveguide_3d, + ) # from . import farfield, bloch TODO diff --git a/meanas/fdfd/bloch.py b/meanas/fdfd/bloch.py index 0d0ac1a..1e15c3a 100644 --- a/meanas/fdfd/bloch.py +++ b/meanas/fdfd/bloch.py @@ -94,18 +94,19 @@ This module contains functions for generating and solving the """ -from typing import Callable, Any, cast, Sequence +from typing import Any, cast +from collections.abc import Callable, Sequence import logging import numpy from numpy import pi, real, trace from numpy.fft import fftfreq from numpy.typing import NDArray, ArrayLike -import scipy # type: ignore -import scipy.optimize # type: ignore -from scipy.linalg import norm # type: ignore -import scipy.sparse.linalg as spalg # type: ignore +import scipy +import scipy.optimize +from scipy.linalg import norm +import scipy.sparse.linalg as spalg -from ..fdmath import fdfield_t, cfdfield_t +from ..fdmath import fdfield, cfdfield, cfdfield_t logger = logging.getLogger(__name__) @@ -114,7 +115,6 @@ logger = logging.getLogger(__name__) try: import pyfftw.interfaces.numpy_fft # type: ignore import pyfftw.interfaces # type: ignore - import multiprocessing logger.info('Using pyfftw') pyfftw.interfaces.cache.enable() @@ -136,6 +136,14 @@ except ImportError: logger.info('Using numpy fft') +def _assemble_hmn_vector( + h_m: NDArray[numpy.complex128], + h_n: NDArray[numpy.complex128], + ) -> NDArray[numpy.complex128]: + stacked = numpy.concatenate((numpy.ravel(h_m), numpy.ravel(h_n))) + return stacked[:, None] + + def generate_kmn( k0: ArrayLike, G_matrix: ArrayLike, @@ -155,7 +163,7 @@ def generate_kmn( All are given in the xyz basis (e.g. `|k|[0,0,0] = norm(G_matrix @ k0)`). """ k0 = numpy.array(k0) - G_matrix = numpy.array(G_matrix, copy=False) + G_matrix = numpy.asarray(G_matrix) Gi_grids = numpy.array(numpy.meshgrid(*(fftfreq(n, 1 / n) for n in shape[:3]), indexing='ij')) Gi = numpy.moveaxis(Gi_grids, 0, -1) @@ -183,8 +191,8 @@ def generate_kmn( def maxwell_operator( k0: ArrayLike, G_matrix: ArrayLike, - epsilon: fdfield_t, - mu: fdfield_t | None = None + epsilon: fdfield, + mu: fdfield | None = None ) -> Callable[[NDArray[numpy.complex128]], NDArray[numpy.complex128]]: """ Generate the Maxwell operator @@ -232,13 +240,13 @@ def maxwell_operator( Raveled conv(1/mu_k, ik x conv(1/eps_k, ik x h_mn)), returned and overwritten in-place of `h`. """ - hin_m, hin_n = [hi.reshape(shape) for hi in numpy.split(h, 2)] + hin_m, hin_n = (hi.reshape(shape) for hi in numpy.split(h, 2)) #{d,e,h}_xyz fields are complex 3-fields in (1/x, 1/y, 1/z) basis # cross product and transform into xyz basis d_xyz = (n * hin_m - - m * hin_n) * k_mag # noqa: E128 + - m * hin_n) * k_mag # divide by epsilon temp = ifftn(d_xyz, axes=range(3)) # reuses d_xyz if using pyfftw @@ -253,8 +261,8 @@ def maxwell_operator( h_m, h_n = b_m, b_n else: # transform from mn to xyz - b_xyz = (m * b_m[:, :, :, None] - + n * b_n[:, :, :, None]) # noqa: E128 + b_xyz = (m * b_m + + n * b_n) # noqa # divide by mu temp = ifftn(b_xyz, axes=range(3)) @@ -265,10 +273,7 @@ def maxwell_operator( h_m = numpy.sum(h_xyz * m, axis=3) h_n = numpy.sum(h_xyz * n, axis=3) - h.shape = (h.size,) - h = numpy.concatenate((h_m.ravel(), h_n.ravel()), axis=None, out=h) # ravel and merge - h.shape = (h.size, 1) - return h + return _assemble_hmn_vector(h_m, h_n) return operator @@ -276,7 +281,7 @@ def maxwell_operator( def hmn_2_exyz( k0: ArrayLike, G_matrix: ArrayLike, - epsilon: fdfield_t, + epsilon: fdfield, ) -> Callable[[NDArray[numpy.complex128]], cfdfield_t]: """ Generate an operator which converts a vectorized spatial-frequency-space @@ -303,12 +308,13 @@ def hmn_2_exyz( k_mag, m, n = generate_kmn(k0, G_matrix, shape) def operator(h: NDArray[numpy.complex128]) -> cfdfield_t: - hin_m, hin_n = [hi.reshape(shape) for hi in numpy.split(h, 2)] + hin_m, hin_n = (hi.reshape(shape) for hi in numpy.split(h, 2)) d_xyz = (n * hin_m - - m * hin_n) * k_mag # noqa: E128 + - m * hin_n) * k_mag # divide by epsilon - return numpy.array([ei for ei in numpy.moveaxis(ifftn(d_xyz, axes=range(3)) / epsilon, 3, 0)]) # TODO avoid copy + exyz = numpy.moveaxis(ifftn(d_xyz, axes=range(3)) / epsilon, 3, 0) + return cfdfield_t(exyz) return operator @@ -316,7 +322,7 @@ def hmn_2_exyz( def hmn_2_hxyz( k0: ArrayLike, G_matrix: ArrayLike, - epsilon: fdfield_t + epsilon: fdfield, ) -> Callable[[NDArray[numpy.complex128]], cfdfield_t]: """ Generate an operator which converts a vectorized spatial-frequency-space @@ -341,10 +347,10 @@ def hmn_2_hxyz( _k_mag, m, n = generate_kmn(k0, G_matrix, shape) def operator(h: NDArray[numpy.complex128]) -> cfdfield_t: - hin_m, hin_n = [hi.reshape(shape) for hi in numpy.split(h, 2)] + hin_m, hin_n = (hi.reshape(shape) for hi in numpy.split(h, 2)) h_xyz = (m * hin_m - + n * hin_n) # noqa: E128 - return numpy.array([ifftn(hi) for hi in numpy.moveaxis(h_xyz, 3, 0)]) + + n * hin_n) + return cfdfield_t(numpy.array([ifftn(hi) for hi in numpy.moveaxis(h_xyz, 3, 0)])) return operator @@ -352,8 +358,8 @@ def hmn_2_hxyz( def inverse_maxwell_operator_approx( k0: ArrayLike, G_matrix: ArrayLike, - epsilon: fdfield_t, - mu: fdfield_t | None = None, + epsilon: fdfield, + mu: fdfield | None = None, ) -> Callable[[NDArray[numpy.complex128]], NDArray[numpy.complex128]]: """ Generate an approximate inverse of the Maxwell operator, @@ -394,7 +400,7 @@ def inverse_maxwell_operator_approx( Returns: Raveled ik x conv(eps_k, ik x conv(mu_k, h_mn)) """ - hin_m, hin_n = [hi.reshape(shape) for hi in numpy.split(h, 2)] + hin_m, hin_n = (hi.reshape(shape) for hi in numpy.split(h, 2)) #{d,e,h}_xyz fields are complex 3-fields in (1/x, 1/y, 1/z) basis @@ -402,8 +408,8 @@ def inverse_maxwell_operator_approx( b_m, b_n = hin_m, hin_n else: # transform from mn to xyz - h_xyz = (m * hin_m[:, :, :, None] - + n * hin_n[:, :, :, None]) # noqa: E128 + h_xyz = (m * hin_m + + n * hin_n) # noqa # multiply by mu temp = ifftn(h_xyz, axes=range(3)) @@ -411,12 +417,12 @@ def inverse_maxwell_operator_approx( b_xyz = fftn(temp, axes=range(3)) # transform back to mn - b_m = numpy.sum(b_xyz * m, axis=3) - b_n = numpy.sum(b_xyz * n, axis=3) + b_m = numpy.sum(b_xyz * m, axis=3, keepdims=True) + b_n = numpy.sum(b_xyz * n, axis=3, keepdims=True) # cross product and transform into xyz basis e_xyz = (n * b_m - - m * b_n) / k_mag # noqa: E128 + - m * b_n) / k_mag # multiply by epsilon temp = ifftn(e_xyz, axes=range(3)) @@ -427,10 +433,7 @@ def inverse_maxwell_operator_approx( h_m = numpy.sum(d_xyz * n, axis=3, keepdims=True) / +k_mag h_n = numpy.sum(d_xyz * m, axis=3, keepdims=True) / -k_mag - h.shape = (h.size,) - h = numpy.concatenate((h_m, h_n), axis=None, out=h) - h.shape = (h.size, 1) - return h + return _assemble_hmn_vector(h_m, h_n) return operator @@ -440,15 +443,15 @@ def find_k( tolerance: float, direction: ArrayLike, G_matrix: ArrayLike, - epsilon: fdfield_t, - mu: fdfield_t | None = None, + epsilon: fdfield, + mu: fdfield | None = None, band: int = 0, k_bounds: tuple[float, float] = (0, 0.5), k_guess: float | None = None, solve_callback: Callable[..., None] | None = None, iter_callback: Callable[..., None] | None = None, v0: NDArray[numpy.complex128] | None = None, - ) -> tuple[float, float, NDArray[numpy.complex128], NDArray[numpy.complex128]]: + ) -> tuple[NDArray[numpy.float64], float, NDArray[numpy.complex128], NDArray[numpy.complex128]]: """ Search for a bloch vector that has a given frequency. @@ -471,7 +474,7 @@ def find_k( `(k, actual_frequency, eigenvalues, eigenvectors)` The found k-vector and its frequency, along with all eigenvalues and eigenvectors. """ - direction = numpy.array(direction) / norm(direction) + direction = numpy.array(direction) / norm(direction) # type: ignore[operator] k_bounds = tuple(sorted(k_bounds)) # type: ignore # we know the length already... assert len(k_bounds) == 2 @@ -493,23 +496,23 @@ def find_k( res = scipy.optimize.minimize_scalar( lambda x: abs(get_f(x, band) - frequency), - k_guess, - method='Bounded', + method='bounded', bounds=k_bounds, options={'xatol': abs(tolerance)}, ) assert n is not None assert v is not None - return float(res.x * direction), float(res.fun + frequency), n, v + actual_frequency = get_f(float(res.x), band) + return direction * float(res.x), float(actual_frequency), n, v # type: ignore[operator,return-value] def eigsolve( num_modes: int, k0: ArrayLike, G_matrix: ArrayLike, - epsilon: fdfield_t, - mu: fdfield_t | None = None, + epsilon: fdfield, + mu: fdfield | None = None, tolerance: float = 1e-7, max_iters: int = 10000, reset_iters: int = 100, @@ -538,7 +541,7 @@ def eigsolve( `(eigenvalues, eigenvectors)` where `eigenvalues[i]` corresponds to the vector `eigenvectors[i, :]` """ - k0 = numpy.array(k0, copy=False) + k0 = numpy.asarray(k0) h_size = 2 * epsilon[0].size @@ -561,11 +564,12 @@ def eigsolve( prev_theta = 0.5 D = numpy.zeros(shape=y_shape, dtype=complex) + rng = numpy.random.default_rng() Z: NDArray[numpy.complex128] if y0 is None: - Z = numpy.random.rand(*y_shape) + 1j * numpy.random.rand(*y_shape) + Z = rng.random(y_shape) + 1j * rng.random(y_shape) else: - Z = numpy.array(y0, copy=False).T + Z = numpy.asarray(y0).T while True: Z *= num_modes / norm(Z) @@ -573,7 +577,7 @@ def eigsolve( try: U = numpy.linalg.inv(ZtZ) except numpy.linalg.LinAlgError: - Z = numpy.random.rand(*y_shape) + 1j * numpy.random.rand(*y_shape) + Z = rng.random(y_shape) + 1j * rng.random(y_shape) continue trace_U = real(trace(U)) @@ -646,17 +650,16 @@ def eigsolve( Qi_memo: list[float | None] = [None, None] - def Qi_func(theta: float) -> float: - nonlocal Qi_memo + def Qi_func(theta: float, Qi_memo=Qi_memo, ZtZ=ZtZ, DtD=DtD, symZtD=symZtD) -> float: # noqa: ANN001 if Qi_memo[0] == theta: - return cast(float, Qi_memo[1]) + return cast('float', Qi_memo[1]) c = numpy.cos(theta) s = numpy.sin(theta) Q = c * c * ZtZ + s * s * DtD + 2 * s * c * symZtD try: Qi = numpy.linalg.inv(Q) - except numpy.linalg.LinAlgError: + except numpy.linalg.LinAlgError as err: logger.info('taylor Qi') # if c or s small, taylor expand if c < 1e-4 * s and c != 0: @@ -666,12 +669,12 @@ def eigsolve( ZtZi = numpy.linalg.inv(ZtZ) Qi = ZtZi / (c * c) - 2 * s / (c * c * c) * (ZtZi @ (ZtZi @ symZtD).conj().T) else: - raise Exception('Inexplicable singularity in trace_func') + raise Exception('Inexplicable singularity in trace_func') from err Qi_memo[0] = theta - Qi_memo[1] = cast(float, Qi) - return cast(float, Qi) + Qi_memo[1] = cast('float', Qi) + return cast('float', Qi) - def trace_func(theta: float) -> float: + def trace_func(theta: float, ZtAZ=ZtAZ, DtAD=DtAD, symZtAD=symZtAD) -> float: # noqa: ANN001 c = numpy.cos(theta) s = numpy.sin(theta) Qi = Qi_func(theta) @@ -680,7 +683,16 @@ def eigsolve( return numpy.abs(trace) if False: - def trace_deriv(theta): + def trace_deriv( + theta: float, + sgn: int = sgn, + ZtAZ=ZtAZ, # noqa: ANN001 + DtAD=DtAD, # noqa: ANN001 + symZtD=symZtD, # noqa: ANN001 + symZtAD=symZtAD, # noqa: ANN001 + ZtZ=ZtZ, # noqa: ANN001 + DtD=DtD, # noqa: ANN001 + ) -> float: Qi = Qi_func(theta) c2 = numpy.cos(2 * theta) s2 = numpy.sin(2 * theta) @@ -722,7 +734,12 @@ def eigsolve( amax=pi, ) - result = scipy.optimize.minimize_scalar(trace_func, bounds=(0, pi), tol=tolerance) + result = scipy.optimize.minimize_scalar( + trace_func, + method='bounded', + bounds=(0, pi), + options={'xatol': tolerance}, + ) new_E = result.fun theta = result.x @@ -751,7 +768,7 @@ def eigsolve( v = eigvecs[:, i] n = eigvals[i] v /= norm(v) - Av = (scipy_op @ v.copy())[:, 0] + Av = numpy.asarray(scipy_op @ v.copy()).reshape(-1) eigness = norm(Av - (v.conj() @ Av) * v) f = numpy.sqrt(-numpy.real(n)) df = numpy.sqrt(-numpy.real(n) + eigness) @@ -799,3 +816,62 @@ def _rtrace_AtB( def _symmetrize(A: NDArray[numpy.complex128]) -> NDArray[numpy.complex128]: return (A + A.conj().T) * 0.5 + + +def inner_product( + eL: cfdfield, + hL: cfdfield, + eR: cfdfield, + hR: cfdfield, + ) -> complex: + # assumes x-axis propagation + + assert numpy.array_equal(eR.shape, hR.shape) + assert numpy.array_equal(eL.shape, hL.shape) + assert numpy.array_equal(eR.shape, eL.shape) + + # Cross product, times 2 since it's

, then divide by 4. # TODO might want to abs() this? + norm2R = (eR[1] * hR[2] - eR[2] * hR[1]).sum() / 2 + norm2L = (eL[1] * hL[2] - eL[2] * hL[1]).sum() / 2 + + # eRxhR_x = numpy.cross(eR.reshape(3, -1), hR.reshape(3, -1), axis=0).reshape(eR.shape)[0] / normR + # logger.info(f'power {eRxhR_x.sum() / 2}) + + eR_norm = eR / numpy.sqrt(abs(norm2R)) + hR_norm = hR / numpy.sqrt(abs(norm2R)) + eL_norm = eL / numpy.sqrt(abs(norm2L)) + hL_norm = hL / numpy.sqrt(abs(norm2L)) + + # (eR x hL)[0] and (eL x hR)[0] + eRxhL_x = eR_norm[1] * hL_norm[2] - eR_norm[2] * hL_norm[1] + eLxhR_x = eL_norm[1] * hR_norm[2] - eL_norm[2] * hR_norm[1] + + #return 1j * (eRxhL_x - eLxhR_x).sum() / numpy.sqrt(norm2R * norm2L) + #return (eRxhL_x.sum() - eLxhR_x.sum()) / numpy.sqrt(norm2R * norm2L) + return eLxhR_x.sum() - eRxhL_x.sum() + + +def trq( + eI: cfdfield, + hI: cfdfield, + eO: cfdfield, + hO: cfdfield, + ) -> tuple[complex, complex]: + pp = inner_product(eO, hO, eI, hI) + pn = inner_product(eO, hO, eI, -hI) + np = inner_product(eO, -hO, eI, hI) + nn = inner_product(eO, -hO, eI, -hI) + + assert numpy.allclose(pp, -nn, atol=1e-12, rtol=1e-12) + assert numpy.allclose(pn, -np, atol=1e-12, rtol=1e-12) + + logger.info(f''' + {pp=:4g} {pn=:4g} + {nn=:4g} {np=:4g} + {nn * pp / pn=:4g} {-np=:4g} + ''') + + r = -pp / pn # -/ = -(-pp) / (-pn) + t = (np - nn * pp / pn) / 4 + + return t, r diff --git a/meanas/fdfd/eme.py b/meanas/fdfd/eme.py new file mode 100644 index 0000000..af745e8 --- /dev/null +++ b/meanas/fdfd/eme.py @@ -0,0 +1,190 @@ +""" +Low-level mode-matching helpers for waveguide / EME workflows. + +These helpers operate on already-solved and already-normalized port fields. +They do not build geometries or solve modes themselves; downstream users are +expected to supply compatible `(E, H)` modal field pairs from +`waveguide_2d`, `waveguide_3d`, or `waveguide_cyl`. + +The returned matrices follow the usual port ordering: + +- `get_tr(...)` returns `(T, R)` for left-incident modes. +- `get_abcd(...)` returns the 2-port block transfer matrix built from the two + directional `T/R` solves. +- `get_s(...)` returns the full block scattering matrix + `[[R12, T12], [T21, R21]]`. + +This module is intentionally a thin library layer rather than an integrated +simulation suite. It provides the overlap algebra that downstream users can +compose into larger workflows. +""" + +from collections.abc import Sequence +import numpy +from numpy.typing import NDArray +from scipy import sparse + +from ..fdmath import dx_lists2_t, vcfdfield2 +from .waveguide_2d import inner_product + +type wavenumber_seq = Sequence[complex] | NDArray[numpy.complexfloating] | NDArray[numpy.floating] + + +def _validate_port_modes( + name: str, + ehs: Sequence[Sequence[vcfdfield2]], + wavenumbers: wavenumber_seq, + ) -> tuple[tuple[int, ...], tuple[int, ...]]: + if len(ehs) != len(wavenumbers): + raise ValueError(f'{name} mode list and wavenumber list must have the same length') + if not ehs: + raise ValueError(f'{name} must contain at least one mode') + + e_shape: tuple[int, ...] | None = None + h_shape: tuple[int, ...] | None = None + for index, mode in enumerate(ehs): + if len(mode) != 2: + raise ValueError(f'{name}[{index}] must be a 2-tuple of (E, H) modal fields') + e_field, h_field = mode + mode_e_shape = numpy.shape(e_field) + mode_h_shape = numpy.shape(h_field) + if mode_e_shape != mode_h_shape: + raise ValueError(f'{name}[{index}] has mismatched E/H field shapes') + if e_shape is None: + e_shape = mode_e_shape + h_shape = mode_h_shape + elif mode_e_shape != e_shape or mode_h_shape != h_shape: + raise ValueError(f'{name} modal fields must all share the same shape') + + assert e_shape is not None + assert h_shape is not None + return e_shape, h_shape + + +def get_tr( + ehLs: Sequence[Sequence[vcfdfield2]], + wavenumbers_L: wavenumber_seq, + ehRs: Sequence[Sequence[vcfdfield2]], + wavenumbers_R: wavenumber_seq, + dxes: dx_lists2_t, + ) -> tuple[NDArray[numpy.complex128], NDArray[numpy.complex128]]: + """ + Compute left-incident transmission and reflection matrices. + + Args: + ehLs: Left-port modes as `(E, H)` field pairs. + wavenumbers_L: Propagation constants for `ehLs`. + ehRs: Right-port modes as `(E, H)` field pairs. + wavenumbers_R: Propagation constants for `ehRs`. + dxes: Two-dimensional Yee-cell edge lengths for the shared port plane. + + Returns: + `(T12, R12)` where columns index left-incident modes and rows index + outgoing right-going / left-going modes respectively. + + Raises: + ValueError: If the port mode lists are empty, malformed, or defined on + incompatible field shapes. + """ + left_e_shape, left_h_shape = _validate_port_modes('ehLs', ehLs, wavenumbers_L) + right_e_shape, right_h_shape = _validate_port_modes('ehRs', ehRs, wavenumbers_R) + if left_e_shape != right_e_shape or left_h_shape != right_h_shape: + raise ValueError('left and right modal fields must share the same E/H shapes') + + nL = len(wavenumbers_L) + nR = len(wavenumbers_R) + A12 = numpy.zeros((nL, nR), dtype=complex) + A21 = numpy.zeros((nL, nR), dtype=complex) + B11 = numpy.zeros((nL,), dtype=complex) + for ll in range(nL): + eL, hL = ehLs[ll] + B11[ll] = inner_product(eL, hL, dxes=dxes, conj_h=False) + for rr in range(nR): + eR, hR = ehRs[rr] + A12[ll, rr] = inner_product(eL, hR, dxes=dxes, conj_h=False) # TODO optimize loop? + A21[ll, rr] = inner_product(eR, hL, dxes=dxes, conj_h=False) + + # tt0 = 2 * numpy.linalg.pinv(A21 + numpy.conj(A12)) + tt0, _resid, _rank, _sing = numpy.linalg.lstsq(A21 + A12, numpy.diag(2 * B11), rcond=None) + + U, st, V = numpy.linalg.svd(tt0) + gain = st > 1 + st[gain] = 1 / st[gain] + tt = U @ numpy.diag(st) @ V + + # rr = 0.5 * (A21 - numpy.conj(A12)) @ tt + rr = numpy.diag(0.5 / B11) @ (A21 - A12) @ tt + + return tt, rr + + +def get_abcd( + ehLs: Sequence[Sequence[vcfdfield2]], + wavenumbers_L: wavenumber_seq, + ehRs: Sequence[Sequence[vcfdfield2]], + wavenumbers_R: wavenumber_seq, + **kwargs, + ) -> sparse.sparray: + """ + Build the 2-port block transfer matrix for an interface. + + The blocks are assembled from the forward and reverse `get_tr(...)` + solutions using the standard + + `[[A, B], [C, D]] = [[T12 - R21 T21^-1 R12, R21 T21^-1], [-T21^-1 R12, T21^-1]]` + + convention. + """ + t12, r12 = get_tr(ehLs, wavenumbers_L, ehRs, wavenumbers_R, **kwargs) + t21, r21 = get_tr(ehRs, wavenumbers_R, ehLs, wavenumbers_L, **kwargs) + t21i = numpy.linalg.pinv(t21) + A = t12 - r21 @ t21i @ r12 + B = r21 @ t21i + C = -t21i @ r12 + D = t21i + return sparse.block_array( + [ + [sparse.csr_array(A), sparse.csr_array(B)], + [sparse.csr_array(C), sparse.csr_array(D)], + ], + format='csr', + ) + + +def get_s( + ehLs: Sequence[Sequence[vcfdfield2]], + wavenumbers_L: wavenumber_seq, + ehRs: Sequence[Sequence[vcfdfield2]], + wavenumbers_R: wavenumber_seq, + force_nogain: bool = False, + force_reciprocal: bool = False, + **kwargs, + ) -> NDArray[numpy.complex128]: + """ + Build the full block scattering matrix for a two-sided interface. + + The returned matrix is ordered as `[[R12, T12], [T21, R21]]`, where the + first block-row/column corresponds to the left port and the second to the + right port. + + Args: + force_nogain: If `True`, clamp singular values of the assembled + scattering matrix to at most one. + force_reciprocal: If `True`, symmetrize the assembled matrix as + `0.5 * (S + S.T)`. + """ + t12, r12 = get_tr(ehLs, wavenumbers_L, ehRs, wavenumbers_R, **kwargs) + t21, r21 = get_tr(ehRs, wavenumbers_R, ehLs, wavenumbers_L, **kwargs) + + ss = numpy.block([[r12, t12], + [t21, r21]]) + + if force_nogain: + # force S @ S.H diagonal + U, sing, Vh = numpy.linalg.svd(ss) + ss = U @ numpy.diag(numpy.minimum(sing, 1.0)) @ Vh + + if force_reciprocal: + ss = 0.5 * (ss + ss.T) + + return ss diff --git a/meanas/fdfd/farfield.py b/meanas/fdfd/farfield.py index 5c1caf0..06f705b 100644 --- a/meanas/fdfd/farfield.py +++ b/meanas/fdfd/farfield.py @@ -1,20 +1,24 @@ """ Functions for performing near-to-farfield transformation (and the reverse). """ -from typing import Any, Sequence, cast +from typing import Any, cast +from collections.abc import Sequence import numpy from numpy.fft import fft2, fftshift, fftfreq, ifft2, ifftshift from numpy import pi +from numpy.typing import NDArray +from numpy import complexfloating -from ..fdmath import cfdfield_t +type farfield_slice = NDArray[complexfloating] +type transverse_slice_pair = Sequence[farfield_slice] def near_to_farfield( - E_near: cfdfield_t, - H_near: cfdfield_t, + E_near: transverse_slice_pair, + H_near: transverse_slice_pair, dx: float, dy: float, - padded_size: list[int] | int | None = None + padded_size: Sequence[int] | int | None = None ) -> dict[str, Any]: """ Compute the farfield, i.e. the distribution of the fields after propagation @@ -55,14 +59,14 @@ def near_to_farfield( raise Exception('H_near must be a length-2 list of ndarrays') s = E_near[0].shape - if not all(s == f.shape for f in E_near + H_near): + if not all(s == f.shape for f in [*E_near, *H_near]): raise Exception('All fields must be the same shape!') if padded_size is None: padded_size = (2**numpy.ceil(numpy.log2(s))).astype(int) if not hasattr(padded_size, '__len__'): padded_size = (padded_size, padded_size) # type: ignore # checked if sequence - padded_shape = cast(Sequence[int], padded_size) + padded_shape = cast('Sequence[int]', padded_size) En_fft = [fftshift(fft2(fftshift(Eni), s=padded_shape)) for Eni in E_near] Hn_fft = [fftshift(fft2(fftshift(Hni), s=padded_shape)) for Hni in H_near] @@ -75,25 +79,22 @@ def near_to_farfield( kx, ky = numpy.meshgrid(kxx, kyy, indexing='ij') kxy2 = kx * kx + ky * ky kxy = numpy.sqrt(kxy2) - kz = numpy.sqrt(k * k - kxy2) + kz = numpy.sqrt(numpy.maximum(0, k * k - kxy2)) - sin_th = ky / kxy - cos_th = kx / kxy + sin_th = numpy.divide(ky, kxy, out=numpy.zeros_like(ky), where=kxy != 0) + cos_th = numpy.divide(kx, kxy, out=numpy.ones_like(kx), where=kxy != 0) cos_phi = kz / k - sin_th[numpy.logical_and(kx == 0, ky == 0)] = 0 - cos_th[numpy.logical_and(kx == 0, ky == 0)] = 1 - # Normalized vector potentials N, L N = [-Hn_fft[1] * cos_phi * cos_th + Hn_fft[0] * cos_phi * sin_th, - Hn_fft[1] * sin_th + Hn_fft[0] * cos_th] # noqa: E127 + Hn_fft[1] * sin_th + Hn_fft[0] * cos_th] # noqa L = [ En_fft[1] * cos_phi * cos_th - En_fft[0] * cos_phi * sin_th, - -En_fft[1] * sin_th - En_fft[0] * cos_th] # noqa: E128 + -En_fft[1] * sin_th - En_fft[0] * cos_th] # noqa E_far = [-L[1] - N[0], - L[0] - N[1]] # noqa: E127 + L[0] - N[1]] # noqa H_far = [-E_far[1], - E_far[0]] # noqa: E127 + E_far[0]] # noqa theta = numpy.arctan2(ky, kx) phi = numpy.arccos(cos_phi) @@ -111,8 +112,8 @@ def near_to_farfield( outputs = { 'E': E_far, 'H': H_far, - 'dkx': kx[1] - kx[0], - 'dky': ky[1] - ky[0], + 'dkx': float(kxx[1] - kxx[0]), + 'dky': float(kyy[1] - kyy[0]), 'kx': kx, 'ky': ky, 'theta': theta, @@ -123,11 +124,11 @@ def near_to_farfield( def far_to_nearfield( - E_far: cfdfield_t, - H_far: cfdfield_t, + E_far: transverse_slice_pair, + H_far: transverse_slice_pair, dkx: float, dky: float, - padded_size: list[int] | int | None = None + padded_size: Sequence[int] | int | None = None ) -> dict[str, Any]: """ Compute the farfield, i.e. the distribution of the fields after propagation @@ -164,32 +165,29 @@ def far_to_nearfield( raise Exception('H_far must be a length-2 list of ndarrays') s = E_far[0].shape - if not all(s == f.shape for f in E_far + H_far): + if not all(s == f.shape for f in [*E_far, *H_far]): raise Exception('All fields must be the same shape!') if padded_size is None: padded_size = (2 ** numpy.ceil(numpy.log2(s))).astype(int) if not hasattr(padded_size, '__len__'): padded_size = (padded_size, padded_size) # type: ignore # checked if sequence - padded_shape = cast(Sequence[int], padded_size) + padded_shape = cast('Sequence[int]', padded_size) k = 2 * pi - kxs = fftshift(fftfreq(s[0], 1 / (s[0] * dkx))) - kys = fftshift(fftfreq(s[0], 1 / (s[1] * dky))) + kxs = dkx * fftshift(fftfreq(s[0], d=1 / s[0])) + kys = dky * fftshift(fftfreq(s[1], d=1 / s[1])) kx, ky = numpy.meshgrid(kxs, kys, indexing='ij') kxy2 = kx * kx + ky * ky kxy = numpy.sqrt(kxy2) - kz = numpy.sqrt(k * k - kxy2) + kz = numpy.sqrt(numpy.maximum(0, k * k - kxy2)) - sin_th = ky / kxy - cos_th = kx / kxy + sin_th = numpy.divide(ky, kxy, out=numpy.zeros_like(ky), where=kxy != 0) + cos_th = numpy.divide(kx, kxy, out=numpy.ones_like(kx), where=kxy != 0) cos_phi = kz / k - sin_th[numpy.logical_and(kx == 0, ky == 0)] = 0 - cos_th[numpy.logical_and(kx == 0, ky == 0)] = 1 - theta = numpy.arctan2(ky, kx) phi = numpy.arccos(cos_phi) theta[numpy.logical_and(kx == 0, ky == 0)] = 0 @@ -205,25 +203,45 @@ def far_to_nearfield( # Normalized vector potentials N, L L = [0.5 * E_far[1], - -0.5 * E_far[0]] # noqa: E128 + -0.5 * E_far[0]] # noqa N = [L[1], - -L[0]] # noqa: E128 + -L[0]] # noqa - En_fft = [-( L[0] * sin_th + L[1] * cos_phi * cos_th) / cos_phi, - -(-L[0] * cos_th + L[1] * cos_phi * sin_th) / cos_phi] + En_fft = [ + numpy.divide( + -(L[0] * sin_th + L[1] * cos_phi * cos_th), + cos_phi, + out=numpy.zeros_like(L[0]), + where=cos_phi != 0, + ), + numpy.divide( + -(-L[0] * cos_th + L[1] * cos_phi * sin_th), + cos_phi, + out=numpy.zeros_like(L[0]), + where=cos_phi != 0, + ), + ] - Hn_fft = [( N[0] * sin_th + N[1] * cos_phi * cos_th) / cos_phi, - (-N[0] * cos_th + N[1] * cos_phi * sin_th) / cos_phi] - - for i in range(2): - En_fft[i][cos_phi == 0] = 0 - Hn_fft[i][cos_phi == 0] = 0 + Hn_fft = [ + numpy.divide( + N[0] * sin_th + N[1] * cos_phi * cos_th, + cos_phi, + out=numpy.zeros_like(N[0]), + where=cos_phi != 0, + ), + numpy.divide( + -N[0] * cos_th + N[1] * cos_phi * sin_th, + cos_phi, + out=numpy.zeros_like(N[0]), + where=cos_phi != 0, + ), + ] E_near = [ifftshift(ifft2(ifftshift(Ei), s=padded_shape)) for Ei in En_fft] H_near = [ifftshift(ifft2(ifftshift(Hi), s=padded_shape)) for Hi in Hn_fft] dx = 2 * pi / (s[0] * dkx) - dy = 2 * pi / (s[0] * dky) + dy = 2 * pi / (s[1] * dky) outputs = { 'E': E_near, @@ -233,4 +251,3 @@ def far_to_nearfield( } return outputs - diff --git a/meanas/fdfd/functional.py b/meanas/fdfd/functional.py index ba2bd70..ddd074b 100644 --- a/meanas/fdfd/functional.py +++ b/meanas/fdfd/functional.py @@ -5,10 +5,10 @@ Functional versions of many FDFD operators. These can be useful for performing The functions generated here expect `cfdfield_t` inputs with shape (3, X, Y, Z), e.g. E = [E_x, E_y, E_z] where each (complex) component has shape (X, Y, Z) """ -from typing import Callable +from collections.abc import Callable import numpy -from ..fdmath import dx_lists_t, fdfield_t, cfdfield_t, cfdfield_updater_t +from ..fdmath import dx_lists_t, cfdfield_t, fdfield, cfdfield, cfdfield_updater_t from ..fdmath.functional import curl_forward, curl_back @@ -18,8 +18,8 @@ __author__ = 'Jan Petykiewicz' def e_full( omega: complex, dxes: dx_lists_t, - epsilon: fdfield_t, - mu: fdfield_t | None = None, + epsilon: fdfield, + mu: fdfield | None = None, ) -> cfdfield_updater_t: """ Wave operator for use with E-field. See `operators.e_full` for details. @@ -37,26 +37,25 @@ def e_full( ch = curl_back(dxes[1]) ce = curl_forward(dxes[0]) - def op_1(e: cfdfield_t) -> cfdfield_t: + def op_1(e: cfdfield) -> cfdfield_t: curls = ch(ce(e)) - return curls - omega ** 2 * epsilon * e + return cfdfield_t(curls - omega ** 2 * epsilon * e) def op_mu(e: cfdfield_t) -> cfdfield_t: - curls = ch(mu * ce(e)) # type: ignore # mu = None ok because we don't return the function - return curls - omega ** 2 * epsilon * e + curls = ch(ce(e) / mu) # type: ignore # mu = None ok because we don't return the function + return cfdfield_t(curls - omega ** 2 * epsilon * e) if mu is None: return op_1 - else: - return op_mu + return op_mu def eh_full( omega: complex, dxes: dx_lists_t, - epsilon: fdfield_t, - mu: fdfield_t | None = None, - ) -> Callable[[cfdfield_t, cfdfield_t], tuple[cfdfield_t, cfdfield_t]]: + epsilon: fdfield, + mu: fdfield | None = None, + ) -> Callable[[cfdfield, cfdfield], tuple[cfdfield_t, cfdfield_t]]: """ Wave operator for full (both E and H) field representation. See `operators.eh_full`. @@ -74,24 +73,23 @@ def eh_full( ch = curl_back(dxes[1]) ce = curl_forward(dxes[0]) - def op_1(e: cfdfield_t, h: cfdfield_t) -> tuple[cfdfield_t, cfdfield_t]: - return (ch(h) - 1j * omega * epsilon * e, - ce(e) + 1j * omega * h) + def op_1(e: cfdfield, h: cfdfield) -> tuple[cfdfield_t, cfdfield_t]: + return (cfdfield_t(ch(h) - 1j * omega * epsilon * e), + cfdfield_t(ce(e) + 1j * omega * h)) - def op_mu(e: cfdfield_t, h: cfdfield_t) -> tuple[cfdfield_t, cfdfield_t]: - return (ch(h) - 1j * omega * epsilon * e, - ce(e) + 1j * omega * mu * h) # type: ignore # mu=None ok + def op_mu(e: cfdfield, h: cfdfield) -> tuple[cfdfield_t, cfdfield_t]: + return (cfdfield_t(ch(h) - 1j * omega * epsilon * e), + cfdfield_t(ce(e) + 1j * omega * mu * h)) # type: ignore # mu=None ok if mu is None: return op_1 - else: - return op_mu + return op_mu def e2h( omega: complex, dxes: dx_lists_t, - mu: fdfield_t | None = None, + mu: fdfield | None = None, ) -> cfdfield_updater_t: """ Utility operator for converting the `E` field into the `H` field. @@ -108,22 +106,21 @@ def e2h( """ ce = curl_forward(dxes[0]) - def e2h_1_1(e: cfdfield_t) -> cfdfield_t: - return ce(e) / (-1j * omega) + def e2h_1_1(e: cfdfield) -> cfdfield_t: + return cfdfield_t(ce(e) / (-1j * omega)) - def e2h_mu(e: cfdfield_t) -> cfdfield_t: - return ce(e) / (-1j * omega * mu) # type: ignore # mu=None ok + def e2h_mu(e: cfdfield) -> cfdfield_t: + return cfdfield_t(ce(e) / (-1j * omega * mu)) # type: ignore # mu=None ok if mu is None: return e2h_1_1 - else: - return e2h_mu + return e2h_mu def m2j( omega: complex, dxes: dx_lists_t, - mu: fdfield_t | None = None, + mu: fdfield | None = None, ) -> cfdfield_updater_t: """ Utility operator for converting magnetic current `M` distribution @@ -142,30 +139,42 @@ def m2j( ch = curl_back(dxes[1]) def m2j_mu(m: cfdfield_t) -> cfdfield_t: - J = ch(m / mu) / (-1j * omega) # type: ignore # mu=None ok - return J + J = ch(m / mu) / (1j * omega) # type: ignore # mu=None ok + return cfdfield_t(J) def m2j_1(m: cfdfield_t) -> cfdfield_t: - J = ch(m) / (-1j * omega) - return J + J = ch(m) / (1j * omega) + return cfdfield_t(J) if mu is None: return m2j_1 - else: - return m2j_mu + return m2j_mu def e_tfsf_source( - TF_region: fdfield_t, + TF_region: fdfield, omega: complex, dxes: dx_lists_t, - epsilon: fdfield_t, - mu: fdfield_t | None = None, + epsilon: fdfield, + mu: fdfield | None = None, ) -> cfdfield_updater_t: - """ + r""" Operator that turns an E-field distribution into a total-field/scattered-field (TFSF) source. + If `A` is the full wave operator from `e_full(...)` and `Q` is the diagonal + mask selecting the total-field region, then the TFSF source is the commutator + + $$ + \frac{A Q - Q A}{-i \omega} E. + $$ + + This vanishes in the interior of the total-field and scattered-field regions + and is supported only at their shared boundary, where the mask discontinuity + makes `A` and `Q` fail to commute. The returned current is therefore the + distributed source needed to inject the desired total field without also + forcing the scattered-field region. + Args: TF_region: mask which is set to 1 in the total-field region, and 0 elsewhere (i.e. in the scattered-field region). @@ -179,20 +188,25 @@ def e_tfsf_source( Function `f` which takes an E field and returns a current distribution, `f(E)` -> `J` """ - # TODO documentation A = e_full(omega, dxes, epsilon, mu) - def op(e: cfdfield_t) -> cfdfield_t: + def op(e: cfdfield) -> cfdfield_t: neg_iwj = A(TF_region * e) - TF_region * A(e) - return neg_iwj / (-1j * omega) + return cfdfield_t(neg_iwj / (-1j * omega)) return op -def poynting_e_cross_h(dxes: dx_lists_t) -> Callable[[cfdfield_t, cfdfield_t], cfdfield_t]: +def poynting_e_cross_h(dxes: dx_lists_t) -> Callable[[cfdfield, cfdfield], cfdfield_t]: r""" Generates a function that takes the single-frequency `E` and `H` fields and calculates the cross product `E` x `H` = $E \times H$ as required - for the Poynting vector, $S = E \times H$ + for the Poynting vector, $S = E \times H$. + + On the Yee grid, the electric and magnetic components are not stored at the + same locations. This helper therefore applies the same one-cell electric-field + shifts used by the sparse `operators.poynting_e_cross(...)` construction so + that the discrete cross product matches the face-centered energy flux used in + `meanas.fdtd.energy.poynting(...)`. Note: This function also shifts the input `E` field by one cell as required @@ -208,9 +222,10 @@ def poynting_e_cross_h(dxes: dx_lists_t) -> Callable[[cfdfield_t, cfdfield_t], c dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` Returns: - Function `f` that returns E x H as required for the poynting vector. + Function `f` that returns the staggered-grid cross product `E \times H`. + For time-average power, call it as `f(E, H.conj())` and take `Re(...) / 2`. """ - def exh(e: cfdfield_t, h: cfdfield_t) -> cfdfield_t: + def exh(e: cfdfield, h: cfdfield) -> cfdfield_t: s = numpy.empty_like(e) ex = e[0] * dxes[0][0][:, None, None] ey = e[1] * dxes[0][1][None, :, None] @@ -221,5 +236,5 @@ def poynting_e_cross_h(dxes: dx_lists_t) -> Callable[[cfdfield_t, cfdfield_t], c s[0] = numpy.roll(ey, -1, axis=0) * hz - numpy.roll(ez, -1, axis=0) * hy s[1] = numpy.roll(ez, -1, axis=1) * hx - numpy.roll(ex, -1, axis=1) * hz s[2] = numpy.roll(ex, -1, axis=2) * hy - numpy.roll(ey, -1, axis=2) * hx - return s + return cfdfield_t(s) return exh diff --git a/meanas/fdfd/operators.py b/meanas/fdfd/operators.py index 3a489a7..6425a29 100644 --- a/meanas/fdfd/operators.py +++ b/meanas/fdfd/operators.py @@ -1,7 +1,7 @@ """ Sparse matrix operators for use with electromagnetic wave equations. -These functions return sparse-matrix (`scipy.sparse.spmatrix`) representations of +These functions return sparse-matrix (`scipy.sparse.sparray`) representations of a variety of operators, intended for use with E and H fields vectorized using the `meanas.fdmath.vectorization.vec()` and `meanas.fdmath.vectorization.unvec()` functions. @@ -28,9 +28,9 @@ The following operators are included: """ import numpy -import scipy.sparse as sparse # type: ignore +from scipy import sparse -from ..fdmath import vec, dx_lists_t, vfdfield_t, vcfdfield_t +from ..fdmath import vec, dx_lists_t, vfdfield, vcfdfield from ..fdmath.operators import shift_with_mirror, shift_circ, curl_forward, curl_back @@ -40,11 +40,11 @@ __author__ = 'Jan Petykiewicz' def e_full( omega: complex, dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, - pec: vfdfield_t | None = None, - pmc: vfdfield_t | None = None, - ) -> sparse.spmatrix: + epsilon: vfdfield | vcfdfield, + mu: vfdfield | None = None, + pec: vfdfield | None = None, + pmc: vfdfield | None = None, + ) -> sparse.sparray: r""" Wave operator $$ \nabla \times (\frac{1}{\mu} \nabla \times) - \Omega^2 \epsilon $$ @@ -64,11 +64,11 @@ def e_full( epsilon: Vectorized dielectric constant mu: Vectorized magnetic permeability (default 1 everywhere). pec: Vectorized mask specifying PEC cells. Any cells where `pec != 0` are interpreted - as containing a perfect electrical conductor (PEC). - The PEC is applied per-field-component (i.e. `pec.size == epsilon.size`) + as containing a perfect electrical conductor (PEC). + The PEC is applied per-field-component (i.e. `pec.size == epsilon.size`) pmc: Vectorized mask specifying PMC cells. Any cells where `pmc != 0` are interpreted - as containing a perfect magnetic conductor (PMC). - The PMC is applied per-field-component (i.e. `pmc.size == epsilon.size`) + as containing a perfect magnetic conductor (PMC). + The PMC is applied per-field-component (i.e. `pmc.size == epsilon.size`) Returns: Sparse matrix containing the wave operator. @@ -77,20 +77,20 @@ def e_full( ce = curl_forward(dxes[0]) if pec is None: - pe = sparse.eye(epsilon.size) + pe = sparse.eye_array(epsilon.size) else: - pe = sparse.diags(numpy.where(pec, 0, 1)) # Set pe to (not PEC) + pe = sparse.diags_array(numpy.where(pec, 0, 1)) # Set pe to (not PEC) if pmc is None: - pm = sparse.eye(epsilon.size) + pm = sparse.eye_array(epsilon.size) else: - pm = sparse.diags(numpy.where(pmc, 0, 1)) # set pm to (not PMC) + pm = sparse.diags_array(numpy.where(pmc, 0, 1)) # set pm to (not PMC) - e = sparse.diags(epsilon) + e = sparse.diags_array(epsilon) if mu is None: - m_div = sparse.eye(epsilon.size) + m_div = sparse.eye_array(epsilon.size) else: - m_div = sparse.diags(1 / mu) + m_div = sparse.diags_array(1 / mu) op = pe @ (ch @ pm @ m_div @ ce - omega**2 * e) @ pe return op @@ -98,7 +98,7 @@ def e_full( def e_full_preconditioners( dxes: dx_lists_t, - ) -> tuple[sparse.spmatrix, sparse.spmatrix]: + ) -> tuple[sparse.sparray, sparse.sparray]: """ Left and right preconditioners `(Pl, Pr)` for symmetrizing the `e_full` wave operator. @@ -118,19 +118,19 @@ def e_full_preconditioners( dxes[1][0][:, None, None] * dxes[1][1][None, :, None] * dxes[0][2][None, None, :]] p_vector = numpy.sqrt(vec(p_squared)) - P_left = sparse.diags(p_vector) - P_right = sparse.diags(1 / p_vector) + P_left = sparse.diags_array(p_vector) + P_right = sparse.diags_array(1 / p_vector) return P_left, P_right def h_full( omega: complex, dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, - pec: vfdfield_t | None = None, - pmc: vfdfield_t | None = None, - ) -> sparse.spmatrix: + epsilon: vfdfield, + mu: vfdfield | None = None, + pec: vfdfield | None = None, + pmc: vfdfield | None = None, + ) -> sparse.sparray: r""" Wave operator $$ \nabla \times (\frac{1}{\epsilon} \nabla \times) - \omega^2 \mu $$ @@ -148,11 +148,11 @@ def h_full( epsilon: Vectorized dielectric constant mu: Vectorized magnetic permeability (default 1 everywhere) pec: Vectorized mask specifying PEC cells. Any cells where `pec != 0` are interpreted - as containing a perfect electrical conductor (PEC). - The PEC is applied per-field-component (i.e. `pec.size == epsilon.size`) + as containing a perfect electrical conductor (PEC). + The PEC is applied per-field-component (i.e. `pec.size == epsilon.size`) pmc: Vectorized mask specifying PMC cells. Any cells where `pmc != 0` are interpreted - as containing a perfect magnetic conductor (PMC). - The PMC is applied per-field-component (i.e. `pmc.size == epsilon.size`) + as containing a perfect magnetic conductor (PMC). + The PMC is applied per-field-component (i.e. `pmc.size == epsilon.size`) Returns: Sparse matrix containing the wave operator. @@ -161,20 +161,20 @@ def h_full( ce = curl_forward(dxes[0]) if pec is None: - pe = sparse.eye(epsilon.size) + pe = sparse.eye_array(epsilon.size) else: - pe = sparse.diags(numpy.where(pec, 0, 1)) # set pe to (not PEC) + pe = sparse.diags_array(numpy.where(pec, 0, 1)) # set pe to (not PEC) if pmc is None: - pm = sparse.eye(epsilon.size) + pm = sparse.eye_array(epsilon.size) else: - pm = sparse.diags(numpy.where(pmc, 0, 1)) # Set pe to (not PMC) + pm = sparse.diags_array(numpy.where(pmc, 0, 1)) # Set pe to (not PMC) - e_div = sparse.diags(1 / epsilon) + e_div = sparse.diags_array(1 / epsilon) if mu is None: - m = sparse.eye(epsilon.size) + m = sparse.eye_array(epsilon.size) else: - m = sparse.diags(mu) + m = sparse.diags_array(mu) A = pm @ (ce @ pe @ e_div @ ch - omega**2 * m) @ pm return A @@ -183,11 +183,11 @@ def h_full( def eh_full( omega: complex, dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, - pec: vfdfield_t | None = None, - pmc: vfdfield_t | None = None, - ) -> sparse.spmatrix: + epsilon: vfdfield, + mu: vfdfield | None = None, + pec: vfdfield | None = None, + pmc: vfdfield | None = None, + ) -> sparse.sparray: r""" Wave operator for `[E, H]` field representation. This operator implements Maxwell's equations without cancelling out either E or H. The operator is @@ -217,45 +217,47 @@ def eh_full( epsilon: Vectorized dielectric constant mu: Vectorized magnetic permeability (default 1 everywhere) pec: Vectorized mask specifying PEC cells. Any cells where `pec != 0` are interpreted - as containing a perfect electrical conductor (PEC). - The PEC is applied per-field-component (i.e. `pec.size == epsilon.size`) + as containing a perfect electrical conductor (PEC). + The PEC is applied per-field-component (i.e. `pec.size == epsilon.size`) pmc: Vectorized mask specifying PMC cells. Any cells where `pmc != 0` are interpreted - as containing a perfect magnetic conductor (PMC). - The PMC is applied per-field-component (i.e. `pmc.size == epsilon.size`) + as containing a perfect magnetic conductor (PMC). + The PMC is applied per-field-component (i.e. `pmc.size == epsilon.size`) Returns: Sparse matrix containing the wave operator. """ if pec is None: - pe = sparse.eye(epsilon.size) + pe = sparse.eye_array(epsilon.size) else: - pe = sparse.diags(numpy.where(pec, 0, 1)) # set pe to (not PEC) + pe = sparse.diags_array(numpy.where(pec, 0, 1)) # set pe to (not PEC) if pmc is None: - pm = sparse.eye(epsilon.size) + pm = sparse.eye_array(epsilon.size) else: - pm = sparse.diags(numpy.where(pmc, 0, 1)) # set pm to (not PMC) + pm = sparse.diags_array(numpy.where(pmc, 0, 1)) # set pm to (not PMC) iwe = pe @ (1j * omega * sparse.diags(epsilon)) @ pe - iwm = 1j * omega - if mu is not None: - iwm *= sparse.diags(mu) + if mu is None: + iwm = 1j * omega * sparse.eye(epsilon.size) + else: + iwm = 1j * omega * sparse.diags(mu) + iwm = pm @ iwm @ pm A1 = pe @ curl_back(dxes[1]) @ pm A2 = pm @ curl_forward(dxes[0]) @ pe - A = sparse.bmat([[-iwe, A1], - [A2, iwm]]) + A = sparse.block_array([[-iwe, A1], + [A2, iwm]]) return A def e2h( omega: complex, dxes: dx_lists_t, - mu: vfdfield_t | None = None, - pmc: vfdfield_t | None = None, - ) -> sparse.spmatrix: + mu: vfdfield | None = None, + pmc: vfdfield | None = None, + ) -> sparse.sparray: """ Utility operator for converting the E field into the H field. For use with `e_full()` -- assumes that there is no magnetic current M. @@ -265,8 +267,8 @@ def e2h( dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` mu: Vectorized magnetic permeability (default 1 everywhere) pmc: Vectorized mask specifying PMC cells. Any cells where `pmc != 0` are interpreted - as containing a perfect magnetic conductor (PMC). - The PMC is applied per-field-component (i.e. `pmc.size == epsilon.size`) + as containing a perfect magnetic conductor (PMC). + The PMC is applied per-field-component (i.e. `pmc.size == epsilon.size`) Returns: Sparse matrix for converting E to H. @@ -274,10 +276,10 @@ def e2h( op = curl_forward(dxes[0]) / (-1j * omega) if mu is not None: - op = sparse.diags(1 / mu) @ op + op = sparse.diags_array(1 / mu) @ op if pmc is not None: - op = sparse.diags(numpy.where(pmc, 0, 1)) @ op + op = sparse.diags_array(numpy.where(pmc, 0, 1)) @ op return op @@ -285,8 +287,8 @@ def e2h( def m2j( omega: complex, dxes: dx_lists_t, - mu: vfdfield_t | None = None, - ) -> sparse.spmatrix: + mu: vfdfield | None = None, + ) -> sparse.sparray: """ Operator for converting a magnetic current M into an electric current J. For use with eg. `e_full()`. @@ -302,79 +304,108 @@ def m2j( op = curl_back(dxes[1]) / (1j * omega) if mu is not None: - op = op @ sparse.diags(1 / mu) + op = op @ sparse.diags_array(1 / mu) return op -def poynting_e_cross(e: vcfdfield_t, dxes: dx_lists_t) -> sparse.spmatrix: - """ - Operator for computing the Poynting vector, containing the - (E x) portion of the Poynting vector. +def poynting_e_cross(e: vcfdfield, dxes: dx_lists_t) -> sparse.sparray: + r""" + Operator for computing the staggered-grid `(E \times)` part of the Poynting vector. + + On the Yee grid the E and H components live on different edges, so the + electric field must be shifted by one cell in the appropriate direction + before forming the discrete cross product. This sparse operator encodes that + shifted cross product directly and is the matrix equivalent of + `functional.poynting_e_cross_h(...)`. Args: e: Vectorized E-field for the ExH cross product dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` Returns: - Sparse matrix containing (E x) portion of Poynting cross product. + Sparse matrix containing the `(E \times)` part of the staggered Poynting + cross product. """ shape = [len(dx) for dx in dxes[0]] - fx, fy, fz = [shift_circ(i, shape, 1) for i in range(3)] + fx, fy, fz = (shift_circ(i, shape, 1) for i in range(3)) dxag = [dx.ravel(order='C') for dx in numpy.meshgrid(*dxes[0], indexing='ij')] dxbg = [dx.ravel(order='C') for dx in numpy.meshgrid(*dxes[1], indexing='ij')] - Ex, Ey, Ez = [ei * da for ei, da in zip(numpy.split(e, 3), dxag)] + Ex, Ey, Ez = (ei * da for ei, da in zip(numpy.split(e, 3), dxag, strict=True)) block_diags = [[ None, fx @ -Ez, fx @ Ey], [ fy @ Ez, None, fy @ -Ex], [ fz @ -Ey, fz @ Ex, None]] - block_matrix = sparse.bmat([[sparse.diags(x) if x is not None else None for x in row] - for row in block_diags]) - P = block_matrix @ sparse.diags(numpy.concatenate(dxbg)) + block_matrix = sparse.block_array([[sparse.diags_array(x) if x is not None else None for x in row] + for row in block_diags]) + P = block_matrix @ sparse.diags_array(numpy.concatenate(dxbg)) return P -def poynting_h_cross(h: vcfdfield_t, dxes: dx_lists_t) -> sparse.spmatrix: - """ - Operator for computing the Poynting vector, containing the (H x) portion of the Poynting vector. +def poynting_h_cross(h: vcfdfield, dxes: dx_lists_t) -> sparse.sparray: + r""" + Operator for computing the staggered-grid `(H \times)` part of the Poynting vector. + + Together with `poynting_e_cross(...)`, this provides the matrix form of the + Yee-grid cross product used in the flux helpers. The two are related by the + usual antisymmetry of the cross product, + + $$ + H \times E = -(E \times H), + $$ + + once the same staggered field placement is used on both sides. Args: h: Vectorized H-field for the HxE cross product dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` Returns: - Sparse matrix containing (H x) portion of Poynting cross product. + Sparse matrix containing the `(H \times)` part of the staggered Poynting + cross product. """ shape = [len(dx) for dx in dxes[0]] - fx, fy, fz = [shift_circ(i, shape, 1) for i in range(3)] + fx, fy, fz = (shift_circ(i, shape, 1) for i in range(3)) dxag = [dx.ravel(order='C') for dx in numpy.meshgrid(*dxes[0], indexing='ij')] dxbg = [dx.ravel(order='C') for dx in numpy.meshgrid(*dxes[1], indexing='ij')] - Hx, Hy, Hz = [sparse.diags(hi * db) for hi, db in zip(numpy.split(h, 3), dxbg)] + Hx, Hy, Hz = (sparse.diags_array(hi * db) for hi, db in zip(numpy.split(h, 3), dxbg, strict=True)) - P = (sparse.bmat( + P = (sparse.block_array( [[ None, -Hz @ fx, Hy @ fx], [ Hz @ fy, None, -Hx @ fy], [-Hy @ fz, Hx @ fz, None]]) - @ sparse.diags(numpy.concatenate(dxag))) + @ sparse.diags_array(numpy.concatenate(dxag))) return P def e_tfsf_source( - TF_region: vfdfield_t, + TF_region: vfdfield, omega: complex, dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, - ) -> sparse.spmatrix: - """ + epsilon: vfdfield, + mu: vfdfield | None = None, + ) -> sparse.sparray: + r""" Operator that turns a desired E-field distribution into a total-field/scattered-field (TFSF) source. - TODO: Reference Rumpf paper + Let `A` be the full wave operator from `e_full(...)`, and let + `Q = \mathrm{diag}(TF_region)` be the projector onto the total-field region. + Then the TFSF current operator is the commutator + + $$ + \frac{A Q - Q A}{-i \omega}. + $$ + + Inside regions where `Q` is locally constant, `A` and `Q` commute and the + source vanishes. Only cells at the TF/SF boundary contribute nonzero current, + which is exactly the desired distributed source for injecting the chosen + field into the total-field region without directly forcing the + scattered-field region. Args: TF_region: Mask, which is set to 1 inside the total-field region and 0 in the @@ -386,27 +417,31 @@ def e_tfsf_source( Returns: Sparse matrix that turns an E-field into a current (J) distribution. - """ - # TODO documentation A = e_full(omega, dxes, epsilon, mu) - Q = sparse.diags(TF_region) + Q = sparse.diags_array(TF_region) return (A @ Q - Q @ A) / (-1j * omega) def e_boundary_source( - mask: vfdfield_t, + mask: vfdfield, omega: complex, dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, + epsilon: vfdfield, + mu: vfdfield | None = None, periodic_mask_edges: bool = False, - ) -> sparse.spmatrix: - """ + ) -> sparse.sparray: + r""" Operator that turns an E-field distrubtion into a current (J) distribution along the edges (external and internal) of the provided mask. This is just an `e_tfsf_source()` with an additional masking step. + Equivalently, this helper first constructs the TFSF commutator source for the + full mask and then zeroes out all cells except the mask boundary. The + boundary is defined as the set of cells whose mask value changes under a + one-cell shift in any Cartesian direction. With `periodic_mask_edges=False` + the shifts mirror at the domain boundary; with `True` they wrap periodically. + Args: mask: The current distribution is generated at the edges of the mask, i.e. any points where shifting the mask by one cell in any direction @@ -424,10 +459,10 @@ def e_boundary_source( shape = [len(dxe) for dxe in dxes[0]] jmask = numpy.zeros_like(mask, dtype=bool) - def shift_rot(axis: int, polarity: int) -> sparse.spmatrix: + def shift_rot(axis: int, polarity: int) -> sparse.sparray: return shift_circ(axis=axis, shape=shape, shift_distance=polarity) - def shift_mir(axis: int, polarity: int) -> sparse.spmatrix: + def shift_mir(axis: int, polarity: int) -> sparse.sparray: return shift_with_mirror(axis=axis, shape=shape, shift_distance=polarity) shift = shift_rot if periodic_mask_edges else shift_mir @@ -436,7 +471,7 @@ def e_boundary_source( if shape[axis] == 1: continue for polarity in (-1, +1): - r = shift(axis, polarity) - sparse.eye(numpy.prod(shape)) # shifted minus original + r = shift(axis, polarity) - sparse.eye_array(numpy.prod(shape)) # shifted minus original r3 = sparse.block_diag((r, r, r)) jmask = numpy.logical_or(jmask, numpy.abs(r3 @ mask)) @@ -447,5 +482,4 @@ def e_boundary_source( # (numpy.roll(mask, -1, axis=2) != mask) | # (numpy.roll(mask, +1, axis=2) != mask)) - return sparse.diags(jmask.astype(int)) @ full - + return sparse.diags_array(jmask.astype(int)) @ full diff --git a/meanas/fdfd/scpml.py b/meanas/fdfd/scpml.py index bc056e1..7030876 100644 --- a/meanas/fdfd/scpml.py +++ b/meanas/fdfd/scpml.py @@ -2,7 +2,7 @@ Functions for creating stretched coordinate perfectly matched layer (PML) absorbers. """ -from typing import Sequence, Callable +from collections.abc import Sequence, Callable import numpy from numpy.typing import NDArray @@ -128,6 +128,11 @@ def stretch_with_scpml( dx_ai = dxes[0][axis].astype(complex) dx_bi = dxes[1][axis].astype(complex) + if thickness == 0: + dxes[0][axis] = dx_ai + dxes[1][axis] = dx_bi + return dxes + pos = numpy.hstack((0, dx_ai.cumsum())) pos_a = (pos[:-1] + pos[1:]) / 2 pos_b = pos[:-1] @@ -153,10 +158,7 @@ def stretch_with_scpml( def l_d(x: NDArray[numpy.float64]) -> NDArray[numpy.float64]: return (x - bound) / (pos[-1] - bound) - if thickness == 0: - slc = slice(None) - else: - slc = slice(-thickness, None) + slc = slice(-thickness, None) dx_ai[slc] *= 1 + 1j * s_function(l_d(pos_a[slc])) / d / s_correction dx_bi[slc] *= 1 + 1j * s_function(l_d(pos_b[slc])) / d / s_correction diff --git a/meanas/fdfd/solvers.py b/meanas/fdfd/solvers.py index 8ac157c..e1f394c 100644 --- a/meanas/fdfd/solvers.py +++ b/meanas/fdfd/solvers.py @@ -2,15 +2,16 @@ Solvers and solver interface for FDFD problems. """ -from typing import Callable, Dict, Any, Optional +from typing import Any +from collections.abc import Callable import logging import numpy from numpy.typing import ArrayLike, NDArray from numpy.linalg import norm -import scipy.sparse.linalg # type: ignore +import scipy.sparse.linalg -from ..fdmath import dx_lists_t, vfdfield_t, vcfdfield_t +from ..fdmath import dx_lists_t, vfdfield, vcfdfield, vcfdfield_t from . import operators @@ -18,7 +19,7 @@ logger = logging.getLogger(__name__) def _scipy_qmr( - A: scipy.sparse.csr_matrix, + A: scipy.sparse.csr_array, b: ArrayLike, **kwargs: Any, ) -> NDArray[numpy.float64]: @@ -34,31 +35,32 @@ def _scipy_qmr( Guess for solution (returned even if didn't converge) """ - ''' - Report on our progress - ''' + # + #Report on our progress + # ii = 0 def log_residual(xk: ArrayLike) -> None: nonlocal ii ii += 1 if ii % 100 == 0: - cur_norm = norm(A @ xk - b) + cur_norm = norm(A @ xk - b) / norm(b) logger.info(f'Solver residual at iteration {ii} : {cur_norm}') if 'callback' in kwargs: + callback = kwargs['callback'] + def augmented_callback(xk: ArrayLike) -> None: log_residual(xk) - kwargs['callback'](xk) + callback(xk) kwargs['callback'] = augmented_callback else: kwargs['callback'] = log_residual - ''' - Run the actual solve - ''' - + # + # Run the actual solve + # x, _ = scipy.sparse.linalg.qmr(A, b, **kwargs) return x @@ -66,14 +68,16 @@ def _scipy_qmr( def generic( omega: complex, dxes: dx_lists_t, - J: vcfdfield_t, - epsilon: vfdfield_t, - mu: Optional[vfdfield_t] = None, - pec: Optional[vfdfield_t] = None, - pmc: Optional[vfdfield_t] = None, + J: vcfdfield, + epsilon: vfdfield, + mu: vfdfield | None = None, + *, + pec: vfdfield | None = None, + pmc: vfdfield | None = None, adjoint: bool = False, matrix_solver: Callable[..., ArrayLike] = _scipy_qmr, - matrix_solver_opts: Optional[Dict[str, Any]] = None, + matrix_solver_opts: dict[str, Any] | None = None, + E_guess: vcfdfield | None = None, ) -> vcfdfield_t: """ Conjugate gradient FDFD solver using CSR sparse matrices. @@ -93,13 +97,15 @@ def generic( (at H-field locations; non-zero value indicates PMC is present) adjoint: If true, solves the adjoint problem. matrix_solver: Called as `matrix_solver(A, b, **matrix_solver_opts) -> x`, - where `A`: `scipy.sparse.csr_matrix`; + where `A`: `scipy.sparse.csr_array`; `b`: `ArrayLike`; `x`: `ArrayLike`; Default is a wrapped version of `scipy.sparse.linalg.qmr()` which doesn't return convergence info and logs the residual every 100 iterations. matrix_solver_opts: Passed as kwargs to `matrix_solver(...)` + E_guess: Guess at the solution E-field. `matrix_solver` must accept an + `x0` argument with the same purpose. Returns: E-field which solves the system. @@ -114,17 +120,24 @@ def generic( Pl, Pr = operators.e_full_preconditioners(dxes) if adjoint: - A = (Pl @ A0 @ Pr).H - b = Pr.H @ b0 + A = (Pl @ A0 @ Pr).T.conjugate() + b = Pr.T.conjugate() @ b0 else: A = Pl @ A0 @ Pr b = Pl @ b0 + if E_guess is not None: + if adjoint: + x0 = Pr.T.conjugate() @ E_guess + else: + x0 = Pl @ E_guess + matrix_solver_opts['x0'] = x0 + x = matrix_solver(A.tocsr(), b, **matrix_solver_opts) if adjoint: - x0 = Pl.H @ x + x0 = Pl.T.conjugate() @ x else: x0 = Pr @ x - return x0 + return vcfdfield_t(x0) diff --git a/meanas/fdfd/waveguide_2d.py b/meanas/fdfd/waveguide_2d.py index 399574d..e67160e 100644 --- a/meanas/fdfd/waveguide_2d.py +++ b/meanas/fdfd/waveguide_2d.py @@ -18,8 +18,8 @@ $$ \begin{aligned} \nabla \times \vec{E}(x, y, z) &= -\imath \omega \mu \vec{H} \\ \nabla \times \vec{H}(x, y, z) &= \imath \omega \epsilon \vec{E} \\ -\vec{E}(x,y,z) &= (\vec{E}_t(x, y) + E_z(x, y)\vec{z}) e^{-\gamma z} \\ -\vec{H}(x,y,z) &= (\vec{H}_t(x, y) + H_z(x, y)\vec{z}) e^{-\gamma z} \\ +\vec{E}(x,y,z) &= (\vec{E}_t(x, y) + E_z(x, y)\vec{z}) e^{-\imath \beta z} \\ +\vec{H}(x,y,z) &= (\vec{H}_t(x, y) + H_z(x, y)\vec{z}) e^{-\imath \beta z} \\ \end{aligned} $$ @@ -40,56 +40,57 @@ Substituting in our expressions for $\vec{E}$, $\vec{H}$ and discretizing: $$ \begin{aligned} --\imath \omega \mu_{xx} H_x &= \tilde{\partial}_y E_z + \gamma E_y \\ --\imath \omega \mu_{yy} H_y &= -\gamma E_x - \tilde{\partial}_x E_z \\ +-\imath \omega \mu_{xx} H_x &= \tilde{\partial}_y E_z + \imath \beta E_y \\ +-\imath \omega \mu_{yy} H_y &= -\imath \beta E_x - \tilde{\partial}_x E_z \\ -\imath \omega \mu_{zz} H_z &= \tilde{\partial}_x E_y - \tilde{\partial}_y E_x \\ -\imath \omega \epsilon_{xx} E_x &= \hat{\partial}_y H_z + \gamma H_y \\ -\imath \omega \epsilon_{yy} E_y &= -\gamma H_x - \hat{\partial}_x H_z \\ +\imath \omega \epsilon_{xx} E_x &= \hat{\partial}_y H_z + \imath \beta H_y \\ +\imath \omega \epsilon_{yy} E_y &= -\imath \beta H_x - \hat{\partial}_x H_z \\ \imath \omega \epsilon_{zz} E_z &= \hat{\partial}_x H_y - \hat{\partial}_y H_x \\ \end{aligned} $$ Rewrite the last three equations as + $$ \begin{aligned} -\gamma H_y &= \imath \omega \epsilon_{xx} E_x - \hat{\partial}_y H_z \\ -\gamma H_x &= -\imath \omega \epsilon_{yy} E_y - \hat{\partial}_x H_z \\ +\imath \beta H_y &= \imath \omega \epsilon_{xx} E_x - \hat{\partial}_y H_z \\ +\imath \beta H_x &= -\imath \omega \epsilon_{yy} E_y - \hat{\partial}_x H_z \\ \imath \omega E_z &= \frac{1}{\epsilon_{zz}} \hat{\partial}_x H_y - \frac{1}{\epsilon_{zz}} \hat{\partial}_y H_x \\ \end{aligned} $$ -Now apply $\gamma \tilde{\partial}_x$ to the last equation, -then substitute in for $\gamma H_x$ and $\gamma H_y$: +Now apply $\imath \beta \tilde{\partial}_x$ to the last equation, +then substitute in for $\imath \beta H_x$ and $\imath \beta H_y$: $$ \begin{aligned} -\gamma \tilde{\partial}_x \imath \omega E_z &= \gamma \tilde{\partial}_x \frac{1}{\epsilon_{zz}} \hat{\partial}_x H_y - - \gamma \tilde{\partial}_x \frac{1}{\epsilon_{zz}} \hat{\partial}_y H_x \\ +\imath \beta \tilde{\partial}_x \imath \omega E_z &= \imath \beta \tilde{\partial}_x \frac{1}{\epsilon_{zz}} \hat{\partial}_x H_y + - \imath \beta \tilde{\partial}_x \frac{1}{\epsilon_{zz}} \hat{\partial}_y H_x \\ &= \tilde{\partial}_x \frac{1}{\epsilon_{zz}} \hat{\partial}_x ( \imath \omega \epsilon_{xx} E_x - \hat{\partial}_y H_z) - \tilde{\partial}_x \frac{1}{\epsilon_{zz}} \hat{\partial}_y (-\imath \omega \epsilon_{yy} E_y - \hat{\partial}_x H_z) \\ &= \tilde{\partial}_x \frac{1}{\epsilon_{zz}} \hat{\partial}_x ( \imath \omega \epsilon_{xx} E_x) - \tilde{\partial}_x \frac{1}{\epsilon_{zz}} \hat{\partial}_y (-\imath \omega \epsilon_{yy} E_y) \\ -\gamma \tilde{\partial}_x E_z &= \tilde{\partial}_x \frac{1}{\epsilon_{zz}} \hat{\partial}_x (\epsilon_{xx} E_x) - + \tilde{\partial}_x \frac{1}{\epsilon_{zz}} \hat{\partial}_y (\epsilon_{yy} E_y) \\ +\imath \beta \tilde{\partial}_x E_z &= \tilde{\partial}_x \frac{1}{\epsilon_{zz}} \hat{\partial}_x (\epsilon_{xx} E_x) + + \tilde{\partial}_x \frac{1}{\epsilon_{zz}} \hat{\partial}_y (\epsilon_{yy} E_y) \\ \end{aligned} $$ -With a similar approach (but using $\gamma \tilde{\partial}_y$ instead), we can get +With a similar approach (but using $\imath \beta \tilde{\partial}_y$ instead), we can get $$ \begin{aligned} -\gamma \tilde{\partial}_y E_z &= \tilde{\partial}_y \frac{1}{\epsilon_{zz}} \hat{\partial}_x (\epsilon_{xx} E_x) - + \tilde{\partial}_y \frac{1}{\epsilon_{zz}} \hat{\partial}_y (\epsilon_{yy} E_y) \\ +\imath \beta \tilde{\partial}_y E_z &= \tilde{\partial}_y \frac{1}{\epsilon_{zz}} \hat{\partial}_x (\epsilon_{xx} E_x) + + \tilde{\partial}_y \frac{1}{\epsilon_{zz}} \hat{\partial}_y (\epsilon_{yy} E_y) \\ \end{aligned} $$ -We can combine this equation for $\gamma \tilde{\partial}_y E_z$ with +We can combine this equation for $\imath \beta \tilde{\partial}_y E_z$ with the unused $\imath \omega \mu_{xx} H_x$ and $\imath \omega \mu_{yy} H_y$ equations to get $$ \begin{aligned} --\imath \omega \mu_{xx} \gamma H_x &= \gamma^2 E_y + \gamma \tilde{\partial}_y E_z \\ --\imath \omega \mu_{xx} \gamma H_x &= \gamma^2 E_y + \tilde{\partial}_y ( +-\imath \omega \mu_{xx} \imath \beta H_x &= -\beta^2 E_y + \imath \beta \tilde{\partial}_y E_z \\ +-\imath \omega \mu_{xx} \imath \beta H_x &= -\beta^2 E_y + \tilde{\partial}_y ( \frac{1}{\epsilon_{zz}} \hat{\partial}_x (\epsilon_{xx} E_x) + \frac{1}{\epsilon_{zz}} \hat{\partial}_y (\epsilon_{yy} E_y) )\\ @@ -100,25 +101,24 @@ and $$ \begin{aligned} --\imath \omega \mu_{yy} \gamma H_y &= -\gamma^2 E_x - \gamma \tilde{\partial}_x E_z \\ --\imath \omega \mu_{yy} \gamma H_y &= -\gamma^2 E_x - \tilde{\partial}_x ( +-\imath \omega \mu_{yy} \imath \beta H_y &= \beta^2 E_x - \imath \beta \tilde{\partial}_x E_z \\ +-\imath \omega \mu_{yy} \imath \beta H_y &= \beta^2 E_x - \tilde{\partial}_x ( \frac{1}{\epsilon_{zz}} \hat{\partial}_x (\epsilon_{xx} E_x) + \frac{1}{\epsilon_{zz}} \hat{\partial}_y (\epsilon_{yy} E_y) )\\ \end{aligned} $$ -However, based on our rewritten equation for $\gamma H_x$ and the so-far unused +However, based on our rewritten equation for $\imath \beta H_x$ and the so-far unused equation for $\imath \omega \mu_{zz} H_z$ we can also write $$ \begin{aligned} --\imath \omega \mu_{xx} (\gamma H_x) &= -\imath \omega \mu_{xx} (-\imath \omega \epsilon_{yy} E_y - \hat{\partial}_x H_z) \\ - &= -\omega^2 \mu_{xx} \epsilon_{yy} E_y - +\imath \omega \mu_{xx} \hat{\partial}_x ( - \frac{1}{-\imath \omega \mu_{zz}} (\tilde{\partial}_x E_y - \tilde{\partial}_y E_x)) \\ - &= -\omega^2 \mu_{xx} \epsilon_{yy} E_y - -\mu_{xx} \hat{\partial}_x \frac{1}{\mu_{zz}} (\tilde{\partial}_x E_y - \tilde{\partial}_y E_x) \\ +-\imath \omega \mu_{xx} (\imath \beta H_x) &= -\imath \omega \mu_{xx} (-\imath \omega \epsilon_{yy} E_y - \hat{\partial}_x H_z) \\ + &= -\omega^2 \mu_{xx} \epsilon_{yy} E_y + \imath \omega \mu_{xx} \hat{\partial}_x ( + \frac{1}{-\imath \omega \mu_{zz}} (\tilde{\partial}_x E_y - \tilde{\partial}_y E_x)) \\ + &= -\omega^2 \mu_{xx} \epsilon_{yy} E_y + -\mu_{xx} \hat{\partial}_x \frac{1}{\mu_{zz}} (\tilde{\partial}_x E_y - \tilde{\partial}_y E_x) \\ \end{aligned} $$ @@ -126,7 +126,7 @@ and, similarly, $$ \begin{aligned} --\imath \omega \mu_{yy} (\gamma H_y) &= \omega^2 \mu_{yy} \epsilon_{xx} E_x +-\imath \omega \mu_{yy} (\imath \beta H_y) &= \omega^2 \mu_{yy} \epsilon_{xx} E_x +\mu_{yy} \hat{\partial}_y \frac{1}{\mu_{zz}} (\tilde{\partial}_x E_y - \tilde{\partial}_y E_x) \\ \end{aligned} $$ @@ -135,12 +135,12 @@ By combining both pairs of expressions, we get $$ \begin{aligned} --\gamma^2 E_x - \tilde{\partial}_x ( +\beta^2 E_x - \tilde{\partial}_x ( \frac{1}{\epsilon_{zz}} \hat{\partial}_x (\epsilon_{xx} E_x) + \frac{1}{\epsilon_{zz}} \hat{\partial}_y (\epsilon_{yy} E_y) ) &= \omega^2 \mu_{yy} \epsilon_{xx} E_x +\mu_{yy} \hat{\partial}_y \frac{1}{\mu_{zz}} (\tilde{\partial}_x E_y - \tilde{\partial}_y E_x) \\ -\gamma^2 E_y + \tilde{\partial}_y ( +-\beta^2 E_y + \tilde{\partial}_y ( \frac{1}{\epsilon_{zz}} \hat{\partial}_x (\epsilon_{xx} E_x) + \frac{1}{\epsilon_{zz}} \hat{\partial}_y (\epsilon_{yy} E_y) ) &= -\omega^2 \mu_{xx} \epsilon_{yy} E_y @@ -165,27 +165,25 @@ $$ E_y \end{bmatrix} $$ -where $\gamma = \imath\beta$. In the literature, $\beta$ is usually used to denote -the lossless/real part of the propagation constant, but in `meanas` it is allowed to -be complex. +In the literature, $\beta$ is usually used to denote the lossless/real part of the propagation constant, +but in `meanas` it is allowed to be complex. An equivalent eigenvalue problem can be formed using the $H_x$ and $H_y$ fields, if those are more convenient. -Note that $E_z$ was never discretized, so $\gamma$ and $\beta$ will need adjustment -to account for numerical dispersion if the result is introduced into a space with a discretized z-axis. +Note that $E_z$ was never discretized, so $\beta$ will need adjustment to account for numerical dispersion +if the result is introduced into a space with a discretized z-axis. """ -# TODO update module docs - from typing import Any +from collections.abc import Sequence import numpy -from numpy.typing import NDArray, ArrayLike +from numpy.typing import NDArray from numpy.linalg import norm -import scipy.sparse as sparse # type: ignore +from scipy import sparse from ..fdmath.operators import deriv_forward, deriv_back, cross -from ..fdmath import vec, unvec, dx_lists_t, vfdfield_t, vcfdfield_t +from ..fdmath import vec, unvec, dx_lists2_t, vcfdfield2_t, vcfdslice_t, vcfdfield2, vfdslice, vcfdslice from ..eigensolvers import signed_eigensolve, rayleigh_quotient_iteration @@ -194,10 +192,10 @@ __author__ = 'Jan Petykiewicz' def operator_e( omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, - ) -> sparse.spmatrix: + dxes: dx_lists2_t, + epsilon: vfdslice, + mu: vfdslice | None = None, + ) -> sparse.sparray: r""" Waveguide operator of the form @@ -246,12 +244,12 @@ def operator_e( Dbx, Dby = deriv_back(dxes[1]) eps_parts = numpy.split(epsilon, 3) - eps_xy = sparse.diags(numpy.hstack((eps_parts[0], eps_parts[1]))) - eps_z_inv = sparse.diags(1 / eps_parts[2]) + eps_xy = sparse.diags_array(numpy.hstack((eps_parts[0], eps_parts[1]))) + eps_z_inv = sparse.diags_array(1 / eps_parts[2]) mu_parts = numpy.split(mu, 3) - mu_yx = sparse.diags(numpy.hstack((mu_parts[1], mu_parts[0]))) - mu_z_inv = sparse.diags(1 / mu_parts[2]) + mu_yx = sparse.diags_array(numpy.hstack((mu_parts[1], mu_parts[0]))) + mu_z_inv = sparse.diags_array(1 / mu_parts[2]) op = ( omega * omega * mu_yx @ eps_xy @@ -263,10 +261,10 @@ def operator_e( def operator_h( omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, - ) -> sparse.spmatrix: + dxes: dx_lists2_t, + epsilon: vfdslice, + mu: vfdslice | None = None, + ) -> sparse.sparray: r""" Waveguide operator of the form @@ -315,12 +313,12 @@ def operator_h( Dbx, Dby = deriv_back(dxes[1]) eps_parts = numpy.split(epsilon, 3) - eps_yx = sparse.diags(numpy.hstack((eps_parts[1], eps_parts[0]))) - eps_z_inv = sparse.diags(1 / eps_parts[2]) + eps_yx = sparse.diags_array(numpy.hstack((eps_parts[1], eps_parts[0]))) + eps_z_inv = sparse.diags_array(1 / eps_parts[2]) mu_parts = numpy.split(mu, 3) - mu_xy = sparse.diags(numpy.hstack((mu_parts[0], mu_parts[1]))) - mu_z_inv = sparse.diags(1 / mu_parts[2]) + mu_xy = sparse.diags_array(numpy.hstack((mu_parts[0], mu_parts[1]))) + mu_z_inv = sparse.diags_array(1 / mu_parts[2]) op = ( omega * omega * eps_yx @ mu_xy @@ -331,15 +329,15 @@ def operator_h( def normalized_fields_e( - e_xy: ArrayLike, + e_xy: vcfdfield2, wavenumber: complex, omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, + dxes: dx_lists2_t, + epsilon: vfdslice, + mu: vfdslice | None = None, prop_phase: float = 0, - ) -> tuple[vcfdfield_t, vcfdfield_t]: - """ + ) -> tuple[vcfdslice_t, vcfdslice_t]: + r""" Given a vector `e_xy` containing the vectorized E_x and E_y fields, returns normalized, vectorized E and H fields for the system. @@ -357,24 +355,40 @@ def normalized_fields_e( Returns: `(e, h)`, where each field is vectorized, normalized, and contains all three vector components. + + Notes: + `e_xy` is only the transverse electric eigenvector. This helper first + reconstructs the full three-component `E` and `H` fields with `exy2e(...)` + and `exy2h(...)`, then normalizes them to unit forward power using + `_normalized_fields(...)`. + + The normalization target is + + $$ + \Re\left[\mathrm{inner\_product}(e, h, \mathrm{conj\_h}=True)\right] = 1, + $$ + + so the returned fields represent a unit-power forward mode under the + discrete Yee-grid Poynting inner product. """ e = exy2e(wavenumber=wavenumber, dxes=dxes, epsilon=epsilon) @ e_xy h = exy2h(wavenumber=wavenumber, omega=omega, dxes=dxes, epsilon=epsilon, mu=mu) @ e_xy - e_norm, h_norm = _normalized_fields(e=e, h=h, omega=omega, dxes=dxes, epsilon=epsilon, - mu=mu, prop_phase=prop_phase) + e_norm, h_norm = _normalized_fields( + e=e, h=h, dxes=dxes, epsilon=epsilon, prop_phase=prop_phase, + ) return e_norm, h_norm def normalized_fields_h( - h_xy: ArrayLike, + h_xy: vcfdfield2, wavenumber: complex, omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, + dxes: dx_lists2_t, + epsilon: vfdslice, + mu: vfdslice | None = None, prop_phase: float = 0, - ) -> tuple[vcfdfield_t, vcfdfield_t]: - """ + ) -> tuple[vcfdslice_t, vcfdslice_t]: + r""" Given a vector `h_xy` containing the vectorized H_x and H_y fields, returns normalized, vectorized E and H fields for the system. @@ -392,39 +406,55 @@ def normalized_fields_h( Returns: `(e, h)`, where each field is vectorized, normalized, and contains all three vector components. + + Notes: + This is the `H_x/H_y` analogue of `normalized_fields_e(...)`. The final + normalized mode should describe the same physical solution, but because + the overall complex phase and sign are chosen heuristically, + `normalized_fields_e(...)` and `normalized_fields_h(...)` need not return + identical representatives for nearly symmetric modes. """ e = hxy2e(wavenumber=wavenumber, omega=omega, dxes=dxes, epsilon=epsilon, mu=mu) @ h_xy h = hxy2h(wavenumber=wavenumber, dxes=dxes, mu=mu) @ h_xy - e_norm, h_norm = _normalized_fields(e=e, h=h, omega=omega, dxes=dxes, epsilon=epsilon, - mu=mu, prop_phase=prop_phase) + e_norm, h_norm = _normalized_fields( + e=e, h=h, dxes=dxes, epsilon=epsilon, prop_phase=prop_phase, + ) return e_norm, h_norm def _normalized_fields( - e: vcfdfield_t, - h: vcfdfield_t, - omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, + e: vcfdslice, + h: vcfdslice, + dxes: dx_lists2_t, + epsilon: vfdslice, prop_phase: float = 0, - ) -> tuple[vcfdfield_t, vcfdfield_t]: - # TODO documentation - shape = [s.size for s in dxes[0]] - dxes_real = [[numpy.real(d) for d in numpy.meshgrid(*dxes[v], indexing='ij')] for v in (0, 1)] + ) -> tuple[vcfdslice_t, vcfdslice_t]: + r""" + Normalize a reconstructed waveguide mode to unit forward power. - E = unvec(e, shape) - H = unvec(h, shape) + The eigenproblem solved by `solve_mode(s)` determines only the mode shape and + propagation constant. The overall complex amplitude and sign are still free. + This helper fixes those remaining degrees of freedom in two steps: + + 1. Compute the discrete longitudinal Poynting flux with + `inner_product(e, h, conj_h=True)`, including the half-cell longitudinal + phase adjustment controlled by `prop_phase`. + 2. Multiply both fields by a scalar chosen so that the real forward power is + `1`, then choose a reproducible phase/sign representative by making a + dominant-energy sample real and using a weighted quadrant sum to break + mirror-symmetry ties. + + The sign heuristic is intentionally pragmatic rather than fundamental: it is + only there to make downstream tests and source/overlap construction choose a + consistent representative when the physical mode is symmetric. + """ + shape = [s.size for s in dxes[0]] # Find time-averaged Sz and normalize to it - # H phase is adjusted by a half-cell forward shift for Yee cell, and 1-cell reverse shift for Poynting - phase = numpy.exp(-1j * -prop_phase / 2) - Sz_a = E[0] * numpy.conj(H[1] * phase) * dxes_real[0][1] * dxes_real[1][0] - Sz_b = E[1] * numpy.conj(H[0] * phase) * dxes_real[0][0] * dxes_real[1][1] - Sz_tavg = numpy.real(Sz_a.sum() - Sz_b.sum()) * 0.5 # 0.5 since E, H are assumed to be peak (not RMS) amplitudes + Sz_tavg = inner_product(e, h, dxes=dxes, prop_phase=prop_phase, conj_h=True).real assert Sz_tavg > 0, f'Found a mode propagating in the wrong direction! {Sz_tavg=}' - energy = epsilon * e.conj() * e + energy = numpy.real(epsilon * e.conj() * e) norm_amplitude = 1 / numpy.sqrt(Sz_tavg) norm_angle = -numpy.angle(e[energy.argmax()]) # Will randomly add a negative sign when mode is symmetric @@ -434,22 +464,23 @@ def _normalized_fields( sign = numpy.sign(E_weighted[:, :max(shape[0] // 2, 1), :max(shape[1] // 2, 1)].real.sum()) + assert sign != 0 norm_factor = sign * norm_amplitude * numpy.exp(1j * norm_angle) e *= norm_factor h *= norm_factor - return e, h + return vcfdslice_t(e), vcfdslice_t(h) def exy2h( wavenumber: complex, omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None - ) -> sparse.spmatrix: + dxes: dx_lists2_t, + epsilon: vfdslice, + mu: vfdslice | None = None + ) -> sparse.sparray: """ Operator which transforms the vector `e_xy` containing the vectorized E_x and E_y fields, into a vectorized H containing all three H components @@ -472,10 +503,10 @@ def exy2h( def hxy2e( wavenumber: complex, omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None - ) -> sparse.spmatrix: + dxes: dx_lists2_t, + epsilon: vfdslice, + mu: vfdslice | None = None + ) -> sparse.sparray: """ Operator which transforms the vector `h_xy` containing the vectorized H_x and H_y fields, into a vectorized E containing all three E components @@ -497,9 +528,9 @@ def hxy2e( def hxy2h( wavenumber: complex, - dxes: dx_lists_t, - mu: vfdfield_t | None = None - ) -> sparse.spmatrix: + dxes: dx_lists2_t, + mu: vfdslice | None = None + ) -> sparse.sparray: """ Operator which transforms the vector `h_xy` containing the vectorized H_x and H_y fields, into a vectorized H containing all three H components @@ -518,26 +549,53 @@ def hxy2h( if mu is not None: mu_parts = numpy.split(mu, 3) - mu_xy = sparse.diags(numpy.hstack((mu_parts[0], mu_parts[1]))) - mu_z_inv = sparse.diags(1 / mu_parts[2]) + mu_xy = sparse.diags_array(numpy.hstack((mu_parts[0], mu_parts[1]))) + mu_z_inv = sparse.diags_array(1 / mu_parts[2]) hxy2hz = mu_z_inv @ hxy2hz @ mu_xy n_pts = dxes[1][0].size * dxes[1][1].size - op = sparse.vstack((sparse.eye(2 * n_pts), + op = sparse.vstack((sparse.eye_array(2 * n_pts), hxy2hz)) return op def exy2e( wavenumber: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - ) -> sparse.spmatrix: - """ + dxes: dx_lists2_t, + epsilon: vfdslice, + ) -> sparse.sparray: + r""" Operator which transforms the vector `e_xy` containing the vectorized E_x and E_y fields, into a vectorized E containing all three E components + From the operator derivation (see module docs), we have + + $$ + \imath \omega \epsilon_{zz} E_z = \hat{\partial}_x H_y - \hat{\partial}_y H_x \\ + $$ + + as well as the intermediate equations + + $$ + \begin{aligned} + \imath \beta H_y &= \imath \omega \epsilon_{xx} E_x - \hat{\partial}_y H_z \\ + \imath \beta H_x &= -\imath \omega \epsilon_{yy} E_y - \hat{\partial}_x H_z \\ + \end{aligned} + $$ + + Combining these, we get + + $$ + \begin{aligned} + E_z &= \frac{1}{- \omega \beta \epsilon_{zz}} (( + \hat{\partial}_y \hat{\partial}_x H_z + -\hat{\partial}_x \hat{\partial}_y H_z) + + \imath \omega (\hat{\partial}_x \epsilon_{xx} E_x + \hat{\partial}_y \epsilon{yy} E_y)) + &= \frac{1}{\imath \beta \epsilon_{zz}} (\hat{\partial}_x \epsilon_{xx} E_x + \hat{\partial}_y \epsilon{yy} E_y) + \end{aligned} + $$ + Args: wavenumber: Wavenumber assuming fields have z-dependence of `exp(-i * wavenumber * z)` It should satisfy `operator_e() @ e_xy == wavenumber**2 * e_xy` @@ -552,13 +610,13 @@ def exy2e( if epsilon is not None: epsilon_parts = numpy.split(epsilon, 3) - epsilon_xy = sparse.diags(numpy.hstack((epsilon_parts[0], epsilon_parts[1]))) - epsilon_z_inv = sparse.diags(1 / epsilon_parts[2]) + epsilon_xy = sparse.diags_array(numpy.hstack((epsilon_parts[0], epsilon_parts[1]))) + epsilon_z_inv = sparse.diags_array(1 / epsilon_parts[2]) exy2ez = epsilon_z_inv @ exy2ez @ epsilon_xy n_pts = dxes[0][0].size * dxes[0][1].size - op = sparse.vstack((sparse.eye(2 * n_pts), + op = sparse.vstack((sparse.eye_array(2 * n_pts), exy2ez)) return op @@ -566,12 +624,12 @@ def exy2e( def e2h( wavenumber: complex, omega: complex, - dxes: dx_lists_t, - mu: vfdfield_t | None = None - ) -> sparse.spmatrix: + dxes: dx_lists2_t, + mu: vfdslice | None = None + ) -> sparse.sparray: """ Returns an operator which, when applied to a vectorized E eigenfield, produces - the vectorized H eigenfield. + the vectorized H eigenfield slice. Args: wavenumber: Wavenumber assuming fields have z-dependence of `exp(-i * wavenumber * z)` @@ -584,19 +642,19 @@ def e2h( """ op = curl_e(wavenumber, dxes) / (-1j * omega) if mu is not None: - op = sparse.diags(1 / mu) @ op + op = sparse.diags_array(1 / mu) @ op return op def h2e( wavenumber: complex, omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t - ) -> sparse.spmatrix: + dxes: dx_lists2_t, + epsilon: vfdslice, + ) -> sparse.sparray: """ Returns an operator which, when applied to a vectorized H eigenfield, produces - the vectorized E eigenfield. + the vectorized E eigenfield slice. Args: wavenumber: Wavenumber assuming fields have z-dependence of `exp(-i * wavenumber * z)` @@ -607,13 +665,13 @@ def h2e( Returns: Sparse matrix representation of the operator. """ - op = sparse.diags(1 / (1j * omega * epsilon)) @ curl_h(wavenumber, dxes) + op = sparse.diags_array(1 / (1j * omega * epsilon)) @ curl_h(wavenumber, dxes) return op -def curl_e(wavenumber: complex, dxes: dx_lists_t) -> sparse.spmatrix: +def curl_e(wavenumber: complex, dxes: dx_lists2_t) -> sparse.sparray: """ - Discretized curl operator for use with the waveguide E field. + Discretized curl operator for use with the waveguide E field slice. Args: wavenumber: Wavenumber assuming fields have z-dependence of `exp(-i * wavenumber * z)` @@ -622,18 +680,18 @@ def curl_e(wavenumber: complex, dxes: dx_lists_t) -> sparse.spmatrix: Returns: Sparse matrix representation of the operator. """ - n = 1 - for d in dxes[0]: - n *= len(d) + nn = 1 + for dd in dxes[0]: + nn *= len(dd) - Bz = -1j * wavenumber * sparse.eye(n) + Bz = -1j * wavenumber * sparse.eye_array(nn) Dfx, Dfy = deriv_forward(dxes[0]) return cross([Dfx, Dfy, Bz]) -def curl_h(wavenumber: complex, dxes: dx_lists_t) -> sparse.spmatrix: +def curl_h(wavenumber: complex, dxes: dx_lists2_t) -> sparse.sparray: """ - Discretized curl operator for use with the waveguide H field. + Discretized curl operator for use with the waveguide H field slice. Args: wavenumber: Wavenumber assuming fields have z-dependence of `exp(-i * wavenumber * z)` @@ -642,22 +700,22 @@ def curl_h(wavenumber: complex, dxes: dx_lists_t) -> sparse.spmatrix: Returns: Sparse matrix representation of the operator. """ - n = 1 - for d in dxes[1]: - n *= len(d) + nn = 1 + for dd in dxes[1]: + nn *= len(dd) - Bz = -1j * wavenumber * sparse.eye(n) + Bz = -1j * wavenumber * sparse.eye_array(nn) Dbx, Dby = deriv_back(dxes[1]) return cross([Dbx, Dby, Bz]) def h_err( - h: vcfdfield_t, + h: vcfdslice, wavenumber: complex, omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None + dxes: dx_lists2_t, + epsilon: vfdslice, + mu: vfdslice | None = None ) -> float: """ Calculates the relative error in the H field @@ -676,7 +734,7 @@ def h_err( ce = curl_e(wavenumber, dxes) ch = curl_h(wavenumber, dxes) - eps_inv = sparse.diags(1 / epsilon) + eps_inv = sparse.diags_array(1 / epsilon) if mu is None: op = ce @ eps_inv @ ch @ h - omega ** 2 * h @@ -687,12 +745,12 @@ def h_err( def e_err( - e: vcfdfield_t, + e: vcfdslice, wavenumber: complex, omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, + dxes: dx_lists2_t, + epsilon: vfdslice, + mu: vfdslice | None = None, ) -> float: """ Calculates the relative error in the E field @@ -714,21 +772,21 @@ def e_err( if mu is None: op = ch @ ce @ e - omega ** 2 * (epsilon * e) else: - mu_inv = sparse.diags(1 / mu) + mu_inv = sparse.diags_array(1 / mu) op = ch @ mu_inv @ ce @ e - omega ** 2 * (epsilon * e) return float(norm(op) / norm(e)) def sensitivity( - e_norm: vcfdfield_t, - h_norm: vcfdfield_t, + e_norm: vcfdslice, + h_norm: vcfdslice, wavenumber: complex, omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, - ) -> vcfdfield_t: + dxes: dx_lists2_t, + epsilon: vfdslice, + mu: vfdslice | None = None, + ) -> vcfdslice_t: r""" Given a waveguide structure (`dxes`, `epsilon`, `mu`) and mode fields (`e_norm`, `h_norm`, `wavenumber`, `omega`), calculates the sensitivity of the wavenumber @@ -802,11 +860,11 @@ def sensitivity( Dbx, Dby = deriv_back(dxes[1]) eps_x, eps_y, eps_z = numpy.split(epsilon, 3) - eps_xy = sparse.diags(numpy.hstack((eps_x, eps_y))) - eps_z_inv = sparse.diags(1 / eps_z) + eps_xy = sparse.diags_array(numpy.hstack((eps_x, eps_y))) + eps_z_inv = sparse.diags_array(1 / eps_z) mu_x, mu_y, _mu_z = numpy.split(mu, 3) - mu_yx = sparse.diags(numpy.hstack((mu_y, mu_x))) + mu_yx = sparse.diags_array(numpy.hstack((mu_y, mu_x))) da_exxhyy = vec(dxes[1][0][:, None] * dxes[0][1][None, :]) da_eyyhxx = vec(dxes[1][1][None, :] * dxes[0][0][:, None]) @@ -820,15 +878,15 @@ def sensitivity( norm = hv_yx_conj @ ev_xy sens_tot = numpy.concatenate([sens_xy1 + sens_xy2, sens_z]) / (2 * wavenumber * norm) - return sens_tot + return vcfdslice_t(sens_tot) def solve_modes( - mode_numbers: list[int], + mode_numbers: Sequence[int], omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - mu: vfdfield_t | None = None, + dxes: dx_lists2_t, + epsilon: vfdslice, + mu: vfdslice | None = None, mode_margin: int = 2, ) -> tuple[NDArray[numpy.complex128], NDArray[numpy.complex128]]: """ @@ -845,32 +903,38 @@ def solve_modes( ability to find the correct mode. Default 2. Returns: - e_xys: list of vfdfield_t specifying fields + e_xys: NDArray of vfdfield_t specifying fields. First dimension is mode number. wavenumbers: list of wavenumbers """ - ''' - Solve for the largest-magnitude eigenvalue of the real operator - ''' + # + # Solve for the largest-magnitude eigenvalue of the real operator + # dxes_real = [[numpy.real(dx) for dx in dxi] for dxi in dxes] mu_real = None if mu is None else numpy.real(mu) A_r = operator_e(numpy.real(omega), dxes_real, numpy.real(epsilon), mu_real) eigvals, eigvecs = signed_eigensolve(A_r, max(mode_numbers) + mode_margin) - e_xys = eigvecs[:, -(numpy.array(mode_numbers) + 1)] + keep_inds = -(numpy.array(mode_numbers) + 1) + e_xys = eigvecs[:, keep_inds].T + eigvals = eigvals[keep_inds] - ''' - Now solve for the eigenvector of the full operator, using the real operator's - eigenvector as an initial guess for Rayleigh quotient iteration. - ''' + # + # Now solve for the eigenvector of the full operator, using the real operator's + # eigenvector as an initial guess for Rayleigh quotient iteration. + # A = operator_e(omega, dxes, epsilon, mu) for nn in range(len(mode_numbers)): - eigvals[nn], e_xys[:, nn] = rayleigh_quotient_iteration(A, e_xys[:, nn]) + eigvals[nn], e_xys[nn, :] = rayleigh_quotient_iteration(A, e_xys[nn, :]) # Calculate the wave-vector (force the real part to be positive) wavenumbers = numpy.sqrt(eigvals) wavenumbers *= numpy.sign(numpy.real(wavenumbers)) + order = wavenumbers.argsort()[::-1] + e_xys = e_xys[order] + wavenumbers = wavenumbers[order] + return e_xys, wavenumbers @@ -878,7 +942,7 @@ def solve_mode( mode_number: int, *args: Any, **kwargs: Any, - ) -> tuple[vcfdfield_t, complex]: + ) -> tuple[vcfdfield2_t, complex]: """ Wrapper around `solve_modes()` that solves for a single mode. @@ -892,4 +956,66 @@ def solve_mode( """ kwargs['mode_numbers'] = [mode_number] e_xys, wavenumbers = solve_modes(*args, **kwargs) - return e_xys[:, 0], wavenumbers[0] + return vcfdfield2_t(e_xys[0]), wavenumbers[0] + + +def inner_product( + e1: vcfdfield2, + h2: vcfdfield2, + dxes: dx_lists2_t, + prop_phase: float = 0, + conj_h: bool = False, + trapezoid: bool = False, + ) -> complex: + r""" + Compute the discrete waveguide overlap / Poynting inner product. + + This is the 2D transverse integral corresponding to the time-averaged + longitudinal Poynting flux, + + $$ + \frac{1}{2}\int (E_x H_y - E_y H_x) \, dx \, dy + $$ + + with the Yee-grid staggering and optional propagation-phase adjustment used + by the waveguide helpers in this module. + + Args: + e1: Vectorized electric field, typically from `exy2e(...)` or + `normalized_fields_e(...)`. + h2: Vectorized magnetic field, typically from `hxy2h(...)`, + `exy2h(...)`, or one of the normalization helpers. + dxes: Two-dimensional Yee-grid spacing lists `[dx_e, dx_h]`. + prop_phase: Phase advance over one propagation cell. This is used to + shift the H field into the same longitudinal reference plane as the + E field. + conj_h: Whether to conjugate `h2` before forming the overlap. Use + `True` for the usual time-averaged power normalization. + trapezoid: Whether to use trapezoidal quadrature instead of the default + rectangular Yee-cell sum. + + Returns: + Complex overlap / longitudinal power integral. + """ + + shape = [s.size for s in dxes[0]] + + # H phase is adjusted by a half-cell forward shift for Yee cell, and 1-cell reverse shift for Poynting + phase = numpy.exp(-1j * -prop_phase / 2) + + E1 = unvec(e1, shape) + H2 = unvec(h2, shape) * phase + + if conj_h: + H2 = numpy.conj(H2) + + # Find time-averaged Sz and normalize to it + dxes_real = [[numpy.real(dxyz) for dxyz in dxeh] for dxeh in dxes] + if trapezoid: + Sz_a = numpy.trapezoid(numpy.trapezoid(E1[0] * H2[1], numpy.cumsum(dxes_real[0][1])), numpy.cumsum(dxes_real[1][0])) + Sz_b = numpy.trapezoid(numpy.trapezoid(E1[1] * H2[0], numpy.cumsum(dxes_real[0][0])), numpy.cumsum(dxes_real[1][1])) + else: + Sz_a = E1[0] * H2[1] * dxes_real[1][0][:, None] * dxes_real[0][1][None, :] + Sz_b = E1[1] * H2[0] * dxes_real[0][0][:, None] * dxes_real[1][1][None, :] + Sz = 0.5 * (Sz_a.sum() - Sz_b.sum()) + return Sz diff --git a/meanas/fdfd/waveguide_3d.py b/meanas/fdfd/waveguide_3d.py index 7f994d3..c77c8d4 100644 --- a/meanas/fdfd/waveguide_3d.py +++ b/meanas/fdfd/waveguide_3d.py @@ -3,15 +3,40 @@ Tools for working with waveguide modes in 3D domains. This module relies heavily on `waveguide_2d` and mostly just transforms its parameters into 2D equivalents and expands the results back into 3D. + +The intended workflow is: + +1. Select a single-cell slice normal to the propagation axis. +2. Solve the corresponding 2D mode problem with `solve_mode(...)`. +3. Turn that mode into a one-sided source with `compute_source(...)`. +4. Build an overlap window with `compute_overlap_e(...)` for port readout. + +`polarity` is part of the public convention throughout this module: + +- `+1` means forward propagation toward increasing index along `axis` +- `-1` means backward propagation toward decreasing index along `axis` + +That same convention controls which side of the selected slice is used for the +overlap window and how the expanded field is phased. """ -from typing import Sequence, Any +from typing import Any, TypedDict, cast +import warnings +from collections.abc import Sequence import numpy from numpy.typing import NDArray +from numpy import complexfloating -from ..fdmath import vec, unvec, dx_lists_t, fdfield_t, cfdfield_t +from ..fdmath import vec, unvec, dx_lists_t, cfdfield_t, fdfield, cfdfield from . import operators, waveguide_2d +class Waveguide3DMode(TypedDict): + wavenumber: complex + wavenumber_2d: complex + H: NDArray[complexfloating] + E: NDArray[complexfloating] + + def solve_mode( mode_number: int, omega: complex, @@ -19,12 +44,12 @@ def solve_mode( axis: int, polarity: int, slices: Sequence[slice], - epsilon: fdfield_t, - mu: fdfield_t | None = None, - ) -> dict[str, complex | NDArray[numpy.float_]]: - """ + epsilon: fdfield, + mu: fdfield | None = None, + ) -> Waveguide3DMode: + r""" Given a 3D grid, selects a slice from the grid and attempts to - solve for an eigenmode propagating through that slice. + solve for an eigenmode propagating through that slice. Args: mode_number: Number of the mode, 0-indexed @@ -33,27 +58,31 @@ def solve_mode( axis: Propagation axis (0=x, 1=y, 2=z) polarity: Propagation direction (+1 for +ve, -1 for -ve) slices: `epsilon[tuple(slices)]` is used to select the portion of the grid to use - as the waveguide cross-section. `slices[axis]` should select only one item. + as the waveguide cross-section. `slices[axis]` must select exactly one item. epsilon: Dielectric constant mu: Magnetic permeability (default 1 everywhere) Returns: - ``` - { - 'E': list[NDArray[numpy.float_]], - 'H': list[NDArray[numpy.float_]], - 'wavenumber': complex, - } - ``` + Dictionary containing: + + - `E`: full-grid electric field for the solved mode + - `H`: full-grid magnetic field for the solved mode + - `wavenumber`: propagation constant corrected for the discretized + propagation axis + - `wavenumber_2d`: propagation constant of the reduced 2D eigenproblem + + Notes: + The returned fields are normalized through the `waveguide_2d` + normalization convention before being expanded back to 3D. """ if mu is None: mu = numpy.ones_like(epsilon) slices = tuple(slices) - ''' - Solve the 2D problem in the specified plane - ''' + # + # Solve the 2D problem in the specified plane + # # Define rotation to set z as propagation direction order = numpy.roll(range(3), 2 - axis) reverse_order = numpy.roll(range(3), axis - 2) @@ -71,9 +100,10 @@ def solve_mode( } e_xy, wavenumber_2d = waveguide_2d.solve_mode(mode_number, **args_2d) - ''' - Apply corrections and expand to 3D - ''' + # + # Apply corrections and expand to 3D + # + # Correct wavenumber to account for numerical dispersion. wavenumber = 2 / dx_prop * numpy.arcsin(wavenumber_2d * dx_prop / 2) @@ -92,11 +122,12 @@ def solve_mode( # Expand E, H to full epsilon space we were given E = numpy.zeros_like(epsilon, dtype=complex) H = numpy.zeros_like(epsilon, dtype=complex) - for a, o in enumerate(reverse_order): - E[(a, *slices)] = e[o][:, :, None].transpose(reverse_order) - H[(a, *slices)] = h[o][:, :, None].transpose(reverse_order) + for aa, oo in enumerate(reverse_order): + iii = cast('tuple[slice | int]', (aa, *slices)) + E[iii] = e[oo][:, :, None].transpose(reverse_order) + H[iii] = h[oo][:, :, None].transpose(reverse_order) - results = { + results: Waveguide3DMode = { 'wavenumber': wavenumber, 'wavenumber_2d': wavenumber_2d, 'H': H, @@ -106,15 +137,15 @@ def solve_mode( def compute_source( - E: cfdfield_t, + E: cfdfield, wavenumber: complex, omega: complex, dxes: dx_lists_t, axis: int, polarity: int, slices: Sequence[slice], - epsilon: fdfield_t, - mu: fdfield_t | None = None, + epsilon: fdfield, + mu: fdfield | None = None, ) -> cfdfield_t: """ Given an eigenmode obtained by `solve_mode`, returns the current source distribution @@ -132,7 +163,14 @@ def compute_source( mu: Magnetic permeability (default 1 everywhere) Returns: - J distribution for the unidirectional source + `J` distribution for a one-sided electric-current source. + + Notes: + The source is built from the expanded mode field and a boundary-source + operator. The resulting current is intended to be injected with the + same sign convention used elsewhere in the package: + + `E -= dt * J / epsilon` """ E_expanded = expand_e(E=E, dxes=dxes, wavenumber=wavenumber, axis=axis, polarity=polarity, slices=slices) @@ -148,66 +186,113 @@ def compute_source( masked_e2j = operators.e_boundary_source(mask=vec(mask), omega=omega, dxes=dxes, epsilon=vec(epsilon), mu=vec(mu)) J = unvec(masked_e2j @ vec(E_expanded), E.shape[1:]) - return J + return cfdfield_t(J) def compute_overlap_e( - E: cfdfield_t, - wavenumber: complex, - dxes: dx_lists_t, - axis: int, - polarity: int, - slices: Sequence[slice], - ) -> cfdfield_t: # TODO DOCS - """ - Given an eigenmode obtained by `solve_mode`, calculates an overlap_e for the - mode orthogonality relation Integrate(((E x H_mode) + (E_mode x H)) dot dn) - [assumes reflection symmetry]. - - TODO: add reference - - Args: - E: E-field of the mode - H: H-field of the mode (advanced by half of a Yee cell from E) - wavenumber: Wavenumber of the mode - omega: Angular frequency of the simulation - dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` - axis: Propagation axis (0=x, 1=y, 2=z) - polarity: Propagation direction (+1 for +ve, -1 for -ve) - slices: `epsilon[tuple(slices)]` is used to select the portion of the grid to use - as the waveguide cross-section. slices[axis] should select only one item. - mu: Magnetic permeability (default 1 everywhere) - - Returns: - overlap_e such that `numpy.sum(overlap_e * other_e.conj())` computes the overlap integral - """ - slices = tuple(slices) - - Ee = expand_e(E=E, wavenumber=wavenumber, dxes=dxes, - axis=axis, polarity=polarity, slices=slices) - - start, stop = sorted((slices[axis].start, slices[axis].start - 2 * polarity)) - - slices2_l = list(slices) - slices2_l[axis] = slice(start, stop) - slices2 = (slice(None), *slices2_l) - - Etgt = numpy.zeros_like(Ee) - Etgt[slices2] = Ee[slices2] - - Etgt /= (Etgt.conj() * Etgt).sum() - return Etgt - - -def expand_e( - E: cfdfield_t, + E: cfdfield, wavenumber: complex, dxes: dx_lists_t, axis: int, polarity: int, slices: Sequence[slice], ) -> cfdfield_t: + r""" + Build an overlap field for projecting another 3D electric field onto a mode. + + The returned field is intended for the discrete overlap expression + + $$ + \sum \mathrm{overlap\_e} \; E_\mathrm{other}^* + $$ + + where the sum is over the full Yee-grid field storage. + + The construction uses a two-cell window immediately upstream of the selected + slice: + + - for `polarity=+1`, the two cells just before `slices[axis].start` + - for `polarity=-1`, the two cells just after `slices[axis].stop` + + The window is clipped to the simulation domain if necessary. A clipped but + non-empty window raises `RuntimeWarning`; an empty window raises + `ValueError`. + + The derivation below assumes reflection symmetry and the standard waveguide + overlap relation involving + + $$ + \int ((E \times H_\mathrm{mode}) + (E_\mathrm{mode} \times H)) \cdot dn. + $$ + + E x H_mode + E_mode x H + -> Ex Hmy - EyHmx + Emx Hy - Emy Hx (Z-prop) + Ex we/B Emx + Ex i/B dy Hmz - Ey (-we/B Emy) - Ey i/B dx Hmz + we/B (Ex Emx + Ey Emy) + i/B (Ex dy Hmz - Ey dx Hmz) + we/B (Ex Emx + Ey Emy) + i/B (Ex dy (dx Emy - dy Emx) - Ey dx (dx Emy - dy Emx)) + we/B (Ex Emx + Ey Emy) + i/B (Ex dy dx Emy - Ex dy dy Emx - Ey dx dx Emy - Ey dx dy Emx) + + Ex j/wu (-jB Emx - dx Emz) - Ey j/wu (dy Emz + jB Emy) + B/wu (Ex Emx + Ey Emy) - j/wu (Ex dx Emz + Ey dy Emz) + + + Args: + E: E-field of the mode + wavenumber: Wavenumber of the mode + dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` + axis: Propagation axis (0=x, 1=y, 2=z) + polarity: Propagation direction (+1 for +ve, -1 for -ve) + slices: `epsilon[tuple(slices)]` is used to select the portion of the grid to use + as the waveguide cross-section. slices[axis] should select only one item. + + Returns: + `overlap_e` normalized so that `numpy.sum(overlap_e * E.conj()) == 1` + over the retained overlap window. """ + slices = tuple(slices) + + Ee = expand_e(E=E, wavenumber=wavenumber, dxes=dxes, + axis=axis, polarity=polarity, slices=slices) + + axis_size = E.shape[axis + 1] + if polarity > 0: + start = slices[axis].start - 2 + stop = slices[axis].start + else: + start = slices[axis].stop + stop = slices[axis].stop + 2 + + clipped_start = max(0, start) + clipped_stop = min(axis_size, stop) + if clipped_start >= clipped_stop: + raise ValueError('Requested overlap window lies outside the domain') + if clipped_start != start or clipped_stop != stop: + warnings.warn('Requested overlap window was clipped to fit within the domain', RuntimeWarning, stacklevel=2) + + slices2_l = list(slices) + slices2_l[axis] = slice(clipped_start, clipped_stop) + slices2 = (slice(None), *slices2_l) + + Etgt = numpy.zeros_like(Ee) + Etgt[slices2] = Ee[slices2] + + # Note: We normalize so that (Etgt @ E.conj()) == 1, so (Etgt @ Etgt.conj) != 1 + norm = (Etgt.conj() * Etgt).sum() + if norm == 0: + raise ValueError('Requested overlap window contains no overlap field support') + Etgt = Etgt / norm + return cfdfield_t(Etgt) + + +def expand_e( + E: cfdfield, + wavenumber: complex, + dxes: dx_lists_t, + axis: int, + polarity: int, + slices: Sequence[slice], + ) -> cfdfield_t: + r""" Given an eigenmode obtained by `solve_mode`, expands the E-field from the 2D slice where the mode was calculated to the entire domain (along the propagation axis). This assumes the epsilon cross-section remains constant throughout the @@ -225,6 +310,16 @@ def expand_e( Returns: `E`, with the original field expanded along the specified `axis`. + + Notes: + This helper assumes that the waveguide cross-section remains constant + along the propagation axis and applies the phase factor + + $$ + e^{-i \, \mathrm{polarity} \, wavenumber \, \Delta z} + $$ + + to each copied slice. """ slices = tuple(slices) @@ -245,4 +340,4 @@ def expand_e( slices_in = (slice(None), *slices) E_expanded[slices_exp] = phase_E * numpy.array(E)[slices_in] - return E_expanded + return cfdfield_t(E_expanded) diff --git a/meanas/fdfd/waveguide_cyl.py b/meanas/fdfd/waveguide_cyl.py index d476caa..f2cb5c3 100644 --- a/meanas/fdfd/waveguide_cyl.py +++ b/meanas/fdfd/waveguide_cyl.py @@ -1,49 +1,181 @@ -""" +r""" Operators and helper functions for cylindrical waveguides with unchanging cross-section. -WORK IN PROGRESS, CURRENTLY BROKEN +Waveguide operator is derived according to 10.1364/OL.33.001848. -As the z-dependence is known, all the functions in this file assume a 2D grid - (i.e. `dxes = [[[dr_e_0, dx_e_1, ...], [dy_e_0, ...]], [[dr_h_0, ...], [dy_h_0, ...]]]`). +As in `waveguide_2d`, the propagation dependence is separated from the +transverse solve. Here the propagation coordinate is the bend angle `\theta`, +and the fields are assumed to have the form + +$$ +\vec{E}(r, y, \theta), \vec{H}(r, y, \theta) \propto e^{-\imath m \theta}, +$$ + +where `m` is the angular wavenumber returned by `solve_mode(s)`. It is often +convenient to introduce the corresponding linear wavenumber + +$$ +\beta = \frac{m}{r_{\min}}, +$$ + +so that the cylindrical problem resembles the straight-waveguide problem with +additional metric factors. + +Those metric factors live on the staggered radial Yee grids. If the left edge of +the computational window is at `r = r_{\min}`, define the electric-grid and +magnetic-grid radial sample locations by + +$$ +\begin{aligned} +r_a(n) &= r_{\min} + \sum_{j \le n} \Delta r_{e, j}, \\ +r_b\!\left(n + \tfrac{1}{2}\right) &= r_{\min} + \tfrac{1}{2}\Delta r_{e, n} + + \sum_{j < n} \Delta r_{h, j}, +\end{aligned} +$$ + +and from them the diagonal metric matrices + +$$ +\begin{aligned} +T_a &= \operatorname{diag}(r_a / r_{\min}), \\ +T_b &= \operatorname{diag}(r_b / r_{\min}). +\end{aligned} +$$ + +With the same forward/backward derivative notation used in `waveguide_2d`, the +coordinate-transformed discrete curl equations used here are + +$$ +\begin{aligned} +-\imath \omega \mu_{rr} H_r &= \tilde{\partial}_y E_z + \imath \beta T_a^{-1} E_y, \\ +-\imath \omega \mu_{yy} H_y &= -\imath \beta T_b^{-1} E_r + - T_b^{-1} \tilde{\partial}_r (T_a E_z), \\ +-\imath \omega \mu_{zz} H_z &= \tilde{\partial}_r E_y - \tilde{\partial}_y E_r, \\ +\imath \beta H_y &= -\imath \omega T_b \epsilon_{rr} E_r - T_b \hat{\partial}_y H_z, \\ +\imath \beta H_r &= \imath \omega T_a \epsilon_{yy} E_y + - T_b T_a^{-1} \hat{\partial}_r (T_b H_z), \\ +\imath \omega E_z &= T_a \epsilon_{zz}^{-1} + \left(\hat{\partial}_r H_y - \hat{\partial}_y H_r\right). +\end{aligned} +$$ + +The first three equations are the cylindrical analogue of the straight-guide +relations for `H_r`, `H_y`, and `H_z`. The next two are the metric-weighted +versions of the straight-guide identities for `\imath \beta H_y` and +`\imath \beta H_r`, and the last equation plays the same role as the +longitudinal `E_z` reconstruction in `waveguide_2d`. + +Following the same elimination steps as in `waveguide_2d`, apply +`\imath \beta \tilde{\partial}_r` and `\imath \beta \tilde{\partial}_y` to the +equation for `E_z`, substitute for `\imath \beta H_r` and `\imath \beta H_y`, +and then eliminate `H_z` with + +$$ +H_z = \frac{1}{-\imath \omega \mu_{zz}} +\left(\tilde{\partial}_r E_y - \tilde{\partial}_y E_r\right). +$$ + +This yields the transverse electric eigenproblem implemented by +`cylindrical_operator(...)`: + +$$ +\beta^2 +\begin{bmatrix} E_r \\ E_y \end{bmatrix} += +\left( +\omega^2 +\begin{bmatrix} +T_b^2 \mu_{yy} \epsilon_{xx} & 0 \\ +0 & T_a^2 \mu_{xx} \epsilon_{yy} +\end{bmatrix} ++ +\begin{bmatrix} +-T_b \mu_{yy} \hat{\partial}_y \\ + T_a \mu_{xx} \hat{\partial}_x +\end{bmatrix} +T_b \mu_{zz}^{-1} +\begin{bmatrix} +-\tilde{\partial}_y & \tilde{\partial}_x +\end{bmatrix} ++ +\begin{bmatrix} +\tilde{\partial}_x \\ +\tilde{\partial}_y +\end{bmatrix} +T_a \epsilon_{zz}^{-1} +\begin{bmatrix} +\hat{\partial}_x T_b \epsilon_{xx} & +\hat{\partial}_y T_a \epsilon_{yy} +\end{bmatrix} +\right) +\begin{bmatrix} E_r \\ E_y \end{bmatrix}. +$$ + +Since `\beta = m / r_{\min}`, the solver implemented in this file returns the +angular wavenumber `m`, while the operator itself is most naturally written in +terms of the linear quantity `\beta`. The helpers below reconstruct the full +field components from the solved transverse eigenvector and then normalize the +mode to unit forward power with the same discrete longitudinal Poynting inner +product used by `waveguide_2d`. + +As in the straight-waveguide case, all functions here assume a 2D grid: + +`dxes = [[[dr_e_0, dr_e_1, ...], [dy_e_0, ...]], [[dr_h_0, ...], [dy_h_0, ...]]]`. """ -# TODO update module docs +from typing import Any, cast +from collections.abc import Sequence +import logging import numpy -import scipy.sparse as sparse # type: ignore +from numpy.typing import NDArray, ArrayLike +from scipy import sparse -from ..fdmath import vec, unvec, dx_lists_t, fdfield_t, vfdfield_t, cfdfield_t +from ..fdmath import vec, unvec, dx_lists2_t, vcfdslice_t, vfdslice, vcfdslice, vcfdfield2 from ..fdmath.operators import deriv_forward, deriv_back from ..eigensolvers import signed_eigensolve, rayleigh_quotient_iteration +from . import waveguide_2d + +logger = logging.getLogger(__name__) def cylindrical_operator( - omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - r0: float, - ) -> sparse.spmatrix: - """ + omega: float, + dxes: dx_lists2_t, + epsilon: vfdslice, + rmin: float, + ) -> sparse.sparray: + r""" Cylindrical coordinate waveguide operator of the form - (NOTE: See 10.1364/OL.33.001848) - TODO: consider 10.1364/OE.20.021583 - - TODO + $$ + (\omega^2 \begin{bmatrix} T_b T_b \mu_{yy} \epsilon_{xx} & 0 \\ + 0 & T_a T_a \mu_{xx} \epsilon_{yy} \end{bmatrix} + + \begin{bmatrix} -T_b \mu_{yy} \hat{\partial}_y \\ + T_a \mu_{xx} \hat{\partial}_x \end{bmatrix} T_b \mu_{zz}^{-1} + \begin{bmatrix} -\tilde{\partial}_y & \tilde{\partial}_x \end{bmatrix} + + \begin{bmatrix} \tilde{\partial}_x \\ + \tilde{\partial}_y \end{bmatrix} T_a \epsilon_{zz}^{-1} + \begin{bmatrix} \hat{\partial}_x T_b \epsilon_{xx} & \hat{\partial}_y T_a \epsilon_{yy} \end{bmatrix}) + \begin{bmatrix} E_r \\ + E_y \end{bmatrix} + $$ for use with a field vector of the form `[E_r, E_y]`. This operator can be used to form an eigenvalue problem of the form - A @ [E_r, E_y] = wavenumber**2 * [E_r, E_y] + A @ [E_r, E_y] = beta**2 * [E_r, E_y] which can then be solved for the eigenmodes of the system - (an `exp(-i * wavenumber * theta)` theta-dependence is assumed for the fields). + (an `exp(-i * angular_wavenumber * theta)` theta-dependence is assumed for + the fields, with `beta = angular_wavenumber / rmin`). + + (NOTE: See module docs and 10.1364/OL.33.001848) Args: omega: The angular frequency of the system dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` (2D) epsilon: Vectorized dielectric constant grid - r0: Radius of curvature for the simulation. This should be the minimum value of - r within the simulation domain. + rmin: Radius at the left edge of the simulation domain (at minimum 'x') Returns: Sparse matrix representation of the operator @@ -52,97 +184,409 @@ def cylindrical_operator( Dfx, Dfy = deriv_forward(dxes[0]) Dbx, Dby = deriv_back(dxes[1]) - rx = r0 + numpy.cumsum(dxes[0][0]) - ry = r0 + dxes[0][0] / 2.0 + numpy.cumsum(dxes[1][0]) - tx = rx / r0 - ty = ry / r0 - - Tx = sparse.diags(vec(tx[:, None].repeat(dxes[0][1].size, axis=1))) - Ty = sparse.diags(vec(ty[:, None].repeat(dxes[1][1].size, axis=1))) + Ta, Tb = dxes2T(dxes=dxes, rmin=rmin) eps_parts = numpy.split(epsilon, 3) - eps_x = sparse.diags(eps_parts[0]) - eps_y = sparse.diags(eps_parts[1]) - eps_z_inv = sparse.diags(1 / eps_parts[2]) - - pa = sparse.vstack((Dfx, Dfy)) @ Tx @ eps_z_inv @ sparse.hstack((Dbx, Dby)) - pb = sparse.vstack((Dfx, Dfy)) @ Tx @ eps_z_inv @ sparse.hstack((Dby, Dbx)) - a0 = Ty @ eps_x + omega**-2 * Dby @ Ty @ Dfy - a1 = Tx @ eps_y + omega**-2 * Dbx @ Ty @ Dfx - b0 = Dbx @ Ty @ Dfy - b1 = Dby @ Ty @ Dfx - - diag = sparse.block_diag + eps_x = sparse.diags_array(eps_parts[0]) + eps_y = sparse.diags_array(eps_parts[1]) + eps_z_inv = sparse.diags_array(1 / eps_parts[2]) omega2 = omega * omega + diag = sparse.block_diag - op = ( - (omega2 * diag((Tx, Ty)) + pa) @ diag((a0, a1)) - - (sparse.bmat(((None, Ty), (Tx, None))) + pb / omega2) @ diag((b0, b1)) - ) + sq0 = omega2 * diag((Tb @ Tb @ eps_x, + Ta @ Ta @ eps_y)) + lin0 = sparse.vstack((-Tb @ Dby, Ta @ Dbx)) @ Tb @ sparse.hstack((-Dfy, Dfx)) + lin1 = sparse.vstack((Dfx, Dfy)) @ Ta @ eps_z_inv @ sparse.hstack((Dbx @ Tb @ eps_x, + Dby @ Ta @ eps_y)) + op = sq0 + lin0 + lin1 return op -def solve_mode( - mode_number: int, - omega: complex, - dxes: dx_lists_t, - epsilon: vfdfield_t, - r0: float, - ) -> dict[str, complex | cfdfield_t]: +def solve_modes( + mode_numbers: Sequence[int], + omega: float, + dxes: dx_lists2_t, + epsilon: vfdslice, + rmin: float, + mode_margin: int = 2, + ) -> tuple[NDArray[numpy.complex128], NDArray[numpy.complex128]]: """ - TODO: fixup Given a 2d (r, y) slice of epsilon, attempts to solve for the eigenmode of the bent waveguide with the specified mode number. Args: - mode_number: Number of the mode, 0-indexed + mode_numbers: Mode numbers to solve, 0-indexed. omega: Angular frequency of the simulation dxes: Grid parameters [dx_e, dx_h] as described in meanas.fdmath.types. - The first coordinate is assumed to be r, the second is y. + The first coordinate is assumed to be r, the second is y. epsilon: Dielectric constant - r0: Radius of curvature for the simulation. This should be the minimum value of + rmin: Radius of curvature for the simulation. This should be the minimum value of r within the simulation domain. Returns: - ``` - { - 'E': list[NDArray[numpy.complex_]], - 'H': list[NDArray[numpy.complex_]], - 'wavenumber': complex, - } - ``` + e_xys: NDArray of vfdfield_t specifying fields. First dimension is mode number. + angular_wavenumbers: list of wavenumbers in 1/rad units. """ - ''' - Solve for the largest-magnitude eigenvalue of the real operator - ''' + # + # Solve for the largest-magnitude eigenvalue of the real operator + # dxes_real = [[numpy.real(dx) for dx in dxi] for dxi in dxes] - A_r = cylindrical_operator(numpy.real(omega), dxes_real, numpy.real(epsilon), r0) - eigvals, eigvecs = signed_eigensolve(A_r, mode_number + 3) - e_xy = eigvecs[:, -(mode_number + 1)] + A_r = cylindrical_operator(numpy.real(omega), dxes_real, numpy.real(epsilon), rmin=rmin) + eigvals, eigvecs = signed_eigensolve(A_r, max(mode_numbers) + mode_margin) + keep_inds = -(numpy.array(mode_numbers) + 1) + e_xys = eigvecs[:, keep_inds].T + eigvals = eigvals[keep_inds] - ''' - Now solve for the eigenvector of the full operator, using the real operator's - eigenvector as an initial guess for Rayleigh quotient iteration. - ''' - A = cylindrical_operator(omega, dxes, epsilon, r0) - eigval, e_xy = rayleigh_quotient_iteration(A, e_xy) + # + # Now solve for the eigenvector of the full operator, using the real operator's + # eigenvector as an initial guess for Rayleigh quotient iteration. + # + A = cylindrical_operator(omega, dxes, epsilon, rmin=rmin) + for nn in range(len(mode_numbers)): + eigvals[nn], e_xys[nn, :] = rayleigh_quotient_iteration(A, e_xys[nn, :]) # Calculate the wave-vector (force the real part to be positive) - wavenumber = numpy.sqrt(eigval) - wavenumber *= numpy.sign(numpy.real(wavenumber)) + wavenumbers = numpy.sqrt(eigvals) + wavenumbers *= numpy.sign(numpy.real(wavenumbers)) - # TODO: Perform correction on wavenumber to account for numerical dispersion. + # Wavenumbers assume the mode is at rmin, which is unlikely + # Instead, return the wavenumber in inverse radians + angular_wavenumbers = wavenumbers * cast('complex', rmin) - shape = [d.size for d in dxes[0]] - e_xy = numpy.hstack((e_xy, numpy.zeros(shape[0] * shape[1]))) - fields = { - 'wavenumber': wavenumber, - 'E': unvec(e_xy, shape), - # 'E': unvec(e, shape), - # 'H': unvec(h, shape), - } + order = angular_wavenumbers.argsort()[::-1] + e_xys = e_xys[order] + angular_wavenumbers = angular_wavenumbers[order] - return fields + return e_xys, angular_wavenumbers + + +def solve_mode( + mode_number: int, + *args: Any, + **kwargs: Any, + ) -> tuple[vcfdfield2, complex]: + """ + Wrapper around `solve_modes()` that solves for a single mode. + + Args: + mode_number: 0-indexed mode number to solve for + *args: passed to `solve_modes()` + **kwargs: passed to `solve_modes()` + + Returns: + (e_xy, angular_wavenumber) + """ + kwargs['mode_numbers'] = [mode_number] + e_xys, angular_wavenumbers = solve_modes(*args, **kwargs) + return e_xys[0], angular_wavenumbers[0] + + +def linear_wavenumbers( + e_xys: Sequence[vcfdfield2] | NDArray[numpy.complex128], + angular_wavenumbers: ArrayLike, + epsilon: vfdslice, + dxes: dx_lists2_t, + rmin: float, + ) -> NDArray[numpy.complex128]: + """ + Calculate linear wavenumbers (1/distance) based on angular wavenumbers (1/rad) + and the mode's energy distribution. + + Args: + e_xys: Vectorized mode fields with shape (num_modes, 2 * x *y) + angular_wavenumbers: Wavenumbers assuming fields have theta-dependence of + `exp(-i * angular_wavenumber * theta)`. They should satisfy + `operator_e() @ e_xy == (angular_wavenumber / rmin) ** 2 * e_xy` + epsilon: Vectorized dielectric constant grid with shape (3, x, y) + dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` (2D) + rmin: Radius at the left edge of the simulation domain (at minimum 'x') + + Returns: + NDArray containing the calculated linear (1/distance) wavenumbers + """ + angular_wavenumbers = numpy.asarray(angular_wavenumbers) + mode_radii = numpy.empty_like(angular_wavenumbers, dtype=float) + + shape2d = (len(dxes[0][0]), len(dxes[0][1])) + epsilon2d = unvec(epsilon, shape2d)[:2] + grid_radii = rmin + numpy.cumsum(dxes[0][0]) + for ii in range(angular_wavenumbers.size): + efield = unvec(e_xys[ii], shape2d, 2) + energy = numpy.real((efield * efield.conj()) * epsilon2d) + energy_vs_x = energy.sum(axis=(0, 2)) + mode_radii[ii] = (grid_radii * energy_vs_x).sum() / energy_vs_x.sum() + + logger.info(f'{mode_radii=}') + lin_wavenumbers = angular_wavenumbers / mode_radii + return lin_wavenumbers + + +def exy2h( + angular_wavenumber: complex, + omega: float, + dxes: dx_lists2_t, + rmin: float, + epsilon: vfdslice, + mu: vfdslice | None = None + ) -> sparse.sparray: + """ + Operator which transforms the vector `e_xy` containing the vectorized E_r and E_y fields, + into a vectorized H containing all three H components + + Args: + angular_wavenumber: Wavenumber assuming fields have theta-dependence of + `exp(-i * angular_wavenumber * theta)`. It should satisfy + `operator_e() @ e_xy == (angular_wavenumber / rmin) ** 2 * e_xy` + omega: The angular frequency of the system + dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` (2D) + rmin: Radius at the left edge of the simulation domain (at minimum 'x') + epsilon: Vectorized dielectric constant grid + mu: Vectorized magnetic permeability grid (default 1 everywhere) + + Returns: + Sparse matrix representing the operator. + """ + e2hop = e2h(angular_wavenumber=angular_wavenumber, omega=omega, dxes=dxes, rmin=rmin, mu=mu) + return e2hop @ exy2e(angular_wavenumber=angular_wavenumber, omega=omega, dxes=dxes, rmin=rmin, epsilon=epsilon) + + +def exy2e( + angular_wavenumber: complex, + omega: float, + dxes: dx_lists2_t, + rmin: float, + epsilon: vfdslice, + ) -> sparse.sparray: + """ + Operator which transforms the vector `e_xy` containing the vectorized E_r and E_y fields, + into a vectorized E containing all three E components + + Unlike the straight waveguide case, the H_z components do not cancel and must be calculated + from E_r and E_y in order to then calculate E_z. + + Args: + angular_wavenumber: Wavenumber assuming fields have theta-dependence of + `exp(-i * angular_wavenumber * theta)`. It should satisfy + `operator_e() @ e_xy == (angular_wavenumber / rmin) ** 2 * e_xy` + omega: The angular frequency of the system + dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` (2D) + rmin: Radius at the left edge of the simulation domain (at minimum 'x') + epsilon: Vectorized dielectric constant grid + + Returns: + Sparse matrix representing the operator. + """ + Dfx, Dfy = deriv_forward(dxes[0]) + Dbx, Dby = deriv_back(dxes[1]) + wavenumber = angular_wavenumber / rmin + + Ta, Tb = dxes2T(dxes=dxes, rmin=rmin) + Tai = sparse.diags_array(1 / Ta.diagonal()) + #Tbi = sparse.diags_array(1 / Tb.diagonal()) + + epsilon_parts = numpy.split(epsilon, 3) + epsilon_x, epsilon_y = (sparse.diags_array(epsi) for epsi in epsilon_parts[:2]) + epsilon_z_inv = sparse.diags_array(1 / epsilon_parts[2]) + + n_pts = dxes[0][0].size * dxes[0][1].size + zeros = sparse.coo_array((n_pts, n_pts)) + + mu_z = numpy.ones(n_pts) + mu_z_inv = sparse.diags_array(1 / mu_z) + exy2hz = 1 / (-1j * omega) * mu_z_inv @ sparse.hstack((Dfy, -Dfx)) + hxy2ez = 1 / (1j * omega) * epsilon_z_inv @ sparse.hstack((Dby, -Dbx)) + + exy2hy = Tb / (1j * wavenumber) @ (-1j * omega * sparse.hstack((epsilon_x, zeros)) - Dby @ exy2hz) + exy2hx = Tb / (1j * wavenumber) @ ( 1j * omega * sparse.hstack((zeros, epsilon_y)) - Tai @ Dbx @ Tb @ exy2hz) + + exy2ez = hxy2ez @ sparse.vstack((exy2hx, exy2hy)) + + op = sparse.vstack((sparse.eye_array(2 * n_pts), + exy2ez)) + return op + + +def e2h( + angular_wavenumber: complex, + omega: float, + dxes: dx_lists2_t, + rmin: float, + mu: vfdslice | None = None + ) -> sparse.sparray: + r""" + Returns an operator which, when applied to a vectorized E eigenfield, produces + the vectorized H eigenfield. + + This operator is created directly from the initial coordinate-transformed equations: + $$ + \begin{aligned} + -\imath \omega \mu_{rr} H_r &= \tilde{\partial}_y E_z + \imath \beta T_a^{-1} E_y, \\ + -\imath \omega \mu_{yy} H_y &= -\imath \beta T_b^{-1} E_r + - T_b^{-1} \tilde{\partial}_r (T_a E_z), \\ + -\imath \omega \mu_{zz} H_z &= \tilde{\partial}_r E_y - \tilde{\partial}_y E_r, + \end{aligned} + $$ + + Args: + angular_wavenumber: Wavenumber assuming fields have theta-dependence of + `exp(-i * angular_wavenumber * theta)`. It should satisfy + `operator_e() @ e_xy == (angular_wavenumber / rmin) ** 2 * e_xy` + omega: The angular frequency of the system + dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` (2D) + rmin: Radius at the left edge of the simulation domain (at minimum 'x') + mu: Vectorized magnetic permeability grid (default 1 everywhere) + + Returns: + Sparse matrix representation of the operator. + """ + Dfx, Dfy = deriv_forward(dxes[0]) + Ta, Tb = dxes2T(dxes=dxes, rmin=rmin) + Tai = sparse.diags_array(1 / Ta.diagonal()) + Tbi = sparse.diags_array(1 / Tb.diagonal()) + + jB = 1j * angular_wavenumber / rmin + op = sparse.block_array([[ None, -jB * Tai, -Dfy], + [jB * Tbi, None, Tbi @ Dfx @ Ta], + [ Dfy, -Dfx, None]]) / (-1j * omega) + if mu is not None: + op = sparse.diags_array(1 / mu) @ op + return op + + +def dxes2T( + dxes: dx_lists2_t, + rmin: float, + ) -> tuple[NDArray[numpy.float64], NDArray[numpy.float64]]: + r""" + Construct the cylindrical metric matrices $T_a$ and $T_b$. + + `T_a` is sampled on the E-grid radial locations, while `T_b` is sampled on + the staggered H-grid radial locations. These are the diagonal matrices that + convert the straight-waveguide algebra into its cylindrical counterpart. + + Args: + dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` (2D) + rmin: Radius at the left edge of the simulation domain (at minimum 'x') + + Returns: + Sparse diagonal matrices `(T_a, T_b)`. + """ + ra = rmin + numpy.cumsum(dxes[0][0]) # Radius at Ey points + rb = rmin + dxes[0][0] / 2.0 + numpy.cumsum(dxes[1][0]) # Radius at Ex points + ta = ra / rmin + tb = rb / rmin + + Ta = sparse.diags_array(vec(ta[:, None].repeat(dxes[0][1].size, axis=1))) + Tb = sparse.diags_array(vec(tb[:, None].repeat(dxes[1][1].size, axis=1))) + return Ta, Tb + + +def normalized_fields_e( + e_xy: vcfdfield2, + angular_wavenumber: complex, + omega: float, + dxes: dx_lists2_t, + rmin: float, + epsilon: vfdslice, + mu: vfdslice | None = None, + prop_phase: float = 0, + ) -> tuple[vcfdslice_t, vcfdslice_t]: + r""" + Given a vector `e_xy` containing the vectorized E_r and E_y fields, + returns normalized, vectorized E and H fields for the system. + + Args: + e_xy: Vector containing E_r and E_y fields + angular_wavenumber: Wavenumber assuming fields have theta-dependence of + `exp(-i * angular_wavenumber * theta)`. It should satisfy + `operator_e() @ e_xy == (angular_wavenumber / rmin) ** 2 * e_xy` + omega: The angular frequency of the system + dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types` (2D) + rmin: Radius at the left edge of the simulation domain (at minimum 'x') + epsilon: Vectorized dielectric constant grid + mu: Vectorized magnetic permeability grid (default 1 everywhere) + prop_phase: Phase shift `(dz * corrected_wavenumber)` over 1 cell in propagation direction. + Default 0 (continuous propagation direction, i.e. dz->0). + + Returns: + `(e, h)`, where each field is vectorized, normalized, + and contains all three vector components. + + Notes: + The normalization step is delegated to `_normalized_fields(...)`, which + enforces unit forward power under the discrete inner product + + $$ + \frac{1}{2}\int (E_r H_y^* - E_y H_r^*) \, dr \, dy. + $$ + + The angular wavenumber `m` is first converted into the full three-component + fields, then the overall complex phase and sign are fixed so the result is + reproducible for symmetric modes. + """ + e = exy2e(angular_wavenumber=angular_wavenumber, omega=omega, dxes=dxes, rmin=rmin, epsilon=epsilon) @ e_xy + h = exy2h(angular_wavenumber=angular_wavenumber, omega=omega, dxes=dxes, rmin=rmin, epsilon=epsilon, mu=mu) @ e_xy + e_norm, h_norm = _normalized_fields( + e=e, h=h, dxes=dxes, epsilon=epsilon, prop_phase=prop_phase, + ) + return e_norm, h_norm + + +def _normalized_fields( + e: vcfdslice, + h: vcfdslice, + dxes: dx_lists2_t, + epsilon: vfdslice, + prop_phase: float = 0, + ) -> tuple[vcfdslice_t, vcfdslice_t]: + r""" + Normalize a cylindrical waveguide mode to unit forward power. + + The cylindrical helpers reuse the straight-waveguide inner product after the + field reconstruction step. The extra metric factors have already been folded + into the reconstructed `e`/`h` fields through `dxes2T(...)` and the + cylindrical `exy2e(...)` / `exy2h(...)` operators, so the same discrete + longitudinal Poynting integral can be used here. + + The normalization procedure is: + + 1. Flip the magnetic field sign so the reconstructed `(e, h)` pair follows + the same forward-power convention as `waveguide_2d`. + 2. Compute the time-averaged forward power with + `waveguide_2d.inner_product(..., conj_h=True)`. + 3. Scale by `1 / sqrt(S_z)` so the resulting mode has unit forward power. + 4. Remove the arbitrary complex phase and apply a quadrant-sum sign heuristic + so symmetric modes choose a stable representative. + + `prop_phase` has the same meaning as in `waveguide_2d`: it compensates for + the half-cell longitudinal staggering between the E and H fields when the + propagation direction is itself discretized. + """ + h *= -1 + shape = [s.size for s in dxes[0]] + + # Find time-averaged Sz and normalize to it + # H phase is adjusted by a half-cell forward shift for Yee cell, and 1-cell reverse shift for Poynting + Sz_tavg = waveguide_2d.inner_product(e, h, dxes=dxes, prop_phase=prop_phase, conj_h=True).real # Note, using linear poynting vector + assert Sz_tavg > 0, f'Found a mode propagating in the wrong direction! {Sz_tavg=}' + + energy = numpy.real(epsilon * e.conj() * e) + + norm_amplitude = 1 / numpy.sqrt(Sz_tavg) + norm_angle = -numpy.angle(e[energy.argmax()]) # Will randomly add a negative sign when mode is symmetric + + # Try to break symmetry to assign a consistent sign [experimental] + E_weighted = unvec(e * energy * numpy.exp(1j * norm_angle), shape) + sign = numpy.sign(E_weighted[:, + :max(shape[0] // 2, 1), + :max(shape[1] // 2, 1)].real.sum()) + assert sign != 0 + + norm_factor = sign * norm_amplitude * numpy.exp(1j * norm_angle) + + e *= norm_factor + h *= norm_factor + return vcfdslice_t(e), vcfdslice_t(h) diff --git a/meanas/fdmath/__init__.py b/meanas/fdmath/__init__.py index 8a6b784..857cf18 100644 --- a/meanas/fdmath/__init__.py +++ b/meanas/fdmath/__init__.py @@ -741,8 +741,46 @@ the true values can be multiplied back in after the simulation is complete if no normalized results are needed. """ -from .types import fdfield_t, vfdfield_t, cfdfield_t, vcfdfield_t, dx_lists_t, dx_lists_mut -from .types import fdfield_updater_t, cfdfield_updater_t -from .vectorization import vec, unvec -from . import operators, functional, types, vectorization +from .types import ( + fdfield_t as fdfield_t, + vfdfield_t as vfdfield_t, + cfdfield_t as cfdfield_t, + vcfdfield_t as vcfdfield_t, + fdfield2_t as fdfield2_t, + vfdfield2_t as vfdfield2_t, + cfdfield2_t as cfdfield2_t, + vcfdfield2_t as vcfdfield2_t, + fdfield as fdfield, + vfdfield as vfdfield, + cfdfield as cfdfield, + vcfdfield as vcfdfield, + fdfield2 as fdfield2, + vfdfield2 as vfdfield2, + cfdfield2 as cfdfield2, + vcfdfield2 as vcfdfield2, + fdslice_t as fdslice_t, + vfdslice_t as vfdslice_t, + cfdslice_t as cfdslice_t, + vcfdslice_t as vcfdslice_t, + fdslice as fdslice, + vfdslice as vfdslice, + cfdslice as cfdslice, + vcfdslice as vcfdslice, + dx_lists_t as dx_lists_t, + dx_lists2_t as dx_lists2_t, + dx_lists_mut as dx_lists_mut, + dx_lists2_mut as dx_lists2_mut, + fdfield_updater_t as fdfield_updater_t, + cfdfield_updater_t as cfdfield_updater_t, + ) +from .vectorization import ( + vec as vec, + unvec as unvec, + ) +from . import ( + operators as operators, + functional as functional, + types as types, + vectorization as vectorization, + ) diff --git a/meanas/fdmath/functional.py b/meanas/fdmath/functional.py index 3a10a00..27d368a 100644 --- a/meanas/fdmath/functional.py +++ b/meanas/fdmath/functional.py @@ -3,16 +3,18 @@ Math functions for finite difference simulations Basic discrete calculus etc. """ -from typing import Sequence, Callable +from typing import TypeVar +from collections.abc import Sequence, Callable import numpy from numpy.typing import NDArray +from numpy import floating, complexfloating -from .types import fdfield_t, fdfield_updater_t +from .types import fdfield, fdfield_updater_t def deriv_forward( - dx_e: Sequence[NDArray[numpy.float_]] | None = None, + dx_e: Sequence[NDArray[floating | complexfloating]] | None = None, ) -> tuple[fdfield_updater_t, fdfield_updater_t, fdfield_updater_t]: """ Utility operators for taking discretized derivatives (backward variant). @@ -36,7 +38,7 @@ def deriv_forward( def deriv_back( - dx_h: Sequence[NDArray[numpy.float_]] | None = None, + dx_h: Sequence[NDArray[floating | complexfloating]] | None = None, ) -> tuple[fdfield_updater_t, fdfield_updater_t, fdfield_updater_t]: """ Utility operators for taking discretized derivatives (forward variant). @@ -59,9 +61,12 @@ def deriv_back( return derivs +TT = TypeVar('TT', bound='NDArray[floating | complexfloating]') + + def curl_forward( - dx_e: Sequence[NDArray[numpy.float_]] | None = None, - ) -> fdfield_updater_t: + dx_e: Sequence[NDArray[floating | complexfloating]] | None = None, + ) -> Callable[[TT], TT]: r""" Curl operator for use with the E field. @@ -75,7 +80,7 @@ def curl_forward( """ Dx, Dy, Dz = deriv_forward(dx_e) - def ce_fun(e: fdfield_t) -> fdfield_t: + def ce_fun(e: TT) -> TT: output = numpy.empty_like(e) output[0] = Dy(e[2]) output[1] = Dz(e[0]) @@ -89,8 +94,8 @@ def curl_forward( def curl_back( - dx_h: Sequence[NDArray[numpy.float_]] | None = None, - ) -> fdfield_updater_t: + dx_h: Sequence[NDArray[floating | complexfloating]] | None = None, + ) -> Callable[[TT], TT]: r""" Create a function which takes the backward curl of a field. @@ -104,7 +109,7 @@ def curl_back( """ Dx, Dy, Dz = deriv_back(dx_h) - def ch_fun(h: fdfield_t) -> fdfield_t: + def ch_fun(h: TT) -> TT: output = numpy.empty_like(h) output[0] = Dy(h[2]) output[1] = Dz(h[0]) @@ -118,11 +123,11 @@ def curl_back( def curl_forward_parts( - dx_e: Sequence[NDArray[numpy.float_]] | None = None, + dx_e: Sequence[NDArray[floating | complexfloating]] | None = None, ) -> Callable: Dx, Dy, Dz = deriv_forward(dx_e) - def mkparts_fwd(e: fdfield_t) -> tuple[tuple[fdfield_t, fdfield_t], ...]: + def mkparts_fwd(e: fdfield) -> tuple[tuple[fdfield, fdfield], ...]: return ((-Dz(e[1]), Dy(e[2])), ( Dz(e[0]), -Dx(e[2])), (-Dy(e[0]), Dx(e[1]))) @@ -131,11 +136,11 @@ def curl_forward_parts( def curl_back_parts( - dx_h: Sequence[NDArray[numpy.float_]] | None = None, + dx_h: Sequence[NDArray[floating | complexfloating]] | None = None, ) -> Callable: Dx, Dy, Dz = deriv_back(dx_h) - def mkparts_back(h: fdfield_t) -> tuple[tuple[fdfield_t, fdfield_t], ...]: + def mkparts_back(h: fdfield) -> tuple[tuple[fdfield, fdfield], ...]: return ((-Dz(h[1]), Dy(h[2])), ( Dz(h[0]), -Dx(h[2])), (-Dy(h[0]), Dx(h[1]))) diff --git a/meanas/fdmath/operators.py b/meanas/fdmath/operators.py index 9d5988d..8b7cabc 100644 --- a/meanas/fdmath/operators.py +++ b/meanas/fdmath/operators.py @@ -3,19 +3,20 @@ Matrix operators for finite difference simulations Basic discrete calculus etc. """ -from typing import Sequence +from collections.abc import Sequence import numpy from numpy.typing import NDArray -import scipy.sparse as sparse # type: ignore +from numpy import floating, complexfloating +from scipy import sparse -from .types import vfdfield_t +from .types import vfdfield def shift_circ( axis: int, shape: Sequence[int], shift_distance: int = 1, - ) -> sparse.spmatrix: + ) -> sparse.sparray: """ Utility operator for performing a circular shift along a specified axis by a specified number of elements. @@ -33,8 +34,8 @@ def shift_circ( if axis not in range(len(shape)): raise Exception(f'Invalid direction: {axis}, shape is {shape}') - shifts = [abs(shift_distance) if a == axis else 0 for a in range(3)] - shifted_diags = [(numpy.arange(n) + s) % n for n, s in zip(shape, shifts)] + shifts = [abs(shift_distance) if a == axis else 0 for a in range(len(shape))] + shifted_diags = [(numpy.arange(n) + s) % n for n, s in zip(shape, shifts, strict=True)] ijk = numpy.meshgrid(*shifted_diags, indexing='ij') n = numpy.prod(shape) @@ -43,7 +44,7 @@ def shift_circ( vij = (numpy.ones(n), (i_ind, j_ind.ravel(order='C'))) - d = sparse.csr_matrix(vij, shape=(n, n)) + d = sparse.csr_array(vij, shape=(n, n)) if shift_distance < 0: d = d.T @@ -55,7 +56,7 @@ def shift_with_mirror( axis: int, shape: Sequence[int], shift_distance: int = 1, - ) -> sparse.spmatrix: + ) -> sparse.sparray: """ Utility operator for performing an n-element shift along a specified axis, with mirror boundary conditions applied to the cells beyond the receding edge. @@ -81,8 +82,8 @@ def shift_with_mirror( v = numpy.where(v < 0, - 1 - v, v) return v - shifts = [shift_distance if a == axis else 0 for a in range(3)] - shifted_diags = [mirrored_range(n, s) for n, s in zip(shape, shifts)] + shifts = [shift_distance if a == axis else 0 for a in range(len(shape))] + shifted_diags = [mirrored_range(n, s) for n, s in zip(shape, shifts, strict=True)] ijk = numpy.meshgrid(*shifted_diags, indexing='ij') n = numpy.prod(shape) @@ -91,13 +92,13 @@ def shift_with_mirror( vij = (numpy.ones(n), (i_ind, j_ind.ravel(order='C'))) - d = sparse.csr_matrix(vij, shape=(n, n)) + d = sparse.csr_array(vij, shape=(n, n)) return d def deriv_forward( - dx_e: Sequence[NDArray[numpy.float_]], - ) -> list[sparse.spmatrix]: + dx_e: Sequence[NDArray[floating | complexfloating]], + ) -> list[sparse.sparray]: """ Utility operators for taking discretized derivatives (forward variant). @@ -113,18 +114,18 @@ def deriv_forward( dx_e_expanded = numpy.meshgrid(*dx_e, indexing='ij') - def deriv(axis: int) -> sparse.spmatrix: - return shift_circ(axis, shape, 1) - sparse.eye(n) + def deriv(axis: int) -> sparse.sparray: + return shift_circ(axis, shape, 1) - sparse.eye_array(n) - Ds = [sparse.diags(+1 / dx.ravel(order='C')) @ deriv(a) + Ds = [sparse.diags_array(+1 / dx.ravel(order='C')) @ deriv(a) for a, dx in enumerate(dx_e_expanded)] return Ds def deriv_back( - dx_h: Sequence[NDArray[numpy.float_]], - ) -> list[sparse.spmatrix]: + dx_h: Sequence[NDArray[floating | complexfloating]], + ) -> list[sparse.sparray]: """ Utility operators for taking discretized derivatives (backward variant). @@ -140,36 +141,37 @@ def deriv_back( dx_h_expanded = numpy.meshgrid(*dx_h, indexing='ij') - def deriv(axis: int) -> sparse.spmatrix: - return shift_circ(axis, shape, -1) - sparse.eye(n) + def deriv(axis: int) -> sparse.sparray: + return shift_circ(axis, shape, -1) - sparse.eye_array(n) - Ds = [sparse.diags(-1 / dx.ravel(order='C')) @ deriv(a) + Ds = [sparse.diags_array(-1 / dx.ravel(order='C')) @ deriv(a) for a, dx in enumerate(dx_h_expanded)] return Ds def cross( - B: Sequence[sparse.spmatrix], - ) -> sparse.spmatrix: + B: Sequence[sparse.sparray], + ) -> sparse.sparray: """ Cross product operator Args: B: List `[Bx, By, Bz]` of sparse matrices corresponding to the x, y, z - portions of the operator on the left side of the cross product. + portions of the operator on the left side of the cross product. Returns: Sparse matrix corresponding to (B x), where x is the cross product. """ n = B[0].shape[0] - zero = sparse.csr_matrix((n, n)) - return sparse.bmat([[zero, -B[2], B[1]], - [B[2], zero, -B[0]], - [-B[1], B[0], zero]]) + zero = sparse.csr_array((n, n)) + return sparse.block_array([ + [zero, -B[2], B[1]], + [B[2], zero, -B[0]], + [-B[1], B[0], zero]]) -def vec_cross(b: vfdfield_t) -> sparse.spmatrix: +def vec_cross(b: vfdfield) -> sparse.sparray: """ Vector cross product operator @@ -181,11 +183,11 @@ def vec_cross(b: vfdfield_t) -> sparse.spmatrix: Sparse matrix corresponding to (b x), where x is the cross product. """ - B = [sparse.diags(c) for c in numpy.split(b, 3)] + B = [sparse.diags_array(c) for c in numpy.split(b, 3)] return cross(B) -def avg_forward(axis: int, shape: Sequence[int]) -> sparse.spmatrix: +def avg_forward(axis: int, shape: Sequence[int]) -> sparse.sparray: """ Forward average operator `(x4 = (x4 + x5) / 2)` @@ -200,10 +202,10 @@ def avg_forward(axis: int, shape: Sequence[int]) -> sparse.spmatrix: raise Exception(f'Invalid shape: {shape}') n = numpy.prod(shape) - return 0.5 * (sparse.eye(n) + shift_circ(axis, shape)) + return 0.5 * (sparse.eye_array(n) + shift_circ(axis, shape)) -def avg_back(axis: int, shape: Sequence[int]) -> sparse.spmatrix: +def avg_back(axis: int, shape: Sequence[int]) -> sparse.sparray: """ Backward average operator `(x4 = (x4 + x3) / 2)` @@ -218,8 +220,8 @@ def avg_back(axis: int, shape: Sequence[int]) -> sparse.spmatrix: def curl_forward( - dx_e: Sequence[NDArray[numpy.float_]], - ) -> sparse.spmatrix: + dx_e: Sequence[NDArray[floating | complexfloating]], + ) -> sparse.sparray: """ Curl operator for use with the E field. @@ -234,8 +236,8 @@ def curl_forward( def curl_back( - dx_h: Sequence[NDArray[numpy.float_]], - ) -> sparse.spmatrix: + dx_h: Sequence[NDArray[floating | complexfloating]], + ) -> sparse.sparray: """ Curl operator for use with the H field. diff --git a/meanas/fdmath/types.py b/meanas/fdmath/types.py index aae9594..b82a5ae 100644 --- a/meanas/fdmath/types.py +++ b/meanas/fdmath/types.py @@ -1,26 +1,65 @@ """ Types shared across multiple submodules """ -from typing import Sequence, Callable, MutableSequence -import numpy +from typing import NewType +from collections.abc import Sequence, Callable, MutableSequence from numpy.typing import NDArray +from numpy import floating, complexfloating # Field types -fdfield_t = NDArray[numpy.float_] +fdfield_t = NewType('fdfield_t', NDArray[floating]) +type fdfield = fdfield_t | NDArray[floating] """Vector field with shape (3, X, Y, Z) (e.g. `[E_x, E_y, E_z]`)""" -vfdfield_t = NDArray[numpy.float_] +vfdfield_t = NewType('vfdfield_t', NDArray[floating]) +type vfdfield = vfdfield_t | NDArray[floating] """Linearized vector field (single vector of length 3*X*Y*Z)""" -cfdfield_t = NDArray[numpy.complex_] +cfdfield_t = NewType('cfdfield_t', NDArray[complexfloating]) +type cfdfield = cfdfield_t | NDArray[complexfloating] """Complex vector field with shape (3, X, Y, Z) (e.g. `[E_x, E_y, E_z]`)""" -vcfdfield_t = NDArray[numpy.complex_] +vcfdfield_t = NewType('vcfdfield_t', NDArray[complexfloating]) +type vcfdfield = vcfdfield_t | NDArray[complexfloating] """Linearized complex vector field (single vector of length 3*X*Y*Z)""" -dx_lists_t = Sequence[Sequence[NDArray[numpy.float_]]] +fdslice_t = NewType('fdslice_t', NDArray[floating]) +type fdslice = fdslice_t | NDArray[floating] +"""Vector field slice with shape (3, X, Y) (e.g. `[E_x, E_y, E_z]` at a single Z position)""" + +vfdslice_t = NewType('vfdslice_t', NDArray[floating]) +type vfdslice = vfdslice_t | NDArray[floating] +"""Linearized vector field slice (single vector of length 3*X*Y)""" + +cfdslice_t = NewType('cfdslice_t', NDArray[complexfloating]) +type cfdslice = cfdslice_t | NDArray[complexfloating] +"""Complex vector field slice with shape (3, X, Y) (e.g. `[E_x, E_y, E_z]` at a single Z position)""" + +vcfdslice_t = NewType('vcfdslice_t', NDArray[complexfloating]) +type vcfdslice = vcfdslice_t | NDArray[complexfloating] +"""Linearized complex vector field slice (single vector of length 3*X*Y)""" + + +fdfield2_t = NewType('fdfield2_t', NDArray[floating]) +type fdfield2 = fdfield2_t | NDArray[floating] +"""2D Vector field with shape (2, X, Y) (e.g. `[E_x, E_y]`)""" + +vfdfield2_t = NewType('vfdfield2_t', NDArray[floating]) +type vfdfield2 = vfdfield2_t | NDArray[floating] +"""2D Linearized vector field (single vector of length 2*X*Y)""" + +cfdfield2_t = NewType('cfdfield2_t', NDArray[complexfloating]) +type cfdfield2 = cfdfield2_t | NDArray[complexfloating] +"""2D Complex vector field with shape (2, X, Y) (e.g. `[E_x, E_y]`)""" + +vcfdfield2_t = NewType('vcfdfield2_t', NDArray[complexfloating]) +type vcfdfield2 = vcfdfield2_t | NDArray[complexfloating] +"""2D Linearized complex vector field (single vector of length 2*X*Y)""" + + +dx_lists_t = Sequence[Sequence[NDArray[floating | complexfloating]]] """ 'dxes' datastructure which contains grid cell width information in the following format: @@ -31,12 +70,26 @@ dx_lists_t = Sequence[Sequence[NDArray[numpy.float_]]] and `dy_h[0]` is the y-width of the `y=0` cells, as used when calculating dH/dy, etc. """ -dx_lists_mut = MutableSequence[MutableSequence[NDArray[numpy.float_]]] +dx_lists2_t = Sequence[Sequence[NDArray[floating | complexfloating]]] +""" + 2D 'dxes' datastructure which contains grid cell width information in the following format: + + [[[dx_e[0], dx_e[1], ...], [dy_e[0], ...]], + [[dx_h[0], dx_h[1], ...], [dy_h[0], ...]]] + + where `dx_e[0]` is the x-width of the `x=0` cells, as used when calculating dE/dx, + and `dy_h[0]` is the y-width of the `y=0` cells, as used when calculating dH/dy, etc. +""" + +dx_lists_mut = MutableSequence[MutableSequence[NDArray[floating | complexfloating]]] """Mutable version of `dx_lists_t`""" +dx_lists2_mut = MutableSequence[MutableSequence[NDArray[floating | complexfloating]]] +"""Mutable version of `dx_lists2_t`""" -fdfield_updater_t = Callable[..., fdfield_t] -"""Convenience type for functions which take and return an fdfield_t""" -cfdfield_updater_t = Callable[..., cfdfield_t] -"""Convenience type for functions which take and return an cfdfield_t""" +fdfield_updater_t = Callable[..., fdfield] +"""Convenience type for functions which take and return a real `fdfield`""" + +cfdfield_updater_t = Callable[..., cfdfield] +"""Convenience type for functions which take and return a complex `cfdfield`""" diff --git a/meanas/fdmath/vectorization.py b/meanas/fdmath/vectorization.py index 0a9f8ad..77b722f 100644 --- a/meanas/fdmath/vectorization.py +++ b/meanas/fdmath/vectorization.py @@ -4,75 +4,122 @@ and a 1D array representation of that field `[f_x0, f_x1, f_x2,... f_y0,... f_z0 Vectorized versions of the field use row-major (ie., C-style) ordering. """ -from typing import overload, Sequence +from typing import overload +from collections.abc import Sequence import numpy -from numpy.typing import ArrayLike +from numpy.typing import ArrayLike, NDArray -from .types import fdfield_t, vfdfield_t, cfdfield_t, vcfdfield_t +from .types import ( + fdfield_t, vfdfield_t, cfdfield_t, vcfdfield_t, + fdslice_t, vfdslice_t, cfdslice_t, vcfdslice_t, + fdfield2_t, vfdfield2_t, cfdfield2_t, vcfdfield2_t, + ) @overload def vec(f: None) -> None: - pass + pass # pragma: no cover @overload def vec(f: fdfield_t) -> vfdfield_t: - pass + pass # pragma: no cover @overload def vec(f: cfdfield_t) -> vcfdfield_t: - pass + pass # pragma: no cover @overload -def vec(f: ArrayLike) -> vfdfield_t | vcfdfield_t: - pass +def vec(f: fdfield2_t) -> vfdfield2_t: + pass # pragma: no cover -def vec(f: fdfield_t | cfdfield_t | ArrayLike | None) -> vfdfield_t | vcfdfield_t | None: +@overload +def vec(f: cfdfield2_t) -> vcfdfield2_t: + pass # pragma: no cover + +@overload +def vec(f: fdslice_t) -> vfdslice_t: + pass # pragma: no cover + +@overload +def vec(f: cfdslice_t) -> vcfdslice_t: + pass # pragma: no cover + +@overload +def vec(f: ArrayLike) -> NDArray: + pass # pragma: no cover + +def vec( + f: fdfield_t | cfdfield_t | fdfield2_t | cfdfield2_t | fdslice_t | cfdslice_t | ArrayLike | None, + ) -> vfdfield_t | vcfdfield_t | vfdfield2_t | vcfdfield2_t | vfdslice_t | vcfdslice_t | NDArray | None: """ - Create a 1D ndarray from a 3D vector field which spans a 1-3D region. + Create a 1D ndarray from a vector field which spans a 1-3D region. Returns `None` if called with `f=None`. Args: - f: A vector field, `[f_x, f_y, f_z]` where each `f_` component is a 1- to - 3-D ndarray (`f_*` should all be the same size). Doesn't fail with `f=None`. + f: A vector field, e.g. `[f_x, f_y, f_z]` where each `f_` component is a 1- to + 3-D ndarray (`f_*` should all be the same size). Doesn't fail with `f=None`. Returns: 1D ndarray containing the linearized field (or `None`) """ if f is None: return None - return numpy.ravel(f, order='C') + return numpy.ravel(f, order='C') # type: ignore @overload -def unvec(v: None, shape: Sequence[int]) -> None: +def unvec(v: None, shape: Sequence[int], nvdim: int = 3) -> None: + pass # pragma: no cover + +@overload +def unvec(v: vfdfield_t, shape: Sequence[int], nvdim: int = 3) -> fdfield_t: + pass # pragma: no cover + +@overload +def unvec(v: vcfdfield_t, shape: Sequence[int], nvdim: int = 3) -> cfdfield_t: + pass # pragma: no cover + +@overload +def unvec(v: vfdfield2_t, shape: Sequence[int], nvdim: int = 3) -> fdfield2_t: pass @overload -def unvec(v: vfdfield_t, shape: Sequence[int]) -> fdfield_t: +def unvec(v: vcfdfield2_t, shape: Sequence[int], nvdim: int = 3) -> cfdfield2_t: pass @overload -def unvec(v: vcfdfield_t, shape: Sequence[int]) -> cfdfield_t: +def unvec(v: vfdslice_t, shape: Sequence[int], nvdim: int = 3) -> fdslice_t: pass -def unvec(v: vfdfield_t | vcfdfield_t | None, shape: Sequence[int]) -> fdfield_t | cfdfield_t | None: +@overload +def unvec(v: vcfdslice_t, shape: Sequence[int], nvdim: int = 3) -> cfdslice_t: + pass + +@overload +def unvec(v: ArrayLike, shape: Sequence[int], nvdim: int = 3) -> NDArray: + pass + +def unvec( + v: vfdfield_t | vcfdfield_t | vfdfield2_t | vcfdfield2_t | vfdslice_t | vcfdslice_t | ArrayLike | None, + shape: Sequence[int], + nvdim: int = 3, + ) -> fdfield_t | cfdfield_t | fdfield2_t | cfdfield2_t | fdslice_t | cfdslice_t | NDArray | None: """ - Perform the inverse of vec(): take a 1D ndarray and output a 3D field - of form `[f_x, f_y, f_z]` where each of `f_*` is a len(shape)-dimensional + Perform the inverse of vec(): take a 1D ndarray and output an `nvdim`-component field + of form e.g. `[f_x, f_y, f_z]` (`nvdim=3`) where each of `f_*` is a len(shape)-dimensional ndarray. Returns `None` if called with `v=None`. Args: - v: 1D ndarray representing a 3D vector field of shape shape (or None) + v: 1D ndarray representing a vector field of shape shape (or None) shape: shape of the vector field + nvdim: Number of components in each vector Returns: `[f_x, f_y, f_z]` where each `f_` is a `len(shape)` dimensional ndarray (or `None`) """ if v is None: return None - return v.reshape((3, *shape), order='C') - + return v.reshape((nvdim, *shape), order='C') # type: ignore diff --git a/meanas/fdtd/__init__.py b/meanas/fdtd/__init__.py index 171c4f4..6291815 100644 --- a/meanas/fdtd/__init__.py +++ b/meanas/fdtd/__init__.py @@ -144,6 +144,50 @@ It is often useful to excite the simulation with an arbitrary broadband pulse an extract the frequency-domain response by performing an on-the-fly Fourier transform of the time-domain fields. +`accumulate_phasor` in `meanas.fdtd.phasor` performs the phase accumulation for one +or more target frequencies, while leaving source normalization and simulation-loop +policy to the caller. `temporal_phasor(...)` and `temporal_phasor_scale(...)` +apply the same Fourier sum to a scalar waveform, which is useful when a pulsed +source envelope must be normalized before being applied to a point source or +mode source. `real_injection_scale(...)` is the corresponding helper for the +common real-valued injection pattern `numpy.real(scale * waveform)`. Convenience +wrappers `accumulate_phasor_e`, `accumulate_phasor_h`, and `accumulate_phasor_j` +apply the usual Yee time offsets. `reconstruct_real(...)` and the corresponding +`reconstruct_real_e/h/j(...)` wrappers perform the inverse operation, converting +phasors back into real-valued field snapshots at explicit Yee-aligned times. +For scalar `omega`, the reconstruction helpers accept either a plain field +phasor or the batched `(1, *sample_shape)` form used by the accumulator helpers. +The helpers accumulate + +$$ \Delta_t \sum_l w_l e^{-i \omega t_l} f_l $$ + +with caller-provided sample times and weights. In this codebase the matching +electric-current convention is typically `E -= dt * J / epsilon` in FDTD and +`-i \omega J` on the right-hand side of the FDFD wave equation. + +For FDTD/FDFD equivalence, this phasor path is the primary comparison workflow. +It isolates the guided `+\omega` response that the frequency-domain solver +targets directly, regardless of whether the underlying FDTD run used real- or +complex-valued fields. + +For exact pulsed FDTD/FDFD equivalence it is often simplest to keep the +injected source, fields, and CPML auxiliary state complex-valued. The +`real_injection_scale(...)` helper is instead for the more ordinary one-run +real-valued source path, where the intended positive-frequency waveform is +injected through `numpy.real(scale * waveform)` and any remaining negative- +frequency leakage is controlled by the pulse bandwidth and run length. + +`reconstruct_real(...)` is for a different question: given a phasor, what late +real-valued field snapshot should it produce? That raw-snapshot comparison is +stricter and noisier because a monitor plane generally contains both the guided +field and the remaining orthogonal content, + +$$ E_{\text{monitor}} = E_{\text{guided}} + E_{\text{residual}} . $$ + +Phasor/modal comparisons mostly validate the guided `+\omega` term. Raw +real-field comparisons expose both terms at once, so they should be treated as +secondary diagnostics rather than the main solver-equivalence benchmark. + The Ricker wavelet (normalized second derivative of a Gaussian) is commonly used for the pulse shape. It can be written @@ -156,11 +200,75 @@ t=0 (assuming the source is off for t<0 this gives $\sim 10^{-3}$ error at t=0). Boundary conditions =================== -# TODO notes about boundaries / PMLs + +`meanas.fdtd` exposes two boundary-related building blocks: + +- `conducting_boundary(...)` for simple perfect-electric-conductor style field + clamping at one face of the domain. +- `cpml_params(...)` and `updates_with_cpml(...)` for convolutional perfectly + matched layers (CPMLs) attached to one or more faces of the Yee grid. + +`updates_with_cpml(...)` accepts a three-by-two table of CPML parameter blocks: + +``` +cpml_params[axis][polarity_index] +``` + +where `axis` is `0`, `1`, or `2` and `polarity_index` corresponds to `(-1, +1)`. +Passing `None` for one entry disables CPML on that face while leaving the other +directions unchanged. This is how mixed boundary setups such as "absorbing in x, +periodic in y/z" are expressed. + +When comparing an FDTD run against an FDFD solve, use the same stretched +coordinate system in both places: + +1. Build the FDTD update with the desired CPML parameters. +2. Stretch the FDFD `dxes` with the matching SCPML transform. +3. Compare the extracted phasor against the FDFD field or residual on those + stretched `dxes`. + +The electric-current sign convention used throughout the examples and tests is + +$$ +E \leftarrow E - \Delta_t J / \epsilon +$$ + +which matches the FDFD right-hand side + +$$ +-i \omega J. +$$ """ -from .base import maxwell_e, maxwell_h -from .pml import cpml_params, updates_with_cpml -from .energy import (poynting, poynting_divergence, energy_hstep, energy_estep, - delta_energy_h2e, delta_energy_j) -from .boundaries import conducting_boundary +from .base import ( + maxwell_e as maxwell_e, + maxwell_h as maxwell_h, + ) +from .pml import ( + cpml_params as cpml_params, + updates_with_cpml as updates_with_cpml, + ) +from .energy import ( + poynting as poynting, + poynting_divergence as poynting_divergence, + energy_hstep as energy_hstep, + energy_estep as energy_estep, + delta_energy_h2e as delta_energy_h2e, + delta_energy_j as delta_energy_j, + ) +from .boundaries import ( + conducting_boundary as conducting_boundary, + ) +from .phasor import ( + accumulate_phasor as accumulate_phasor, + accumulate_phasor_e as accumulate_phasor_e, + accumulate_phasor_h as accumulate_phasor_h, + accumulate_phasor_j as accumulate_phasor_j, + real_injection_scale as real_injection_scale, + reconstruct_real as reconstruct_real, + reconstruct_real_e as reconstruct_real_e, + reconstruct_real_h as reconstruct_real_h, + reconstruct_real_j as reconstruct_real_j, + temporal_phasor as temporal_phasor, + temporal_phasor_scale as temporal_phasor_scale, + ) diff --git a/meanas/fdtd/base.py b/meanas/fdtd/base.py index 3891e28..480ed87 100644 --- a/meanas/fdtd/base.py +++ b/meanas/fdtd/base.py @@ -3,7 +3,7 @@ Basic FDTD field updates """ -from ..fdmath import dx_lists_t, fdfield_t, fdfield_updater_t +from ..fdmath import dx_lists_t, fdfield, fdfield_updater_t from ..fdmath.functional import curl_forward, curl_back @@ -47,7 +47,7 @@ def maxwell_e( else: curl_h_fun = curl_back() - def me_fun(e: fdfield_t, h: fdfield_t, epsilon: fdfield_t | float) -> fdfield_t: + def me_fun(e: fdfield, h: fdfield, epsilon: fdfield | float) -> fdfield: """ Update the E-field. @@ -103,7 +103,7 @@ def maxwell_h( else: curl_e_fun = curl_forward() - def mh_fun(e: fdfield_t, h: fdfield_t, mu: fdfield_t | float | None = None) -> fdfield_t: + def mh_fun(e: fdfield, h: fdfield, mu: fdfield | float | None = None) -> fdfield: """ Update the H-field. diff --git a/meanas/fdtd/boundaries.py b/meanas/fdtd/boundaries.py index 131d741..ca8940d 100644 --- a/meanas/fdtd/boundaries.py +++ b/meanas/fdtd/boundaries.py @@ -6,7 +6,7 @@ Boundary conditions from typing import Any -from ..fdmath import fdfield_t, fdfield_updater_t +from ..fdmath import fdfield, fdfield_updater_t def conducting_boundary( @@ -15,7 +15,7 @@ def conducting_boundary( ) -> tuple[fdfield_updater_t, fdfield_updater_t]: dirs = [0, 1, 2] if direction not in dirs: - raise Exception(f'Invalid direction: {direction}') + raise ValueError(f'Invalid direction: {direction}') dirs.remove(direction) u, v = dirs @@ -28,17 +28,19 @@ def conducting_boundary( shifted1_slice = [slice(None)] * 3 boundary_slice[direction] = 0 shifted1_slice[direction] = 1 + boundary = tuple(boundary_slice) + shifted1 = tuple(shifted1_slice) - def en(e: fdfield_t) -> fdfield_t: - e[direction][boundary_slice] = 0 - e[u][boundary_slice] = e[u][shifted1_slice] - e[v][boundary_slice] = e[v][shifted1_slice] + def en(e: fdfield) -> fdfield: + e[direction][boundary] = 0 + e[u][boundary] = e[u][shifted1] + e[v][boundary] = e[v][shifted1] return e - def hn(h: fdfield_t) -> fdfield_t: - h[direction][boundary_slice] = h[direction][shifted1_slice] - h[u][boundary_slice] = 0 - h[v][boundary_slice] = 0 + def hn(h: fdfield) -> fdfield: + h[direction][boundary] = h[direction][shifted1] + h[u][boundary] = 0 + h[v][boundary] = 0 return h return en, hn @@ -50,22 +52,25 @@ def conducting_boundary( boundary_slice[direction] = -1 shifted1_slice[direction] = -2 shifted2_slice[direction] = -3 + boundary = tuple(boundary_slice) + shifted1 = tuple(shifted1_slice) + shifted2 = tuple(shifted2_slice) - def ep(e: fdfield_t) -> fdfield_t: - e[direction][boundary_slice] = -e[direction][shifted2_slice] - e[direction][shifted1_slice] = 0 - e[u][boundary_slice] = e[u][shifted1_slice] - e[v][boundary_slice] = e[v][shifted1_slice] + def ep(e: fdfield) -> fdfield: + e[direction][boundary] = -e[direction][shifted2] + e[direction][shifted1] = 0 + e[u][boundary] = e[u][shifted1] + e[v][boundary] = e[v][shifted1] return e - def hp(h: fdfield_t) -> fdfield_t: - h[direction][boundary_slice] = h[direction][shifted1_slice] - h[u][boundary_slice] = -h[u][shifted2_slice] - h[u][shifted1_slice] = 0 - h[v][boundary_slice] = -h[v][shifted2_slice] - h[v][shifted1_slice] = 0 + def hp(h: fdfield) -> fdfield: + h[direction][boundary] = h[direction][shifted1] + h[u][boundary] = -h[u][shifted2] + h[u][shifted1] = 0 + h[v][boundary] = -h[v][shifted2] + h[v][shifted1] = 0 return h return ep, hp - raise Exception(f'Bad polarity: {polarity}') + raise ValueError(f'Bad polarity: {polarity}') diff --git a/meanas/fdtd/energy.py b/meanas/fdtd/energy.py index 43ea3a1..57387aa 100644 --- a/meanas/fdtd/energy.py +++ b/meanas/fdtd/energy.py @@ -1,15 +1,29 @@ import numpy -from ..fdmath import dx_lists_t, fdfield_t +from ..fdmath import dx_lists_t, fdfield_t, fdfield from ..fdmath.functional import deriv_back -# TODO documentation +""" +Energy- and flux-accounting helpers for Yee-grid FDTD fields. + +These functions complement the derivation in `meanas.fdtd`: + +- `poynting(...)` and `poynting_divergence(...)` evaluate the discrete flux terms + from the exact time-domain Poynting identity. +- `energy_hstep(...)` / `energy_estep(...)` evaluate the two staggered energy + expressions. +- `delta_energy_*` helpers evaluate the corresponding energy changes between + adjacent half-steps. + +The helpers are intended for diagnostics, regression tests, and consistency +checks between source work, field energy, and flux through cell faces. +""" def poynting( - e: fdfield_t, - h: fdfield_t, + e: fdfield, + h: fdfield, dxes: dx_lists_t | None = None, ) -> fdfield_t: r""" @@ -43,6 +57,7 @@ def poynting( (see `meanas.tests.test_fdtd.test_poynting_planes`) The full relationship is + $$ \begin{aligned} (U_{l+\frac{1}{2}} - U_l) / \Delta_t @@ -84,14 +99,14 @@ def poynting( s[0] = numpy.roll(ey, -1, axis=0) * hz - numpy.roll(ez, -1, axis=0) * hy s[1] = numpy.roll(ez, -1, axis=1) * hx - numpy.roll(ex, -1, axis=1) * hz s[2] = numpy.roll(ex, -1, axis=2) * hy - numpy.roll(ey, -1, axis=2) * hx - return s + return fdfield_t(s) def poynting_divergence( - s: fdfield_t | None = None, + s: fdfield | None = None, *, - e: fdfield_t | None = None, - h: fdfield_t | None = None, + e: fdfield | None = None, + h: fdfield | None = None, dxes: dx_lists_t | None = None, ) -> fdfield_t: """ @@ -122,15 +137,15 @@ def poynting_divergence( Dx, Dy, Dz = deriv_back() ds = Dx(s[0]) + Dy(s[1]) + Dz(s[2]) - return ds + return fdfield_t(ds) def energy_hstep( - e0: fdfield_t, - h1: fdfield_t, - e2: fdfield_t, - epsilon: fdfield_t | None = None, - mu: fdfield_t | None = None, + e0: fdfield, + h1: fdfield, + e2: fdfield, + epsilon: fdfield | None = None, + mu: fdfield | None = None, dxes: dx_lists_t | None = None, ) -> fdfield_t: """ @@ -150,15 +165,15 @@ def energy_hstep( Energy, at the time of the H-field `h1`. """ u = dxmul(e0 * e2, h1 * h1, epsilon, mu, dxes) - return u + return fdfield_t(u) def energy_estep( - h0: fdfield_t, - e1: fdfield_t, - h2: fdfield_t, - epsilon: fdfield_t | None = None, - mu: fdfield_t | None = None, + h0: fdfield, + e1: fdfield, + h2: fdfield, + epsilon: fdfield | None = None, + mu: fdfield | None = None, dxes: dx_lists_t | None = None, ) -> fdfield_t: """ @@ -178,17 +193,17 @@ def energy_estep( Energy, at the time of the E-field `e1`. """ u = dxmul(e1 * e1, h0 * h2, epsilon, mu, dxes) - return u + return fdfield_t(u) def delta_energy_h2e( dt: float, - e0: fdfield_t, - h1: fdfield_t, - e2: fdfield_t, - h3: fdfield_t, - epsilon: fdfield_t | None = None, - mu: fdfield_t | None = None, + e0: fdfield, + h1: fdfield, + e2: fdfield, + h3: fdfield, + epsilon: fdfield | None = None, + mu: fdfield | None = None, dxes: dx_lists_t | None = None, ) -> fdfield_t: """ @@ -211,17 +226,17 @@ def delta_energy_h2e( de = e2 * (e2 - e0) / dt dh = h1 * (h3 - h1) / dt du = dxmul(de, dh, epsilon, mu, dxes) - return du + return fdfield_t(du) def delta_energy_e2h( dt: float, - h0: fdfield_t, - e1: fdfield_t, - h2: fdfield_t, - e3: fdfield_t, - epsilon: fdfield_t | None = None, - mu: fdfield_t | None = None, + h0: fdfield, + e1: fdfield, + h2: fdfield, + e3: fdfield, + epsilon: fdfield | None = None, + mu: fdfield | None = None, dxes: dx_lists_t | None = None, ) -> fdfield_t: """ @@ -244,21 +259,31 @@ def delta_energy_e2h( de = e1 * (e3 - e1) / dt dh = h2 * (h2 - h0) / dt du = dxmul(de, dh, epsilon, mu, dxes) - return du + return fdfield_t(du) def delta_energy_j( - j0: fdfield_t, - e1: fdfield_t, + j0: fdfield, + e1: fdfield, dxes: dx_lists_t | None = None, ) -> fdfield_t: - """ - Calculate + r""" + Calculate the electric-current work term $J \cdot E$ on the Yee grid. - Note that each value of $J$ contributes to the energy twice (i.e. once per field update) - despite only causing the value of $E$ to change once (same for $M$ and $H$). + This is the source contribution that appears beside the flux divergence in + the discrete Poynting identities documented in `meanas.fdtd`. + Note that each value of `J` contributes twice in a full Yee cycle (once per + half-step energy balance) even though it directly changes `E` only once. + Args: + j0: Electric-current density sampled at the same half-step as the + current work term. + e1: Electric field sampled at the matching integer timestep. + dxes: Grid description; defaults to unit spacing. + + Returns: + Per-cell source-work contribution with the scalar field shape. """ if dxes is None: dxes = tuple(tuple(numpy.ones(1) for _ in range(3)) for _ in range(2)) @@ -267,16 +292,30 @@ def delta_energy_j( * dxes[0][0][:, None, None] * dxes[0][1][None, :, None] * dxes[0][2][None, None, :]) - return du + return fdfield_t(du) def dxmul( - ee: fdfield_t, - hh: fdfield_t, - epsilon: fdfield_t | float | None = None, - mu: fdfield_t | float | None = None, + ee: fdfield, + hh: fdfield, + epsilon: fdfield | float | None = None, + mu: fdfield | float | None = None, dxes: dx_lists_t | None = None, ) -> fdfield_t: + """ + Multiply E- and H-like field products by material weights and cell volumes. + + Args: + ee: Three-component electric-field product, such as `e0 * e2`. + hh: Three-component magnetic-field product, such as `h1 * h1`. + epsilon: Electric material weight; defaults to `1`. + mu: Magnetic material weight; defaults to `1`. + dxes: Grid description; defaults to unit spacing. + + Returns: + Scalar field containing the weighted electric plus magnetic contribution + for each Yee cell. + """ if epsilon is None: epsilon = 1 if mu is None: @@ -292,4 +331,4 @@ def dxmul( * dxes[1][0][:, None, None] * dxes[1][1][None, :, None] * dxes[1][2][None, None, :]) - return result + return fdfield_t(result) diff --git a/meanas/fdtd/misc.py b/meanas/fdtd/misc.py new file mode 100644 index 0000000..585c745 --- /dev/null +++ b/meanas/fdtd/misc.py @@ -0,0 +1,180 @@ +from collections.abc import Callable +import logging +from typing import cast + +import numpy +from numpy.typing import NDArray, ArrayLike +from numpy import pi + + +logger = logging.getLogger(__name__) + + +type pulse_scalar_t = float | NDArray[numpy.floating] +pulse_fn_t = Callable[[ArrayLike], tuple[pulse_scalar_t, pulse_scalar_t, pulse_scalar_t]] + + +def _scalar_or_array(values: NDArray[numpy.floating]) -> pulse_scalar_t: + if values.ndim == 0: + return float(values) + return cast('NDArray[numpy.floating]', values) + + +def gaussian_packet( + wl: float, + dwl: float, + dt: float, + turn_on: float = 1e-10, + one_sided: bool = False, + ) -> tuple[pulse_fn_t, float]: + """ + Gaussian pulse (or gaussian ramp) for FDTD excitation + + exp(-a*t*t) ==> exp(-omega * omega / (4 * a)) [fourier, ignoring leading const.] + + FWHM_time is 2 * sqrt(2 * log(2)) * sqrt(2 / a) + FWHM_omega is 2 * sqrt(2 * log(2)) * sqrt(2 * a) = 4 * sqrt(log(2) * a) + + Args: + wl: wavelength + dwl: Gaussian's FWHM in wavelength space + dt: Timestep + turn_on: Max allowable amplitude at t=0 + one_sided: If `True`, source amplitude never decreases after reaching max + + Returns: + Source function: src(timestep) -> (envelope[tt], cos[... * tt], sin[... * tt]) + Delay: number of initial timesteps for which envelope[tt] will be 0 + """ + logger.warning('meanas.fdtd.misc functions are still very WIP!') # TODO + # dt * dw = 4 * ln(2) + + omega = 2 * pi / wl + freq = 1 / wl + fwhm_omega = dwl * omega * omega / (2 * pi) # dwl -> d_omega (approx) + alpha = (fwhm_omega * fwhm_omega) * numpy.log(2) / 8 + delay = numpy.sqrt(-numpy.log(turn_on) / alpha) + delay = numpy.ceil(delay * freq) / freq # force delay to integer number of periods to maintain phase + logger.info(f'src_time {2 * delay / dt}') + + def source_phasor(ii: ArrayLike) -> tuple[pulse_scalar_t, pulse_scalar_t, pulse_scalar_t]: + ii_array = numpy.asarray(ii, dtype=float) + t0 = ii_array * dt - delay + envelope = numpy.sqrt(numpy.sqrt(2 * alpha / pi)) * numpy.exp(-alpha * t0 * t0) + + if one_sided: + envelope = numpy.where(t0 > 0, 1.0, envelope) + + cc = numpy.cos(omega * t0) + ss = numpy.sin(omega * t0) + + return _scalar_or_array(envelope), _scalar_or_array(cc), _scalar_or_array(ss) + + # nrm = numpy.exp(-omega * omega / alpha) / 2 + + return source_phasor, delay + + +def ricker_pulse( + wl: float, + dt: float, + turn_on: float = 1e-10, + ) -> tuple[pulse_fn_t, float]: + """ + Ricker wavelet (second derivative of a gaussian pulse) + + t0 = ii * dt - delay + R = w_peak * t0 / 2 + f(t) = (1 - 2 * (pi * f_peak * t0) ** 2) * exp(-(pi * f_peak * t0)**2 + = (1 - (w_peak * t0)**2 / 2 exp(-(w_peak * t0 / 2) **2) + = (1 - 2 * R * R) * exp(-R * R) + + # NOTE: don't use cosine/sine for J, just for phasor readout + + Args: + wl: wavelength + dt: Timestep + turn_on: Max allowable amplitude at t=0 + + Returns: + Source function: src(timestep) -> (envelope[tt], cos[... * tt], sin[... * tt]) + Delay: number of initial timesteps for which envelope[tt] will be 0 + """ + logger.warning('meanas.fdtd.misc functions are still very WIP!') # TODO + omega = 2 * pi / wl + freq = 1 / wl + + from scipy.optimize import root_scalar + delay_results = root_scalar( + lambda tt: (1 - omega * omega * tt * tt / 2) * numpy.exp(-omega * omega * tt * tt / 4) - turn_on, + x0=0, + x1=-2 / omega, + ) + + delay = delay_results.root + delay = numpy.ceil(delay * freq) / freq # force delay to integer number of periods to maintain phase + + def source_phasor(ii: ArrayLike) -> tuple[pulse_scalar_t, pulse_scalar_t, pulse_scalar_t]: + ii_array = numpy.asarray(ii, dtype=float) + t0 = ii_array * dt - delay + rr = omega * t0 / 2 + ff = (1 - 2 * rr * rr) * numpy.exp(-rr * rr) + + cc = numpy.cos(omega * t0) + ss = numpy.sin(omega * t0) + + return _scalar_or_array(ff), _scalar_or_array(cc), _scalar_or_array(ss) + + return source_phasor, delay + + +def gaussian_beam( + xyz: list[NDArray], + center: ArrayLike, + waist_radius: float, + wl: float, + tilt: float = 0, + ) -> NDArray[numpy.complex128]: + """ + Gaussian beam + (solution to paraxial Helmholtz equation) + + Default (no tilt) corresponds to a beam propagating in the -z direction. + + Args: + xyz: List of [[x0, x1, ...], [y0, ...], [z0, ...]] positions specifying grid + locations at which the field will be sampled. + center: [x, y, z] location of beam waist + waist_radius: Beam radius at the waist + wl: Wavelength + tilt: Rotation around y axis. Default (0) has beam propagating in -z direction. + """ + logger.warning('meanas.fdtd.misc functions are still very WIP!') # TODO + w0 = waist_radius + grids = numpy.asarray(numpy.meshgrid(*xyz, indexing='ij')) + grids -= numpy.asarray(center)[:, None, None, None] + + rot = numpy.array([ + [ numpy.cos(tilt), 0, numpy.sin(tilt)], + [ 0, 1, 0], + [-numpy.sin(tilt), 0, numpy.cos(tilt)], + ]) + + xx, yy, zz = numpy.einsum('ij,jxyz->ixyz', rot, grids) + r2 = xx * xx + yy * yy + z2 = zz * zz + + zr = pi * w0 * w0 / wl + zr2 = zr * zr + wz2 = w0 * w0 * (1 + z2 / zr2) + wz = numpy.sqrt(wz2) # == fwhm(z) / sqrt(2 * ln(2)) + + kk = 2 * pi / wl + inv_Rz = numpy.divide(zz, z2 + zr2, out=numpy.zeros_like(zz), where=(z2 + zr2) != 0) + gouy = numpy.arctan(zz / zr) + + gaussian = w0 / wz * numpy.exp(-r2 / wz2) * numpy.exp(1j * (kk * zz + kk * r2 * inv_Rz / 2 - gouy)) + + row = gaussian[:, :, gaussian.shape[2] // 2] + norm = numpy.linalg.norm(row) + return gaussian / norm diff --git a/meanas/fdtd/phasor.py b/meanas/fdtd/phasor.py new file mode 100644 index 0000000..d5a01cd --- /dev/null +++ b/meanas/fdtd/phasor.py @@ -0,0 +1,319 @@ +""" +Helpers for extracting single- or multi-frequency phasors from FDTD samples. + +These helpers are intentionally low-level: callers own the accumulator arrays and +the sampling policy. The accumulated quantity is + + dt * sum(weight * exp(-1j * omega * t_step) * sample_step) + +where `t_step = (step + offset_steps) * dt`. + +The usual Yee offsets are: + +- `accumulate_phasor_e(..., step=l)` for `E_l` +- `accumulate_phasor_h(..., step=l)` for `H_{l + 1/2}` +- `accumulate_phasor_j(..., step=l)` for `J_{l + 1/2}` + +`temporal_phasor(...)` and `temporal_phasor_scale(...)` apply the same Fourier +sum to a 1D scalar waveform. They are useful for normalizing a pulsed source +before that scalar waveform is applied to a point source or spatial mode source. +`real_injection_scale(...)` is a companion helper for the common real-valued +injection pattern `numpy.real(scale * waveform)`, where `waveform` is the +analytic positive-frequency signal and the injected real current should still +produce a desired phasor response. +`reconstruct_real(...)` and its `E/H/J` wrappers perform the inverse operation: +they turn one or more phasors back into real-valued field snapshots at explicit +Yee-aligned sample times. For a scalar target frequency they accept either a +plain field phasor or the batched `(1, *sample_shape)` form used elsewhere in +this module. + +These helpers do not choose warmup/accumulation windows or pulse-envelope +normalization. They also do not impose a current sign convention. In this +codebase, electric-current injection normally appears as `E -= dt * J / epsilon`, +which matches the FDFD right-hand side `-1j * omega * J`. +""" +from collections.abc import Sequence + +import numpy +from numpy.typing import ArrayLike, NDArray + + +def _normalize_omegas( + omegas: float | complex | Sequence[float | complex] | NDArray, + ) -> NDArray[numpy.complexfloating]: + omega_array = numpy.atleast_1d(numpy.asarray(omegas, dtype=complex)) + if omega_array.ndim != 1 or omega_array.size == 0: + raise ValueError('omegas must be a scalar or non-empty 1D sequence') + return omega_array + + +def _normalize_weight( + weight: ArrayLike, + omega_shape: tuple[int, ...], + ) -> NDArray[numpy.complexfloating]: + weight_array = numpy.asarray(weight, dtype=complex) + if weight_array.ndim == 0: + return numpy.full(omega_shape, weight_array, dtype=complex) + if weight_array.shape == omega_shape: + return weight_array + raise ValueError(f'weight must be scalar or have shape {omega_shape}, got {weight_array.shape}') + + +def _normalize_temporal_samples( + samples: ArrayLike, + ) -> NDArray[numpy.complexfloating]: + sample_array = numpy.asarray(samples, dtype=complex) + if sample_array.ndim != 1 or sample_array.size == 0: + raise ValueError('samples must be a non-empty 1D sequence') + return sample_array + + +def _validate_reconstruction_inputs( + phasors: ArrayLike, + omegas: float | complex | Sequence[float | complex] | NDArray, + dt: float, + ) -> tuple[NDArray[numpy.complexfloating], NDArray[numpy.complexfloating], bool]: + if dt <= 0: + raise ValueError('dt must be positive') + + omega_array = _normalize_omegas(omegas) + phasor_array = numpy.asarray(phasors, dtype=complex) + expected_leading = omega_array.size + if phasor_array.ndim == 0: + raise ValueError( + f'phasors must have shape ({expected_leading}, *sample_shape) or sample_shape for scalar omega, got {phasor_array.shape}', + ) + added_axis = False + if expected_leading == 1 and (phasor_array.ndim == 1 or phasor_array.shape[0] != expected_leading): + phasor_array = phasor_array[numpy.newaxis, ...] + added_axis = True + elif phasor_array.shape[0] != expected_leading: + raise ValueError( + f'phasors must have shape ({expected_leading}, *sample_shape) or sample_shape for scalar omega, got {phasor_array.shape}', + ) + return omega_array, phasor_array, added_axis + + +def accumulate_phasor( + accumulator: NDArray[numpy.complexfloating], + omegas: float | complex | Sequence[float | complex] | NDArray, + dt: float, + sample: ArrayLike, + step: int, + *, + offset_steps: float = 0.0, + weight: ArrayLike = 1.0, + ) -> NDArray[numpy.complexfloating]: + """ + Add one time-domain sample into a phasor accumulator. + + The added quantity is + + dt * weight * exp(-1j * omega * t_step) * sample + + where `t_step = (step + offset_steps) * dt`. + + Note: + This helper already multiplies by `dt`. If the caller's normalization + factor was derived from a discrete sum that already includes `dt`, pass + `weight / dt` here. + """ + if dt <= 0: + raise ValueError('dt must be positive') + + omega_array = _normalize_omegas(omegas) + sample_array = numpy.asarray(sample) + expected_shape = (omega_array.size, *sample_array.shape) + if accumulator.shape != expected_shape: + raise ValueError(f'accumulator must have shape {expected_shape}, got {accumulator.shape}') + + weight_array = _normalize_weight(weight, omega_array.shape) + time = (step + offset_steps) * dt + phase = numpy.exp(-1j * omega_array * time) + scaled = dt * (weight_array * phase).reshape((-1,) + (1,) * sample_array.ndim) + accumulator += scaled * sample_array + return accumulator + + +def temporal_phasor( + samples: ArrayLike, + omegas: float | complex | Sequence[float | complex] | NDArray, + dt: float, + *, + start_step: int = 0, + offset_steps: float = 0.0, + ) -> NDArray[numpy.complexfloating]: + """ + Fourier-project a 1D temporal waveform onto one or more angular frequencies. + + The returned quantity is + + dt * sum(exp(-1j * omega * t_step) * samples[step_index]) + + where `t_step = (start_step + step_index + offset_steps) * dt`. + """ + if dt <= 0: + raise ValueError('dt must be positive') + + omega_array = _normalize_omegas(omegas) + sample_array = _normalize_temporal_samples(samples) + steps = start_step + numpy.arange(sample_array.size, dtype=float) + offset_steps + phase = numpy.exp(-1j * omega_array[:, None] * (steps[None, :] * dt)) + return dt * (phase @ sample_array) + + +def temporal_phasor_scale( + samples: ArrayLike, + omegas: float | complex | Sequence[float | complex] | NDArray, + dt: float, + *, + start_step: int = 0, + offset_steps: float = 0.0, + target: ArrayLike = 1.0, + ) -> NDArray[numpy.complexfloating]: + """ + Return the scalar multiplier that gives a desired temporal phasor response. + + The returned scale satisfies + + temporal_phasor(scale * samples, omegas, dt, ...) == target + + for each target frequency. The result keeps a leading frequency axis even + when `omegas` is scalar. + """ + response = temporal_phasor(samples, omegas, dt, start_step=start_step, offset_steps=offset_steps) + target_array = _normalize_weight(target, response.shape) + if numpy.any(numpy.abs(response) <= numpy.finfo(float).eps): + raise ValueError('cannot normalize a waveform with zero temporal phasor response') + return target_array / response + + +def real_injection_scale( + samples: ArrayLike, + omegas: float | complex | Sequence[float | complex] | NDArray, + dt: float, + *, + start_step: int = 0, + offset_steps: float = 0.0, + target: ArrayLike = 1.0, + ) -> NDArray[numpy.complexfloating]: + """ + Return the scale for a real-valued injection built from an analytic waveform. + + If the time-domain source is applied as + + numpy.real(scale * samples[step]) + + then the desired positive-frequency phasor is obtained by compensating for + the 1/2 factor between the real-valued source and its analytic component: + + scale = 2 * target / temporal_phasor(samples, ...) + + This helper normalizes only the intended positive-frequency component. Any + residual negative-frequency leakage is controlled by the waveform design and + the accumulation window. + """ + response = temporal_phasor(samples, omegas, dt, start_step=start_step, offset_steps=offset_steps) + target_array = _normalize_weight(target, response.shape) + if numpy.any(numpy.abs(response) <= numpy.finfo(float).eps): + raise ValueError('cannot normalize a waveform with zero temporal phasor response') + return 2 * target_array / response + + +def reconstruct_real( + phasors: ArrayLike, + omegas: float | complex | Sequence[float | complex] | NDArray, + dt: float, + step: int, + *, + offset_steps: float = 0.0, + ) -> NDArray[numpy.floating]: + """ + Reconstruct a real-valued field snapshot from one or more phasors. + + The returned quantity is + + real(phasor * exp(1j * omega * t_step)) + + where `t_step = (step + offset_steps) * dt`. + + For multi-frequency inputs, the leading frequency axis is preserved. For a + scalar `omega`, callers may pass either `(1, *sample_shape)` or + `sample_shape`; the return shape matches that choice. + """ + omega_array, phasor_array, added_axis = _validate_reconstruction_inputs(phasors, omegas, dt) + time = (step + offset_steps) * dt + phase = numpy.exp(1j * omega_array * time).reshape((-1,) + (1,) * (phasor_array.ndim - 1)) + reconstructed = numpy.real(phasor_array * phase) + if added_axis: + return reconstructed[0] + return reconstructed + + +def accumulate_phasor_e( + accumulator: NDArray[numpy.complexfloating], + omegas: float | complex | Sequence[float | complex] | NDArray, + dt: float, + sample: ArrayLike, + step: int, + *, + weight: ArrayLike = 1.0, + ) -> NDArray[numpy.complexfloating]: + """Accumulate an E-field sample taken at integer timestep `step`.""" + return accumulate_phasor(accumulator, omegas, dt, sample, step, offset_steps=0.0, weight=weight) + + +def accumulate_phasor_h( + accumulator: NDArray[numpy.complexfloating], + omegas: float | complex | Sequence[float | complex] | NDArray, + dt: float, + sample: ArrayLike, + step: int, + *, + weight: ArrayLike = 1.0, + ) -> NDArray[numpy.complexfloating]: + """Accumulate an H-field sample corresponding to `H_{step + 1/2}`.""" + return accumulate_phasor(accumulator, omegas, dt, sample, step, offset_steps=0.5, weight=weight) + + +def accumulate_phasor_j( + accumulator: NDArray[numpy.complexfloating], + omegas: float | complex | Sequence[float | complex] | NDArray, + dt: float, + sample: ArrayLike, + step: int, + *, + weight: ArrayLike = 1.0, + ) -> NDArray[numpy.complexfloating]: + """Accumulate a current sample corresponding to `J_{step + 1/2}`.""" + return accumulate_phasor(accumulator, omegas, dt, sample, step, offset_steps=0.5, weight=weight) + + +def reconstruct_real_e( + phasors: ArrayLike, + omegas: float | complex | Sequence[float | complex] | NDArray, + dt: float, + step: int, + ) -> NDArray[numpy.floating]: + """Reconstruct a real E-field snapshot taken at integer timestep `step`.""" + return reconstruct_real(phasors, omegas, dt, step, offset_steps=0.0) + + +def reconstruct_real_h( + phasors: ArrayLike, + omegas: float | complex | Sequence[float | complex] | NDArray, + dt: float, + step: int, + ) -> NDArray[numpy.floating]: + """Reconstruct a real H-field snapshot corresponding to `H_{step + 1/2}`.""" + return reconstruct_real(phasors, omegas, dt, step, offset_steps=0.5) + + +def reconstruct_real_j( + phasors: ArrayLike, + omegas: float | complex | Sequence[float | complex] | NDArray, + dt: float, + step: int, + ) -> NDArray[numpy.floating]: + """Reconstruct a real current snapshot corresponding to `J_{step + 1/2}`.""" + return reconstruct_real(phasors, omegas, dt, step, offset_steps=0.5) diff --git a/meanas/fdtd/pml.py b/meanas/fdtd/pml.py index 65d71e6..aba9cb7 100644 --- a/meanas/fdtd/pml.py +++ b/meanas/fdtd/pml.py @@ -1,18 +1,29 @@ """ -PML implementations +Convolutional perfectly matched layer (CPML) support for FDTD updates. -#TODO discussion of PMLs -#TODO cpml documentation +The helpers in this module construct per-face CPML parameters and then wrap the +standard Yee updates with the additional auxiliary `psi` fields needed by the +CPML recurrence. +The intended call pattern is: + +1. Build a `cpml_params[axis][polarity_index]` table with `cpml_params(...)`. +2. Pass that table into `updates_with_cpml(...)` together with `dt`, `dxes`, and + `epsilon`. +3. Advance the returned `update_E` / `update_H` closures in the simulation loop. + +Each face can be enabled or disabled independently by replacing one table entry +with `None`. """ # TODO retest pmls! -from typing import Callable, Sequence, Any +from typing import Any +from collections.abc import Callable, Sequence from copy import deepcopy import numpy from numpy.typing import NDArray, DTypeLike -from ..fdmath import fdfield_t, dx_lists_t +from ..fdmath import fdfield, dx_lists_t from ..fdmath.functional import deriv_forward, deriv_back @@ -31,18 +42,41 @@ def cpml_params( ma: float = 1, cfs_alpha: float = 0, ) -> dict[str, Any]: + """ + Construct the parameter block for one CPML face. + + Args: + axis: Which Cartesian axis the CPML is normal to (`0`, `1`, or `2`). + polarity: Which face along that axis (`-1` for the low-index face, + `+1` for the high-index face). + dt: Timestep used by the Yee update. + thickness: Number of Yee cells occupied by the CPML region. + ln_R_per_layer: Logarithmic attenuation target per layer. + epsilon_eff: Effective permittivity used when choosing the CPML scaling. + mu_eff: Effective permeability used when choosing the CPML scaling. + m: Polynomial grading exponent for `sigma` and `kappa`. + ma: Polynomial grading exponent for the complex-frequency shift `alpha`. + cfs_alpha: Maximum complex-frequency shift parameter. + + Returns: + Dictionary with: + + - `param_e`: `(p0, p1, p2)` arrays for the E update + - `param_h`: `(p0, p1, p2)` arrays for the H update + - `region`: slice tuple selecting the CPML cells on that face + """ if axis not in range(3): - raise Exception(f'Invalid axis: {axis}') + raise ValueError(f'Invalid axis: {axis}') if polarity not in (-1, 1): - raise Exception(f'Invalid polarity: {polarity}') + raise ValueError(f'Invalid polarity: {polarity}') if thickness <= 2: - raise Exception('It would be wise to have a pml with 4+ cells of thickness') + raise ValueError('It would be wise to have a pml with 4+ cells of thickness') if epsilon_eff <= 0: - raise Exception('epsilon_eff must be positive') + raise ValueError('epsilon_eff must be positive') sigma_max = -ln_R_per_layer / 2 * (m + 1) kappa_max = numpy.sqrt(epsilon_eff * mu_eff) @@ -56,8 +90,6 @@ def cpml_params( xh -= 0.5 xe = xe[::-1] xh = xh[::-1] - else: - raise Exception('Bad polarity!') expand_slice_l: list[Any] = [None, None, None] expand_slice_l[axis] = slice(None) @@ -81,8 +113,6 @@ def cpml_params( region_list[axis] = slice(None, thickness) elif polarity > 0: region_list[axis] = slice(-thickness, None) - else: - raise Exception('Bad polarity!') region = tuple(region_list) return { @@ -96,11 +126,31 @@ def updates_with_cpml( cpml_params: Sequence[Sequence[dict[str, Any] | None]], dt: float, dxes: dx_lists_t, - epsilon: fdfield_t, + epsilon: fdfield, *, dtype: DTypeLike = numpy.float32, - ) -> tuple[Callable[[fdfield_t, fdfield_t, fdfield_t], None], - Callable[[fdfield_t, fdfield_t, fdfield_t], None]]: + ) -> tuple[Callable[..., None], Callable[..., None]]: + """ + Build Yee-step update closures augmented with CPML terms. + + Args: + cpml_params: Three-by-two sequence indexed as `[axis][polarity_index]`. + Entries are the dictionaries returned by `cpml_params(...)`; use + `None` to disable CPML on one face. + dt: Timestep. + dxes: Yee-grid spacing lists `[dx_e, dx_h]`. + epsilon: Electric material distribution used by the E update. + dtype: Storage dtype for the auxiliary CPML state arrays. + + Returns: + `(update_E, update_H)` closures with the same call shape as the basic + Yee updates: + + - `update_E(e, h, epsilon)` + - `update_H(e, h, mu)` + + The closures retain the CPML auxiliary state internally. + """ Dfx, Dfy, Dfz = deriv_forward(dxes[1]) Dbx, Dby, Dbz = deriv_back(dxes[1]) @@ -111,7 +161,7 @@ def updates_with_cpml( params_H: list[list[tuple[Any, Any, Any, Any]]] = deepcopy(params_E) for axis in range(3): - for pp, polarity in enumerate((-1, 1)): + for pp, _polarity in enumerate((-1, 1)): cpml_param = cpml_params[axis][pp] if cpml_param is None: psi_E[axis][pp] = (None, None) @@ -136,9 +186,9 @@ def updates_with_cpml( pH = numpy.empty_like(epsilon, dtype=dtype) def update_E( - e: fdfield_t, - h: fdfield_t, - epsilon: fdfield_t, + e: fdfield, + h: fdfield, + epsilon: fdfield, ) -> None: dyHx = Dby(h[0]) dzHx = Dbz(h[0]) @@ -182,9 +232,9 @@ def updates_with_cpml( e[2] += dt / epsilon[2] * (dxHy - dyHx + pE[2]) def update_H( - e: fdfield_t, - h: fdfield_t, - mu: fdfield_t = numpy.ones(3), + e: fdfield, + h: fdfield, + mu: fdfield | tuple[int, int, int] = (1, 1, 1), ) -> None: dyEx = Dfy(e[0]) dzEx = Dfz(e[0]) diff --git a/meanas/test/_bloch_case.py b/meanas/test/_bloch_case.py new file mode 100644 index 0000000..430cd06 --- /dev/null +++ b/meanas/test/_bloch_case.py @@ -0,0 +1,37 @@ +import numpy + + +SHAPE = (2, 2, 2) +G_MATRIX = numpy.eye(3) +K0_GENERAL = numpy.array([0.1, 0.2, 0.3], dtype=float) +K0_AXIAL = numpy.array([0.0, 0.0, 0.25], dtype=float) +K0_X = numpy.array([0.1, 0.0, 0.0], dtype=float) +EPSILON = numpy.ones((3, *SHAPE), dtype=float) +MU = numpy.stack([ + numpy.linspace(2.0, 2.7, numpy.prod(SHAPE)).reshape(SHAPE), + numpy.linspace(2.1, 2.8, numpy.prod(SHAPE)).reshape(SHAPE), + numpy.linspace(2.2, 2.9, numpy.prod(SHAPE)).reshape(SHAPE), +]) +H_SIZE = 2 * numpy.prod(SHAPE) +H_MN = (numpy.arange(H_SIZE) + 0.25j).astype(complex) +ZERO_H_MN = numpy.zeros_like(H_MN) +Y0 = (numpy.arange(H_SIZE, dtype=float) + 1j * numpy.linspace(0.1, 0.9, H_SIZE))[None, :] +Y0_TWO_MODE = numpy.vstack( + [ + numpy.arange(H_SIZE, dtype=float) + 1j * numpy.linspace(0.1, 0.9, H_SIZE), + numpy.linspace(2.0, 3.5, H_SIZE) - 0.5j * numpy.arange(H_SIZE, dtype=float), + ], +) + + +def build_overlap_fixture() -> tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray]: + e_in = numpy.zeros((3, *SHAPE), dtype=complex) + h_in = numpy.zeros_like(e_in) + e_out = numpy.zeros_like(e_in) + h_out = numpy.zeros_like(e_in) + + e_in[1] = 1.0 + h_in[2] = 2.0 + e_out[1] = 3.0 + h_out[2] = 4.0 + return e_in, h_in, e_out, h_out diff --git a/meanas/test/_fdfd_case.py b/meanas/test/_fdfd_case.py new file mode 100644 index 0000000..35284f6 --- /dev/null +++ b/meanas/test/_fdfd_case.py @@ -0,0 +1,49 @@ +import numpy + +from ..fdmath import vec, unvec + + +OMEGA = 1 / 1500 +SHAPE = (2, 3, 2) +DXES = [ + [numpy.array([1.0, 1.5]), numpy.array([0.75, 1.25, 1.5]), numpy.array([1.2, 0.8])], + [numpy.array([0.9, 1.4]), numpy.array([0.8, 1.1, 1.4]), numpy.array([1.0, 0.7])], +] + +EPSILON = numpy.stack([ + numpy.linspace(1.0, 2.2, numpy.prod(SHAPE)).reshape(SHAPE), + numpy.linspace(1.1, 2.3, numpy.prod(SHAPE)).reshape(SHAPE), + numpy.linspace(1.2, 2.4, numpy.prod(SHAPE)).reshape(SHAPE), +]) +MU = numpy.stack([ + numpy.linspace(2.0, 3.2, numpy.prod(SHAPE)).reshape(SHAPE), + numpy.linspace(2.1, 3.3, numpy.prod(SHAPE)).reshape(SHAPE), + numpy.linspace(2.2, 3.4, numpy.prod(SHAPE)).reshape(SHAPE), +]) + +E_FIELD = (numpy.arange(3 * numpy.prod(SHAPE)).reshape((3, *SHAPE)) + 0.5j).astype(complex) +H_FIELD = (numpy.arange(3 * numpy.prod(SHAPE)).reshape((3, *SHAPE)) * 0.25 - 0.75j).astype(complex) + +PEC = numpy.zeros((3, *SHAPE), dtype=float) +PEC[1, 0, 1, 0] = 1.0 +PMC = numpy.zeros((3, *SHAPE), dtype=float) +PMC[2, 1, 2, 1] = 1.0 + +TF_REGION = numpy.zeros((3, *SHAPE), dtype=float) +TF_REGION[:, 0, 1, 0] = 1.0 + +BOUNDARY_SHAPE = (3, 4, 3) +BOUNDARY_DXES = [ + [numpy.array([1.0, 1.5, 0.8]), numpy.array([0.75, 1.25, 1.5, 0.9]), numpy.array([1.2, 0.8, 1.1])], + [numpy.array([0.9, 1.4, 1.0]), numpy.array([0.8, 1.1, 1.4, 1.0]), numpy.array([1.0, 0.7, 1.3])], +] +BOUNDARY_EPSILON = numpy.stack([ + numpy.linspace(1.0, 2.2, numpy.prod(BOUNDARY_SHAPE)).reshape(BOUNDARY_SHAPE), + numpy.linspace(1.1, 2.3, numpy.prod(BOUNDARY_SHAPE)).reshape(BOUNDARY_SHAPE), + numpy.linspace(1.2, 2.4, numpy.prod(BOUNDARY_SHAPE)).reshape(BOUNDARY_SHAPE), +]) +BOUNDARY_FIELD = (numpy.arange(3 * numpy.prod(BOUNDARY_SHAPE)).reshape((3, *BOUNDARY_SHAPE)) + 0.5j).astype(complex) + + +def apply_fdfd_matrix(op, field: numpy.ndarray, shape: tuple[int, ...] = SHAPE) -> numpy.ndarray: + return unvec(op @ vec(field), shape) diff --git a/meanas/test/_solver_cases.py b/meanas/test/_solver_cases.py new file mode 100644 index 0000000..364e1f0 --- /dev/null +++ b/meanas/test/_solver_cases.py @@ -0,0 +1,56 @@ +import dataclasses +import numpy +from scipy import sparse +import scipy.sparse.linalg as spalg + +from ._test_builders import unit_dxes + + +@dataclasses.dataclass(frozen=True) +class DiagonalEigenCase: + operator: sparse.csr_matrix + linear_operator: spalg.LinearOperator + guess_default: numpy.ndarray + guess_sparse: numpy.ndarray + + +@dataclasses.dataclass(frozen=True) +class SolverPlumbingCase: + omega: float + a0: sparse.csr_matrix + pl: sparse.csr_matrix + pr: sparse.csr_matrix + j: numpy.ndarray + guess: numpy.ndarray + solver_result: numpy.ndarray + dxes: tuple[tuple[numpy.ndarray, ...], tuple[numpy.ndarray, ...]] + epsilon: numpy.ndarray + + +def diagonal_eigen_case() -> DiagonalEigenCase: + operator = sparse.diags([5.0, 3.0, 1.0, -2.0]).tocsr() + linear_operator = spalg.LinearOperator( + shape=operator.shape, + dtype=complex, + matvec=lambda vv: operator @ vv, + ) + return DiagonalEigenCase( + operator=operator, + linear_operator=linear_operator, + guess_default=numpy.array([0.0, 1.0, 1e-6, 0.0], dtype=complex), + guess_sparse=numpy.array([1.0, 0.1, 0.0, 0.0], dtype=complex), + ) + + +def solver_plumbing_case() -> SolverPlumbingCase: + return SolverPlumbingCase( + omega=2.0, + a0=sparse.csr_matrix(numpy.array([[1.0 + 2.0j, 2.0], [3.0 - 1.0j, 4.0]])), + pl=sparse.csr_matrix(numpy.array([[2.0, 0.0], [0.0, 3.0j]])), + pr=sparse.csr_matrix(numpy.array([[0.5, 0.0], [0.0, -2.0j]])), + j=numpy.array([1.0 + 0.5j, -2.0]), + guess=numpy.array([0.25 - 0.75j, 1.5 + 0.5j]), + solver_result=numpy.array([3.0 - 1.0j, -4.0 + 2.0j]), + dxes=unit_dxes((1, 1, 1)), + epsilon=numpy.ones(2), + ) diff --git a/meanas/test/_test_builders.py b/meanas/test/_test_builders.py new file mode 100644 index 0000000..d8b2088 --- /dev/null +++ b/meanas/test/_test_builders.py @@ -0,0 +1,22 @@ +import numpy + + +def real_ramp(shape: tuple[int, ...], *, scale: float = 1.0, offset: float = 0.0) -> numpy.ndarray: + return numpy.arange(numpy.prod(shape), dtype=float).reshape(shape, order='C') * scale + offset + + +def complex_ramp( + shape: tuple[int, ...], + *, + scale: float = 1.0, + offset: float = 0.0, + imag_scale: float = 0.0, + imag_offset: float = 0.0, + ) -> numpy.ndarray: + real = real_ramp(shape, scale=scale, offset=offset) + imag = real_ramp(shape, scale=imag_scale, offset=imag_offset) + return (real + 1j * imag).astype(complex) + + +def unit_dxes(shape: tuple[int, ...]) -> tuple[tuple[numpy.ndarray, ...], tuple[numpy.ndarray, ...]]: + return tuple(tuple(numpy.ones(length) for length in shape) for _ in range(2)) # type: ignore[return-value] diff --git a/meanas/test/conftest.py b/meanas/test/conftest.py index 5dcdbff..5b577c6 100644 --- a/meanas/test/conftest.py +++ b/meanas/test/conftest.py @@ -3,12 +3,13 @@ Test fixtures """ -from typing import Iterable, Any +# ruff: noqa: ARG001 +from typing import Any import numpy from numpy.typing import NDArray import pytest # type: ignore -from .utils import PRNG +from .utils import make_prng FixtureRequest = Any @@ -20,18 +21,18 @@ FixtureRequest = Any (5, 5, 5), # (7, 7, 7), ]) -def shape(request: FixtureRequest) -> Iterable[tuple[int, ...]]: - yield (3, *request.param) +def shape(request: FixtureRequest) -> tuple[int, ...]: + return (3, *request.param) @pytest.fixture(scope='module', params=[1.0, 1.5]) -def epsilon_bg(request: FixtureRequest) -> Iterable[float]: - yield request.param +def epsilon_bg(request: FixtureRequest) -> float: + return request.param @pytest.fixture(scope='module', params=[1.0, 2.5]) -def epsilon_fg(request: FixtureRequest) -> Iterable[float]: - yield request.param +def epsilon_fg(request: FixtureRequest) -> float: + return request.param @pytest.fixture(scope='module', params=['center', '000', 'random']) @@ -40,7 +41,8 @@ def epsilon( shape: tuple[int, ...], epsilon_bg: float, epsilon_fg: float, - ) -> Iterable[NDArray[numpy.float64]]: + ) -> NDArray[numpy.float64]: + prng = make_prng() is3d = (numpy.array(shape) == 1).sum() == 0 if is3d: if request.param == '000': @@ -56,21 +58,23 @@ def epsilon( elif request.param == '000': epsilon[:, 0, 0, 0] = epsilon_fg elif request.param == 'random': - epsilon[:] = PRNG.uniform(low=min(epsilon_bg, epsilon_fg), - high=max(epsilon_bg, epsilon_fg), - size=shape) + epsilon[:] = prng.uniform( + low=min(epsilon_bg, epsilon_fg), + high=max(epsilon_bg, epsilon_fg), + size=shape, + ) - yield epsilon + return epsilon @pytest.fixture(scope='module', params=[1.0]) # 1.5 -def j_mag(request: FixtureRequest) -> Iterable[float]: - yield request.param +def j_mag(request: FixtureRequest) -> float: + return request.param @pytest.fixture(scope='module', params=[1.0, 1.5]) -def dx(request: FixtureRequest) -> Iterable[float]: - yield request.param +def dx(request: FixtureRequest) -> float: + return request.param @pytest.fixture(scope='module', params=['uniform', 'centerbig']) @@ -78,7 +82,8 @@ def dxes( request: FixtureRequest, shape: tuple[int, ...], dx: float, - ) -> Iterable[list[list[NDArray[numpy.float64]]]]: + ) -> list[list[NDArray[numpy.float64]]]: + prng = make_prng() if request.param == 'uniform': dxes = [[numpy.full(s, dx) for s in shape[1:]] for _ in range(2)] elif request.param == 'centerbig': @@ -87,8 +92,7 @@ def dxes( for ax in (0, 1, 2): dxes[eh][ax][dxes[eh][ax].size // 2] *= 1.1 elif request.param == 'random': - dxe = [PRNG.uniform(low=1.0 * dx, high=1.1 * dx, size=s) for s in shape[1:]] + dxe = [prng.uniform(low=1.0 * dx, high=1.1 * dx, size=s) for s in shape[1:]] dxh = [(d + numpy.roll(d, -1)) / 2 for d in dxe] dxes = [dxe, dxh] - yield dxes - + return dxes diff --git a/meanas/test/test_bloch_foundations.py b/meanas/test/test_bloch_foundations.py new file mode 100644 index 0000000..02a547c --- /dev/null +++ b/meanas/test/test_bloch_foundations.py @@ -0,0 +1,73 @@ +import numpy +from numpy.linalg import norm + +from ..fdfd import bloch +from ._bloch_case import EPSILON, G_MATRIX, H_MN, K0_AXIAL, K0_GENERAL, MU, SHAPE, ZERO_H_MN +from .utils import assert_close + +def test_generate_kmn_general_case_returns_orthonormal_basis() -> None: + k_mag, m_vecs, n_vecs = bloch.generate_kmn(K0_GENERAL, G_MATRIX, SHAPE) + + assert k_mag.shape == SHAPE + (1,) + assert m_vecs.shape == SHAPE + (3,) + assert n_vecs.shape == SHAPE + (3,) + assert numpy.isfinite(k_mag).all() + assert numpy.isfinite(m_vecs).all() + assert numpy.isfinite(n_vecs).all() + + assert_close(norm(m_vecs.reshape(-1, 3), axis=1), 1.0) + assert_close(norm(n_vecs.reshape(-1, 3), axis=1), 1.0) + assert_close(numpy.sum(m_vecs * n_vecs, axis=3), 0.0, atol=1e-12) + + +def test_generate_kmn_z_aligned_uses_default_transverse_basis() -> None: + k_mag, m_vecs, n_vecs = bloch.generate_kmn(K0_AXIAL, G_MATRIX, (1, 1, 1)) + + assert numpy.isfinite(k_mag).all() + assert_close(m_vecs[0, 0, 0], [0.0, 1.0, 0.0]) + assert_close(numpy.sum(m_vecs * n_vecs, axis=3), 0.0, atol=1e-12) + assert_close(norm(n_vecs.reshape(-1, 3), axis=1), 1.0) + + +def test_maxwell_operator_returns_finite_column_vector_without_mu() -> None: + operator = bloch.maxwell_operator(K0_GENERAL, G_MATRIX, EPSILON) + + result = operator(H_MN.copy()) + zero_result = operator(ZERO_H_MN.copy()) + + assert result.shape == (2 * numpy.prod(SHAPE), 1) + assert numpy.isfinite(result).all() + assert_close(zero_result, 0.0) + + +def test_maxwell_operator_returns_finite_column_vector_with_mu() -> None: + operator = bloch.maxwell_operator(K0_GENERAL, G_MATRIX, EPSILON, MU) + + result = operator(H_MN.copy()) + zero_result = operator(ZERO_H_MN.copy()) + + assert result.shape == (2 * numpy.prod(SHAPE), 1) + assert numpy.isfinite(result).all() + assert_close(zero_result, 0.0) + + +def test_inverse_maxwell_operator_returns_finite_column_vector_for_both_mu_branches() -> None: + for mu in (None, MU): + operator = bloch.inverse_maxwell_operator_approx(K0_GENERAL, G_MATRIX, EPSILON, mu) + + result = operator(H_MN.copy()) + zero_result = operator(ZERO_H_MN.copy()) + + assert result.shape == (2 * numpy.prod(SHAPE), 1) + assert numpy.isfinite(result).all() + assert_close(zero_result, 0.0) + + +def test_bloch_field_converters_return_finite_fields() -> None: + e_field = bloch.hmn_2_exyz(K0_GENERAL, G_MATRIX, EPSILON)(H_MN.copy()) + h_field = bloch.hmn_2_hxyz(K0_GENERAL, G_MATRIX, EPSILON)(H_MN.copy()) + + assert e_field.shape == (3, *SHAPE) + assert h_field.shape == (3, *SHAPE) + assert numpy.isfinite(e_field).all() + assert numpy.isfinite(h_field).all() diff --git a/meanas/test/test_bloch_interactions.py b/meanas/test/test_bloch_interactions.py new file mode 100644 index 0000000..0628a55 --- /dev/null +++ b/meanas/test/test_bloch_interactions.py @@ -0,0 +1,315 @@ +import numpy +import pytest +from numpy.testing import assert_allclose +from types import SimpleNamespace + +from ..fdfd import bloch +from ._bloch_case import EPSILON, G_MATRIX, H_SIZE, K0_X, Y0, Y0_TWO_MODE, build_overlap_fixture +from .utils import assert_close + + +def test_rtrace_atb_matches_real_frobenius_inner_product() -> None: + a_mat = numpy.array([[1.0 + 2.0j, 3.0 - 1.0j], [2.0j, 4.0]], dtype=complex) + b_mat = numpy.array([[5.0 - 1.0j, 1.0 + 1.0j], [2.0, 3.0j]], dtype=complex) + expected = numpy.real(numpy.sum(a_mat.conj() * b_mat)) + + assert bloch._rtrace_AtB(a_mat, b_mat) == expected + + +def test_symmetrize_returns_hermitian_average() -> None: + matrix = numpy.array([[1.0 + 2.0j, 3.0 - 1.0j], [2.0j, 4.0]], dtype=complex) + result = bloch._symmetrize(matrix) + + assert_close(result, 0.5 * (matrix + matrix.conj().T)) + assert_close(result, result.conj().T) + + +def test_inner_product_is_nonmutating_and_obeys_sign_symmetry() -> None: + e_in, h_in, e_out, h_out = build_overlap_fixture() + originals = (e_in.copy(), h_in.copy(), e_out.copy(), h_out.copy()) + + pp = bloch.inner_product(e_out, h_out, e_in, h_in) + pn = bloch.inner_product(e_out, h_out, e_in, -h_in) + np_term = bloch.inner_product(e_out, -h_out, e_in, h_in) + nn = bloch.inner_product(e_out, -h_out, e_in, -h_in) + + assert_close(pp, 0.8164965809277263 + 0.0j) + assert_close(pp, -nn, atol=1e-12, rtol=1e-12) + assert_close(pn, -np_term, atol=1e-12, rtol=1e-12) + assert numpy.array_equal(e_in, originals[0]) + assert numpy.array_equal(h_in, originals[1]) + assert numpy.array_equal(e_out, originals[2]) + assert numpy.array_equal(h_out, originals[3]) + + +def test_trq_returns_expected_transmission_and_reflection() -> None: + e_in, h_in, e_out, h_out = build_overlap_fixture() + + transmission, reflection = bloch.trq(e_in, h_in, e_out, h_out) + + assert_close(transmission, 0.9797958971132713 + 0.0j, atol=1e-12, rtol=1e-12) + assert_close(reflection, 0.2 + 0.0j, atol=1e-12, rtol=1e-12) + + +def test_eigsolve_returns_finite_modes_with_small_residual() -> None: + callback_count = 0 + + def callback() -> None: + nonlocal callback_count + callback_count += 1 + + eigvals, eigvecs = bloch.eigsolve( + 1, + K0_X, + G_MATRIX, + EPSILON, + tolerance=1e-6, + max_iters=50, + y0=Y0, + callback=callback, + ) + + operator = bloch.maxwell_operator(K0_X, G_MATRIX, EPSILON) + eigvec = eigvecs[0] / numpy.linalg.norm(eigvecs[0]) + residual = numpy.linalg.norm(operator(eigvec).reshape(-1) - eigvals[0] * eigvec) / numpy.linalg.norm(eigvec) + + assert eigvals.shape == (1,) + assert eigvecs.shape == (1, H_SIZE) + assert numpy.isfinite(eigvals).all() + assert numpy.isfinite(eigvecs).all() + assert residual < 1e-5 + assert callback_count > 0 + + +def test_eigsolve_without_initial_guess_returns_finite_modes() -> None: + eigvals, eigvecs = bloch.eigsolve( + 1, + K0_X, + G_MATRIX, + EPSILON, + tolerance=1e-6, + max_iters=20, + y0=None, + ) + + operator = bloch.maxwell_operator(K0_X, G_MATRIX, EPSILON) + eigvec = eigvecs[0] / numpy.linalg.norm(eigvecs[0]) + residual = numpy.linalg.norm(operator(eigvec).reshape(-1) - eigvals[0] * eigvec) / numpy.linalg.norm(eigvec) + + assert eigvals.shape == (1,) + assert eigvecs.shape == (1, H_SIZE) + assert numpy.isfinite(eigvals).all() + assert numpy.isfinite(eigvecs).all() + assert residual < 1e-5 + + +def test_eigsolve_recovers_from_singular_initial_subspace(monkeypatch: pytest.MonkeyPatch) -> None: + class FakeRng: + def __init__(self) -> None: + self.calls = 0 + + def random(self, shape: tuple[int, ...]) -> numpy.ndarray: + self.calls += 1 + return numpy.arange(numpy.prod(shape), dtype=float).reshape(shape) + self.calls + + fake_rng = FakeRng() + singular_y0 = numpy.vstack([Y0_TWO_MODE[0], Y0_TWO_MODE[0]]) + monkeypatch.setattr(bloch.numpy.random, 'default_rng', lambda: fake_rng) + + eigvals, eigvecs = bloch.eigsolve( + 2, + K0_X, + G_MATRIX, + EPSILON, + tolerance=1e-6, + max_iters=20, + y0=singular_y0, + ) + + assert fake_rng.calls == 2 + assert eigvals.shape == (2,) + assert eigvecs.shape == (2, H_SIZE) + assert numpy.isfinite(eigvals).all() + assert numpy.isfinite(eigvecs).all() + + +def test_eigsolve_reconditions_large_trace_initial_subspace(monkeypatch: pytest.MonkeyPatch) -> None: + original_inv = bloch.numpy.linalg.inv + original_sqrtm = bloch.scipy.linalg.sqrtm + sqrtm_calls = 0 + inv_calls = 0 + + def inv_with_large_first_trace(matrix: numpy.ndarray) -> numpy.ndarray: + nonlocal inv_calls + inv_calls += 1 + if inv_calls == 1: + return numpy.eye(matrix.shape[0], dtype=complex) * 1e9 + return original_inv(matrix) + + def sqrtm_wrapper(matrix: numpy.ndarray) -> numpy.ndarray: + nonlocal sqrtm_calls + sqrtm_calls += 1 + return original_sqrtm(matrix) + + monkeypatch.setattr(bloch.numpy.linalg, 'inv', inv_with_large_first_trace) + monkeypatch.setattr(bloch.scipy.linalg, 'sqrtm', sqrtm_wrapper) + + eigvals, eigvecs = bloch.eigsolve( + 2, + K0_X, + G_MATRIX, + EPSILON, + tolerance=1e-6, + max_iters=20, + y0=Y0_TWO_MODE, + ) + + assert sqrtm_calls >= 2 + assert eigvals.shape == (2,) + assert eigvecs.shape == (2, H_SIZE) + assert numpy.isfinite(eigvals).all() + assert numpy.isfinite(eigvecs).all() + + +def test_eigsolve_qi_memoization_reuses_cached_theta(monkeypatch: pytest.MonkeyPatch) -> None: + def fake_minimize_scalar(func, method: str, bounds: tuple[float, float], options: dict[str, float]) -> SimpleNamespace: + theta = 0.3 + first = func(theta) + second = func(theta) + assert_allclose(second, first) + return SimpleNamespace(fun=second, x=theta) + + monkeypatch.setattr(bloch.scipy.optimize, 'minimize_scalar', fake_minimize_scalar) + + eigvals, eigvecs = bloch.eigsolve( + 1, + K0_X, + G_MATRIX, + EPSILON, + tolerance=1e-6, + max_iters=1, + y0=Y0, + ) + + assert eigvals.shape == (1,) + assert eigvecs.shape == (1, H_SIZE) + assert numpy.isfinite(eigvals).all() + assert numpy.isfinite(eigvecs).all() + + +@pytest.mark.parametrize('theta', [numpy.pi / 2 - 1e-8, 1e-8]) +def test_eigsolve_qi_taylor_expansions_return_finite_modes(monkeypatch: pytest.MonkeyPatch, theta: float) -> None: + original_inv = bloch.numpy.linalg.inv + inv_calls = 0 + + def inv_raise_once_for_q(matrix: numpy.ndarray) -> numpy.ndarray: + nonlocal inv_calls + inv_calls += 1 + if inv_calls == 3: + raise numpy.linalg.LinAlgError('forced singular Q') + return original_inv(matrix) + + def fake_minimize_scalar(func, method: str, bounds: tuple[float, float], options: dict[str, float]) -> SimpleNamespace: + value = func(theta) + return SimpleNamespace(fun=value, x=theta) + + monkeypatch.setattr(bloch.numpy.linalg, 'inv', inv_raise_once_for_q) + monkeypatch.setattr(bloch.scipy.optimize, 'minimize_scalar', fake_minimize_scalar) + + eigvals, eigvecs = bloch.eigsolve( + 1, + K0_X, + G_MATRIX, + EPSILON, + tolerance=1e-6, + max_iters=1, + y0=Y0, + ) + + assert eigvals.shape == (1,) + assert eigvecs.shape == (1, H_SIZE) + assert numpy.isfinite(eigvals).all() + assert numpy.isfinite(eigvecs).all() + + +def test_eigsolve_qi_inexplicable_singularity_raises(monkeypatch: pytest.MonkeyPatch) -> None: + original_inv = bloch.numpy.linalg.inv + inv_calls = 0 + + def inv_raise_once_for_q(matrix: numpy.ndarray) -> numpy.ndarray: + nonlocal inv_calls + inv_calls += 1 + if inv_calls == 3: + raise numpy.linalg.LinAlgError('forced singular Q') + return original_inv(matrix) + + def fake_minimize_scalar(func, method: str, bounds: tuple[float, float], options: dict[str, float]) -> SimpleNamespace: + func(numpy.pi / 4) + raise AssertionError('unreachable after trace_func exception') + + monkeypatch.setattr(bloch.numpy.linalg, 'inv', inv_raise_once_for_q) + monkeypatch.setattr(bloch.scipy.optimize, 'minimize_scalar', fake_minimize_scalar) + + with pytest.raises(Exception, match='Inexplicable singularity in trace_func'): + bloch.eigsolve( + 1, + K0_X, + G_MATRIX, + EPSILON, + tolerance=1e-6, + max_iters=1, + y0=Y0, + ) + + +def test_find_k_returns_vector_frequency_and_callbacks() -> None: + target_eigvals, _target_eigvecs = bloch.eigsolve( + 1, + K0_X, + G_MATRIX, + EPSILON, + tolerance=1e-6, + max_iters=50, + y0=Y0, + ) + target_frequency = float(numpy.sqrt(abs(numpy.real(target_eigvals[0])))) + + solve_calls = 0 + iter_calls = 0 + + def solve_callback(k_mag: float, eigvals: numpy.ndarray, eigvecs: numpy.ndarray, frequency: float) -> None: + nonlocal solve_calls + solve_calls += 1 + assert eigvals.shape == (1,) + assert eigvecs.shape == (1, H_SIZE) + assert isinstance(k_mag, float) + assert isinstance(frequency, float) + + def iter_callback() -> None: + nonlocal iter_calls + iter_calls += 1 + + found_k, found_frequency, eigvals, eigvecs = bloch.find_k( + target_frequency, + 1e-4, + [1, 0, 0], + G_MATRIX, + EPSILON, + band=0, + k_bounds=(0.05, 0.15), + v0=Y0, + solve_callback=solve_callback, + iter_callback=iter_callback, + ) + + assert found_k.shape == (3,) + assert numpy.isfinite(found_k).all() + assert_close(numpy.cross(found_k, [1.0, 0.0, 0.0]), 0.0, atol=1e-12, rtol=1e-12) + assert_close(found_k, K0_X, atol=1e-4, rtol=1e-4) + assert abs(found_frequency - target_frequency) <= 1e-4 + assert eigvals.shape == (1,) + assert eigvecs.shape == (1, H_SIZE) + assert numpy.isfinite(eigvals).all() + assert numpy.isfinite(eigvecs).all() + assert solve_calls > 0 + assert iter_calls > 0 diff --git a/meanas/test/test_eigensolvers_numerics.py b/meanas/test/test_eigensolvers_numerics.py new file mode 100644 index 0000000..cf037a6 --- /dev/null +++ b/meanas/test/test_eigensolvers_numerics.py @@ -0,0 +1,101 @@ +import numpy +from numpy.linalg import norm +import pytest + +from ._solver_cases import diagonal_eigen_case +from .utils import assert_close +from ..eigensolvers import power_iteration, rayleigh_quotient_iteration, signed_eigensolve + + +def test_rayleigh_quotient_iteration_with_linear_operator() -> None: + case = diagonal_eigen_case() + + def dense_solver( + shifted_operator, + rhs: numpy.ndarray, + ) -> numpy.ndarray: + basis = numpy.eye(case.operator.shape[0], dtype=complex) + columns = [shifted_operator.matvec(basis[:, ii]) for ii in range(case.operator.shape[0])] + dense_matrix = numpy.column_stack(columns) + return numpy.linalg.lstsq(dense_matrix, rhs, rcond=None)[0] + + eigval, eigvec = rayleigh_quotient_iteration( + case.linear_operator, + case.guess_default, + iterations=8, + solver=dense_solver, + ) + + residual = norm(case.operator @ eigvec - eigval * eigvec) + assert abs(eigval - 3.0) < 1e-12 + assert residual < 1e-12 + + +def test_signed_eigensolve_negative_returns_largest_negative_mode() -> None: + case = diagonal_eigen_case() + + eigvals, eigvecs = signed_eigensolve(case.operator, how_many=1, negative=True) + + assert eigvals.shape == (1,) + assert eigvecs.shape == (4, 1) + assert abs(eigvals[0] + 2.0) < 1e-12 + assert abs(eigvecs[3, 0]) > 0.99 + + +def test_rayleigh_quotient_iteration_uses_default_linear_operator_solver() -> None: + case = diagonal_eigen_case() + + eigval, eigvec = rayleigh_quotient_iteration( + case.linear_operator, + case.guess_default, + iterations=8, + ) + + residual = norm(case.operator @ eigvec - eigval * eigvec) + assert abs(eigval - 3.0) < 1e-12 + assert residual < 1e-12 + + +def test_signed_eigensolve_linear_operator_fallback_returns_dominant_positive_mode() -> None: + case = diagonal_eigen_case() + + eigvals, eigvecs = signed_eigensolve(case.linear_operator, how_many=1) + + assert eigvals.shape == (1,) + assert eigvecs.shape == (4, 1) + assert_close(eigvals[0], 5.0, atol=1e-12, rtol=1e-12) + assert abs(eigvecs[0, 0]) > 0.99 + + +def test_power_iteration_finds_dominant_mode() -> None: + case = diagonal_eigen_case() + eigval, eigvec = power_iteration(case.operator, guess_vector=numpy.ones(4, dtype=complex), iterations=20) + + assert eigval == pytest.approx(5.0, rel=1e-6) + assert abs(eigvec[0]) > abs(eigvec[1]) + + +def test_rayleigh_quotient_iteration_refines_known_sparse_mode() -> None: + case = diagonal_eigen_case() + + def solver(matrix, rhs: numpy.ndarray) -> numpy.ndarray: + return numpy.linalg.lstsq(matrix.toarray(), rhs, rcond=None)[0] + + eigval, eigvec = rayleigh_quotient_iteration( + case.operator, + case.guess_sparse, + iterations=8, + solver=solver, + ) + + residual = numpy.linalg.norm(case.operator @ eigvec - eigval * eigvec) + assert eigval == pytest.approx(3.0, rel=1e-6) + assert residual < 1e-8 + + +def test_signed_eigensolve_returns_largest_positive_modes() -> None: + case = diagonal_eigen_case() + eigvals, eigvecs = signed_eigensolve(case.operator, how_many=2) + + assert_close(eigvals, [3.0, 5.0], atol=1e-6) + assert eigvecs.shape == (4, 2) diff --git a/meanas/test/test_eme_numerics.py b/meanas/test/test_eme_numerics.py new file mode 100644 index 0000000..3237c1b --- /dev/null +++ b/meanas/test/test_eme_numerics.py @@ -0,0 +1,491 @@ +from typing import cast + +import numpy +import pytest +from scipy import sparse + +from ..fdmath import vec +from ..fdfd import eme, waveguide_2d, waveguide_cyl +from ._test_builders import complex_ramp, unit_dxes +from .utils import assert_close + + +SHAPE = (3, 2, 2) +DXES = unit_dxes((2, 2)) +WAVENUMBERS_L = numpy.array([1.0, 0.8]) +WAVENUMBERS_R = numpy.array([0.9, 0.7]) +OMEGA = 1 / 1500 +REAL_DXES = unit_dxes((5, 5)) + + +def _mode(scale: float) -> tuple[numpy.ndarray, numpy.ndarray]: + e_field = complex_ramp(SHAPE, offset=1.0 + scale) + h_field = complex_ramp(SHAPE, scale=0.2, offset=2.0, imag_offset=0.05 * scale) + return vec(e_field), vec(h_field) + + +def _mode_sets() -> tuple[list[tuple[numpy.ndarray, numpy.ndarray]], list[tuple[numpy.ndarray, numpy.ndarray]]]: + left_modes = [_mode(0.0), _mode(0.7)] + right_modes = [_mode(1.4), _mode(2.1)] + return left_modes, right_modes + + +def _gain_only_tr(*args, **kwargs) -> tuple[numpy.ndarray, numpy.ndarray]: + return numpy.array([[2.0, 0.0], [0.0, 0.5]]), numpy.zeros((2, 2)) + + +def _gain_and_reflection_tr(*args, **kwargs) -> tuple[numpy.ndarray, numpy.ndarray]: + return numpy.array([[2.0, 0.0], [0.0, 0.5]]), numpy.array([[0.0, 1.0], [2.0, 0.0]]) + + +def _nonsymmetric_tr(left_marker: object): + def fake_get_tr(_eh_left, wavenumbers_left, _eh_right, _wavenumbers_right, **kwargs): + if wavenumbers_left is left_marker: + return ( + numpy.array([[1.0, 2.0], [0.5, 1.0]]), + numpy.array([[0.0, 1.0], [2.0, 0.0]]), + ) + return ( + numpy.array([[1.0, -1.0], [0.0, 1.0]]), + numpy.array([[0.0, 0.5], [1.5, 0.0]]), + ) + + return fake_get_tr + + +def _dummy_modes() -> tuple[list[tuple[numpy.ndarray, numpy.ndarray]], numpy.ndarray]: + return [_mode(0.0), _mode(0.7)], numpy.array([1.0, 0.5]) + + +def test_get_tr_returns_finite_bounded_transfer_matrices() -> None: + left_modes, right_modes = _mode_sets() + + transmission, reflection = eme.get_tr( + left_modes, + WAVENUMBERS_L, + right_modes, + WAVENUMBERS_R, + dxes=DXES, + ) + + singular_values = numpy.linalg.svd(transmission, compute_uv=False) + + assert transmission.shape == (2, 2) + assert reflection.shape == (2, 2) + assert numpy.isfinite(transmission).all() + assert numpy.isfinite(reflection).all() + assert (singular_values <= 1.0 + 1e-12).all() + + +def test_get_abcd_matches_explicit_block_formula() -> None: + left_modes, right_modes = _mode_sets() + t12, r12 = eme.get_tr(left_modes, WAVENUMBERS_L, right_modes, WAVENUMBERS_R, dxes=DXES) + t21, r21 = eme.get_tr(right_modes, WAVENUMBERS_R, left_modes, WAVENUMBERS_L, dxes=DXES) + t21_inv = numpy.linalg.pinv(t21) + + expected = numpy.block([ + [t12 - r21 @ t21_inv @ r12, r21 @ t21_inv], + [-t21_inv @ r12, t21_inv], + ]) + abcd = eme.get_abcd(left_modes, WAVENUMBERS_L, right_modes, WAVENUMBERS_R, dxes=DXES) + + assert sparse.issparse(abcd) + assert abcd.shape == (4, 4) + assert_close(abcd.toarray(), expected) + + +def test_get_s_plain_matches_block_assembly_from_get_tr() -> None: + left_modes, right_modes = _mode_sets() + t12, r12 = eme.get_tr(left_modes, WAVENUMBERS_L, right_modes, WAVENUMBERS_R, dxes=DXES) + t21, r21 = eme.get_tr(right_modes, WAVENUMBERS_R, left_modes, WAVENUMBERS_L, dxes=DXES) + expected = numpy.block([[r12, t12], [t21, r21]]) + + ss = eme.get_s(left_modes, WAVENUMBERS_L, right_modes, WAVENUMBERS_R, dxes=DXES) + + assert ss.shape == (4, 4) + assert numpy.isfinite(ss).all() + assert_close(ss, expected) + + +def test_get_s_force_nogain_caps_singular_values(monkeypatch) -> None: + monkeypatch.setattr(eme, 'get_tr', _gain_only_tr) + modes, wavenumbers = _dummy_modes() + + plain_s = eme.get_s(modes, wavenumbers, modes, wavenumbers) + clipped_s = eme.get_s(modes, wavenumbers, modes, wavenumbers, force_nogain=True) + + plain_singular_values = numpy.linalg.svd(plain_s, compute_uv=False) + clipped_singular_values = numpy.linalg.svd(clipped_s, compute_uv=False) + + assert plain_singular_values.max() > 1.0 + assert (clipped_singular_values <= 1.0 + 1e-12).all() + assert numpy.isfinite(clipped_s).all() + + +def test_get_s_force_reciprocal_symmetrizes_output(monkeypatch) -> None: + left = numpy.array([1.0, 0.5]) + right = numpy.array([0.9, 0.4]) + modes, _wavenumbers = _dummy_modes() + + monkeypatch.setattr(eme, 'get_tr', _nonsymmetric_tr(left)) + ss = eme.get_s(modes, left, modes, right, force_reciprocal=True) + + assert_close(ss, ss.T) + + +def test_get_s_force_nogain_and_reciprocal_returns_finite_output(monkeypatch) -> None: + monkeypatch.setattr(eme, 'get_tr', _gain_and_reflection_tr) + modes, wavenumbers = _dummy_modes() + ss = eme.get_s(modes, wavenumbers, modes, wavenumbers, force_nogain=True, force_reciprocal=True) + + assert ss.shape == (4, 4) + assert numpy.isfinite(ss).all() + assert_close(ss, ss.T) + assert (numpy.linalg.svd(ss, compute_uv=False) <= 1.0 + 1e-12).all() + + +def test_get_tr_rejects_length_mismatches() -> None: + left_modes, right_modes = _mode_sets() + + with pytest.raises(ValueError, match='same length'): + eme.get_tr(left_modes[:1], WAVENUMBERS_L, right_modes, WAVENUMBERS_R, dxes=DXES) + + +def test_get_tr_rejects_malformed_mode_tuples() -> None: + bad_modes = cast(list[tuple[numpy.ndarray, numpy.ndarray]], [(numpy.ones(4, dtype=complex),)]) + + with pytest.raises(ValueError, match='2-tuple'): + eme.get_tr(bad_modes, [1.0], bad_modes, [1.0], dxes=DXES) + + +def test_get_tr_rejects_incompatible_field_shapes() -> None: + left_modes = [(numpy.ones(4, dtype=complex), numpy.ones(4, dtype=complex))] + right_modes = [(numpy.ones(6, dtype=complex), numpy.ones(6, dtype=complex))] + + with pytest.raises(ValueError, match='same E/H shapes'): + eme.get_tr(left_modes, [1.0], right_modes, [1.0], dxes=DXES) + + +def _build_real_epsilon() -> numpy.ndarray: + epsilon = numpy.ones((3, 5, 5), dtype=float) + epsilon[:, 2, 1] = 2.0 + return vec(epsilon) + + +def _build_straight_mode() -> tuple[tuple[numpy.ndarray, numpy.ndarray], complex, numpy.ndarray]: + epsilon = _build_real_epsilon() + e_xy, wavenumber = waveguide_2d.solve_mode( + 0, + omega=OMEGA, + dxes=REAL_DXES, + epsilon=epsilon, + ) + e_field, h_field = waveguide_2d.normalized_fields_e( + e_xy, + wavenumber=wavenumber, + omega=OMEGA, + dxes=REAL_DXES, + epsilon=epsilon, + ) + return (e_field, h_field), wavenumber, epsilon + + +def _build_bend_mode() -> tuple[tuple[numpy.ndarray, numpy.ndarray], complex]: + epsilon = vec(numpy.ones((3, 5, 5), dtype=float)) + rmin = 10.0 + e_xy, angular_wavenumber = waveguide_cyl.solve_mode( + 0, + omega=OMEGA, + dxes=REAL_DXES, + epsilon=epsilon, + rmin=rmin, + ) + linear_wavenumber = waveguide_cyl.linear_wavenumbers( + [e_xy], + [angular_wavenumber], + epsilon=epsilon, + dxes=REAL_DXES, + rmin=rmin, + )[0] + e_field, h_field = waveguide_cyl.normalized_fields_e( + e_xy, + angular_wavenumber=angular_wavenumber, + omega=OMEGA, + dxes=REAL_DXES, + epsilon=epsilon, + rmin=rmin, + ) + return (e_field, h_field), linear_wavenumber + + +def _build_uniform_mode(index: float) -> tuple[tuple[numpy.ndarray, numpy.ndarray], complex]: + area = 25.0 + e_field = numpy.zeros((3, 5, 5), dtype=complex) + h_field = numpy.zeros((3, 5, 5), dtype=complex) + e_field[0] = numpy.sqrt(2.0 / (index * area)) + h_field[1] = numpy.sqrt(2.0 * index / area) + return (vec(e_field), vec(h_field)), complex(index * OMEGA) + + +def _interface_s(n_left: float, n_right: float) -> numpy.ndarray: + left_mode, left_beta = _build_uniform_mode(n_left) + right_mode, right_beta = _build_uniform_mode(n_right) + return eme.get_s([left_mode], [left_beta], [right_mode], [right_beta], dxes=REAL_DXES) + + +def _interface_abcd(n_left: float, n_right: float) -> numpy.ndarray: + left_mode, left_beta = _build_uniform_mode(n_left) + right_mode, right_beta = _build_uniform_mode(n_right) + return eme.get_abcd([left_mode], [left_beta], [right_mode], [right_beta], dxes=REAL_DXES).toarray() + + +def _expected_interface_s(n_left: float, n_right: float) -> numpy.ndarray: + reflection = (n_left - n_right) / (n_left + n_right) + transmission = 2 * numpy.sqrt(n_left * n_right) / (n_left + n_right) + return numpy.array( + [ + [reflection, transmission], + [transmission, -reflection], + ], + dtype=complex, + ) + + +def _propagation_abcd(beta: complex, length: float) -> numpy.ndarray: + phase = numpy.exp(-1j * beta * length) + return numpy.array( + [ + [phase, 0.0], + [0.0, phase ** -1], + ], + dtype=complex, + ) + + +def _abcd_to_s(abcd: numpy.ndarray) -> numpy.ndarray: + aa = abcd[0, 0] + bb = abcd[0, 1] + cc = abcd[1, 0] + dd = abcd[1, 1] + t21 = 1.0 / dd + r21 = bb / dd + r12 = -cc / dd + t12 = aa - bb * cc / dd + return numpy.array( + [ + [r12, t12], + [t21, r21], + ], + dtype=complex, + ) + + +def _expected_bragg_reflector_s(n_low: float, n_high: float, periods: int) -> numpy.ndarray: + ratio = n_high / n_low + reflection = (1 - ratio ** (2 * periods)) / (1 + ratio ** (2 * periods)) + transmission = ((-1) ** periods) * 2 * ratio ** periods / (1 + ratio ** (2 * periods)) + return numpy.array( + [ + [reflection, transmission], + [transmission, -reflection], + ], + dtype=complex, + ) + + +def test_get_s_is_near_identity_for_identical_solved_straight_modes() -> None: + mode, wavenumber, _epsilon = _build_straight_mode() + + ss = eme.get_s([mode], [wavenumber], [mode], [wavenumber], dxes=REAL_DXES) + + assert ss.shape == (2, 2) + assert numpy.isfinite(ss).all() + assert abs(ss[0, 0]) < 1e-6 + assert abs(ss[1, 1]) < 1e-6 + assert abs(abs(ss[0, 1]) - 1.0) < 1e-6 + assert abs(abs(ss[1, 0]) - 1.0) < 1e-6 + assert numpy.linalg.svd(ss, compute_uv=False).max() <= 1.0 + 1e-10 + + +def test_get_s_returns_finite_passive_output_for_small_straight_to_bend_fixture() -> None: + straight_mode, straight_wavenumber, _epsilon = _build_straight_mode() + bend_mode, bend_wavenumber = _build_bend_mode() + + ss = eme.get_s([straight_mode], [straight_wavenumber], [bend_mode], [bend_wavenumber], dxes=REAL_DXES) + + assert ss.shape == (2, 2) + assert numpy.isfinite(ss).all() + assert numpy.linalg.svd(ss, compute_uv=False).max() <= 1.0 + 1e-10 + + +def test_get_s_matches_analytic_fresnel_interface_for_uniform_one_mode_ports() -> None: + """ + For power-normalized one-mode ports at normal incidence, the interface matrix is + + r12 = (n_left - n_right) / (n_left + n_right) + r21 = -r12 + t12 = t21 = 2 * sqrt(n_left * n_right) / (n_left + n_right) + + so + + S = [[r12, t12], [t21, r21]]. + """ + ss = _interface_s(1.0, 2.0) + expected = _expected_interface_s(1.0, 2.0) + + assert ss.shape == (2, 2) + assert numpy.isfinite(ss).all() + assert_close(ss, expected, atol=1e-6, rtol=1e-6) + assert numpy.linalg.svd(ss, compute_uv=False).max() <= 1.0 + 1e-10 + + +def test_quarter_wave_matching_layer_is_nearly_reflectionless_at_design_frequency() -> None: + """ + A single quarter-wave matching layer with + + n1 = sqrt(n0 * n2), beta1 * L = pi / 2 + + cancels the two interface reflections at the design wavelength, so the + normal-incidence stack should satisfy `r = 0` and `|t| = 1`. + """ + n0 = 1.0 + n1 = numpy.sqrt(2.0) + n2 = 2.0 + interface_01 = _interface_abcd(n0, n1) + interface_12 = _interface_abcd(n1, n2) + _mode_1, beta_1 = _build_uniform_mode(float(n1)) + quarter_wave_length = numpy.pi / (2 * numpy.real(beta_1)) + + stack_abcd = interface_01 @ _propagation_abcd(beta_1, quarter_wave_length) @ interface_12 + ss = _abcd_to_s(stack_abcd) + + assert ss.shape == (2, 2) + assert numpy.isfinite(ss).all() + assert abs(ss[0, 0]) < 1e-12 + assert abs(ss[1, 1]) < 1e-12 + assert abs(abs(ss[0, 1]) - 1.0) < 1e-12 + assert abs(abs(ss[1, 0]) - 1.0) < 1e-12 + assert numpy.linalg.svd(ss, compute_uv=False).max() <= 1.0 + 1e-10 + + +def test_quarter_wave_ar_layer_reduces_reflection_relative_to_abrupt_interface() -> None: + """ + Compare the abrupt interface `n0 -> n2` against the quarter-wave matching-layer + stack `n0 -> sqrt(n0 n2) -> n2` at the same design wavelength. + + For the canonical `n0 = 1`, `n2 = 2` case, the abrupt interface has + + |r_abrupt| = |(n0 - n2) / (n0 + n2)| = 1 / 3, + + while the quarter-wave matching layer should cancel the interface reflections + so that `|r_ar|` is essentially zero and `|t_ar|` is correspondingly larger. + """ + n0 = 1.0 + n2 = 2.0 + abrupt = _interface_s(n0, n2) + + n1 = numpy.sqrt(n0 * n2) + interface_01 = _interface_abcd(n0, n1) + interface_12 = _interface_abcd(n1, n2) + _mode_1, beta_1 = _build_uniform_mode(float(n1)) + quarter_wave_length = numpy.pi / (2 * numpy.real(beta_1)) + ar_stack = _abcd_to_s(interface_01 @ _propagation_abcd(beta_1, quarter_wave_length) @ interface_12) + + abrupt_reflection = abs(abrupt[0, 0]) + abrupt_transmission = abs(abrupt[1, 0]) + ar_reflection = abs(ar_stack[0, 0]) + ar_transmission = abs(ar_stack[1, 0]) + + assert numpy.linalg.svd(abrupt, compute_uv=False).max() <= 1.0 + 1e-10 + assert numpy.linalg.svd(ar_stack, compute_uv=False).max() <= 1.0 + 1e-10 + assert ar_reflection < abrupt_reflection + assert ar_transmission > abrupt_transmission + assert ar_reflection < 1e-12 + assert abs(abrupt_reflection - (1.0 / 3.0)) < 1e-12 + + +def test_half_wave_uniform_slab_restores_unit_transmission_between_matched_media() -> None: + """ + For matched exterior media `n0 = n2`, a half-wave slab with + + beta1 * L = pi + + contributes only a global phase, so the stack returns to `r = 0` and + `|t| = 1` at the design wavelength. + """ + n0 = 1.0 + n1 = 2.0 + interface_01 = _interface_abcd(n0, n1) + interface_10 = _interface_abcd(n1, n0) + _mode_1, beta_1 = _build_uniform_mode(n1) + half_wave_length = numpy.pi / numpy.real(beta_1) + + stack_abcd = interface_01 @ _propagation_abcd(beta_1, half_wave_length) @ interface_10 + ss = _abcd_to_s(stack_abcd) + + assert ss.shape == (2, 2) + assert numpy.isfinite(ss).all() + assert abs(ss[0, 0]) < 1e-12 + assert abs(ss[1, 1]) < 1e-12 + assert abs(abs(ss[0, 1]) - 1.0) < 1e-12 + assert abs(abs(ss[1, 0]) - 1.0) < 1e-12 + assert numpy.linalg.svd(ss, compute_uv=False).max() <= 1.0 + 1e-10 + + +def test_strong_uniform_index_mismatch_behaves_like_near_termination() -> None: + """ + In the large-index-ratio limit, the same Fresnel formulas approach a hard-wall + reflector: + + |r| -> 1, |t| -> 0 as n_right / n_left -> infinity. + """ + ss = _interface_s(1.0, 100.0) + expected = _expected_interface_s(1.0, 100.0) + + assert ss.shape == (2, 2) + assert numpy.isfinite(ss).all() + assert_close(ss, expected, atol=1e-6, rtol=1e-6) + assert abs(ss[0, 0]) > 0.9 + assert abs(ss[1, 0]) < 0.25 + assert numpy.linalg.svd(ss, compute_uv=False).max() <= 1.0 + 1e-10 + + +def test_quarter_wave_bragg_reflector_matches_closed_form_stopband_response() -> None: + """ + For `N` quarter-wave high/low periods at the Bragg wavelength with identical + low-index incident and exit media (`n0 = ns = n_low`), + + M_pair = diag(-(n_low / n_high), -(n_high / n_low)) + M_stack = M_pair ** N + + which yields the closed-form scattering amplitudes + + r = (1 - (n_high / n_low) ** (2N)) / (1 + (n_high / n_low) ** (2N)) + t = 2 * (n_high / n_low) ** N / (1 + (n_high / n_low) ** (2N)). + + The reflector should therefore sit deep in the stopband with `|r|` near 1 and + `|t|` correspondingly small. + """ + n_low = 1.0 + n_high = 2.0 + periods = 5 + interface_lh = _interface_abcd(n_low, n_high) + interface_hl = _interface_abcd(n_high, n_low) + _mode_h, beta_h = _build_uniform_mode(n_high) + _mode_l, beta_l = _build_uniform_mode(n_low) + quarter_wave_high = numpy.pi / (2 * numpy.real(beta_h)) + quarter_wave_low = numpy.pi / (2 * numpy.real(beta_l)) + + stack_abcd = numpy.eye(2, dtype=complex) + for _ in range(periods): + stack_abcd = stack_abcd @ interface_lh @ _propagation_abcd(beta_h, quarter_wave_high) + stack_abcd = stack_abcd @ interface_hl @ _propagation_abcd(beta_l, quarter_wave_low) + ss = _abcd_to_s(stack_abcd) + expected = _expected_bragg_reflector_s(n_low, n_high, periods) + + assert ss.shape == (2, 2) + assert numpy.isfinite(ss).all() + assert_close(ss, expected, atol=1e-12, rtol=1e-12) + assert abs(ss[0, 0]) > 0.99 + assert abs(ss[1, 0]) < 0.1 + assert numpy.linalg.svd(ss, compute_uv=False).max() <= 1.0 + 1e-10 diff --git a/meanas/test/test_examples_smoke.py b/meanas/test/test_examples_smoke.py new file mode 100644 index 0000000..b21f90b --- /dev/null +++ b/meanas/test/test_examples_smoke.py @@ -0,0 +1,47 @@ +from pathlib import Path +import os +import subprocess +import sys + +import pytest + + +pytestmark = pytest.mark.complete + +REPO_ROOT = Path(__file__).resolve().parents[2] + + +def _run_example(example_name: str, tmp_path: Path) -> subprocess.CompletedProcess[str]: + env = os.environ.copy() + env['MPLBACKEND'] = 'Agg' + env['MPLCONFIGDIR'] = str(tmp_path / f'mpl-{example_name}') + return subprocess.run( + [sys.executable, str(REPO_ROOT / 'examples' / example_name)], + cwd=REPO_ROOT, + env=env, + text=True, + capture_output=True, + check=False, + timeout=60, + ) + + +def test_eme_example_smoke_runs(tmp_path: Path) -> None: + pytest.importorskip('matplotlib') + + result = _run_example('eme.py', tmp_path) + + assert result.returncode == 0, result.stdout + result.stderr + assert 'left effective indices:' in result.stdout + assert 'fundamental left-to-right transmission' in result.stdout + + +def test_eme_bend_example_smoke_runs(tmp_path: Path) -> None: + pytest.importorskip('matplotlib') + pytest.importorskip('skrf') + + result = _run_example('eme_bend.py', tmp_path) + + assert result.returncode == 0, result.stdout + result.stderr + assert 'straight effective indices:' in result.stdout + assert 'cascaded bend through power' in result.stdout diff --git a/meanas/test/test_fdfd.py b/meanas/test/test_fdfd.py index 009c65b..82587b4 100644 --- a/meanas/test/test_fdfd.py +++ b/meanas/test/test_fdfd.py @@ -1,4 +1,4 @@ -from typing import Iterable +# ruff: noqa: ARG001 import dataclasses import pytest # type: ignore import numpy @@ -6,7 +6,7 @@ from numpy.typing import NDArray #from numpy.testing import assert_allclose, assert_array_equal from .. import fdfd -from ..fdmath import vec, unvec +from ..fdmath import vec, unvec, vcfdfield, vfdfield, dx_lists_t from .utils import assert_close # , assert_fields_close from .conftest import FixtureRequest @@ -61,24 +61,24 @@ def test_poynting_planes(sim: 'FDResult') -> None: # Also see conftest.py @pytest.fixture(params=[1 / 1500]) -def omega(request: FixtureRequest) -> Iterable[float]: - yield request.param +def omega(request: FixtureRequest) -> float: + return request.param @pytest.fixture(params=[None]) -def pec(request: FixtureRequest) -> Iterable[NDArray[numpy.float64] | None]: - yield request.param +def pec(request: FixtureRequest) -> NDArray[numpy.float64] | None: + return request.param @pytest.fixture(params=[None]) -def pmc(request: FixtureRequest) -> Iterable[NDArray[numpy.float64] | None]: - yield request.param +def pmc(request: FixtureRequest) -> NDArray[numpy.float64] | None: + return request.param #@pytest.fixture(scope='module', # params=[(25, 5, 5)]) -#def shape(request): -# yield (3, *request.param) +#def shape(request: FixtureRequest): +# return (3, *request.param) @pytest.fixture(params=['diag']) # 'center' @@ -86,7 +86,7 @@ def j_distribution( request: FixtureRequest, shape: tuple[int, ...], j_mag: float, - ) -> Iterable[NDArray[numpy.float64]]: + ) -> NDArray[numpy.float64]: j = numpy.zeros(shape, dtype=complex) center_mask = numpy.zeros(shape, dtype=bool) center_mask[:, shape[1] // 2, shape[2] // 2, shape[3] // 2] = True @@ -96,22 +96,22 @@ def j_distribution( elif request.param == 'diag': j[numpy.roll(center_mask, [1, 1, 1], axis=(1, 2, 3))] = (1 + 1j) * j_mag j[numpy.roll(center_mask, [-1, -1, -1], axis=(1, 2, 3))] = (1 - 1j) * j_mag - yield j + return j @dataclasses.dataclass() class FDResult: shape: tuple[int, ...] - dxes: list[list[NDArray[numpy.float64]]] - epsilon: NDArray[numpy.float64] + dxes: dx_lists_t + epsilon: vfdfield omega: complex - j: NDArray[numpy.complex128] - e: NDArray[numpy.complex128] - pmc: NDArray[numpy.float64] | None - pec: NDArray[numpy.float64] | None + j: vcfdfield + e: vcfdfield + pmc: vfdfield | None + pec: vfdfield | None -@pytest.fixture() +@pytest.fixture def sim( request: FixtureRequest, shape: tuple[int, ...], @@ -141,11 +141,11 @@ def sim( j_vec = vec(j_distribution) eps_vec = vec(epsilon) e_vec = fdfd.solvers.generic( - J=j_vec, - omega=omega, - dxes=dxes, - epsilon=eps_vec, - matrix_solver_opts={'atol': 1e-15, 'tol': 1e-11}, + J = j_vec, + omega = omega, + dxes = dxes, + epsilon = eps_vec, + matrix_solver_opts = dict(atol=1e-15, rtol=1e-11), ) e = unvec(e_vec, shape[1:]) diff --git a/meanas/test/test_fdfd_algebra_helpers.py b/meanas/test/test_fdfd_algebra_helpers.py new file mode 100644 index 0000000..825edb3 --- /dev/null +++ b/meanas/test/test_fdfd_algebra_helpers.py @@ -0,0 +1,213 @@ +import numpy + +from ..fdmath import vec, unvec +from ..fdmath import functional as fd_functional +from ..fdfd import operators, scpml +from ._fdfd_case import ( + BOUNDARY_DXES, + BOUNDARY_EPSILON, + BOUNDARY_FIELD, + BOUNDARY_SHAPE, + DXES, + EPSILON, + E_FIELD, + MU, + H_FIELD, + OMEGA, + PEC, + PMC, + SHAPE, + apply_fdfd_matrix, +) +from .utils import assert_close, assert_fields_close + + +def _dense_e_full(mu: numpy.ndarray | None) -> numpy.ndarray: + ce = fd_functional.curl_forward(DXES[0]) + ch = fd_functional.curl_back(DXES[1]) + pe = numpy.where(PEC, 0.0, 1.0) + pm = numpy.where(PMC, 0.0, 1.0) + + masked_e = pe * E_FIELD + curl_term = ce(masked_e) + if mu is not None: + curl_term = curl_term / mu + curl_term = pm * curl_term + curl_term = ch(curl_term) + return pe * (curl_term - OMEGA**2 * EPSILON * masked_e) + + +def _dense_h_full(mu: numpy.ndarray | None) -> numpy.ndarray: + ce = fd_functional.curl_forward(DXES[0]) + ch = fd_functional.curl_back(DXES[1]) + pe = numpy.where(PEC, 0.0, 1.0) + pm = numpy.where(PMC, 0.0, 1.0) + magnetic = numpy.ones_like(EPSILON) if mu is None else mu + + masked_h = pm * H_FIELD + curl_term = ch(masked_h) + curl_term = pe * (curl_term / EPSILON) + curl_term = ce(curl_term) + return pm * (curl_term - OMEGA**2 * magnetic * masked_h) + + +def _normalized_distance(u: numpy.ndarray, size: int, thickness: int) -> numpy.ndarray: + return ((thickness - u).clip(0) + (u - (size - thickness)).clip(0)) / thickness + + +def test_h_full_matches_dense_reference_with_and_without_mu() -> None: + for mu in (None, MU): + matrix_result = apply_fdfd_matrix( + operators.h_full(OMEGA, DXES, vec(EPSILON), None if mu is None else vec(mu), vec(PEC), vec(PMC)), + H_FIELD, + ) + dense_result = _dense_h_full(mu) + assert_fields_close(matrix_result, dense_result, atol=1e-10, rtol=1e-10) + + +def test_e_full_matches_dense_reference_with_masks() -> None: + for mu in (None, MU): + matrix_result = apply_fdfd_matrix( + operators.e_full(OMEGA, DXES, vec(EPSILON), None if mu is None else vec(mu), vec(PEC), vec(PMC)), + E_FIELD, + ) + dense_result = _dense_e_full(mu) + assert_fields_close(matrix_result, dense_result, atol=1e-10, rtol=1e-10) + + +def test_h_full_without_masks_matches_dense_reference() -> None: + ce = fd_functional.curl_forward(DXES[0]) + ch = fd_functional.curl_back(DXES[1]) + dense_result = ce(ch(H_FIELD) / EPSILON) - OMEGA**2 * MU * H_FIELD + matrix_result = apply_fdfd_matrix( + operators.h_full(OMEGA, DXES, vec(EPSILON), vec(MU)), + H_FIELD, + ) + assert_fields_close(matrix_result, dense_result, atol=1e-10, rtol=1e-10) + + +def test_eh_full_matches_manual_block_operator_with_masks() -> None: + pe = numpy.where(PEC, 0.0, 1.0) + pm = numpy.where(PMC, 0.0, 1.0) + ce = fd_functional.curl_forward(DXES[0]) + ch = fd_functional.curl_back(DXES[1]) + + matrix_result = operators.eh_full(OMEGA, DXES, vec(EPSILON), vec(MU), vec(PEC), vec(PMC)) @ numpy.concatenate( + [vec(E_FIELD), vec(H_FIELD)], + ) + matrix_e, matrix_h = (unvec(part, SHAPE) for part in numpy.split(matrix_result, 2)) + + dense_e = pe * ch(pm * H_FIELD) - pe * (1j * OMEGA * EPSILON * (pe * E_FIELD)) + dense_h = pm * ce(pe * E_FIELD) + pm * (1j * OMEGA * MU * (pm * H_FIELD)) + + assert_fields_close(matrix_e, dense_e, atol=1e-10, rtol=1e-10) + assert_fields_close(matrix_h, dense_h, atol=1e-10, rtol=1e-10) + + +def test_e2h_pmc_mask_matches_masked_unmasked_result() -> None: + pmc_complement = numpy.where(PMC, 0.0, 1.0) + unmasked = apply_fdfd_matrix(operators.e2h(OMEGA, DXES, vec(MU)), E_FIELD) + masked = apply_fdfd_matrix(operators.e2h(OMEGA, DXES, vec(MU), vec(PMC)), E_FIELD) + + assert_fields_close(masked, pmc_complement * unmasked, atol=1e-10, rtol=1e-10) + + +def test_poynting_h_cross_matches_negative_e_cross_relation() -> None: + h_cross_e = apply_fdfd_matrix(operators.poynting_h_cross(vec(H_FIELD), DXES), E_FIELD) + e_cross_h = apply_fdfd_matrix(operators.poynting_e_cross(vec(E_FIELD), DXES), H_FIELD) + + assert_fields_close(h_cross_e, -e_cross_h, atol=1e-10, rtol=1e-10) + + +def test_e_boundary_source_interior_mask_is_independent_of_periodic_edges() -> None: + mask = numpy.zeros((3, *BOUNDARY_SHAPE), dtype=float) + mask[:, 1, 1, 1] = 1.0 + + periodic = operators.e_boundary_source(vec(mask), OMEGA, BOUNDARY_DXES, vec(BOUNDARY_EPSILON), periodic_mask_edges=True) + mirrored = operators.e_boundary_source(vec(mask), OMEGA, BOUNDARY_DXES, vec(BOUNDARY_EPSILON), periodic_mask_edges=False) + + assert_close(periodic.toarray(), mirrored.toarray()) + + +def test_e_boundary_source_periodic_edges_add_opposite_face_response() -> None: + mask = numpy.zeros((3, *BOUNDARY_SHAPE), dtype=float) + mask[:, 0, 1, 1] = 1.0 + + periodic = operators.e_boundary_source(vec(mask), OMEGA, BOUNDARY_DXES, vec(BOUNDARY_EPSILON), periodic_mask_edges=True) + mirrored = operators.e_boundary_source(vec(mask), OMEGA, BOUNDARY_DXES, vec(BOUNDARY_EPSILON), periodic_mask_edges=False) + diff = unvec((periodic - mirrored) @ vec(BOUNDARY_FIELD), BOUNDARY_SHAPE) + + assert numpy.isfinite(diff).all() + assert_close(diff[:, 1:-1, :, :], 0.0) + assert numpy.linalg.norm(diff[:, -1, :, :]) > 0 + + +def test_prepare_s_function_matches_closed_form_polynomial() -> None: + ln_r = -12.0 + order = 3.0 + distances = numpy.array([0.0, 0.25, 0.5, 1.0]) + s_function = scpml.prepare_s_function(ln_R=ln_r, m=order) + expected = (order + 1) * ln_r / 2 * distances**order + + assert_close(s_function(distances), expected) + + +def test_uniform_grid_scpml_matches_expected_stretch_profile() -> None: + s_function = scpml.prepare_s_function(ln_R=-12.0, m=3.0) + dxes = scpml.uniform_grid_scpml((6, 4, 3), (2, 0, 1), omega=2.0, epsilon_effective=4.0, s_function=s_function) + correction = numpy.sqrt(4.0) * 2.0 + + for axis, size, thickness in ((0, 6, 2), (2, 3, 1)): + grid = numpy.arange(size, dtype=float) + expected_a = 1 + 1j * s_function(_normalized_distance(grid, size, thickness)) / correction + expected_b = 1 + 1j * s_function(_normalized_distance(grid + 0.5, size, thickness)) / correction + assert_close(dxes[0][axis], expected_a) + assert_close(dxes[1][axis], expected_b) + + assert_close(dxes[0][1], 1.0) + assert_close(dxes[1][1], 1.0) + assert numpy.isfinite(dxes[0][0]).all() + assert numpy.isfinite(dxes[1][0]).all() + + +def test_uniform_grid_scpml_default_s_function_matches_explicit_default() -> None: + implicit = scpml.uniform_grid_scpml((6, 4, 3), (2, 0, 1), omega=2.0) + explicit = scpml.uniform_grid_scpml((6, 4, 3), (2, 0, 1), omega=2.0, s_function=scpml.prepare_s_function()) + + for implicit_group, explicit_group in zip(implicit, explicit, strict=True): + for implicit_axis, explicit_axis in zip(implicit_group, explicit_group, strict=True): + assert_close(implicit_axis, explicit_axis) + + +def test_stretch_with_scpml_only_modifies_requested_front_edge() -> None: + s_function = scpml.prepare_s_function(ln_R=-12.0, m=3.0) + base = [[numpy.ones(6), numpy.ones(4), numpy.ones(3)] for _ in range(2)] + stretched = scpml.stretch_with_scpml(base, axis=0, polarity=1, omega=2.0, epsilon_effective=4.0, thickness=2, s_function=s_function) + + assert_close(stretched[0][0][2:], 1.0) + assert_close(stretched[1][0][2:], 1.0) + assert_close(stretched[0][0][-2:], 1.0) + assert_close(stretched[1][0][-2:], 1.0) + assert numpy.linalg.norm(stretched[0][0][:2] - 1.0) > 0 + assert numpy.linalg.norm(stretched[1][0][:2] - 1.0) > 0 + + +def test_stretch_with_scpml_only_modifies_requested_back_edge() -> None: + s_function = scpml.prepare_s_function(ln_R=-12.0, m=3.0) + base = [[numpy.ones(6), numpy.ones(4), numpy.ones(3)] for _ in range(2)] + stretched = scpml.stretch_with_scpml(base, axis=0, polarity=-1, omega=2.0, epsilon_effective=4.0, thickness=2, s_function=s_function) + + assert_close(stretched[0][0][:4], 1.0) + assert_close(stretched[1][0][:4], 1.0) + assert numpy.linalg.norm(stretched[0][0][-2:] - 1.0) > 0 + assert numpy.linalg.norm(stretched[1][0][-2:] - 1.0) > 0 + + +def test_stretch_with_scpml_thickness_zero_is_noop() -> None: + s_function = scpml.prepare_s_function(ln_R=-12.0, m=3.0) + base = [[numpy.ones(6), numpy.ones(4), numpy.ones(3)] for _ in range(2)] + stretched = scpml.stretch_with_scpml(base, axis=0, polarity=-1, omega=2.0, epsilon_effective=4.0, thickness=0, s_function=s_function) + + for grid_group in stretched: + for axis_grid in grid_group: + assert_close(axis_grid, 1.0) diff --git a/meanas/test/test_fdfd_farfield.py b/meanas/test/test_fdfd_farfield.py new file mode 100644 index 0000000..5e2daab --- /dev/null +++ b/meanas/test/test_fdfd_farfield.py @@ -0,0 +1,100 @@ +import numpy +import pytest + +from ..fdfd import farfield + + +NEAR_SHAPE = (2, 3) +E_NEAR = [numpy.zeros(NEAR_SHAPE, dtype=complex), numpy.zeros(NEAR_SHAPE, dtype=complex)] +H_NEAR = [numpy.zeros(NEAR_SHAPE, dtype=complex), numpy.zeros(NEAR_SHAPE, dtype=complex)] + + +def test_near_to_farfield_rejects_wrong_length_inputs() -> None: + with pytest.raises(Exception, match='E_near must be a length-2 list'): + farfield.near_to_farfield(E_NEAR[:1], H_NEAR, dx=0.2, dy=0.3) + + with pytest.raises(Exception, match='H_near must be a length-2 list'): + farfield.near_to_farfield(E_NEAR, H_NEAR[:1], dx=0.2, dy=0.3) + + +def test_near_to_farfield_rejects_mismatched_shapes() -> None: + bad_h_near = [H_NEAR[0], numpy.zeros((2, 4), dtype=complex)] + + with pytest.raises(Exception, match='All fields must be the same shape'): + farfield.near_to_farfield(E_NEAR, bad_h_near, dx=0.2, dy=0.3) + + +def test_near_to_farfield_uses_default_and_scalar_padding_shapes() -> None: + default_result = farfield.near_to_farfield(E_NEAR, H_NEAR, dx=0.2, dy=0.3) + scalar_result = farfield.near_to_farfield(E_NEAR, H_NEAR, dx=0.2, dy=0.3, padded_size=8) + + assert default_result['E'][0].shape == (2, 4) + assert default_result['H'][0].shape == (2, 4) + assert scalar_result['E'][0].shape == (8, 8) + assert scalar_result['H'][0].shape == (8, 8) + + +def test_far_to_nearfield_rejects_wrong_length_inputs() -> None: + ff = farfield.near_to_farfield(E_NEAR, H_NEAR, dx=0.2, dy=0.3, padded_size=8) + + with pytest.raises(Exception, match='E_far must be a length-2 list'): + farfield.far_to_nearfield(ff['E'][:1], ff['H'], ff['dkx'], ff['dky']) + + with pytest.raises(Exception, match='H_far must be a length-2 list'): + farfield.far_to_nearfield(ff['E'], ff['H'][:1], ff['dkx'], ff['dky']) + + +def test_far_to_nearfield_rejects_mismatched_shapes() -> None: + ff = farfield.near_to_farfield(E_NEAR, H_NEAR, dx=0.2, dy=0.3, padded_size=8) + bad_h_far = [ff['H'][0], numpy.zeros((8, 4), dtype=complex)] + + with pytest.raises(Exception, match='All fields must be the same shape'): + farfield.far_to_nearfield(ff['E'], bad_h_far, ff['dkx'], ff['dky']) + + +def test_far_to_nearfield_uses_default_and_scalar_padding_shapes() -> None: + ff = farfield.near_to_farfield(E_NEAR, H_NEAR, dx=0.2, dy=0.3, padded_size=8) + default_result = farfield.far_to_nearfield( + [field.copy() for field in ff['E']], + [field.copy() for field in ff['H']], + ff['dkx'], + ff['dky'], + ) + scalar_result = farfield.far_to_nearfield( + [field.copy() for field in ff['E']], + [field.copy() for field in ff['H']], + ff['dkx'], + ff['dky'], + padded_size=4, + ) + + assert default_result['E'][0].shape == (8, 8) + assert default_result['H'][0].shape == (8, 8) + assert scalar_result['E'][0].shape == (4, 4) + assert scalar_result['H'][0].shape == (4, 4) + + +def test_farfield_roundtrip_supports_rectangular_arrays() -> None: + e_near = [numpy.zeros((4, 8), dtype=complex), numpy.zeros((4, 8), dtype=complex)] + h_near = [numpy.zeros((4, 8), dtype=complex), numpy.zeros((4, 8), dtype=complex)] + e_near[0][1, 3] = 1.0 + 0.25j + h_near[1][2, 5] = -0.5j + + ff = farfield.near_to_farfield(e_near, h_near, dx=0.2, dy=0.3, padded_size=(4, 8)) + restored = farfield.far_to_nearfield( + [field.copy() for field in ff['E']], + [field.copy() for field in ff['H']], + ff['dkx'], + ff['dky'], + padded_size=(4, 8), + ) + + assert isinstance(ff['dkx'], float) + assert isinstance(ff['dky'], float) + assert ff['E'][0].shape == (4, 8) + assert restored['E'][0].shape == (4, 8) + assert restored['H'][0].shape == (4, 8) + assert restored['dx'] == pytest.approx(0.2) + assert restored['dy'] == pytest.approx(0.3) + assert numpy.isfinite(restored['E'][0]).all() + assert numpy.isfinite(restored['H'][0]).all() diff --git a/meanas/test/test_fdfd_functional.py b/meanas/test/test_fdfd_functional.py new file mode 100644 index 0000000..9c1f771 --- /dev/null +++ b/meanas/test/test_fdfd_functional.py @@ -0,0 +1,122 @@ +import numpy + +from ..fdmath import unvec, vec +from ..fdfd import functional, operators +from ._fdfd_case import DXES, EPSILON, E_FIELD, H_FIELD, MU, OMEGA, SHAPE, TF_REGION, apply_fdfd_matrix +from .utils import assert_fields_close + + +ATOL = 1e-9 +RTOL = 1e-9 + + +def assert_fields_match(actual: numpy.ndarray, expected: numpy.ndarray) -> None: + assert_fields_close(actual, expected, atol=ATOL, rtol=RTOL) + + +def test_e_full_matches_sparse_operator_without_mu() -> None: + matrix_result = apply_fdfd_matrix( + operators.e_full(OMEGA, DXES, vec(EPSILON)), + E_FIELD, + ) + functional_result = functional.e_full(OMEGA, DXES, EPSILON)(E_FIELD) + + assert_fields_match(functional_result, matrix_result) + + +def test_e_full_matches_sparse_operator_with_mu() -> None: + matrix_result = apply_fdfd_matrix( + operators.e_full(OMEGA, DXES, vec(EPSILON), vec(MU)), + E_FIELD, + ) + functional_result = functional.e_full(OMEGA, DXES, EPSILON, MU)(E_FIELD) + + assert_fields_match(functional_result, matrix_result) + + +def test_eh_full_matches_sparse_operator_with_mu() -> None: + matrix_result = operators.eh_full(OMEGA, DXES, vec(EPSILON), vec(MU)) @ numpy.concatenate([vec(E_FIELD), vec(H_FIELD)]) + matrix_e, matrix_h = (unvec(part, SHAPE) for part in numpy.split(matrix_result, 2)) + functional_e, functional_h = functional.eh_full(OMEGA, DXES, EPSILON, MU)(E_FIELD, H_FIELD) + + assert_fields_match(functional_e, matrix_e) + assert_fields_match(functional_h, matrix_h) + + +def test_eh_full_matches_sparse_operator_without_mu() -> None: + matrix_result = operators.eh_full(OMEGA, DXES, vec(EPSILON)) @ numpy.concatenate([vec(E_FIELD), vec(H_FIELD)]) + matrix_e, matrix_h = (unvec(part, SHAPE) for part in numpy.split(matrix_result, 2)) + functional_e, functional_h = functional.eh_full(OMEGA, DXES, EPSILON)(E_FIELD, H_FIELD) + + assert_fields_match(functional_e, matrix_e) + assert_fields_match(functional_h, matrix_h) + + +def test_e2h_matches_sparse_operator_with_mu() -> None: + matrix_result = apply_fdfd_matrix( + operators.e2h(OMEGA, DXES, vec(MU)), + E_FIELD, + ) + functional_result = functional.e2h(OMEGA, DXES, MU)(E_FIELD) + + assert_fields_match(functional_result, matrix_result) + + +def test_e2h_matches_sparse_operator_without_mu() -> None: + matrix_result = apply_fdfd_matrix( + operators.e2h(OMEGA, DXES), + E_FIELD, + ) + functional_result = functional.e2h(OMEGA, DXES)(E_FIELD) + + assert_fields_match(functional_result, matrix_result) + + +def test_m2j_matches_sparse_operator_without_mu() -> None: + matrix_result = apply_fdfd_matrix( + operators.m2j(OMEGA, DXES), + H_FIELD, + ) + functional_result = functional.m2j(OMEGA, DXES)(H_FIELD) + + assert_fields_match(functional_result, matrix_result) + + +def test_m2j_matches_sparse_operator_with_mu() -> None: + matrix_result = apply_fdfd_matrix( + operators.m2j(OMEGA, DXES, vec(MU)), + H_FIELD, + ) + functional_result = functional.m2j(OMEGA, DXES, MU)(H_FIELD) + + assert_fields_match(functional_result, matrix_result) + + +def test_e_tfsf_source_matches_sparse_operator_without_mu() -> None: + matrix_result = apply_fdfd_matrix( + operators.e_tfsf_source(vec(TF_REGION), OMEGA, DXES, vec(EPSILON)), + E_FIELD, + ) + functional_result = functional.e_tfsf_source(TF_REGION, OMEGA, DXES, EPSILON)(E_FIELD) + + assert_fields_match(functional_result, matrix_result) + + +def test_e_tfsf_source_matches_sparse_operator_with_mu() -> None: + matrix_result = apply_fdfd_matrix( + operators.e_tfsf_source(vec(TF_REGION), OMEGA, DXES, vec(EPSILON), vec(MU)), + E_FIELD, + ) + functional_result = functional.e_tfsf_source(TF_REGION, OMEGA, DXES, EPSILON, MU)(E_FIELD) + + assert_fields_match(functional_result, matrix_result) + + +def test_poynting_e_cross_h_matches_sparse_operator() -> None: + matrix_result = apply_fdfd_matrix( + operators.poynting_e_cross(vec(E_FIELD), DXES), + H_FIELD, + ) + functional_result = functional.poynting_e_cross_h(DXES)(E_FIELD, H_FIELD) + + assert_fields_match(functional_result, matrix_result) diff --git a/meanas/test/test_fdfd_pml.py b/meanas/test/test_fdfd_pml.py index d752491..1a8d66c 100644 --- a/meanas/test/test_fdfd_pml.py +++ b/meanas/test/test_fdfd_pml.py @@ -1,11 +1,11 @@ -from typing import Iterable +# ruff: noqa: ARG001 import pytest # type: ignore import numpy from numpy.typing import NDArray from numpy.testing import assert_allclose from .. import fdfd -from ..fdmath import vec, unvec, dx_lists_mut +from ..fdmath import vec, unvec, dx_lists_mut, vfdfield, cfdfield_t #from .utils import assert_close, assert_fields_close from .test_fdfd import FDResult from .conftest import FixtureRequest @@ -44,49 +44,51 @@ def test_pml(sim: FDResult, src_polarity: int) -> None: # Also see conftest.py @pytest.fixture(params=[1 / 1500]) -def omega(request: FixtureRequest) -> Iterable[float]: - yield request.param +def omega(request: FixtureRequest) -> float: + return request.param @pytest.fixture(params=[None]) -def pec(request: FixtureRequest) -> Iterable[NDArray[numpy.float64] | None]: - yield request.param +def pec(request: FixtureRequest) -> NDArray[numpy.float64] | None: + return request.param @pytest.fixture(params=[None]) -def pmc(request: FixtureRequest) -> Iterable[NDArray[numpy.float64] | None]: - yield request.param +def pmc(request: FixtureRequest) -> NDArray[numpy.float64] | None: + return request.param @pytest.fixture(params=[(30, 1, 1), (1, 30, 1), (1, 1, 30)]) -def shape(request: FixtureRequest) -> Iterable[tuple[int, ...]]: - yield (3, *request.param) +def shape(request: FixtureRequest) -> tuple[int, int, int]: + return (3, *request.param) @pytest.fixture(params=[+1, -1]) -def src_polarity(request: FixtureRequest) -> Iterable[int]: - yield request.param +def src_polarity(request: FixtureRequest) -> int: + return request.param -@pytest.fixture() +@pytest.fixture def j_distribution( request: FixtureRequest, shape: tuple[int, ...], - epsilon: NDArray[numpy.float64], + epsilon: vfdfield, dxes: dx_lists_mut, omega: float, src_polarity: int, - ) -> Iterable[NDArray[numpy.complex128]]: + ) -> cfdfield_t: j = numpy.zeros(shape, dtype=complex) dim = numpy.where(numpy.array(shape[1:]) > 1)[0][0] # Propagation axis other_dims = [0, 1, 2] other_dims.remove(dim) - dx_prop = (dxes[0][dim][shape[dim + 1] // 2] - + dxes[1][dim][shape[dim + 1] // 2]) / 2 # noqa: E128 # TODO is this right for nonuniform dxes? + dx_prop = ( + dxes[0][dim][shape[dim + 1] // 2] + + dxes[1][dim][shape[dim + 1] // 2] + ) / 2 # TODO is this right for nonuniform dxes? # Mask only contains components orthogonal to propagation direction center_mask = numpy.zeros(shape, dtype=bool) @@ -106,18 +108,18 @@ def j_distribution( j = fdfd.waveguide_3d.compute_source(E=e, wavenumber=wavenumber_corrected, omega=omega, dxes=dxes, axis=dim, polarity=src_polarity, slices=slices, epsilon=epsilon) - yield j + return j -@pytest.fixture() +@pytest.fixture def epsilon( request: FixtureRequest, shape: tuple[int, ...], epsilon_bg: float, epsilon_fg: float, - ) -> Iterable[NDArray[numpy.float64]]: + ) -> NDArray[numpy.float64]: epsilon = numpy.full(shape, epsilon_fg, dtype=float) - yield epsilon + return epsilon @pytest.fixture(params=['uniform']) @@ -127,7 +129,7 @@ def dxes( dx: float, omega: float, epsilon_fg: float, - ) -> Iterable[list[list[NDArray[numpy.float64]]]]: + ) -> list[list[NDArray[numpy.float64]]]: if request.param == 'uniform': dxes = [[numpy.full(s, dx) for s in shape[1:]] for _ in range(2)] dim = numpy.where(numpy.array(shape[1:]) > 1)[0][0] # Propagation axis @@ -141,10 +143,10 @@ def dxes( epsilon_effective=epsilon_fg, thickness=10, ) - yield dxes + return dxes -@pytest.fixture() +@pytest.fixture def sim( request: FixtureRequest, shape: tuple[int, ...], @@ -162,7 +164,7 @@ def sim( omega=omega, dxes=dxes, epsilon=eps_vec, - matrix_solver_opts={'atol': 1e-15, 'tol': 1e-11}, + matrix_solver_opts={'atol': 1e-15, 'rtol': 1e-11}, ) e = unvec(e_vec, shape[1:]) diff --git a/meanas/test/test_fdfd_solvers.py b/meanas/test/test_fdfd_solvers.py new file mode 100644 index 0000000..de39d70 --- /dev/null +++ b/meanas/test/test_fdfd_solvers.py @@ -0,0 +1,128 @@ +from typing import cast + +import numpy + +from ..fdfd import solvers +from ._solver_cases import solver_plumbing_case +from .utils import assert_close + + +def test_scipy_qmr_wraps_user_callback_without_recursion(monkeypatch) -> None: + seen: list[tuple[float, ...]] = [] + + def fake_qmr(a, b: numpy.ndarray, **kwargs): + kwargs['callback'](numpy.array([1.0, 2.0])) + return numpy.array([3.0, 4.0]), 0 + + monkeypatch.setattr(solvers.scipy.sparse.linalg, 'qmr', fake_qmr) + result = solvers._scipy_qmr( + solver_plumbing_case().a0, + numpy.array([1.0, 0.0]), + callback=lambda xk: seen.append(tuple(xk)), + ) + + assert_close(result, [3.0, 4.0]) + assert seen == [(1.0, 2.0)] + + +def test_scipy_qmr_installs_logging_callback_when_missing(monkeypatch) -> None: + callback_seen: list[numpy.ndarray] = [] + + def fake_qmr(a, b: numpy.ndarray, **kwargs): + callback = kwargs['callback'] + callback(numpy.array([5.0, 6.0])) + callback_seen.append(b.copy()) + return numpy.array([7.0, 8.0]), 0 + + monkeypatch.setattr(solvers.scipy.sparse.linalg, 'qmr', fake_qmr) + result = solvers._scipy_qmr(solver_plumbing_case().a0, numpy.array([1.0, 0.0])) + + assert_close(result, [7.0, 8.0]) + assert len(callback_seen) == 1 + + +def test_generic_forward_preconditions_system_and_guess(monkeypatch) -> None: + case = solver_plumbing_case() + captured: dict[str, numpy.ndarray | float | object] = {} + + monkeypatch.setattr(solvers.operators, 'e_full', lambda *args, **kwargs: case.a0) + monkeypatch.setattr(solvers.operators, 'e_full_preconditioners', lambda dxes: (case.pl, case.pr)) + + def fake_solver(a, b: numpy.ndarray, **kwargs): + captured['a'] = a + captured['b'] = b + captured['x0'] = kwargs['x0'] + captured['atol'] = kwargs['atol'] + return case.solver_result + + result = solvers.generic( + omega=case.omega, + dxes=case.dxes, + J=case.j, + epsilon=case.epsilon, + matrix_solver=fake_solver, + matrix_solver_opts={'atol': 1e-12}, + E_guess=case.guess, + ) + + assert_close(cast(object, captured['a']).toarray(), (case.pl @ case.a0 @ case.pr).toarray()) # type: ignore[attr-defined] + assert_close(cast(numpy.ndarray, captured['b']), case.pl @ (-1j * case.omega * case.j)) + assert_close(cast(numpy.ndarray, captured['x0']), case.pl @ case.guess) + assert captured['atol'] == 1e-12 + assert_close(result, case.pr @ case.solver_result) + + +def test_generic_adjoint_preconditions_system_and_guess(monkeypatch) -> None: + case = solver_plumbing_case() + captured: dict[str, numpy.ndarray | float | object] = {} + + monkeypatch.setattr(solvers.operators, 'e_full', lambda *args, **kwargs: case.a0) + monkeypatch.setattr(solvers.operators, 'e_full_preconditioners', lambda dxes: (case.pl, case.pr)) + + def fake_solver(a, b: numpy.ndarray, **kwargs): + captured['a'] = a + captured['b'] = b + captured['x0'] = kwargs['x0'] + captured['rtol'] = kwargs['rtol'] + return case.solver_result + + result = solvers.generic( + omega=case.omega, + dxes=case.dxes, + J=case.j, + epsilon=case.epsilon, + matrix_solver=fake_solver, + matrix_solver_opts={'rtol': 1e-9}, + E_guess=case.guess, + adjoint=True, + ) + + expected_matrix = (case.pl @ case.a0 @ case.pr).T.conjugate() + assert_close(cast(object, captured['a']).toarray(), expected_matrix.toarray()) # type: ignore[attr-defined] + assert_close(cast(numpy.ndarray, captured['b']), case.pr.T.conjugate() @ (-1j * case.omega * case.j)) + assert_close(cast(numpy.ndarray, captured['x0']), case.pr.T.conjugate() @ case.guess) + assert captured['rtol'] == 1e-9 + assert_close(result, case.pl.T.conjugate() @ case.solver_result) + + +def test_generic_without_guess_does_not_inject_x0(monkeypatch) -> None: + case = solver_plumbing_case() + captured: dict[str, object] = {} + + monkeypatch.setattr(solvers.operators, 'e_full', lambda *args, **kwargs: case.a0) + monkeypatch.setattr(solvers.operators, 'e_full_preconditioners', lambda dxes: (case.pl, case.pr)) + + def fake_solver(a, b: numpy.ndarray, **kwargs): + captured['kwargs'] = kwargs + return numpy.array([1.0, -1.0]) + + result = solvers.generic( + omega=1.0, + dxes=case.dxes, + J=numpy.array([2.0, 3.0]), + epsilon=case.epsilon, + matrix_solver=fake_solver, + ) + + assert 'x0' not in cast(dict[str, object], captured['kwargs']) + assert_close(result, case.pr @ numpy.array([1.0, -1.0])) diff --git a/meanas/test/test_fdmath_functional.py b/meanas/test/test_fdmath_functional.py new file mode 100644 index 0000000..368eba3 --- /dev/null +++ b/meanas/test/test_fdmath_functional.py @@ -0,0 +1,60 @@ +import numpy + +from ..fdmath import functional as fd_functional +from ..fdmath import operators as fd_operators +from ..fdmath import vec, unvec +from .utils import assert_close, assert_fields_close + + +SHAPE = (2, 3, 2) +DX_E = [numpy.array([1.0, 1.5]), numpy.array([0.75, 1.25, 1.5]), numpy.array([1.2, 0.8])] +DX_H = [numpy.array([0.9, 1.4]), numpy.array([0.8, 1.1, 1.4]), numpy.array([1.0, 0.7])] + +SCALAR_FIELD = ( + numpy.arange(numpy.prod(SHAPE)).reshape(SHAPE) + + 0.1j * numpy.arange(numpy.prod(SHAPE)).reshape(SHAPE) +).astype(complex) +VECTOR_FIELD = (numpy.arange(3 * numpy.prod(SHAPE)).reshape((3, *SHAPE)) + 0.25j).astype(complex) + + +def test_deriv_forward_without_dx_matches_numpy_roll() -> None: + for axis, deriv in enumerate(fd_functional.deriv_forward()): + expected = numpy.roll(SCALAR_FIELD, -1, axis=axis) - SCALAR_FIELD + assert_close(deriv(SCALAR_FIELD), expected) + + +def test_deriv_back_without_dx_matches_numpy_roll() -> None: + for axis, deriv in enumerate(fd_functional.deriv_back()): + expected = SCALAR_FIELD - numpy.roll(SCALAR_FIELD, 1, axis=axis) + assert_close(deriv(SCALAR_FIELD), expected) + + +def test_curl_parts_sum_to_full_curl() -> None: + curl_forward = fd_functional.curl_forward(DX_E)(VECTOR_FIELD) + curl_back = fd_functional.curl_back(DX_H)(VECTOR_FIELD) + forward_parts = fd_functional.curl_forward_parts(DX_E)(VECTOR_FIELD) + back_parts = fd_functional.curl_back_parts(DX_H)(VECTOR_FIELD) + + for axis in range(3): + assert_close(forward_parts[axis][0] + forward_parts[axis][1], curl_forward[axis]) + assert_close(back_parts[axis][0] + back_parts[axis][1], curl_back[axis]) + + +def test_derivatives_match_sparse_operators_on_nonuniform_grid() -> None: + for axis, deriv in enumerate(fd_functional.deriv_forward(DX_E)): + matrix_result = (fd_operators.deriv_forward(DX_E)[axis] @ SCALAR_FIELD.ravel(order='C')).reshape(SHAPE, order='C') + assert_close(deriv(SCALAR_FIELD), matrix_result, atol=1e-12, rtol=1e-12) + + for axis, deriv in enumerate(fd_functional.deriv_back(DX_H)): + matrix_result = (fd_operators.deriv_back(DX_H)[axis] @ SCALAR_FIELD.ravel(order='C')).reshape(SHAPE, order='C') + assert_close(deriv(SCALAR_FIELD), matrix_result, atol=1e-12, rtol=1e-12) + + +def test_curls_match_sparse_operators_on_nonuniform_grid() -> None: + curl_forward = fd_functional.curl_forward(DX_E)(VECTOR_FIELD) + curl_back = fd_functional.curl_back(DX_H)(VECTOR_FIELD) + matrix_forward = unvec(fd_operators.curl_forward(DX_E) @ vec(VECTOR_FIELD), SHAPE) + matrix_back = unvec(fd_operators.curl_back(DX_H) @ vec(VECTOR_FIELD), SHAPE) + + assert_fields_close(curl_forward, matrix_forward, atol=1e-12, rtol=1e-12) + assert_fields_close(curl_back, matrix_back, atol=1e-12, rtol=1e-12) diff --git a/meanas/test/test_fdmath_operators.py b/meanas/test/test_fdmath_operators.py new file mode 100644 index 0000000..9b1dec0 --- /dev/null +++ b/meanas/test/test_fdmath_operators.py @@ -0,0 +1,90 @@ +import numpy +import pytest + +from ..fdmath import operators, unvec, vec +from ._test_builders import real_ramp +from .utils import assert_close + + +SHAPE = (2, 3, 2) +SCALAR_FIELD = real_ramp(SHAPE) +VECTOR_LEFT = real_ramp((3, *SHAPE), offset=0.5) +VECTOR_RIGHT = real_ramp((3, *SHAPE), scale=1 / 3, offset=2.0) + + +def _apply_scalar_matrix(op: operators.sparse.spmatrix) -> numpy.ndarray: + return (op @ SCALAR_FIELD.ravel(order='C')).reshape(SHAPE, order='C') + + +def _mirrored_indices(size: int, shift_distance: int) -> numpy.ndarray: + indices = numpy.arange(size) + shift_distance + indices = numpy.where(indices >= size, 2 * size - indices - 1, indices) + indices = numpy.where(indices < 0, -1 - indices, indices) + return indices + + +@pytest.mark.parametrize(('axis', 'shift_distance'), [(0, 1), (1, -1), (2, 1)]) +def test_shift_circ_matches_numpy_roll(axis: int, shift_distance: int) -> None: + matrix_result = _apply_scalar_matrix(operators.shift_circ(axis, SHAPE, shift_distance)) + expected = numpy.roll(SCALAR_FIELD, -shift_distance, axis=axis) + assert_close(matrix_result, expected) + + +@pytest.mark.parametrize(('axis', 'shift_distance'), [(0, 1), (1, -1), (2, 1)]) +def test_shift_with_mirror_matches_explicit_mirrored_indices(axis: int, shift_distance: int) -> None: + matrix_result = _apply_scalar_matrix(operators.shift_with_mirror(axis, SHAPE, shift_distance)) + indices = [numpy.arange(length) for length in SHAPE] + indices[axis] = _mirrored_indices(SHAPE[axis], shift_distance) + expected = SCALAR_FIELD[numpy.ix_(*indices)] + assert_close(matrix_result, expected) + + +@pytest.mark.parametrize( + ('args', 'message'), + [ + ((0, (2,), 1), 'Invalid shape'), + ((3, SHAPE, 1), 'Invalid direction'), + ], + ) +def test_shift_circ_rejects_invalid_arguments(args: tuple[int, tuple[int, ...], int], message: str) -> None: + with pytest.raises(Exception, match=message): + operators.shift_circ(*args) + + +@pytest.mark.parametrize( + ('args', 'message'), + [ + ((0, (2,), 1), 'Invalid shape'), + ((3, SHAPE, 1), 'Invalid direction'), + ((0, SHAPE, SHAPE[0]), 'too large'), + ], + ) +def test_shift_with_mirror_rejects_invalid_arguments(args: tuple[int, tuple[int, ...], int], message: str) -> None: + with pytest.raises(Exception, match=message): + operators.shift_with_mirror(*args) + + +def test_vec_cross_matches_pointwise_cross_product() -> None: + matrix_result = unvec(operators.vec_cross(vec(VECTOR_LEFT)) @ vec(VECTOR_RIGHT), SHAPE) + expected = numpy.empty_like(VECTOR_LEFT) + expected[0] = VECTOR_LEFT[1] * VECTOR_RIGHT[2] - VECTOR_LEFT[2] * VECTOR_RIGHT[1] + expected[1] = VECTOR_LEFT[2] * VECTOR_RIGHT[0] - VECTOR_LEFT[0] * VECTOR_RIGHT[2] + expected[2] = VECTOR_LEFT[0] * VECTOR_RIGHT[1] - VECTOR_LEFT[1] * VECTOR_RIGHT[0] + assert_close(matrix_result, expected) + + +def test_avg_forward_matches_half_sum_with_forward_neighbor() -> None: + matrix_result = _apply_scalar_matrix(operators.avg_forward(1, SHAPE)) + expected = 0.5 * (SCALAR_FIELD + numpy.roll(SCALAR_FIELD, -1, axis=1)) + assert_close(matrix_result, expected) + + +def test_avg_back_matches_half_sum_with_backward_neighbor() -> None: + matrix_result = _apply_scalar_matrix(operators.avg_back(1, SHAPE)) + expected = 0.5 * (SCALAR_FIELD + numpy.roll(SCALAR_FIELD, 1, axis=1)) + assert_close(matrix_result, expected) + + +def test_avg_forward_rejects_invalid_shape() -> None: + with pytest.raises(Exception, match='Invalid shape'): + operators.avg_forward(0, (2,)) diff --git a/meanas/test/test_fdmath_vectorization.py b/meanas/test/test_fdmath_vectorization.py new file mode 100644 index 0000000..c55f7cd --- /dev/null +++ b/meanas/test/test_fdmath_vectorization.py @@ -0,0 +1,46 @@ +import numpy + +from ..fdmath import unvec, vec +from ._test_builders import complex_ramp, real_ramp +from .utils import assert_close + + +SHAPE = (2, 3, 2) +FIELD = real_ramp((3, *SHAPE)) +COMPLEX_FIELD = complex_ramp((3, *SHAPE), imag_scale=0.5) + + +def test_vec_and_unvec_return_none_for_none_input() -> None: + assert vec(None) is None + assert unvec(None, SHAPE) is None + + +def test_real_field_round_trip_preserves_shape_and_values() -> None: + vector = vec(FIELD) + assert vector is not None + restored = unvec(vector, SHAPE) + assert restored is not None + assert restored.shape == (3, *SHAPE) + assert_close(restored, FIELD) + + +def test_complex_field_round_trip_preserves_shape_and_values() -> None: + vector = vec(COMPLEX_FIELD) + assert vector is not None + restored = unvec(vector, SHAPE) + assert restored is not None + assert restored.shape == (3, *SHAPE) + assert_close(restored, COMPLEX_FIELD) + + +def test_unvec_with_two_components_round_trips_vector() -> None: + vector = numpy.arange(2 * numpy.prod(SHAPE), dtype=float) + field = unvec(vector, SHAPE, nvdim=2) + assert field is not None + assert field.shape == (2, *SHAPE) + assert_close(vec(field), vector) + + +def test_vec_accepts_arraylike_input() -> None: + arraylike = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]] + assert_close(vec(arraylike), numpy.ravel(arraylike, order='C')) diff --git a/meanas/test/test_fdtd.py b/meanas/test/test_fdtd.py index 0a92c73..469c220 100644 --- a/meanas/test/test_fdtd.py +++ b/meanas/test/test_fdtd.py @@ -1,4 +1,5 @@ -from typing import Iterable, Any +# ruff: noqa: ARG001 +from typing import Any import dataclasses import pytest # type: ignore import numpy @@ -6,7 +7,7 @@ from numpy.typing import NDArray #from numpy.testing import assert_allclose, assert_array_equal from .. import fdtd -from .utils import assert_close, assert_fields_close, PRNG +from .utils import assert_close, assert_fields_close, make_prng from .conftest import FixtureRequest @@ -150,8 +151,8 @@ def test_poynting_planes(sim: 'TDResult') -> None: @pytest.fixture(params=[0.3]) -def dt(request: FixtureRequest) -> Iterable[float]: - yield request.param +def dt(request: FixtureRequest) -> float: + return request.param @dataclasses.dataclass() @@ -168,8 +169,8 @@ class TDResult: @pytest.fixture(params=[(0, 4, 8)]) # (0,) -def j_steps(request: FixtureRequest) -> Iterable[tuple[int, ...]]: - yield request.param +def j_steps(request: FixtureRequest) -> tuple[int, ...]: + return request.param @pytest.fixture(params=['center', 'random']) @@ -177,18 +178,19 @@ def j_distribution( request: FixtureRequest, shape: tuple[int, ...], j_mag: float, - ) -> Iterable[NDArray[numpy.float64]]: + ) -> NDArray[numpy.float64]: + prng = make_prng() j = numpy.zeros(shape) if request.param == 'center': j[:, shape[1] // 2, shape[2] // 2, shape[3] // 2] = j_mag elif request.param == '000': j[:, 0, 0, 0] = j_mag elif request.param == 'random': - j[:] = PRNG.uniform(low=-j_mag, high=j_mag, size=shape) - yield j + j[:] = prng.uniform(low=-j_mag, high=j_mag, size=shape) + return j -@pytest.fixture() +@pytest.fixture def sim( request: FixtureRequest, shape: tuple[int, ...], @@ -199,9 +201,8 @@ def sim( j_steps: tuple[int, ...], ) -> TDResult: is3d = (numpy.array(shape) == 1).sum() == 0 - if is3d: - if dt != 0.3: - pytest.skip('Skipping dt != 0.3 because test is 3D (for speed)') + if is3d and dt != 0.3: + pytest.skip('Skipping dt != 0.3 because test is 3D (for speed)') sim = TDResult( shape=shape, diff --git a/meanas/test/test_fdtd_base.py b/meanas/test/test_fdtd_base.py new file mode 100644 index 0000000..c8246d5 --- /dev/null +++ b/meanas/test/test_fdtd_base.py @@ -0,0 +1,43 @@ +from ..fdmath import functional as fd_functional +from ..fdtd import base +from ._test_builders import real_ramp +from .utils import assert_close + + +DT = 0.25 +SHAPE = (3, 2, 2, 2) +E_FIELD = real_ramp(SHAPE, scale=1 / 5) +H_FIELD = real_ramp(SHAPE, scale=1 / 7, offset=1 / 7) +EPSILON = 1.5 + E_FIELD / 10.0 +MU_FIELD = 2.0 + H_FIELD / 8.0 +MU_SCALAR = 3.0 + + +def test_maxwell_e_without_dxes_matches_unit_spacing_update() -> None: + updater = base.maxwell_e(dt=DT) + expected = E_FIELD + DT * fd_functional.curl_back()(H_FIELD) / EPSILON + + updated = updater(E_FIELD.copy(), H_FIELD.copy(), EPSILON) + + assert_close(updated, expected) + + +def test_maxwell_h_without_dxes_and_without_mu_matches_unit_spacing_update() -> None: + updater = base.maxwell_h(dt=DT) + expected = H_FIELD - DT * fd_functional.curl_forward()(E_FIELD) + + updated = updater(E_FIELD.copy(), H_FIELD.copy()) + + assert_close(updated, expected) + + +def test_maxwell_h_without_dxes_accepts_scalar_and_field_mu() -> None: + updater = base.maxwell_h(dt=DT) + + updated_scalar = updater(E_FIELD.copy(), H_FIELD.copy(), MU_SCALAR) + expected_scalar = H_FIELD - DT * fd_functional.curl_forward()(E_FIELD) / MU_SCALAR + assert_close(updated_scalar, expected_scalar) + + updated_field = updater(E_FIELD.copy(), H_FIELD.copy(), MU_FIELD) + expected_field = H_FIELD - DT * fd_functional.curl_forward()(E_FIELD) / MU_FIELD + assert_close(updated_field, expected_field) diff --git a/meanas/test/test_fdtd_boundaries.py b/meanas/test/test_fdtd_boundaries.py new file mode 100644 index 0000000..d60ca7a --- /dev/null +++ b/meanas/test/test_fdtd_boundaries.py @@ -0,0 +1,62 @@ +import numpy +import pytest +from numpy.testing import assert_allclose + +from ..fdtd.boundaries import conducting_boundary + + +def _axis_index(axis: int, index: int) -> tuple[slice | int, ...]: + coords: list[slice | int] = [slice(None), slice(None), slice(None)] + coords[axis] = index + return tuple(coords) + + +@pytest.mark.parametrize('direction', [0, 1, 2]) +@pytest.mark.parametrize('polarity', [-1, 1]) +def test_conducting_boundary_updates_expected_faces(direction: int, polarity: int) -> None: + e = numpy.arange(3 * 4 * 4 * 4, dtype=float).reshape(3, 4, 4, 4) + h = e.copy() + e0 = e.copy() + h0 = h.copy() + + update_e, update_h = conducting_boundary(direction, polarity) + update_e(e) + update_h(h) + + dirs = [0, 1, 2] + dirs.remove(direction) + u, v = dirs + + if polarity < 0: + boundary = _axis_index(direction, 0) + shifted1 = _axis_index(direction, 1) + + assert_allclose(e[direction][boundary], 0) + assert_allclose(e[u][boundary], e0[u][shifted1]) + assert_allclose(e[v][boundary], e0[v][shifted1]) + assert_allclose(h[direction][boundary], h0[direction][shifted1]) + assert_allclose(h[u][boundary], 0) + assert_allclose(h[v][boundary], 0) + else: + boundary = _axis_index(direction, -1) + shifted1 = _axis_index(direction, -2) + shifted2 = _axis_index(direction, -3) + + assert_allclose(e[direction][boundary], -e0[direction][shifted2]) + assert_allclose(e[direction][shifted1], 0) + assert_allclose(e[u][boundary], e0[u][shifted1]) + assert_allclose(e[v][boundary], e0[v][shifted1]) + assert_allclose(h[direction][boundary], h0[direction][shifted1]) + assert_allclose(h[u][boundary], -h0[u][shifted2]) + assert_allclose(h[u][shifted1], 0) + assert_allclose(h[v][boundary], -h0[v][shifted2]) + assert_allclose(h[v][shifted1], 0) + + +@pytest.mark.parametrize( + ('direction', 'polarity'), + [(-1, 1), (3, 1), (0, 0)], +) +def test_conducting_boundary_rejects_invalid_arguments(direction: int, polarity: int) -> None: + with pytest.raises(ValueError, match='Invalid direction|Bad polarity'): + conducting_boundary(direction, polarity) diff --git a/meanas/test/test_fdtd_energy.py b/meanas/test/test_fdtd_energy.py new file mode 100644 index 0000000..84830cf --- /dev/null +++ b/meanas/test/test_fdtd_energy.py @@ -0,0 +1,99 @@ +import numpy + +from .. import fdtd +from ..fdtd import energy as fdtd_energy +from ._test_builders import real_ramp, unit_dxes +from .utils import assert_close + + +SHAPE = (2, 2, 2) +DT = 0.25 +UNIT_DXES = unit_dxes(SHAPE) +DXES = ( + ( + numpy.array([1.0, 1.5]), + numpy.array([0.75, 1.25]), + numpy.array([1.1, 0.9]), + ), + ( + numpy.array([0.8, 1.2]), + numpy.array([1.4, 0.6]), + numpy.array([0.7, 1.3]), + ), +) +E0 = real_ramp((3, *SHAPE)) +E1 = E0 + 0.5 +E2 = E0 + 1.0 +E3 = E0 + 1.5 +H0 = real_ramp((3, *SHAPE), scale=1 / 3, offset=2 / 3) +H1 = H0 + 0.25 +H2 = H0 + 0.5 +H3 = H0 + 0.75 +J0 = (E0 + 2.0) / 5.0 +EPSILON = 1.0 + E0 / 20.0 +MU = 1.5 + H0 / 10.0 + + +def test_poynting_default_spacing_matches_explicit_unit_spacing() -> None: + default_spacing = fdtd.poynting(E1, H1) + explicit_spacing = fdtd.poynting(E1, H1, dxes=UNIT_DXES) + assert_close(default_spacing, explicit_spacing) + + +def test_poynting_divergence_matches_precomputed_poynting_vector() -> None: + s = fdtd.poynting(E2, H2, dxes=DXES) + from_fields = fdtd.poynting_divergence(e=E2, h=H2, dxes=DXES) + from_vector = fdtd.poynting_divergence(s=s) + assert_close(from_fields, from_vector) + + +def test_delta_energy_h2e_matches_direct_dxmul_formula() -> None: + expected = fdtd_energy.dxmul( + E2 * (E2 - E0) / DT, + H1 * (H3 - H1) / DT, + EPSILON, + MU, + DXES, + ) + actual = fdtd.delta_energy_h2e( + dt=DT, + e0=E0, + h1=H1, + e2=E2, + h3=H3, + epsilon=EPSILON, + mu=MU, + dxes=DXES, + ) + assert_close(actual, expected) + + +def test_delta_energy_e2h_matches_direct_dxmul_formula() -> None: + expected = fdtd_energy.dxmul( + E1 * (E3 - E1) / DT, + H2 * (H2 - H0) / DT, + EPSILON, + MU, + DXES, + ) + actual = fdtd_energy.delta_energy_e2h( + dt=DT, + h0=H0, + e1=E1, + h2=H2, + e3=E3, + epsilon=EPSILON, + mu=MU, + dxes=DXES, + ) + assert_close(actual, expected) + + +def test_delta_energy_j_defaults_to_unit_cell_volume() -> None: + expected = (J0 * E1).sum(axis=0) + assert_close(fdtd.delta_energy_j(j0=J0, e1=E1), expected) + + +def test_dxmul_defaults_to_unit_materials_and_spacing() -> None: + expected = E1.sum(axis=0) + H1.sum(axis=0) + assert_close(fdtd_energy.dxmul(E1, H1), expected) diff --git a/meanas/test/test_fdtd_misc.py b/meanas/test/test_fdtd_misc.py new file mode 100644 index 0000000..3688c6c --- /dev/null +++ b/meanas/test/test_fdtd_misc.py @@ -0,0 +1,45 @@ +import numpy +import pytest + +from ..fdtd.misc import gaussian_beam, gaussian_packet, ricker_pulse + + +@pytest.mark.parametrize('one_sided', [False, True]) +def test_gaussian_packet_accepts_array_input(one_sided: bool) -> None: + dt = 0.01 + source, delay = gaussian_packet(1.55, 0.1, dt, one_sided=one_sided) + steps = numpy.array([0, int(numpy.ceil(delay / dt)) + 5]) + envelope, cc, ss = source(steps) + assert isinstance(envelope, numpy.ndarray) + assert isinstance(cc, numpy.ndarray) + assert isinstance(ss, numpy.ndarray) + + assert envelope.shape == (2,) + assert numpy.isfinite(envelope).all() + assert numpy.isfinite(cc).all() + assert numpy.isfinite(ss).all() + if one_sided: + assert envelope[-1] == pytest.approx(1.0) + + +def test_ricker_pulse_returns_finite_values() -> None: + source, delay = ricker_pulse(1.55, 0.01) + envelope, cc, ss = source(numpy.array([0, 1, 2])) + + assert numpy.isfinite(delay) + assert numpy.isfinite(envelope).all() + assert numpy.isfinite(cc).all() + assert numpy.isfinite(ss).all() + + +def test_gaussian_beam_centered_grid_is_finite_and_normalized() -> None: + beam = gaussian_beam( + xyz=[numpy.linspace(-1, 1, 3), numpy.linspace(-1, 1, 3), numpy.linspace(-1, 1, 3)], + center=[0, 0, 0], + waist_radius=1.0, + wl=1.55, + ) + + row = beam[:, :, beam.shape[2] // 2] + assert numpy.isfinite(beam).all() + assert numpy.linalg.norm(row) == pytest.approx(1.0) diff --git a/meanas/test/test_fdtd_phasor.py b/meanas/test/test_fdtd_phasor.py new file mode 100644 index 0000000..9d28ee3 --- /dev/null +++ b/meanas/test/test_fdtd_phasor.py @@ -0,0 +1,403 @@ +import dataclasses +from functools import lru_cache + +import numpy +import pytest +import scipy.sparse.linalg + +from .. import fdfd, fdtd +from ..fdtd.misc import gaussian_packet +from ..fdmath import unvec, vec +from ._test_builders import unit_dxes +from .utils import assert_close, assert_fields_close + + +@dataclasses.dataclass(frozen=True) +class ContinuousWaveCase: + omega: float + dt: float + dxes: tuple[tuple[numpy.ndarray, ...], tuple[numpy.ndarray, ...]] + epsilon: numpy.ndarray + e_ph: numpy.ndarray + h_ph: numpy.ndarray + j_ph: numpy.ndarray + snapshots: tuple['RealFieldSnapshot', ...] + + +@dataclasses.dataclass(frozen=True) +class RealPulseCase: + omega: float + dt: float + j_ph: numpy.ndarray + target_j_ph: numpy.ndarray + + +@dataclasses.dataclass(frozen=True) +class RealFieldSnapshot: + step: int + j_field: numpy.ndarray + e_field: numpy.ndarray + h_field: numpy.ndarray + + +def test_phasor_accumulator_matches_direct_sum_for_multi_frequency_weights() -> None: + omegas = numpy.array([0.25, 0.5]) + dt = 0.2 + sample_0 = numpy.array([[1.0, 2.0], [3.0, 4.0]]) + sample_1 = numpy.array([[0.5, 1.5], [2.5, 3.5]]) + weight_0 = numpy.array([1.0, 2.0]) + weight_1 = 0.75 + accumulator = numpy.zeros((omegas.size, *sample_0.shape), dtype=complex) + + fdtd.accumulate_phasor(accumulator, omegas, dt, sample_0, 0, weight=weight_0) + fdtd.accumulate_phasor(accumulator, omegas, dt, sample_1, 3, offset_steps=0.5, weight=weight_1) + + expected = numpy.zeros((2, *sample_0.shape), dtype=complex) + for idx, omega in enumerate(omegas): + expected[idx] += dt * weight_0[idx] * numpy.exp(-1j * omega * 0.0) * sample_0 + expected[idx] += dt * weight_1 * numpy.exp(-1j * omega * ((3 + 0.5) * dt)) * sample_1 + + assert_close(accumulator, expected) + + +def test_phasor_accumulator_convenience_methods_apply_yee_offsets() -> None: + omega = 1.25 + dt = 0.1 + sample = numpy.arange(6, dtype=float).reshape(2, 3) + e_acc = numpy.zeros((1, *sample.shape), dtype=complex) + h_acc = numpy.zeros((1, *sample.shape), dtype=complex) + j_acc = numpy.zeros((1, *sample.shape), dtype=complex) + + fdtd.accumulate_phasor_e(e_acc, omega, dt, sample, 4) + fdtd.accumulate_phasor_h(h_acc, omega, dt, sample, 4) + fdtd.accumulate_phasor_j(j_acc, omega, dt, sample, 4) + + expected_e = dt * numpy.exp(-1j * omega * (4 * dt)) * sample + expected_h = dt * numpy.exp(-1j * omega * ((4.5) * dt)) * sample + + assert_close(e_acc[0], expected_e) + assert_close(h_acc[0], expected_h) + assert_close(j_acc[0], expected_h) + + +def test_phasor_accumulator_matches_delayed_weighted_example_pattern() -> None: + omega = 0.75 + dt = 0.2 + delay = 0.6 + phasor_norm = 0.5 + steps = numpy.arange(5) + samples = numpy.arange(20, dtype=float).reshape(5, 2, 2) + 1.0 + accumulator = numpy.zeros((1, 2, 2), dtype=complex) + + for step, sample in zip(steps, samples, strict=True): + fdtd.accumulate_phasor( + accumulator, + omega, + dt, + sample, + int(step), + offset_steps=0.5 - delay / dt, + weight=phasor_norm / dt, + ) + + expected = numpy.zeros((2, 2), dtype=complex) + for step, sample in zip(steps, samples, strict=True): + time = (step + 0.5 - delay / dt) * dt + expected += dt * (phasor_norm / dt) * numpy.exp(-1j * omega * time) * sample + + assert_close(accumulator[0], expected) + + +def test_temporal_phasor_matches_direct_sum_for_offset_waveform() -> None: + omegas = numpy.array([0.75, 1.25]) + dt = 0.2 + samples = numpy.array([1.0 + 0.5j, 0.5 - 0.25j, -0.75 + 0.1j]) + + result = fdtd.temporal_phasor(samples, omegas, dt, start_step=2, offset_steps=0.5) + + expected = numpy.zeros(omegas.shape, dtype=complex) + for idx, omega in enumerate(omegas): + for step, sample in enumerate(samples, start=2): + expected[idx] += dt * numpy.exp(-1j * omega * ((step + 0.5) * dt)) * sample + + assert_close(result, expected) + + +def test_temporal_phasor_scale_normalizes_waveform_to_target_response() -> None: + omega = 0.75 + dt = 0.2 + delay = 0.6 + samples = numpy.arange(5, dtype=float) + 1.0 + scale = fdtd.temporal_phasor_scale(samples, omega, dt, offset_steps=0.5 - delay / dt, target=0.5) + normalized = fdtd.temporal_phasor(scale[0] * samples, omega, dt, offset_steps=0.5 - delay / dt) + + assert_close(normalized[0], 0.5) + + +def test_real_injection_scale_matches_positive_frequency_normalization() -> None: + omega = 0.75 + dt = 0.2 + samples = numpy.array([1.0 + 0.5j, 0.5 - 0.25j, -0.75 + 0.1j]) + scale = fdtd.real_injection_scale(samples, omega, dt, offset_steps=0.5, target=0.5) + normalized = 0.5 * scale[0] * fdtd.temporal_phasor(samples, omega, dt, offset_steps=0.5)[0] + + assert_close(normalized, 0.5) + + +def test_reconstruct_real_matches_direct_formula_and_yee_wrappers() -> None: + omegas = numpy.array([0.75, 1.25]) + dt = 0.2 + phasors = numpy.array( + [ + [[1.0 + 2.0j, -0.5 + 0.25j]], + [[-1.5 + 0.5j, 0.75 - 0.125j]], + ], + dtype=complex, + ) + + reconstructed = fdtd.reconstruct_real(phasors, omegas, dt, 3, offset_steps=0.5) + expected = numpy.stack( + [ + numpy.real(phasors[idx] * numpy.exp(1j * omega * ((3.5) * dt))) + for idx, omega in enumerate(omegas) + ], + ) + + assert_close(reconstructed, expected) + assert_close(fdtd.reconstruct_real_e(phasors[:1], omegas[0], dt, 3)[0], numpy.real(phasors[0] * numpy.exp(1j * omegas[0] * (3 * dt)))) + assert_close(fdtd.reconstruct_real_h(phasors[:1], omegas[0], dt, 3)[0], numpy.real(phasors[0] * numpy.exp(1j * omegas[0] * ((3.5) * dt)))) + assert_close(fdtd.reconstruct_real_j(phasors[:1], omegas[0], dt, 3)[0], numpy.real(phasors[0] * numpy.exp(1j * omegas[0] * ((3.5) * dt)))) + + +def test_reconstruct_real_accepts_scalar_frequency_without_leading_axis() -> None: + omega = 0.75 + dt = 0.2 + phasor = numpy.array([[1.0 + 0.5j, -0.25 + 0.75j]]) + + reconstructed = fdtd.reconstruct_real(phasor, omega, dt, 3, offset_steps=0.5) + expected = numpy.real(phasor * numpy.exp(1j * omega * ((3.5) * dt))) + + assert_close(reconstructed, expected) + assert_close(fdtd.reconstruct_real_e(phasor, omega, dt, 3), numpy.real(phasor * numpy.exp(1j * omega * (3 * dt)))) + assert_close(fdtd.reconstruct_real_h(phasor, omega, dt, 3), expected) + assert_close(fdtd.reconstruct_real_j(phasor, omega, dt, 3), expected) + + +def test_phasor_accumulator_validation_reset_and_temporal_validation() -> None: + with pytest.raises(ValueError, match='dt must be positive'): + fdtd.accumulate_phasor(numpy.zeros((1, 2, 2), dtype=complex), [1.0], 0.0, numpy.ones((2, 2)), 0) + + with pytest.raises(ValueError, match='omegas must be a scalar or non-empty 1D sequence'): + fdtd.accumulate_phasor(numpy.zeros((1, 2, 2), dtype=complex), numpy.ones((2, 2)), 0.2, numpy.ones((2, 2)), 0) + + accumulator = numpy.zeros((2, 2, 2), dtype=complex) + + with pytest.raises(ValueError, match='accumulator must have shape'): + fdtd.accumulate_phasor(accumulator, [1.0], 0.2, numpy.ones((2, 2)), 0) + + with pytest.raises(ValueError, match='weight must be scalar'): + fdtd.accumulate_phasor(accumulator, [1.0, 2.0], 0.2, numpy.ones((2, 2)), 0, weight=numpy.ones((2, 2))) + + fdtd.accumulate_phasor(accumulator, [1.0, 2.0], 0.2, numpy.ones((2, 2)), 0) + accumulator.fill(0) + assert_close(accumulator, 0.0) + + with pytest.raises(ValueError, match='samples must be a non-empty 1D sequence'): + fdtd.temporal_phasor(numpy.ones((2, 2)), [1.0], 0.2) + + with pytest.raises(ValueError, match='cannot normalize a waveform with zero temporal phasor response'): + fdtd.temporal_phasor_scale(numpy.zeros(4), [1.0], 0.2) + + with pytest.raises(ValueError, match='cannot normalize a waveform with zero temporal phasor response'): + fdtd.real_injection_scale(numpy.zeros(4), [1.0], 0.2) + + with pytest.raises(ValueError, match='dt must be positive'): + fdtd.reconstruct_real(numpy.ones((1, 2, 2), dtype=complex), [1.0], 0.0, 0) + + with pytest.raises(ValueError, match='omegas must be a scalar or non-empty 1D sequence'): + fdtd.reconstruct_real(numpy.ones((1, 2, 2), dtype=complex), numpy.ones((2, 2)), 0.2, 0) + + with pytest.raises(ValueError, match='phasors must have shape'): + fdtd.reconstruct_real(numpy.ones((3, 2, 2), dtype=complex), [1.0, 2.0], 0.2, 0) + + +@lru_cache(maxsize=1) +def _continuous_wave_case() -> ContinuousWaveCase: + spatial_shape = (5, 1, 5) + full_shape = (3, *spatial_shape) + dt = 0.25 + period_steps = 64 + warmup_periods = 8 + accumulation_periods = 8 + omega = 2 * numpy.pi / (period_steps * dt) + total_steps = period_steps * (warmup_periods + accumulation_periods) + warmup_steps = period_steps * warmup_periods + accumulation_steps = period_steps * accumulation_periods + source_amplitude = 1.0 + source_index = (1, spatial_shape[0] // 2, spatial_shape[1] // 2, spatial_shape[2] // 2) + + dxes = unit_dxes(spatial_shape) + epsilon = numpy.ones(full_shape, dtype=float) + e_field = numpy.zeros(full_shape, dtype=float) + h_field = numpy.zeros(full_shape, dtype=float) + update_e = fdtd.maxwell_e(dt=dt, dxes=dxes) + update_h = fdtd.maxwell_h(dt=dt, dxes=dxes) + + e_accumulator = numpy.zeros((1, *full_shape), dtype=complex) + h_accumulator = numpy.zeros((1, *full_shape), dtype=complex) + j_accumulator = numpy.zeros((1, *full_shape), dtype=complex) + snapshot_offsets = (0, period_steps // 4, period_steps // 2, 3 * period_steps // 4) + snapshot_steps = { + warmup_steps + accumulation_steps - period_steps + offset + for offset in snapshot_offsets + } + snapshots: list[RealFieldSnapshot] = [] + + for step in range(total_steps): + update_e(e_field, h_field, epsilon) + + j_step = numpy.zeros_like(e_field) + current_density = source_amplitude * numpy.cos(omega * (step + 0.5) * dt) + j_step[source_index] = current_density + e_field -= dt * j_step / epsilon + + if step >= warmup_steps: + fdtd.accumulate_phasor_j(j_accumulator, omega, dt, j_step, step) + fdtd.accumulate_phasor_e(e_accumulator, omega, dt, e_field, step + 1) + + update_h(e_field, h_field) + + if step in snapshot_steps: + snapshots.append( + RealFieldSnapshot( + step=step, + j_field=j_step.copy(), + e_field=e_field.copy(), + h_field=h_field.copy(), + ), + ) + + if step >= warmup_steps: + fdtd.accumulate_phasor_h(h_accumulator, omega, dt, h_field, step + 1) + + return ContinuousWaveCase( + omega=omega, + dt=dt, + dxes=dxes, + epsilon=epsilon, + e_ph=e_accumulator[0], + h_ph=h_accumulator[0], + j_ph=j_accumulator[0], + snapshots=tuple(snapshots), + ) + + +def test_continuous_wave_current_phasor_matches_analytic_discrete_sum() -> None: + case = _continuous_wave_case() + + accumulation_indices = numpy.arange(64 * 8, 64 * 16) + times = (accumulation_indices + 0.5) * case.dt + expected = numpy.zeros_like(case.j_ph) + expected[1, 2, 0, 2] = case.dt * numpy.sum( + numpy.exp(-1j * case.omega * times) * numpy.cos(case.omega * times), + ) + + assert_fields_close(case.j_ph, expected, atol=1e-12, rtol=1e-12) + + +def test_continuous_wave_electric_phasor_matches_fdfd_solution() -> None: + case = _continuous_wave_case() + operator = fdfd.operators.e_full(case.omega, case.dxes, vec(case.epsilon)).tocsr() + rhs = -1j * case.omega * vec(case.j_ph) + e_fdfd = unvec(scipy.sparse.linalg.spsolve(operator, rhs), case.epsilon.shape[1:]) + + rel_err = numpy.linalg.norm(vec(case.e_ph - e_fdfd)) / numpy.linalg.norm(vec(e_fdfd)) + assert rel_err < 5e-2 + + +def test_continuous_wave_magnetic_phasor_matches_fdfd_conversion() -> None: + case = _continuous_wave_case() + operator = fdfd.operators.e_full(case.omega, case.dxes, vec(case.epsilon)).tocsr() + rhs = -1j * case.omega * vec(case.j_ph) + e_fdfd = unvec(scipy.sparse.linalg.spsolve(operator, rhs), case.epsilon.shape[1:]) + h_fdfd = fdfd.functional.e2h(case.omega, case.dxes)(e_fdfd) + + rel_err = numpy.linalg.norm(vec(case.h_ph - h_fdfd)) / numpy.linalg.norm(vec(h_fdfd)) + assert rel_err < 5e-2 + + +def test_continuous_wave_extracted_electric_phasor_has_small_fdfd_residual() -> None: + case = _continuous_wave_case() + operator = fdfd.operators.e_full(case.omega, case.dxes, vec(case.epsilon)).tocsr() + rhs = -1j * case.omega * vec(case.j_ph) + residual = operator @ vec(case.e_ph) - rhs + rel_residual = numpy.linalg.norm(residual) / numpy.linalg.norm(rhs) + + assert rel_residual < 5e-2 + + +def test_continuous_wave_real_source_matches_reconstructed_source() -> None: + case = _continuous_wave_case() + accumulation_indices = numpy.arange(64 * 8, 64 * 16) + accumulation_times = (accumulation_indices + 0.5) * case.dt + accumulation_response = case.dt * numpy.sum( + numpy.exp(-1j * case.omega * accumulation_times) * numpy.cos(case.omega * accumulation_times), + ) + normalized_j_ph = case.j_ph / accumulation_response + + for snapshot in case.snapshots: + reconstructed_j = fdtd.reconstruct_real_j(normalized_j_ph, case.omega, case.dt, snapshot.step) + assert_fields_close(snapshot.j_field, reconstructed_j, atol=1e-12, rtol=1e-12) + + +@lru_cache(maxsize=1) +def _real_pulse_case() -> RealPulseCase: + spatial_shape = (5, 1, 5) + full_shape = (3, *spatial_shape) + dt = 0.25 + period_steps = 64 + total_periods = 40 + omega = 2 * numpy.pi / (period_steps * dt) + wavelength = 2 * numpy.pi / omega + total_steps = period_steps * total_periods + source_index = (1, spatial_shape[0] // 2, spatial_shape[1] // 2, spatial_shape[2] // 2) + + dxes = unit_dxes(spatial_shape) + epsilon = numpy.ones(full_shape, dtype=float) + e_field = numpy.zeros(full_shape, dtype=float) + h_field = numpy.zeros(full_shape, dtype=float) + update_e = fdtd.maxwell_e(dt=dt, dxes=dxes) + update_h = fdtd.maxwell_h(dt=dt, dxes=dxes) + + source_phasor, _delay = gaussian_packet(wl=wavelength, dwl=1.0, dt=dt, turn_on=1e-5) + aa, cc, ss = source_phasor(numpy.arange(total_steps) + 0.5) + waveform = numpy.asarray(aa * (cc + 1j * ss), dtype=complex) + scale = fdtd.real_injection_scale(waveform, omega, dt, offset_steps=0.5)[0] + + j_accumulator = numpy.zeros((1, *full_shape), dtype=complex) + target_j_ph = numpy.zeros(full_shape, dtype=complex) + target_j_ph[source_index] = 1.0 + + for step in range(total_steps): + update_e(e_field, h_field, epsilon) + + j_step = numpy.zeros_like(e_field) + j_step[source_index] = numpy.real(scale * waveform[step]) + e_field -= dt * j_step / epsilon + + fdtd.accumulate_phasor_j(j_accumulator, omega, dt, j_step, step) + + update_h(e_field, h_field) + + return RealPulseCase( + omega=omega, + dt=dt, + j_ph=j_accumulator[0], + target_j_ph=target_j_ph, + ) + + +def test_real_pulse_current_phasor_matches_target_source() -> None: + case = _real_pulse_case() + rel_err = numpy.linalg.norm(vec(case.j_ph - case.target_j_ph)) / numpy.linalg.norm(vec(case.target_j_ph)) + assert rel_err < 0.005 diff --git a/meanas/test/test_fdtd_pml.py b/meanas/test/test_fdtd_pml.py new file mode 100644 index 0000000..319260f --- /dev/null +++ b/meanas/test/test_fdtd_pml.py @@ -0,0 +1,249 @@ +from typing import Any + +import numpy +import pytest + +from .. import fdtd +from ..fdtd.base import maxwell_e, maxwell_h +from ..fdtd.pml import cpml_params, updates_with_cpml +from .utils import assert_close + + +@pytest.mark.parametrize( + ('axis', 'polarity', 'thickness', 'epsilon_eff'), + [(3, 1, 4, 1.0), (0, 0, 4, 1.0), (0, 1, 2, 1.0), (0, 1, 4, 0.0)], +) +def test_cpml_params_reject_invalid_arguments(axis: int, polarity: int, thickness: int, epsilon_eff: float) -> None: + with pytest.raises(ValueError, match='Invalid axis|Invalid polarity|wise to have a pml|epsilon_eff must be positive'): + cpml_params(axis=axis, polarity=polarity, dt=0.1, thickness=thickness, epsilon_eff=epsilon_eff) + + +def test_cpml_params_shapes_and_region() -> None: + params = cpml_params(axis=1, polarity=1, dt=0.1, thickness=3) + p0e, p1e, p2e = params['param_e'] + p0h, p1h, p2h = params['param_h'] + + assert p0e.shape == (1, 3, 1) + assert p1e.shape == (1, 3, 1) + assert p2e.shape == (1, 3, 1) + assert p0h.shape == (1, 3, 1) + assert p1h.shape == (1, 3, 1) + assert p2h.shape == (1, 3, 1) + assert params['region'][1] == slice(-3, None) + + +def test_updates_with_cpml_keeps_zero_fields_zero() -> None: + shape = (3, 4, 4, 4) + epsilon = numpy.ones(shape, dtype=float) + e = numpy.zeros(shape, dtype=float) + h = numpy.zeros(shape, dtype=float) + dxes = [[numpy.ones(4), numpy.ones(4), numpy.ones(4)] for _ in range(2)] + params: list[list[dict[str, Any] | None]] = [[None, None] for _ in range(3)] + params[0][0] = cpml_params(axis=0, polarity=-1, dt=0.1, thickness=3) + + update_e, update_h = updates_with_cpml(params, dt=0.1, dxes=dxes, epsilon=epsilon) + update_e(e, h, epsilon) + update_h(e, h) + + assert not e.any() + assert not h.any() + + +def _unit_dxes(shape: tuple[int, int, int, int]) -> list[list[numpy.ndarray]]: + return [[numpy.ones(n, dtype=float) for n in shape[1:]] for _ in range(2)] + + +def _real_field(shape: tuple[int, int, int, int], start: float) -> numpy.ndarray: + total = numpy.prod(shape, dtype=int) + return numpy.arange(start, start + total, dtype=float).reshape(shape) / total + + +def _complex_field(shape: tuple[int, int, int, int], start: float) -> numpy.ndarray: + real = _real_field(shape, start) + imag = _real_field(shape, start + real.size) + return real + 1j * imag + + +def test_updates_with_cpml_matches_base_updates_when_all_faces_disabled() -> None: + shape = (3, 4, 5, 6) + epsilon = _real_field(shape, 1.0) + 2.0 + mu = _real_field(shape, 4.0) + 1.5 + e = _real_field(shape, 10.0) + h = _real_field(shape, 100.0) + dxes = _unit_dxes(shape) + params: list[list[dict[str, Any] | None]] = [[None, None] for _ in range(3)] + + update_e_cpml, update_h_cpml = updates_with_cpml(params, dt=0.1, dxes=dxes, epsilon=epsilon) + update_e_base = maxwell_e(dt=0.1, dxes=dxes) + update_h_base = maxwell_h(dt=0.1, dxes=dxes) + + e_cpml = e.copy() + h_cpml = h.copy() + e_base = e.copy() + h_base = h.copy() + + update_e_cpml(e_cpml, h_cpml, epsilon) + update_e_base(e_base, h_base, epsilon) + update_h_cpml(e_cpml, h_cpml, mu) + update_h_base(e_base, h_base, mu) + + assert_close(e_cpml, e_base) + assert_close(h_cpml, h_base) + + +def test_updates_with_cpml_matches_base_updates_with_complex_dtype_when_all_faces_disabled() -> None: + shape = (3, 4, 5, 6) + epsilon = _real_field(shape, 1.0) + 2.0 + mu = _real_field(shape, 4.0) + 1.5 + e = _complex_field(shape, 10.0) + h = _complex_field(shape, 100.0) + dxes = _unit_dxes(shape) + params: list[list[dict[str, Any] | None]] = [[None, None] for _ in range(3)] + + update_e_cpml, update_h_cpml = updates_with_cpml(params, dt=0.1, dxes=dxes, epsilon=epsilon, dtype=complex) + update_e_base = maxwell_e(dt=0.1, dxes=dxes) + update_h_base = maxwell_h(dt=0.1, dxes=dxes) + + e_cpml = e.copy() + h_cpml = h.copy() + e_base = e.copy() + h_base = h.copy() + + update_e_cpml(e_cpml, h_cpml, epsilon) + update_e_base(e_base, h_base, epsilon) + update_h_cpml(e_cpml, h_cpml, mu) + update_h_base(e_base, h_base, mu) + + assert_close(e_cpml, e_base) + assert_close(h_cpml, h_base) + + +def test_updates_with_cpml_only_changes_the_configured_face_region() -> None: + shape = (3, 6, 6, 6) + epsilon = numpy.ones(shape, dtype=float) + mu = numpy.ones(shape, dtype=float) + e = _real_field(shape, 1.0) + h = _real_field(shape, 100.0) + dxes = _unit_dxes(shape) + thickness = 3 + + params: list[list[dict[str, Any] | None]] = [[None, None] for _ in range(3)] + params[0][0] = cpml_params(axis=0, polarity=-1, dt=0.1, thickness=thickness) + + update_e_cpml, update_h_cpml = updates_with_cpml(params, dt=0.1, dxes=dxes, epsilon=epsilon) + update_e_base = maxwell_e(dt=0.1, dxes=dxes) + update_h_base = maxwell_h(dt=0.1, dxes=dxes) + + e_cpml = e.copy() + h_cpml = h.copy() + e_base = e.copy() + h_base = h.copy() + + update_e_cpml(e_cpml, h_cpml, epsilon) + update_e_base(e_base, h_base, epsilon) + update_h_cpml(e_cpml, h_cpml, mu) + update_h_base(e_base, h_base, mu) + + e_untouched = slice(thickness, None) + h_untouched = slice(thickness, -1) + assert_close(e_cpml[:, e_untouched, :, :], e_base[:, e_untouched, :, :]) + assert_close(h_cpml[:, h_untouched, :, :], h_base[:, h_untouched, :, :]) + + changed_e = numpy.any(numpy.abs(e_cpml[:, :thickness, :, :] - e_base[:, :thickness, :, :]) > 1e-12) + changed_h = numpy.any(numpy.abs(h_cpml[:, :thickness, :, :] - h_base[:, :thickness, :, :]) > 1e-12) + assert changed_e + assert changed_h + + +def test_cpml_plane_wave_phasor_decays_monotonically_through_outgoing_pml() -> None: + dt = 0.4 + period_steps = 24 + omega = 2 * numpy.pi / (period_steps * dt) + shape = (3, 80, 1, 1) + thickness = 8 + source_x = 16 + warmup_periods = 10 + accumulation_periods = 6 + total_steps = period_steps * (warmup_periods + accumulation_periods) + + epsilon = numpy.ones(shape, dtype=float) + dxes = _unit_dxes(shape) + params: list[list[dict[str, Any] | None]] = [[None, None] for _ in range(3)] + for polarity_index, polarity in enumerate((-1, 1)): + params[0][polarity_index] = cpml_params(axis=0, polarity=polarity, dt=dt, thickness=thickness) + + update_e, update_h = updates_with_cpml(params, dt=dt, dxes=dxes, epsilon=epsilon) + + e = numpy.zeros(shape, dtype=float) + h = numpy.zeros(shape, dtype=float) + e_accumulator = numpy.zeros((1, *shape), dtype=complex) + + for step in range(total_steps): + update_e(e, h, epsilon) + + source = numpy.cos(omega * (step + 0.5) * dt) + e[1, source_x, 0, 0] -= dt * source + + if step >= period_steps * warmup_periods: + fdtd.accumulate_phasor_e(e_accumulator, omega, dt, e, step + 1) + + update_h(e, h) + + profile = numpy.abs(e_accumulator[0, 1, :, 0, 0]) + right_pml = profile[-thickness:] + interior = profile[-thickness - 6:-thickness] + interior_level = interior.mean() + + assert interior_level > 1.0 + assert right_pml[-1] < interior_level / 100 + assert profile[0] < interior_level / 100 + assert numpy.all(numpy.diff(right_pml) <= interior_level * 1e-3) + + +@pytest.mark.complete +def test_cpml_point_source_total_energy_reaches_late_time_plateau() -> None: + dt = 0.3 + period_steps = 24 + omega = 2 * numpy.pi / (period_steps * dt) + cycles = 1000 + sample_every_cycles = 50 + sample_stride = period_steps * sample_every_cycles + shape = (3, 9, 9, 9) + thickness = 3 + center = shape[1] // 2 + + epsilon = numpy.ones(shape, dtype=float) + dxes = _unit_dxes(shape) + params: list[list[dict[str, Any] | None]] = [[None, None] for _ in range(3)] + for axis in range(3): + for polarity_index, polarity in enumerate((-1, 1)): + params[axis][polarity_index] = cpml_params(axis=axis, polarity=polarity, dt=dt, thickness=thickness) + + update_e, update_h = updates_with_cpml(params, dt=dt, dxes=dxes, epsilon=epsilon) + + e = numpy.zeros(shape, dtype=float) + h = numpy.zeros(shape, dtype=float) + sampled_energies: list[float] = [] + + for step in range(period_steps * cycles): + h_before = h.copy() + update_e(e, h, epsilon) + + source = numpy.cos(omega * (step + 0.5) * dt) + e[1, center, center, center] -= dt * source + + update_h(e, h) + + if (step + 1) % sample_stride == 0: + total_energy = fdtd.energy_estep(h0=h_before, e1=e, h2=h, epsilon=epsilon, dxes=dxes).sum().real + sampled_energies.append(total_energy) + + energies = numpy.asarray(sampled_energies) + late_window = energies[-5:] + previous_window = energies[-10:-5] + late_mean = late_window.mean() + + assert energies.size == cycles // sample_every_cycles + assert late_mean > 0.1 + assert (late_window.max() - late_window.min()) / late_mean < 1e-4 + assert abs(late_mean - previous_window.mean()) / late_mean < 1e-4 diff --git a/meanas/test/test_import_fallbacks.py b/meanas/test/test_import_fallbacks.py new file mode 100644 index 0000000..e332d1b --- /dev/null +++ b/meanas/test/test_import_fallbacks.py @@ -0,0 +1,60 @@ +import builtins +import importlib +import pathlib +from types import ModuleType +from typing import Any + +import pytest +import meanas +from ..fdfd import bloch + + +def _reload(module: ModuleType) -> ModuleType: + return importlib.reload(module) + + +def _restore_reloaded(monkeypatch: pytest.MonkeyPatch, module: ModuleType) -> ModuleType: + monkeypatch.undo() + return _reload(module) + + +def test_meanas_import_survives_readme_open_failure(monkeypatch: pytest.MonkeyPatch) -> None: + expected_version = meanas.__version__ + original_open = pathlib.Path.open + + def failing_open(self: pathlib.Path, *args: Any, **kwargs: Any) -> Any: + if self.name == 'README.md': + raise FileNotFoundError('forced README failure') + return original_open(self, *args, **kwargs) + + monkeypatch.setattr(pathlib.Path, 'open', failing_open) + reloaded = _reload(meanas) + + assert reloaded.__version__ == expected_version + assert reloaded.__author__ == 'Jan Petykiewicz' + assert reloaded.__doc__ is not None + + _restore_reloaded(monkeypatch, meanas) + + +def test_bloch_reloads_with_numpy_fft_when_pyfftw_is_unavailable(monkeypatch: pytest.MonkeyPatch) -> None: + original_import = builtins.__import__ + + def fake_import( + name: str, + globals: dict[str, Any] | None = None, + locals: dict[str, Any] | None = None, + fromlist: tuple[str, ...] = (), + level: int = 0, + ) -> Any: + if name.startswith('pyfftw'): + raise ImportError('forced pyfftw failure') + return original_import(name, globals, locals, fromlist, level) + + monkeypatch.setattr(builtins, '__import__', fake_import) + reloaded = _reload(bloch) + + assert reloaded.fftn.__module__ == 'numpy.fft' + assert reloaded.ifftn.__module__ == 'numpy.fft' + + _restore_reloaded(monkeypatch, bloch) diff --git a/meanas/test/test_waveguide_2d_numerics.py b/meanas/test/test_waveguide_2d_numerics.py new file mode 100644 index 0000000..0005584 --- /dev/null +++ b/meanas/test/test_waveguide_2d_numerics.py @@ -0,0 +1,284 @@ +import numpy +from numpy.linalg import norm +from numpy.testing import assert_allclose + +from ..fdmath import vec +from ..fdfd import waveguide_2d + + +OMEGA = 1 / 1500 +GRID_SHAPE = (5, 5) +DXES_2D = [[numpy.ones(GRID_SHAPE[0]), numpy.ones(GRID_SHAPE[1])] for _ in range(2)] +DXES_2D_NONUNIFORM = [[ + numpy.array([1.0, 1.2, 0.9, 1.1, 1.3]), + numpy.array([0.8, 1.1, 1.0, 1.2, 0.9]), +] for _ in range(2)] + + +def build_asymmetric_epsilon() -> numpy.ndarray: + epsilon = numpy.ones((3, *GRID_SHAPE), dtype=float) + epsilon[:, 2, 1] = 2.0 + return vec(epsilon) + + +def build_mu_profile() -> numpy.ndarray: + return numpy.linspace(1.5, 2.2, 3 * GRID_SHAPE[0] * GRID_SHAPE[1]) + + +def test_waveguide_2d_solved_modes_are_ordered_and_low_residual() -> None: + epsilon = build_asymmetric_epsilon() + operator_e = waveguide_2d.operator_e(OMEGA, DXES_2D, epsilon) + + e_xys, wavenumbers = waveguide_2d.solve_modes( + [0, 1], + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + ) + + assert numpy.all(numpy.diff(numpy.real(wavenumbers)) <= 0) + + for e_xy, wavenumber in zip(e_xys, wavenumbers, strict=True): + residual = norm(operator_e @ e_xy - (wavenumber ** 2) * e_xy) / norm(e_xy) + assert residual < 1e-6 + + +def test_waveguide_2d_normalized_fields_are_consistent() -> None: + epsilon = build_asymmetric_epsilon() + operator_h = waveguide_2d.operator_h(OMEGA, DXES_2D, epsilon) + + e_xy, wavenumber = waveguide_2d.solve_mode( + 0, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + ) + e_field, h_field = waveguide_2d.normalized_fields_e( + e_xy, + wavenumber=wavenumber, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + ) + h_xy = numpy.concatenate(numpy.split(h_field, 3)[:2]) + + overlap = waveguide_2d.inner_product(e_field, h_field, DXES_2D, conj_h=True) + h_residual = norm(operator_h @ h_xy - (wavenumber ** 2) * h_xy) / norm(h_xy) + + assert abs(overlap.real - 1.0) < 1e-10 + assert abs(overlap.imag) < 1e-10 + assert waveguide_2d.e_err(e_field, wavenumber, OMEGA, DXES_2D, epsilon) < 1e-6 + assert waveguide_2d.h_err(h_field, wavenumber, OMEGA, DXES_2D, epsilon) < 1e-6 + assert h_residual < 1e-6 + + +def test_waveguide_2d_sensitivity_matches_finite_difference() -> None: + epsilon = build_asymmetric_epsilon() + e_xy, wavenumber = waveguide_2d.solve_mode( + 0, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + ) + e_field, h_field = waveguide_2d.normalized_fields_e( + e_xy, + wavenumber=wavenumber, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + ) + sensitivity = waveguide_2d.sensitivity( + e_field, + h_field, + wavenumber=wavenumber, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + ) + + target_index = int(numpy.argmax(numpy.abs(sensitivity))) + delta = 1e-4 + epsilon_perturbed = epsilon.copy() + epsilon_perturbed[target_index] += delta + + _, perturbed_wavenumber = waveguide_2d.solve_mode( + 0, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon_perturbed, + ) + finite_difference = (perturbed_wavenumber - wavenumber) / delta + + assert numpy.isfinite(sensitivity[target_index]) + assert numpy.isfinite(finite_difference) + assert abs(sensitivity[target_index].imag) < 1e-10 + assert abs(finite_difference.imag) < 1e-10 + + ratio = abs(sensitivity[target_index] / finite_difference) + assert sensitivity[target_index].real > 0 + assert finite_difference.real > 0 + assert 0.4 < ratio < 1.8 + + +def test_waveguide_2d_normalized_fields_h_are_finite_and_unit_normalized_with_mu() -> None: + epsilon = build_asymmetric_epsilon() + mu = build_mu_profile() + + e_xy, wavenumber = waveguide_2d.solve_mode( + 0, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + ) + _e_ref, h_ref = waveguide_2d.normalized_fields_e( + e_xy, + wavenumber=wavenumber, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + mu=mu, + ) + h_xy = numpy.concatenate(numpy.split(h_ref, 3)[:2]) + + e_field, h_field = waveguide_2d.normalized_fields_h( + h_xy, + wavenumber=wavenumber, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + mu=mu, + ) + overlap = waveguide_2d.inner_product(e_field, h_field, DXES_2D, conj_h=True) + + assert e_field.shape == (3 * GRID_SHAPE[0] * GRID_SHAPE[1],) + assert h_field.shape == (3 * GRID_SHAPE[0] * GRID_SHAPE[1],) + assert numpy.isfinite(e_field).all() + assert numpy.isfinite(h_field).all() + assert abs(overlap.real - 1.0) < 1e-10 + assert abs(overlap.imag) < 1e-10 + + +def test_waveguide_2d_helper_operators_with_mu_return_finite_outputs() -> None: + epsilon = build_asymmetric_epsilon() + mu = build_mu_profile() + + e_xy, wavenumber = waveguide_2d.solve_mode( + 0, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + ) + _e_ref, h_ref = waveguide_2d.normalized_fields_e( + e_xy, + wavenumber=wavenumber, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + mu=mu, + ) + h_xy = numpy.concatenate(numpy.split(h_ref, 3)[:2]) + n_pts = GRID_SHAPE[0] * GRID_SHAPE[1] + + operators = [ + ('exy2h', waveguide_2d.exy2h(wavenumber, OMEGA, DXES_2D, epsilon, mu), e_xy), + ('hxy2e', waveguide_2d.hxy2e(wavenumber, OMEGA, DXES_2D, epsilon, mu), h_xy), + ('hxy2h', waveguide_2d.hxy2h(wavenumber, DXES_2D, mu), h_xy), + ] + + for _name, operator, vector in operators: + result = operator @ vector + assert operator.shape == (3 * n_pts, 2 * n_pts) + assert numpy.isfinite(operator.data).all() + assert result.shape == (3 * n_pts,) + assert numpy.isfinite(result).all() + + +def test_waveguide_2d_error_helpers_with_mu_return_finite_values() -> None: + epsilon = build_asymmetric_epsilon() + mu = build_mu_profile() + + e_xy, wavenumber = waveguide_2d.solve_mode( + 0, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + ) + e_field, h_field = waveguide_2d.normalized_fields_e( + e_xy, + wavenumber=wavenumber, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + mu=mu, + ) + + h_error = waveguide_2d.h_err(h_field, wavenumber, OMEGA, DXES_2D, epsilon, mu) + e_error = waveguide_2d.e_err(e_field, wavenumber, OMEGA, DXES_2D, epsilon, mu) + + assert numpy.isfinite(h_error) + assert numpy.isfinite(e_error) + assert 0 < h_error < 0.1 + assert 0 < e_error < 2.0 + + +def test_waveguide_2d_inner_product_phase_and_conjugation_branches() -> None: + epsilon = build_asymmetric_epsilon() + mu = build_mu_profile() + + e_xy, wavenumber = waveguide_2d.solve_mode( + 0, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + ) + e_field, h_field = waveguide_2d.normalized_fields_e( + e_xy, + wavenumber=wavenumber, + omega=OMEGA, + dxes=DXES_2D, + epsilon=epsilon, + mu=mu, + ) + + overlap_no_conj = waveguide_2d.inner_product(e_field, h_field, DXES_2D, conj_h=False) + overlap_conj = waveguide_2d.inner_product(e_field, h_field, DXES_2D, conj_h=True) + overlap_phase = waveguide_2d.inner_product(e_field, h_field, DXES_2D, conj_h=True, prop_phase=0.3) + + assert numpy.isfinite(overlap_no_conj) + assert numpy.isfinite(overlap_phase) + assert abs(overlap_no_conj.real - 1.0) < 1e-10 + assert abs(overlap_no_conj.imag) < 1e-10 + assert_allclose(overlap_phase / overlap_conj, numpy.exp(-0.15j), atol=1e-12, rtol=1e-12) + + +def test_waveguide_2d_inner_product_trapezoid_branch_on_nonuniform_grid() -> None: + epsilon = build_asymmetric_epsilon() + + e_xy, wavenumber = waveguide_2d.solve_mode( + 0, + omega=OMEGA, + dxes=DXES_2D_NONUNIFORM, + epsilon=epsilon, + ) + e_field, h_field = waveguide_2d.normalized_fields_e( + e_xy, + wavenumber=wavenumber, + omega=OMEGA, + dxes=DXES_2D_NONUNIFORM, + epsilon=epsilon, + ) + + overlap_rect = waveguide_2d.inner_product(e_field, h_field, DXES_2D_NONUNIFORM, conj_h=True) + overlap_trap = waveguide_2d.inner_product( + e_field, + h_field, + DXES_2D_NONUNIFORM, + conj_h=True, + trapezoid=True, + ) + + assert numpy.isfinite(overlap_rect) + assert numpy.isfinite(overlap_trap) + assert abs(overlap_rect.imag) < 1e-10 + assert abs(overlap_trap.imag) < 1e-10 + assert abs(overlap_rect - overlap_trap) > 0.1 diff --git a/meanas/test/test_waveguide_fdtd_fdfd.py b/meanas/test/test_waveguide_fdtd_fdfd.py new file mode 100644 index 0000000..0488197 --- /dev/null +++ b/meanas/test/test_waveguide_fdtd_fdfd.py @@ -0,0 +1,803 @@ +import dataclasses +from functools import lru_cache + +import numpy +import pytest + +from .. import fdfd, fdtd +from ..fdtd.misc import gaussian_packet +from ..fdmath import vec, unvec +from ..fdfd import functional, scpml, waveguide_3d + + +pytestmark = pytest.mark.complete + + +DT = 0.25 +PERIOD_STEPS = 64 +OMEGA = 2 * numpy.pi / (PERIOD_STEPS * DT) +WAVELENGTH = 2 * numpy.pi / OMEGA +PULSE_DWL = 4.0 +CPML_THICKNESS = 3 +WARMUP_PERIODS = 9 +ACCUMULATION_PERIODS = 9 +SHAPE = (3, 25, 13, 13) +SOURCE_SLICES = (slice(4, 5), slice(None), slice(None)) +MONITOR_SLICES = (slice(18, 19), slice(None), slice(None)) +CHOSEN_VARIANT = 'base' +REAL_FIELD_SHAPE = (3, 37, 13, 13) +REAL_FIELD_SOURCE_SLICES = (slice(5, 6), slice(None), slice(None)) +REAL_FIELD_MONITOR_SLICES = (slice(30, 31), slice(None), slice(None)) +REAL_FIELD_WARMUP_PERIODS = 16 +REAL_FIELD_SOURCE_PHASE = 0.4 +REAL_FIELD_CORE_SLICES = (slice(None), slice(None), slice(4, 9), slice(4, 9)) +SCATTERING_SHAPE = (3, 35, 15, 15) +SCATTERING_SOURCE_SLICES = (slice(4, 5), slice(None), slice(None)) +SCATTERING_REFLECT_SLICES = (slice(10, 11), slice(None), slice(None)) +SCATTERING_TRANSMIT_SLICES = (slice(29, 30), slice(None), slice(None)) +SCATTERING_STEP_X = 18 +SCATTERING_WARMUP_PERIODS = 10 +SCATTERING_ACCUMULATION_PERIODS = 10 + + +@dataclasses.dataclass(frozen=True) +class WaveguideCalibrationResult: + variant: str + e_ph: numpy.ndarray + h_ph: numpy.ndarray + j_ph: numpy.ndarray + e_fdfd: numpy.ndarray + h_fdfd: numpy.ndarray + overlap_td: complex + overlap_fd: complex + flux_td: float + flux_fd: float + + @property + def overlap_rel_err(self) -> float: + return float(abs(self.overlap_td - self.overlap_fd) / abs(self.overlap_fd)) + + @property + def overlap_mag_rel_err(self) -> float: + return float(abs(abs(self.overlap_td) - abs(self.overlap_fd)) / abs(self.overlap_fd)) + + @property + def overlap_phase_deg(self) -> float: + return float(abs(numpy.degrees(numpy.angle(self.overlap_td / self.overlap_fd)))) + + @property + def flux_rel_err(self) -> float: + return float(abs(self.flux_td - self.flux_fd) / abs(self.flux_fd)) + + @property + def combined_error(self) -> float: + return self.overlap_mag_rel_err + self.flux_rel_err + + +@dataclasses.dataclass(frozen=True) +class WaveguideScatteringResult: + e_ph: numpy.ndarray + h_ph: numpy.ndarray + j_ph: numpy.ndarray + e_fdfd: numpy.ndarray + h_fdfd: numpy.ndarray + reflected_td: complex + reflected_fd: complex + transmitted_td: complex + transmitted_fd: complex + reflected_flux_td: float + reflected_flux_fd: float + transmitted_flux_td: float + transmitted_flux_fd: float + + @property + def reflected_overlap_mag_rel_err(self) -> float: + return float(abs(abs(self.reflected_td) - abs(self.reflected_fd)) / abs(self.reflected_fd)) + + @property + def transmitted_overlap_mag_rel_err(self) -> float: + return float(abs(abs(self.transmitted_td) - abs(self.transmitted_fd)) / abs(self.transmitted_fd)) + + @property + def reflected_flux_rel_err(self) -> float: + return float(abs(self.reflected_flux_td - self.reflected_flux_fd) / abs(self.reflected_flux_fd)) + + @property + def transmitted_flux_rel_err(self) -> float: + return float(abs(self.transmitted_flux_td - self.transmitted_flux_fd) / abs(self.transmitted_flux_fd)) + + +@dataclasses.dataclass(frozen=True) +class MonitorSliceSnapshot: + step: int + e_monitor: numpy.ndarray + h_monitor: numpy.ndarray + + +@dataclasses.dataclass(frozen=True) +class PulsedWaveguideCalibrationResult: + e_ph: numpy.ndarray + h_ph: numpy.ndarray + j_ph: numpy.ndarray + j_target: numpy.ndarray + e_fdfd: numpy.ndarray + h_fdfd: numpy.ndarray + overlap_td: complex + overlap_fd: complex + flux_td: float + flux_fd: float + + @property + def j_rel_err(self) -> float: + return float(numpy.linalg.norm(vec(self.j_ph - self.j_target)) / numpy.linalg.norm(vec(self.j_target))) + + @property + def overlap_rel_err(self) -> float: + return float(abs(self.overlap_td - self.overlap_fd) / abs(self.overlap_fd)) + + @property + def overlap_mag_rel_err(self) -> float: + return float(abs(abs(self.overlap_td) - abs(self.overlap_fd)) / abs(self.overlap_fd)) + + @property + def overlap_phase_deg(self) -> float: + return float(abs(numpy.degrees(numpy.angle(self.overlap_td / self.overlap_fd)))) + + @property + def flux_rel_err(self) -> float: + return float(abs(self.flux_td - self.flux_fd) / abs(self.flux_fd)) + + +@dataclasses.dataclass(frozen=True) +class RealFieldWaveguideResult: + e_fdfd: numpy.ndarray + h_fdfd: numpy.ndarray + e_mode_weight: numpy.ndarray + h_mode_weight: numpy.ndarray + e_mode: numpy.ndarray + h_mode: numpy.ndarray + snapshots: tuple[MonitorSliceSnapshot, ...] + + + + +def _build_uniform_dxes(shape: tuple[int, int, int, int]) -> list[list[numpy.ndarray]]: + return [[numpy.ones(shape[axis + 1]) for axis in range(3)] for _ in range(2)] + + +def _build_base_dxes() -> list[list[numpy.ndarray]]: + return _build_uniform_dxes(SHAPE) + + +def _build_real_field_base_dxes() -> list[list[numpy.ndarray]]: + return _build_uniform_dxes(REAL_FIELD_SHAPE) + + +def _build_stretched_dxes(base_dxes: list[list[numpy.ndarray]]) -> list[list[numpy.ndarray]]: + stretched_dxes = [[dx.copy() for dx in group] for group in base_dxes] + for axis in (0, 1, 2): + for polarity in (-1, 1): + stretched_dxes = scpml.stretch_with_scpml( + stretched_dxes, + axis=axis, + polarity=polarity, + omega=OMEGA, + epsilon_effective=1.0, + thickness=CPML_THICKNESS, + ) + return stretched_dxes + + +def _build_epsilon() -> numpy.ndarray: + epsilon = numpy.ones(SHAPE, dtype=float) + y0 = (SHAPE[2] - 3) // 2 + z0 = (SHAPE[3] - 3) // 2 + epsilon[:, :, y0:y0 + 3, z0:z0 + 3] = 12.0 + return epsilon + + +def _build_real_field_epsilon() -> numpy.ndarray: + epsilon = numpy.ones(REAL_FIELD_SHAPE, dtype=float) + y0 = (REAL_FIELD_SHAPE[2] - 3) // 2 + z0 = (REAL_FIELD_SHAPE[3] - 3) // 2 + epsilon[:, :, y0:y0 + 3, z0:z0 + 3] = 12.0 + return epsilon + + +def _build_scattering_epsilon() -> numpy.ndarray: + epsilon = numpy.ones(SCATTERING_SHAPE, dtype=float) + y0 = SCATTERING_SHAPE[2] // 2 + z0 = SCATTERING_SHAPE[3] // 2 + epsilon[:, :SCATTERING_STEP_X, y0 - 1:y0 + 2, z0 - 1:z0 + 2] = 12.0 + epsilon[:, SCATTERING_STEP_X:, y0 - 2:y0 + 3, z0 - 2:z0 + 3] = 12.0 + return epsilon + + +def _build_cpml_params() -> list[list[dict[str, numpy.ndarray | float]]]: + return [ + [fdtd.cpml_params(axis=axis, polarity=polarity, dt=DT, thickness=CPML_THICKNESS, epsilon_eff=1.0) + for polarity in (-1, 1)] + for axis in range(3) + ] + + +def _build_complex_pulse_waveform(total_steps: int) -> tuple[numpy.ndarray, complex]: + source_phasor, _delay = gaussian_packet(wl=WAVELENGTH, dwl=PULSE_DWL, dt=DT, turn_on=1e-5) + aa, cc, ss = source_phasor(numpy.arange(total_steps) + 0.5) + waveform = numpy.asarray(aa * (cc + 1j * ss), dtype=complex) + scale = fdtd.temporal_phasor_scale(waveform, OMEGA, DT, offset_steps=0.5)[0] + return waveform, scale + + +def _weighted_rel_err( + observed: numpy.ndarray, + reference: numpy.ndarray, + weight: numpy.ndarray, + ) -> float: + return float(numpy.linalg.norm((observed - reference) * weight) / numpy.linalg.norm(reference * weight)) + + +def _project_onto_mode( + observed: numpy.ndarray, + mode: numpy.ndarray, + ) -> tuple[complex, numpy.ndarray, numpy.ndarray]: + coefficient = numpy.vdot(mode, observed) / numpy.vdot(mode, mode) + guided = coefficient * mode + residual = observed - guided + return coefficient, guided, residual + + +@lru_cache(maxsize=1) +def _run_real_field_straight_waveguide_case() -> RealFieldWaveguideResult: + epsilon = _build_real_field_epsilon() + base_dxes = _build_real_field_base_dxes() + stretched_dxes = _build_stretched_dxes(base_dxes) + + source_mode = waveguide_3d.solve_mode( + 0, + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=1, + slices=REAL_FIELD_SOURCE_SLICES, + epsilon=epsilon, + ) + j_mode = waveguide_3d.compute_source( + E=source_mode['E'], + wavenumber=source_mode['wavenumber'], + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=1, + slices=REAL_FIELD_SOURCE_SLICES, + epsilon=epsilon, + ) + j_mode = j_mode * numpy.exp(1j * REAL_FIELD_SOURCE_PHASE) + monitor_mode = waveguide_3d.solve_mode( + 0, + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=1, + slices=REAL_FIELD_MONITOR_SLICES, + epsilon=epsilon, + ) + e_fdfd = unvec( + fdfd.solvers.generic( + J=vec(j_mode), + omega=OMEGA, + dxes=stretched_dxes, + epsilon=vec(epsilon), + matrix_solver_opts={'atol': 1e-10, 'rtol': 1e-7}, + ), + REAL_FIELD_SHAPE[1:], + ) + h_fdfd = functional.e2h(OMEGA, stretched_dxes)(e_fdfd) + + update_e, update_h = fdtd.updates_with_cpml( + cpml_params=_build_cpml_params(), + dt=DT, + dxes=base_dxes, + epsilon=epsilon, + ) + e_field = numpy.zeros_like(epsilon) + h_field = numpy.zeros_like(epsilon) + total_steps = (REAL_FIELD_WARMUP_PERIODS + 1) * PERIOD_STEPS + snapshots: list[MonitorSliceSnapshot] = [] + + for step in range(total_steps): + update_e(e_field, h_field, epsilon) + + t_half = (step + 0.5) * DT + j_real = (j_mode.real * numpy.cos(OMEGA * t_half) - j_mode.imag * numpy.sin(OMEGA * t_half)).real + e_field -= DT * j_real / epsilon + + update_h(e_field, h_field) + + if step >= total_steps - PERIOD_STEPS // 4: + snapshots.append( + MonitorSliceSnapshot( + step=step, + e_monitor=e_field[:, REAL_FIELD_MONITOR_SLICES[0], :, :].copy(), + h_monitor=h_field[:, REAL_FIELD_MONITOR_SLICES[0], :, :].copy(), + ), + ) + + return RealFieldWaveguideResult( + e_fdfd=e_fdfd[:, REAL_FIELD_MONITOR_SLICES[0], :, :], + h_fdfd=h_fdfd[:, REAL_FIELD_MONITOR_SLICES[0], :, :], + e_mode_weight=numpy.abs(monitor_mode['E'][:, REAL_FIELD_MONITOR_SLICES[0], :, :]), + h_mode_weight=numpy.abs(monitor_mode['H'][:, REAL_FIELD_MONITOR_SLICES[0], :, :]), + e_mode=monitor_mode['E'][:, REAL_FIELD_MONITOR_SLICES[0], :, :], + h_mode=monitor_mode['H'][:, REAL_FIELD_MONITOR_SLICES[0], :, :], + snapshots=tuple(snapshots), + ) + + + + +@lru_cache(maxsize=2) +def _run_straight_waveguide_case(variant: str) -> WaveguideCalibrationResult: + assert variant in ('stretched', 'base') + + epsilon = _build_epsilon() + base_dxes = _build_base_dxes() + stretched_dxes = _build_stretched_dxes(base_dxes) + mode_dxes = stretched_dxes if variant == 'stretched' else base_dxes + + source_mode = waveguide_3d.solve_mode( + 0, + omega=OMEGA, + dxes=mode_dxes, + axis=0, + polarity=1, + slices=SOURCE_SLICES, + epsilon=epsilon, + ) + j_mode = waveguide_3d.compute_source( + E=source_mode['E'], + wavenumber=source_mode['wavenumber'], + omega=OMEGA, + dxes=mode_dxes, + axis=0, + polarity=1, + slices=SOURCE_SLICES, + epsilon=epsilon, + ) + monitor_mode = waveguide_3d.solve_mode( + 0, + omega=OMEGA, + dxes=mode_dxes, + axis=0, + polarity=1, + slices=MONITOR_SLICES, + epsilon=epsilon, + ) + overlap_e = waveguide_3d.compute_overlap_e( + E=monitor_mode['E'], + wavenumber=monitor_mode['wavenumber'], + dxes=mode_dxes, + axis=0, + polarity=1, + slices=MONITOR_SLICES, + ) + + update_e, update_h = fdtd.updates_with_cpml(cpml_params=_build_cpml_params(), dt=DT, dxes=base_dxes, epsilon=epsilon) + + e_field = numpy.zeros_like(epsilon) + h_field = numpy.zeros_like(epsilon) + e_accumulator = numpy.zeros((1, *SHAPE), dtype=complex) + h_accumulator = numpy.zeros((1, *SHAPE), dtype=complex) + j_accumulator = numpy.zeros((1, *SHAPE), dtype=complex) + + warmup_steps = WARMUP_PERIODS * PERIOD_STEPS + accumulation_steps = ACCUMULATION_PERIODS * PERIOD_STEPS + for step in range(warmup_steps + accumulation_steps): + update_e(e_field, h_field, epsilon) + + t_half = (step + 0.5) * DT + j_real = (j_mode.real * numpy.cos(OMEGA * t_half) - j_mode.imag * numpy.sin(OMEGA * t_half)).real + e_field -= DT * j_real / epsilon + + if step >= warmup_steps: + fdtd.accumulate_phasor_j(j_accumulator, OMEGA, DT, j_real, step) + fdtd.accumulate_phasor_e(e_accumulator, OMEGA, DT, e_field, step + 1) + + update_h(e_field, h_field) + + if step >= warmup_steps: + fdtd.accumulate_phasor_h(h_accumulator, OMEGA, DT, h_field, step + 1) + + e_ph = e_accumulator[0] + h_ph = h_accumulator[0] + j_ph = j_accumulator[0] + + e_fdfd = unvec( + fdfd.solvers.generic( + J=vec(j_ph), + omega=OMEGA, + dxes=stretched_dxes, + epsilon=vec(epsilon), + matrix_solver_opts={'atol': 1e-10, 'rtol': 1e-7}, + ), + SHAPE[1:], + ) + h_fdfd = functional.e2h(OMEGA, stretched_dxes)(e_fdfd) + + overlap_td = complex(vec(e_ph) @ vec(overlap_e).conj()) + overlap_fd = complex(vec(e_fdfd) @ vec(overlap_e).conj()) + + poynting_td = functional.poynting_e_cross_h(stretched_dxes)(e_ph, h_ph.conj()) + poynting_fd = functional.poynting_e_cross_h(stretched_dxes)(e_fdfd, h_fdfd.conj()) + flux_td = float(0.5 * poynting_td[0, MONITOR_SLICES[0], :, :].real.sum()) + flux_fd = float(0.5 * poynting_fd[0, MONITOR_SLICES[0], :, :].real.sum()) + + return WaveguideCalibrationResult( + variant=variant, + e_ph=e_ph, + h_ph=h_ph, + j_ph=j_ph, + e_fdfd=e_fdfd, + h_fdfd=h_fdfd, + overlap_td=overlap_td, + overlap_fd=overlap_fd, + flux_td=flux_td, + flux_fd=flux_fd, + ) + + +@lru_cache(maxsize=1) +def _run_width_step_scattering_case() -> WaveguideScatteringResult: + epsilon = _build_scattering_epsilon() + base_dxes = _build_uniform_dxes(SCATTERING_SHAPE) + stretched_dxes = _build_stretched_dxes(base_dxes) + + source_mode = waveguide_3d.solve_mode( + 0, + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=1, + slices=SCATTERING_SOURCE_SLICES, + epsilon=epsilon, + ) + j_mode = waveguide_3d.compute_source( + E=source_mode['E'], + wavenumber=source_mode['wavenumber'], + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=1, + slices=SCATTERING_SOURCE_SLICES, + epsilon=epsilon, + ) + reflected_mode = waveguide_3d.solve_mode( + 0, + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=-1, + slices=SCATTERING_REFLECT_SLICES, + epsilon=epsilon, + ) + reflected_overlap = waveguide_3d.compute_overlap_e( + E=reflected_mode['E'], + wavenumber=reflected_mode['wavenumber'], + dxes=base_dxes, + axis=0, + polarity=-1, + slices=SCATTERING_REFLECT_SLICES, + ) + transmitted_mode = waveguide_3d.solve_mode( + 0, + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=1, + slices=SCATTERING_TRANSMIT_SLICES, + epsilon=epsilon, + ) + transmitted_overlap = waveguide_3d.compute_overlap_e( + E=transmitted_mode['E'], + wavenumber=transmitted_mode['wavenumber'], + dxes=base_dxes, + axis=0, + polarity=1, + slices=SCATTERING_TRANSMIT_SLICES, + ) + + update_e, update_h = fdtd.updates_with_cpml(cpml_params=_build_cpml_params(), dt=DT, dxes=base_dxes, epsilon=epsilon) + + e_field = numpy.zeros_like(epsilon) + h_field = numpy.zeros_like(epsilon) + e_accumulator = numpy.zeros((1, *SCATTERING_SHAPE), dtype=complex) + h_accumulator = numpy.zeros((1, *SCATTERING_SHAPE), dtype=complex) + j_accumulator = numpy.zeros((1, *SCATTERING_SHAPE), dtype=complex) + + warmup_steps = SCATTERING_WARMUP_PERIODS * PERIOD_STEPS + accumulation_steps = SCATTERING_ACCUMULATION_PERIODS * PERIOD_STEPS + for step in range(warmup_steps + accumulation_steps): + update_e(e_field, h_field, epsilon) + + t_half = (step + 0.5) * DT + j_real = (j_mode.real * numpy.cos(OMEGA * t_half) - j_mode.imag * numpy.sin(OMEGA * t_half)).real + e_field -= DT * j_real / epsilon + + if step >= warmup_steps: + fdtd.accumulate_phasor_j(j_accumulator, OMEGA, DT, j_real, step) + fdtd.accumulate_phasor_e(e_accumulator, OMEGA, DT, e_field, step + 1) + + update_h(e_field, h_field) + + if step >= warmup_steps: + fdtd.accumulate_phasor_h(h_accumulator, OMEGA, DT, h_field, step + 1) + + e_ph = e_accumulator[0] + h_ph = h_accumulator[0] + j_ph = j_accumulator[0] + + e_fdfd = unvec( + fdfd.solvers.generic( + J=vec(j_ph), + omega=OMEGA, + dxes=stretched_dxes, + epsilon=vec(epsilon), + matrix_solver_opts={'atol': 1e-10, 'rtol': 1e-7}, + ), + SCATTERING_SHAPE[1:], + ) + h_fdfd = functional.e2h(OMEGA, stretched_dxes)(e_fdfd) + + reflected_td = complex(vec(e_ph) @ vec(reflected_overlap).conj()) + reflected_fd = complex(vec(e_fdfd) @ vec(reflected_overlap).conj()) + transmitted_td = complex(vec(e_ph) @ vec(transmitted_overlap).conj()) + transmitted_fd = complex(vec(e_fdfd) @ vec(transmitted_overlap).conj()) + + poynting_td = functional.poynting_e_cross_h(stretched_dxes)(e_ph, h_ph.conj()) + poynting_fd = functional.poynting_e_cross_h(stretched_dxes)(e_fdfd, h_fdfd.conj()) + reflected_flux_td = float(0.5 * poynting_td[0, SCATTERING_REFLECT_SLICES[0], :, :].real.sum()) + reflected_flux_fd = float(0.5 * poynting_fd[0, SCATTERING_REFLECT_SLICES[0], :, :].real.sum()) + transmitted_flux_td = float(0.5 * poynting_td[0, SCATTERING_TRANSMIT_SLICES[0], :, :].real.sum()) + transmitted_flux_fd = float(0.5 * poynting_fd[0, SCATTERING_TRANSMIT_SLICES[0], :, :].real.sum()) + + return WaveguideScatteringResult( + e_ph=e_ph, + h_ph=h_ph, + j_ph=j_ph, + e_fdfd=e_fdfd, + h_fdfd=h_fdfd, + reflected_td=reflected_td, + reflected_fd=reflected_fd, + transmitted_td=transmitted_td, + transmitted_fd=transmitted_fd, + reflected_flux_td=reflected_flux_td, + reflected_flux_fd=reflected_flux_fd, + transmitted_flux_td=transmitted_flux_td, + transmitted_flux_fd=transmitted_flux_fd, + ) + + +@lru_cache(maxsize=1) +def _run_pulsed_straight_waveguide_case() -> PulsedWaveguideCalibrationResult: + epsilon = _build_epsilon() + base_dxes = _build_base_dxes() + stretched_dxes = _build_stretched_dxes(base_dxes) + + source_mode = waveguide_3d.solve_mode( + 0, + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=1, + slices=SOURCE_SLICES, + epsilon=epsilon, + ) + j_mode = waveguide_3d.compute_source( + E=source_mode['E'], + wavenumber=source_mode['wavenumber'], + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=1, + slices=SOURCE_SLICES, + epsilon=epsilon, + ) + monitor_mode = waveguide_3d.solve_mode( + 0, + omega=OMEGA, + dxes=base_dxes, + axis=0, + polarity=1, + slices=MONITOR_SLICES, + epsilon=epsilon, + ) + overlap_e = waveguide_3d.compute_overlap_e( + E=monitor_mode['E'], + wavenumber=monitor_mode['wavenumber'], + dxes=base_dxes, + axis=0, + polarity=1, + slices=MONITOR_SLICES, + ) + + update_e, update_h = fdtd.updates_with_cpml(cpml_params=_build_cpml_params(), dt=DT, dxes=base_dxes, epsilon=epsilon, dtype=complex) + + e_field = numpy.zeros_like(epsilon, dtype=complex) + h_field = numpy.zeros_like(epsilon, dtype=complex) + e_accumulator = numpy.zeros((1, *SHAPE), dtype=complex) + h_accumulator = numpy.zeros((1, *SHAPE), dtype=complex) + j_accumulator = numpy.zeros((1, *SHAPE), dtype=complex) + + total_steps = (WARMUP_PERIODS + ACCUMULATION_PERIODS) * PERIOD_STEPS + waveform, pulse_scale = _build_complex_pulse_waveform(total_steps) + + for step in range(total_steps): + update_e(e_field, h_field, epsilon) + + j_step = pulse_scale * waveform[step] * j_mode + e_field -= DT * j_step / epsilon + + fdtd.accumulate_phasor_j(j_accumulator, OMEGA, DT, j_step, step) + fdtd.accumulate_phasor_e(e_accumulator, OMEGA, DT, e_field, step + 1) + + update_h(e_field, h_field) + + fdtd.accumulate_phasor_h(h_accumulator, OMEGA, DT, h_field, step + 1) + + e_ph = e_accumulator[0] + h_ph = h_accumulator[0] + j_ph = j_accumulator[0] + + e_fdfd = unvec( + fdfd.solvers.generic( + J=vec(j_ph), + omega=OMEGA, + dxes=stretched_dxes, + epsilon=vec(epsilon), + matrix_solver_opts={'atol': 1e-10, 'rtol': 1e-7}, + ), + SHAPE[1:], + ) + h_fdfd = functional.e2h(OMEGA, stretched_dxes)(e_fdfd) + + overlap_td = complex(vec(e_ph) @ vec(overlap_e).conj()) + overlap_fd = complex(vec(e_fdfd) @ vec(overlap_e).conj()) + + poynting_td = functional.poynting_e_cross_h(stretched_dxes)(e_ph, h_ph.conj()) + poynting_fd = functional.poynting_e_cross_h(stretched_dxes)(e_fdfd, h_fdfd.conj()) + flux_td = float(0.5 * poynting_td[0, MONITOR_SLICES[0], :, :].real.sum()) + flux_fd = float(0.5 * poynting_fd[0, MONITOR_SLICES[0], :, :].real.sum()) + + return PulsedWaveguideCalibrationResult( + e_ph=e_ph, + h_ph=h_ph, + j_ph=j_ph, + j_target=j_mode, + e_fdfd=e_fdfd, + h_fdfd=h_fdfd, + overlap_td=overlap_td, + overlap_fd=overlap_fd, + flux_td=flux_td, + flux_fd=flux_fd, + ) + + + + +def test_straight_waveguide_base_variant_outperforms_stretched_variant() -> None: + base_result = _run_straight_waveguide_case('base') + stretched_result = _run_straight_waveguide_case('stretched') + + assert base_result.variant == CHOSEN_VARIANT + assert base_result.combined_error < stretched_result.combined_error + + +def test_straight_waveguide_fdtd_fdfd_overlap_and_flux_agree() -> None: + result = _run_straight_waveguide_case(CHOSEN_VARIANT) + + assert numpy.isfinite(result.e_ph).all() + assert numpy.isfinite(result.h_ph).all() + assert numpy.isfinite(result.j_ph).all() + assert numpy.isfinite(result.e_fdfd).all() + assert numpy.isfinite(result.h_fdfd).all() + assert abs(result.overlap_td) > 0 + assert abs(result.overlap_fd) > 0 + assert abs(result.flux_td) > 0 + assert abs(result.flux_fd) > 0 + + assert result.overlap_mag_rel_err < 0.01 + assert result.flux_rel_err < 0.01 + assert result.overlap_rel_err < 0.01 + assert result.overlap_phase_deg < 0.5 + + +def test_straight_waveguide_real_snapshot_diagnostic_tracks_guided_content_and_bounded_residual() -> None: + # The phasor-based waveguide tests above are the primary FDTD/FDFD + # equivalence benchmark. This raw real-field check is intentionally stricter: + # it validates that late monitor snapshots keep the guided content close to + # the reconstructed FDFD field while the orthogonal residual stays bounded. + result = _run_real_field_straight_waveguide_case() + ranked_snapshots = sorted( + result.snapshots, + key=lambda snapshot: numpy.linalg.norm( + fdtd.reconstruct_real_e(result.e_fdfd, OMEGA, DT, snapshot.step + 1), + ), + reverse=True, + ) + + for snapshot in ranked_snapshots[:3]: + reconstructed_e = fdtd.reconstruct_real_e(result.e_fdfd, OMEGA, DT, snapshot.step + 1) + reconstructed_h = fdtd.reconstruct_real_h(result.h_fdfd, OMEGA, DT, snapshot.step + 1) + + e_rel_err = numpy.linalg.norm(snapshot.e_monitor - reconstructed_e) / numpy.linalg.norm(reconstructed_e) + h_rel_err = numpy.linalg.norm(snapshot.h_monitor - reconstructed_h) / numpy.linalg.norm(reconstructed_h) + e_core_rel_err = numpy.linalg.norm( + snapshot.e_monitor[REAL_FIELD_CORE_SLICES] - reconstructed_e[REAL_FIELD_CORE_SLICES], + ) / numpy.linalg.norm(reconstructed_e[REAL_FIELD_CORE_SLICES]) + h_core_rel_err = numpy.linalg.norm( + snapshot.h_monitor[REAL_FIELD_CORE_SLICES] - reconstructed_h[REAL_FIELD_CORE_SLICES], + ) / numpy.linalg.norm(reconstructed_h[REAL_FIELD_CORE_SLICES]) + e_weighted_rel_err = _weighted_rel_err(snapshot.e_monitor, reconstructed_e, result.e_mode_weight) + h_weighted_rel_err = _weighted_rel_err(snapshot.h_monitor, reconstructed_h, result.h_mode_weight) + e_guided_coeff, _, e_residual = _project_onto_mode(snapshot.e_monitor, result.e_mode) + e_guided_coeff_ref, _, e_residual_ref = _project_onto_mode(reconstructed_e, result.e_mode) + h_guided_coeff, _, h_residual = _project_onto_mode(snapshot.h_monitor, result.h_mode) + h_guided_coeff_ref, _, h_residual_ref = _project_onto_mode(reconstructed_h, result.h_mode) + e_guided_rel_err = abs(e_guided_coeff - e_guided_coeff_ref) / abs(e_guided_coeff_ref) + h_guided_rel_err = abs(h_guided_coeff - h_guided_coeff_ref) / abs(h_guided_coeff_ref) + e_residual_rel_err = numpy.linalg.norm(e_residual - e_residual_ref) / numpy.linalg.norm(e_residual_ref) + h_residual_rel_err = numpy.linalg.norm(h_residual - h_residual_ref) / numpy.linalg.norm(h_residual_ref) + + assert e_rel_err < 0.075 + assert h_rel_err < 0.075 + assert e_core_rel_err < 0.055 + assert h_core_rel_err < 0.055 + assert e_weighted_rel_err < 0.055 + assert h_weighted_rel_err < 0.03 + assert e_guided_rel_err < 0.04 + assert h_guided_rel_err < 0.03 + assert e_residual_rel_err < 0.115 + assert h_residual_rel_err < 0.115 + + +def test_width_step_waveguide_fdtd_fdfd_modal_powers_and_flux_agree() -> None: + result = _run_width_step_scattering_case() + + assert numpy.isfinite(result.e_ph).all() + assert numpy.isfinite(result.h_ph).all() + assert numpy.isfinite(result.j_ph).all() + assert numpy.isfinite(result.e_fdfd).all() + assert numpy.isfinite(result.h_fdfd).all() + assert abs(result.reflected_td) > 0 + assert abs(result.reflected_fd) > 0 + assert abs(result.transmitted_td) > 0 + assert abs(result.transmitted_fd) > 0 + assert abs(result.reflected_flux_td) > 0 + assert abs(result.reflected_flux_fd) > 0 + assert abs(result.transmitted_flux_td) > 0 + assert abs(result.transmitted_flux_fd) > 0 + + assert result.transmitted_overlap_mag_rel_err < 0.03 + assert result.reflected_overlap_mag_rel_err < 0.03 + assert result.transmitted_flux_rel_err < 0.01 + assert result.reflected_flux_rel_err < 0.01 + + +def test_pulsed_straight_waveguide_fdtd_fdfd_overlap_flux_and_source_agree() -> None: + result = _run_pulsed_straight_waveguide_case() + + assert numpy.isfinite(result.e_ph).all() + assert numpy.isfinite(result.h_ph).all() + assert numpy.isfinite(result.j_ph).all() + assert numpy.isfinite(result.e_fdfd).all() + assert numpy.isfinite(result.h_fdfd).all() + assert abs(result.overlap_td) > 0 + assert abs(result.overlap_fd) > 0 + assert abs(result.flux_td) > 0 + assert abs(result.flux_fd) > 0 + + assert result.j_rel_err < 1e-9 + assert result.overlap_mag_rel_err < 0.01 + assert result.flux_rel_err < 0.03 + assert result.overlap_rel_err < 0.01 + assert result.overlap_phase_deg < 0.5 diff --git a/meanas/test/test_waveguide_mode_helpers.py b/meanas/test/test_waveguide_mode_helpers.py new file mode 100644 index 0000000..d3ec7cd --- /dev/null +++ b/meanas/test/test_waveguide_mode_helpers.py @@ -0,0 +1,295 @@ +import contextlib +import io +import numpy +from numpy.linalg import norm +import pytest +import warnings + +from ..fdmath import vec, unvec +from ..fdfd import waveguide_2d, waveguide_3d, waveguide_cyl + + +OMEGA = 1 / 1500 + + +def build_waveguide_3d_mode( + *, + slice_start: int, + polarity: int, + ) -> tuple[numpy.ndarray, list[list[numpy.ndarray]], tuple[slice, slice, slice], waveguide_3d.Waveguide3DMode]: + epsilon = numpy.ones((3, 5, 5, 1), dtype=float) + dxes = [[numpy.ones(5), numpy.ones(5), numpy.ones(1)] for _ in range(2)] + slices = (slice(slice_start, slice_start + 1), slice(None), slice(None)) + result = waveguide_3d.solve_mode( + 0, + omega=OMEGA, + dxes=dxes, + axis=0, + polarity=polarity, + slices=slices, + epsilon=epsilon, + ) + return epsilon, dxes, slices, result + + +def build_waveguide_cyl_fixture( + *, + nonuniform: bool = False, + ) -> tuple[list[list[numpy.ndarray]], numpy.ndarray, float]: + if nonuniform: + dxes = [ + [numpy.array([1.0, 1.5, 1.2, 0.8, 1.1]), numpy.ones(5)], + [numpy.array([0.9, 1.4, 1.0, 0.7, 1.2]), numpy.ones(5)], + ] + else: + dxes = [[numpy.ones(5), numpy.ones(5)] for _ in range(2)] + epsilon = vec(numpy.ones((3, 5, 5), dtype=float)) + return dxes, epsilon, 10.0 + + +def test_waveguide_3d_solve_mode_and_expand_e_are_phase_consistent() -> None: + epsilon, dxes, slices, result = build_waveguide_3d_mode(slice_start=0, polarity=1) + axis = 0 + polarity = 1 + expanded = waveguide_3d.expand_e( + E=result['E'], + wavenumber=result['wavenumber'], + dxes=dxes, + axis=axis, + polarity=polarity, + slices=slices, + ) + + dx_prop = 0.5 * numpy.array([dx[2][slices[2]] for dx in dxes]).sum() + expected_wavenumber = 2 / dx_prop * numpy.arcsin(result['wavenumber_2d'] * dx_prop / 2) + solved_slice = (slice(None), *slices) + + assert result['E'].shape == epsilon.shape + assert result['H'].shape == epsilon.shape + assert numpy.isfinite(result['E']).all() + assert numpy.isfinite(result['H']).all() + assert abs(result['wavenumber'] - expected_wavenumber) < 1e-12 + assert numpy.allclose(expanded[solved_slice], result['E'][solved_slice]) + + component, _x, y_index, z_index = numpy.unravel_index( + numpy.abs(result['E']).argmax(), + result['E'].shape, + ) + values = expanded[component, :, y_index, z_index] + ratios = values[1:] / values[:-1] + expected_ratio = numpy.exp(-1j * result['wavenumber']) + + numpy.testing.assert_allclose(ratios, expected_ratio, rtol=1e-6, atol=1e-9) + + +@pytest.mark.parametrize( + ('polarity', 'expected_range'), + [(1, (0, 1)), (-1, (3, 4))], + ) +def test_waveguide_3d_compute_overlap_e_uses_adjacent_window( + polarity: int, + expected_range: tuple[int, int], + ) -> None: + _epsilon, dxes, slices, result = build_waveguide_3d_mode(slice_start=2, polarity=polarity) + + with warnings.catch_warnings(record=True) as caught: + overlap = waveguide_3d.compute_overlap_e( + E=result['E'], + wavenumber=result['wavenumber'], + dxes=dxes, + axis=0, + polarity=polarity, + slices=slices, + ) + + nonzero = numpy.argwhere(numpy.abs(overlap) > 0) + + assert not caught + assert numpy.isfinite(overlap).all() + assert nonzero[:, 1].min() == expected_range[0] + assert nonzero[:, 1].max() == expected_range[1] + + +@pytest.mark.parametrize( + ('polarity', 'slice_start', 'expected_index'), + [(1, 1, 0), (-1, 3, 4)], + ) +def test_waveguide_3d_compute_overlap_e_warns_when_window_is_clipped( + polarity: int, + slice_start: int, + expected_index: int, + ) -> None: + _epsilon, dxes, slices, result = build_waveguide_3d_mode(slice_start=slice_start, polarity=polarity) + + with pytest.warns(RuntimeWarning, match='clipped'): + overlap = waveguide_3d.compute_overlap_e( + E=result['E'], + wavenumber=result['wavenumber'], + dxes=dxes, + axis=0, + polarity=polarity, + slices=slices, + ) + + nonzero = numpy.argwhere(numpy.abs(overlap) > 0) + + assert numpy.isfinite(overlap).all() + assert nonzero[:, 1].min() == expected_index + assert nonzero[:, 1].max() == expected_index + + +@pytest.mark.parametrize( + ('polarity', 'slice_start'), + [(1, 0), (-1, 4)], + ) +def test_waveguide_3d_compute_overlap_e_rejects_empty_overlap_window( + polarity: int, + slice_start: int, + ) -> None: + _epsilon, dxes, slices, result = build_waveguide_3d_mode(slice_start=slice_start, polarity=polarity) + + with pytest.raises(ValueError, match='outside the domain'): + waveguide_3d.compute_overlap_e( + E=result['E'], + wavenumber=result['wavenumber'], + dxes=dxes, + axis=0, + polarity=polarity, + slices=slices, + ) + + +def test_waveguide_3d_compute_overlap_e_rejects_zero_support_window() -> None: + _epsilon, dxes, slices, result = build_waveguide_3d_mode(slice_start=2, polarity=1) + + with pytest.raises(ValueError, match='no overlap field support'): + waveguide_3d.compute_overlap_e( + E=numpy.zeros_like(result['E']), + wavenumber=result['wavenumber'], + dxes=dxes, + axis=0, + polarity=1, + slices=slices, + ) + + +def test_waveguide_cyl_solved_modes_are_ordered_and_low_residual() -> None: + dxes, epsilon, rmin = build_waveguide_cyl_fixture() + + e_xys, angular_wavenumbers = waveguide_cyl.solve_modes( + [0, 1], + omega=OMEGA, + dxes=dxes, + epsilon=epsilon, + rmin=rmin, + ) + operator = waveguide_cyl.cylindrical_operator(OMEGA, dxes, epsilon, rmin=rmin) + + assert numpy.all(numpy.diff(numpy.real(angular_wavenumbers)) <= 0) + + for e_xy, angular_wavenumber in zip(e_xys, angular_wavenumbers, strict=True): + eigenvalue = (angular_wavenumber / rmin) ** 2 + residual = norm(operator @ e_xy - eigenvalue * e_xy) / norm(e_xy) + assert residual < 1e-6 + + +def test_waveguide_cyl_linear_wavenumbers_are_finite_and_ordered() -> None: + dxes, epsilon, rmin = build_waveguide_cyl_fixture() + + e_xys, angular_wavenumbers = waveguide_cyl.solve_modes( + [0, 1], + omega=OMEGA, + dxes=dxes, + epsilon=epsilon, + rmin=10.0, + ) + linear_wavenumbers = waveguide_cyl.linear_wavenumbers( + e_xys, + angular_wavenumbers, + epsilon=epsilon, + dxes=dxes, + rmin=rmin, + ) + + assert numpy.isfinite(linear_wavenumbers).all() + assert numpy.all(numpy.real(linear_wavenumbers) > 0) + assert numpy.all(numpy.diff(numpy.real(linear_wavenumbers)) <= 0) + + +def test_waveguide_cyl_dxes2t_matches_expected_radius_scaling() -> None: + dxes, _epsilon, rmin = build_waveguide_cyl_fixture(nonuniform=True) + Ta, Tb = waveguide_cyl.dxes2T(dxes, rmin) + + ta = (rmin + numpy.cumsum(dxes[0][0])) / rmin + tb = (rmin + dxes[0][0] / 2 + numpy.cumsum(dxes[1][0])) / rmin + + numpy.testing.assert_allclose(Ta.diagonal(), numpy.repeat(ta, dxes[0][1].size)) + numpy.testing.assert_allclose(Tb.diagonal(), numpy.repeat(tb, dxes[1][1].size)) + + +def test_waveguide_cyl_exy2e_and_exy2h_return_finite_full_fields() -> None: + dxes, epsilon, rmin = build_waveguide_cyl_fixture() + mu = vec(2 * numpy.ones((3, 5, 5), dtype=float)) + e_xy, angular_wavenumber = waveguide_cyl.solve_mode( + 0, + omega=OMEGA, + dxes=dxes, + epsilon=epsilon, + rmin=rmin, + ) + + e_field = waveguide_cyl.exy2e( + angular_wavenumber=angular_wavenumber, + omega=OMEGA, + dxes=dxes, + rmin=rmin, + epsilon=epsilon, + ) @ e_xy + h_field = waveguide_cyl.exy2h( + angular_wavenumber=angular_wavenumber, + omega=OMEGA, + dxes=dxes, + rmin=rmin, + epsilon=epsilon, + mu=mu, + ) @ e_xy + + assert e_field.shape == (3 * 25,) + assert h_field.shape == (3 * 25,) + assert numpy.isfinite(e_field).all() + assert numpy.isfinite(h_field).all() + assert unvec(e_field, (5, 5)).shape == (3, 5, 5) + assert unvec(h_field, (5, 5)).shape == (3, 5, 5) + + +@pytest.mark.parametrize('use_mu', [False, True]) +def test_waveguide_cyl_normalized_fields_are_unit_norm_and_silent(use_mu: bool) -> None: + dxes, epsilon, rmin = build_waveguide_cyl_fixture() + mu = vec(2 * numpy.ones((3, 5, 5), dtype=float)) if use_mu else None + e_xy, angular_wavenumber = waveguide_cyl.solve_mode( + 0, + omega=OMEGA, + dxes=dxes, + epsilon=epsilon, + rmin=rmin, + ) + + output = io.StringIO() + with contextlib.redirect_stdout(output): + e_field, h_field = waveguide_cyl.normalized_fields_e( + e_xy, + angular_wavenumber=angular_wavenumber, + omega=OMEGA, + dxes=dxes, + rmin=rmin, + epsilon=epsilon, + mu=mu, + ) + + overlap = waveguide_2d.inner_product(e_field, h_field, dxes, conj_h=True) + + assert output.getvalue() == '' + assert numpy.isfinite(e_field).all() + assert numpy.isfinite(h_field).all() + assert abs(overlap.real - 1.0) < 1e-10 + assert abs(overlap.imag) < 1e-10 diff --git a/meanas/test/utils.py b/meanas/test/utils.py index 00ed3f1..62afaf0 100644 --- a/meanas/test/utils.py +++ b/meanas/test/utils.py @@ -1,31 +1,33 @@ -from typing import Any - import numpy from numpy.typing import NDArray +from numpy.typing import ArrayLike -PRNG = numpy.random.RandomState(12345) +def make_prng(seed: int = 12345) -> numpy.random.RandomState: + return numpy.random.RandomState(seed) def assert_fields_close( x: NDArray, y: NDArray, - *args: Any, - **kwargs: Any, - ) -> None: - numpy.testing.assert_allclose( - x, y, verbose=False, # type: ignore - err_msg='Fields did not match:\n{}\n{}'.format(numpy.moveaxis(x, -1, 0), - numpy.moveaxis(y, -1, 0)), *args, **kwargs, + ) -> None: + x_disp = numpy.moveaxis(x, -1, 0) + y_disp = numpy.moveaxis(y, -1, 0) + numpy.testing.assert_allclose( + x, # type: ignore + y, # type: ignore + *args, + verbose=False, + err_msg=f'Fields did not match:\n{x_disp}\n{y_disp}', + **kwargs, ) def assert_close( - x: NDArray, - y: NDArray, - *args: Any, - **kwargs: Any, + x: ArrayLike, + y: ArrayLike, + *args, + **kwargs, ) -> None: - numpy.testing.assert_allclose(x, y, *args, **kwargs) - + numpy.testing.assert_allclose(numpy.asarray(x), numpy.asarray(y), *args, **kwargs) diff --git a/mkdocs.yml b/mkdocs.yml new file mode 100644 index 0000000..379af9b --- /dev/null +++ b/mkdocs.yml @@ -0,0 +1,89 @@ +site_name: meanas +site_description: Electromagnetic simulation tools +site_url: !ENV [DOCS_SITE_URL, ""] +repo_url: https://mpxd.net/code/jan/meanas +repo_name: meanas +docs_dir: docs +site_dir: site +strict: false + +theme: + name: material + font: false + palette: + - scheme: slate + primary: blue grey + accent: cyan + toggle: + icon: material/weather-sunny + name: Switch to light mode + - scheme: default + primary: teal + accent: indigo + toggle: + icon: material/weather-night + name: Switch to dark mode + features: + - navigation.indexes + - navigation.sections + - navigation.top + - content.code.copy + - toc.follow + +nav: + - Home: index.md + - API: + - Overview: api/index.md + - meanas: api/meanas.md + - eigensolvers: api/eigensolvers.md + - fdfd: api/fdfd.md + - waveguides: api/waveguides.md + - fdtd: api/fdtd.md + - fdmath: api/fdmath.md + +plugins: + - search + - mkdocstrings: + handlers: + python: + paths: + - !ENV [MKDOCSTRINGS_PYTHON_PATH, "."] + options: + show_root_heading: true + show_root_toc_entry: false + show_source: false + show_signature_annotations: true + show_symbol_type_heading: true + show_symbol_type_toc: true + members_order: source + separate_signature: true + merge_init_into_class: true + docstring_style: google + - print-site + +markdown_extensions: + - admonition + - attr_list + - md_in_html + - tables + - toc: + permalink: true + - pymdownx.arithmatex: + generic: true + - pymdownx.highlight: + anchor_linenums: true + - pymdownx.inlinehilite + - pymdownx.snippets + - pymdownx.superfences + - pymdownx.tabbed: + alternate_style: true + +extra_css: + - stylesheets/extra.css + +extra_javascript: + - javascripts/mathjax.js + - assets/vendor/mathjax/startup.js + +watch: + - meanas diff --git a/pdoc_templates/config.mako b/pdoc_templates/config.mako deleted file mode 100644 index 93cf716..0000000 --- a/pdoc_templates/config.mako +++ /dev/null @@ -1,47 +0,0 @@ -<%! - # Template configuration. Copy over in your template directory - # (used with --template-dir) and adapt as required. - html_lang = 'en' - show_inherited_members = False - extract_module_toc_into_sidebar = True - list_class_variables_in_index = True - sort_identifiers = True - show_type_annotations = True - - # Show collapsed source code block next to each item. - # Disabling this can improve rendering speed of large modules. - show_source_code = True - - # If set, format links to objects in online source code repository - # according to this template. Supported keywords for interpolation - # are: commit, path, start_line, end_line. - #git_link_template = 'https://github.com/USER/PROJECT/blob/{commit}/{path}#L{start_line}-L{end_line}' - #git_link_template = 'https://gitlab.com/USER/PROJECT/blob/{commit}/{path}#L{start_line}-L{end_line}' - #git_link_template = 'https://bitbucket.org/USER/PROJECT/src/{commit}/{path}#lines-{start_line}:{end_line}' - #git_link_template = 'https://CGIT_HOSTNAME/PROJECT/tree/{path}?id={commit}#n{start_line}' - #git_link_template = None - git_link_template = 'https://mpxd.net/code/jan/meanas/src/commit/{commit}/{path}#L{start_line}-L{end_line}' - - # A prefix to use for every HTML hyperlink in the generated documentation. - # No prefix results in all links being relative. - link_prefix = '' - - # Enable syntax highlighting for code/source blocks by including Highlight.js - syntax_highlighting = True - - # Set the style keyword such as 'atom-one-light' or 'github-gist' - # Options: https://github.com/highlightjs/highlight.js/tree/master/src/styles - # Demo: https://highlightjs.org/static/demo/ - hljs_style = 'github' - - # If set, insert Google Analytics tracking code. 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- } - - #http-server-module-list { - display: flex; - flex-flow: column; - } - #http-server-module-list div { - display: flex; - } - #http-server-module-list dt { - min-width: 10%; - } - #http-server-module-list p { - margin-top: 0; - } - - .toc ul, - #index { - list-style-type: none; - margin: 0; - padding: 0; - } - #index code { - background: transparent; - } - #index h3 { - border-bottom: 1px solid #ddd; - } - #index ul { - padding: 0; - } - #index h4 { - font-weight: bold; - } - #index h4 + ul { - margin-bottom:.6em; - } - /* Make TOC lists have 2+ columns when viewport is wide enough. - Assuming ~20-character identifiers and ~30% wide sidebar. */ - @media (min-width: 200ex) { #index .two-column { column-count: 2 } } - @media (min-width: 300ex) { #index .two-column { column-count: 3 } } - - dl { - margin-bottom: 2em; - } - dl dl:last-child { - margin-bottom: 4em; - } - dd { - margin: 0 0 1em 3em; - } - #header-classes + dl > dd { - margin-bottom: 3em; - } - dd dd { - margin-left: 2em; - } - dd p { - margin: 10px 0; - } - .name { - background: #111; - font-weight: bold; - font-size: .85em; - padding: 5px 10px; - display: inline-block; - min-width: 40%; - } - .name:hover { - background: #101010; - } - .name > span:first-child { - white-space: nowrap; - } - .name.class > span:nth-child(2) { - margin-left: .4em; - } - .inherited { - color: #777; - border-left: 5px solid #eee; - padding-left: 1em; - } - .inheritance em { - font-style: normal; - font-weight: bold; - } - - /* Docstrings titles, e.g. in numpydoc format */ - .desc h2 { - font-weight: 400; - font-size: 1.25em; - } - .desc h3 { - font-size: 1em; - } - .desc dt code { - background: inherit; /* Don't grey-back parameters */ - } - - .source summary, - .git-link-div { - color: #aaa; - text-align: right; - font-weight: 400; - font-size: .8em; - text-transform: uppercase; - } - .source summary > * { - white-space: nowrap; - cursor: pointer; - } - .git-link { - color: inherit; - margin-left: 1em; - } - .source pre { - max-height: 500px; - overflow: auto; - margin: 0; - } - .source pre code { - font-size: 12px; - overflow: visible; - } - .hlist { - list-style: none; - } - .hlist li { - display: inline; - } - .hlist li:after { - content: ',\2002'; - } - .hlist li:last-child:after { - content: none; - } - .hlist .hlist { - display: inline; - padding-left: 1em; - } - - img { - max-width: 100%; - } - - .admonition { - padding: .1em .5em; - margin-bottom: 1em; - } - .admonition-title { - font-weight: bold; - } - .admonition.note, - .admonition.info, - .admonition.important { - background: #610; - } - .admonition.todo, - .admonition.versionadded, - .admonition.tip, - .admonition.hint { - background: #202; - } - .admonition.warning, - .admonition.versionchanged, - .admonition.deprecated { - background: #02b; - } - .admonition.error, - .admonition.danger, - .admonition.caution { - background: darkpink; - } - - -<%def name="desktop()" filter="minify_css"> - @media screen and (min-width: 700px) { - #sidebar { - width: 30%; - } - #content { - width: 70%; - max-width: 100ch; - padding: 3em 4em; - border-left: 1px solid #ddd; - } - pre code { - font-size: 1em; - } - .item .name { - font-size: 1em; - } - main { - display: flex; - flex-direction: row-reverse; - justify-content: flex-end; - } - .toc ul ul, - #index ul { - padding-left: 1.5em; - } - .toc > ul > li { - margin-top: .5em; - } - } - - -<%def name="print()" filter="minify_css"> -@media print { - #sidebar h1 { - page-break-before: always; - } - .source { - display: none; - } -} -@media print { - * { - background: transparent !important; - color: #000 !important; /* Black prints faster: h5bp.com/s */ - box-shadow: none !important; - text-shadow: none !important; - } - - a[href]:after { - content: " (" attr(href) ")"; - font-size: 90%; - } - /* Internal, documentation links, recognized by having a title, - don't need the URL explicity stated. */ - a[href][title]:after { - content: none; - } - - abbr[title]:after { - content: " (" attr(title) ")"; - } - - /* - * Don't show links for images, or javascript/internal links - */ - - .ir a:after, - a[href^="javascript:"]:after, - a[href^="#"]:after { - content: ""; - } - - pre, - blockquote { - border: 1px solid #999; - page-break-inside: avoid; - } - - thead { - display: table-header-group; /* h5bp.com/t */ - } - - tr, - img { - page-break-inside: avoid; - } - - img { - max-width: 100% !important; - } - - @page { - margin: 0.5cm; - } - - p, - h2, - h3 { - orphans: 3; - widows: 3; - } - - h1, - h2, - h3, - h4, - h5, - h6 { - page-break-after: avoid; - } -} - diff --git a/pdoc_templates/html.mako b/pdoc_templates/html.mako deleted file mode 100644 index 6b3326f..0000000 --- a/pdoc_templates/html.mako +++ /dev/null @@ -1,445 +0,0 @@ -<% - import os - - import pdoc - from pdoc.html_helpers import extract_toc, glimpse, to_html as _to_html, format_git_link, _md, to_markdown - - from markdown.inlinepatterns import InlineProcessor - from markdown.util import AtomicString, etree - - - def link(d, name=None, fmt='{}'): - name = fmt.format(name or d.qualname + ('()' if isinstance(d, pdoc.Function) else '')) - if not isinstance(d, pdoc.Doc) or isinstance(d, pdoc.External) and not external_links: - return name - url = d.url(relative_to=module, link_prefix=link_prefix, - top_ancestor=not show_inherited_members) - return '{}'.format(d.refname, url, name) - - - # Altered latex delimeters (allow inline $...$, wrap in ) - class _MathPattern(InlineProcessor): - NAME = 'pdoc-math' - PATTERN = r'(? - -<%def name="ident(name)">${name} - -<%def name="show_source(d)"> - % if (show_source_code or git_link_template) and d.source and d.obj is not getattr(d.inherits, 'obj', None): - <% git_link = format_git_link(git_link_template, d) %> - % if show_source_code: -

- - Expand source code - % if git_link: - Browse git - %endif - - 
${d.source | h}
-
- % elif git_link: -
Browse git
- %endif - %endif - - -<%def name="show_desc(d, short=False)"> - <% - inherits = ' inherited' if d.inherits else '' - docstring = glimpse(d.docstring) if short or inherits else d.docstring - %> - % if d.inherits: -

- Inherited from: - % if hasattr(d.inherits, 'cls'): - ${link(d.inherits.cls)}.${link(d.inherits, d.name)} - % else: - ${link(d.inherits)} - % endif -

- % endif -
${docstring | to_html}
- % if not isinstance(d, pdoc.Module): - ${show_source(d)} - % endif - - -<%def name="show_module_list(modules)"> -

Python module list

- -% if not modules: -

No modules found.

-% else: -
- % for name, desc in modules: -
-
${name}
-
${desc | glimpse, to_html}
-
- % endfor -
-% endif - - -<%def name="show_column_list(items)"> - <% - two_column = len(items) >= 6 and all(len(i.name) < 20 for i in items) - %> -
    - % for item in items: -
  • ${link(item, item.name)}
    • - % endfor -
- - -<%def name="show_module(module)"> - <% - variables = module.variables(sort=sort_identifiers) - classes = module.classes(sort=sort_identifiers) - functions = module.functions(sort=sort_identifiers) - submodules = module.submodules() - %> - - <%def name="show_func(f)"> -
- <% - params = ', '.join(f.params(annotate=show_type_annotations, link=link)) - returns = show_type_annotations and f.return_annotation(link=link) or '' - if returns: - returns = ' ->\N{NBSP}' + returns - %> - ${f.funcdef()} ${ident(f.name)}(${params})${returns} -
-
${show_desc(f)}
- - -
- % if http_server: - - % endif -

${'Namespace' if module.is_namespace else 'Module'} ${module.name}

-
- -
- ${module.docstring | to_html} - ${show_source(module)} -
- -
- % if submodules: -

Sub-modules

-
- % for m in submodules: -
${link(m)}
-
${show_desc(m, short=True)}
- % endfor -
- % endif -
- -
- % if variables: -

Global variables

-
- % for v in variables: -
var ${ident(v.name)}
-
${show_desc(v)}
- % endfor -
- % endif -
- -
- % if functions: -

Functions

-
- % for f in functions: - ${show_func(f)} - % endfor -
- % endif -
- -
- % if classes: -

Classes

-
- % for c in classes: - <% - class_vars = c.class_variables(show_inherited_members, sort=sort_identifiers) - smethods = c.functions(show_inherited_members, sort=sort_identifiers) - inst_vars = c.instance_variables(show_inherited_members, sort=sort_identifiers) - methods = c.methods(show_inherited_members, sort=sort_identifiers) - mro = c.mro() - subclasses = c.subclasses() - params = ', '.join(c.params(annotate=show_type_annotations, link=link)) - %> -
- class ${ident(c.name)} - % if params: - (${params}) - % endif -
- -
${show_desc(c)} - - % if mro: -

Ancestors

-
    - % for cls in mro: -
  • ${link(cls)}
    • - % endfor -
- %endif - - % if subclasses: -

Subclasses

-
    - % for sub in subclasses: -
  • ${link(sub)}
    • - % endfor -
- % endif - % if class_vars: -

Class variables

-
- % for v in class_vars: -
var ${ident(v.name)}
-
${show_desc(v)}
- % endfor -
- % endif - % if smethods: -

Static methods

-
- % for f in smethods: - ${show_func(f)} - % endfor -
- % endif - % if inst_vars: -

Instance variables

-
- % for v in inst_vars: -
var ${ident(v.name)}
-
${show_desc(v)}
- % endfor -
- % endif - % if methods: -

Methods

-
- % for f in methods: - ${show_func(f)} - % endfor -
- % endif - - % if not show_inherited_members: - <% - members = c.inherited_members() - %> - % if members: -

Inherited members

-
    - % for cls, mems in members: -
  • ${link(cls)}: -
      - % for m in mems: -
    • ${link(m, name=m.name)}
      • - % endfor -
    - -
    • - % endfor -
- % endif - % endif - -
- % endfor -
- % endif -
- - -<%def name="module_index(module)"> - <% - variables = module.variables(sort=sort_identifiers) - classes = module.classes(sort=sort_identifiers) - functions = module.functions(sort=sort_identifiers) - submodules = module.submodules() - supermodule = module.supermodule - %> - - - - - - - - - - -<% - module_list = 'modules' in context.keys() # Whether we're showing module list in server mode -%> - - % if module_list: - Python module list - - % else: - ${module.name} API documentation - - % endif - - - - % if syntax_highlighting: - - %endif - - <%namespace name="css" file="css.mako" /> - - - - - % if google_analytics: - - % endif - - <%include file="head.mako"/> - - -
- % if module_list: -
- ${show_module_list(modules)} -
- % else: -
- ${show_module(module)} -
- ${module_index(module)} - % endif -
- - - -% if syntax_highlighting: - - -% endif - -% if http_server and module: ## Auto-reload on file change in dev mode - -% endif - - diff --git a/pdoc_templates/html_helpers.py b/pdoc_templates/html_helpers.py deleted file mode 100644 index 5e58405..0000000 --- a/pdoc_templates/html_helpers.py +++ /dev/null @@ -1,539 +0,0 @@ -""" -Helper functions for HTML output. -""" -import inspect -import os -import re -import subprocess -import traceback -from functools import partial, lru_cache -from typing import Callable, Match -from warnings import warn - -import markdown -from markdown.inlinepatterns import InlineProcessor -from markdown.util import AtomicString, etree - -import pdoc - - -@lru_cache() -def minify_css(css: str, - _whitespace=partial(re.compile(r'\s*([,{:;}])\s*').sub, r'\1'), - _comments=partial(re.compile(r'/\*.*?\*/', flags=re.DOTALL).sub, ''), - _trailing_semicolon=partial(re.compile(r';\s*}').sub, '}')): - """ - Minify CSS by removing extraneous whitespace, comments, and trailing semicolons. - """ - return _trailing_semicolon(_whitespace(_comments(css))).strip() - - -def minify_html(html: str, - _minify=partial( - re.compile(r'(.*?)()|(.*)', re.IGNORECASE | re.DOTALL).sub, - lambda m, _norm_space=partial(re.compile(r'\s\s+').sub, '\n'): ( - _norm_space(m.group(1) or '') + - (m.group(2) or '') + - _norm_space(m.group(3) or '')))): - """ - Minify HTML by replacing all consecutive whitespace with a single space - (or newline) character, except inside `
` tags.
-    """
-    return _minify(html)
-
-
-def glimpse(text: str, max_length=153, *, paragraph=True,
-            _split_paragraph=partial(re.compile(r'\s*\n\s*\n\s*').split, maxsplit=1),
-            _trim_last_word=partial(re.compile(r'\S+$').sub, ''),
-            _remove_titles=partial(re.compile(r'^(#+|-{4,}|={4,})', re.MULTILINE).sub, ' ')):
-    """
-    Returns a short excerpt (e.g. first paragraph) of text.
-    If `paragraph` is True, the first paragraph will be returned,
-    but never longer than `max_length` characters.
-    """
-    text = text.lstrip()
-    if paragraph:
-        text, *rest = _split_paragraph(text)
-        if rest:
-            text = text.rstrip('.')
-            text += ' …'
-        text = _remove_titles(text).strip()
-
-    if len(text) > max_length:
-        text = _trim_last_word(text[:max_length - 2])
-        if not text.endswith('.') or not paragraph:
-            text = text.rstrip('. ') + ' …'
-    return text
-
-
-_md = markdown.Markdown(
-    output_format='html5',
-    extensions=[
-        "markdown.extensions.abbr",
-        "markdown.extensions.attr_list",
-        "markdown.extensions.def_list",
-        "markdown.extensions.fenced_code",
-        "markdown.extensions.footnotes",
-        "markdown.extensions.tables",
-        "markdown.extensions.admonition",
-        "markdown.extensions.smarty",
-        "markdown.extensions.toc",
-    ],
-    extension_configs={
-        "markdown.extensions.smarty": dict(
-            smart_dashes=True,
-            smart_ellipses=True,
-            smart_quotes=False,
-            smart_angled_quotes=False,
-        ),
-    },
-)
-
-
-class _ToMarkdown:
-    """
-    This class serves as a namespace for methods converting common
-    documentation formats into markdown our Python-Markdown with
-    addons can ingest.
-
-    If debugging regexs (I can't imagine why that would be necessary
-    — they are all perfect!) an insta-preview tool such as RegEx101.com
-    will come in handy.
-    """
-    @staticmethod
-    def _deflist(name, type, desc,
-                 # Wraps any identifiers and string literals in parameter type spec
-                 # in backticks while skipping common "stopwords" such as 'or', 'of',
-                 # 'optional' ... See §4 Parameters:
-                 # https://numpydoc.readthedocs.io/en/latest/format.html#sections
-                 _type_parts=partial(
-                     re.compile(r'[\w.\'"]+').sub,
-                     lambda m: ('{}' if m.group(0) in ('of', 'or', 'default', 'optional') else
-                                '`{}`').format(m.group(0)))):
-        """
-        Returns `name`, `type`, and `desc` formatted as a
-        Python-Markdown definition list entry. See also:
-        https://python-markdown.github.io/extensions/definition_lists/
-        """
-        type = _type_parts(type or '')
-        desc = desc or ' '
-        assert _ToMarkdown._is_indented_4_spaces(desc)
-        assert name or type
-        ret = ""
-        if name:
-            ret += '**`{}`**'.format(name)
-        if type:
-            ret += ' : {}'.format(type) if ret else type
-        ret += '\n:   {}\n\n'.format(desc)
-        return ret
-
-    @staticmethod
-    def _numpy_params(match,
-                      _name_parts=partial(re.compile(', ').sub, '`**, **`')):
-        """ Converts NumpyDoc parameter (etc.) sections into Markdown. """
-        name, type, desc = match.group("name", "type", "desc")
-        type = type or match.groupdict().get('just_type', None)
-        desc = desc.strip()
-        name = name and _name_parts(name)
-        return _ToMarkdown._deflist(name, type, desc)
-
-    @staticmethod
-    def _numpy_seealso(match):
-        """
-        Converts NumpyDoc "See Also" section either into referenced code,
-        optionally within a definition list.
-        """
-        spec_with_desc, simple_list = match.groups()
-        if spec_with_desc:
-            return '\n\n'.join('`{}`\n:   {}'.format(*map(str.strip, line.split(':', 1)))
-                               for line in filter(None, spec_with_desc.split('\n')))
-        return ', '.join('`{}`'.format(i) for i in simple_list.split(', '))
-
-    @staticmethod
-    def _numpy_sections(match):
-        """
-        Convert sections with parameter, return, and see also lists to Markdown
-        lists.
-        """
-        section, body = match.groups()
-        if section.title() == 'See Also':
-            body = re.sub(r'^((?:\n?[\w.]* ?: .*)+)|(.*\w.*)',
-                          _ToMarkdown._numpy_seealso, body)
-        elif section.title() in ('Returns', 'Yields', 'Raises', 'Warns'):
-            body = re.sub(r'^(?:(?P\*{0,2}\w+(?:, \*{0,2}\w+)*)'
-                          r'(?: ?: (?P.*))|'
-                          r'(?P\w[^\n`*]*))(?(?:\n(?: {4}.*|$))*)',
-                          _ToMarkdown._numpy_params, body, flags=re.MULTILINE)
-        else:
-            body = re.sub(r'^(?P\*{0,2}\w+(?:, \*{0,2}\w+)*)'
-                          r'(?: ?: (?P.*))?(?(?:\n(?: {4}.*|$))*)',
-                          _ToMarkdown._numpy_params, body, flags=re.MULTILINE)
-        return section + '\n-----\n' + body
-
-    @staticmethod
-    def numpy(text):
-        """
-        Convert `text` in numpydoc docstring format to Markdown
-        to be further converted later.
-        """
-        return re.sub(r'^(\w[\w ]+)\n-{3,}\n'
-                      r'((?:(?!.+\n-+).*$\n?)*)',
-                      _ToMarkdown._numpy_sections, text, flags=re.MULTILINE)
-
-    @staticmethod
-    def _is_indented_4_spaces(txt, _3_spaces_or_less=re.compile(r'\n\s{0,3}\S').search):
-        return '\n' not in txt or not _3_spaces_or_less(txt)
-
-    @staticmethod
-    def _fix_indent(name, type, desc):
-        """Maybe fix indent from 2 to 4 spaces."""
-        if not _ToMarkdown._is_indented_4_spaces(desc):
-            desc = desc.replace('\n', '\n  ')
-        return name, type, desc
-
-    @staticmethod
-    def indent(indent, text, *, clean_first=False):
-        if clean_first:
-            text = inspect.cleandoc(text)
-        return re.sub(r'\n', '\n' + indent, indent + text.rstrip())
-
-    @staticmethod
-    def google(text,
-               _googledoc_sections=partial(
-                   re.compile(r'^([A-Z]\w+):$\n((?:\n?(?: {2,}.*|$))+)', re.MULTILINE).sub,
-                   lambda m, _params=partial(
-                           re.compile(r'^([\w*]+)(?: \(([\w.,=\[\] ]+)\))?: '
-                                      r'((?:.*)(?:\n(?: {2,}.*|$))*)', re.MULTILINE).sub,
-                           lambda m: _ToMarkdown._deflist(*_ToMarkdown._fix_indent(*m.groups()))): (
-                       m.group() if not m.group(2) else '\n{}\n-----\n{}'.format(
-                           m.group(1), _params(inspect.cleandoc('\n' + m.group(2))))))):
-        """
-        Convert `text` in Google-style docstring format to Markdown
-        to be further converted later.
-        """
-        return _googledoc_sections(text)
-
-    @staticmethod
-    def _admonition(match, module=None, limit_types=None):
-        indent, type, value, text = match.groups()
-
-        if limit_types and type not in limit_types:
-            return match.group(0)
-
-        if type == 'include' and module:
-            try:
-                return _ToMarkdown._include_file(indent, value,
-                                                 _ToMarkdown._directive_opts(text), module)
-            except Exception as e:
-                raise RuntimeError('`.. include:: {}` error in module {!r}: {}'
-                                   .format(value, module.name, e))
-        if type in ('image', 'figure'):
-            return '{}![{}]({})\n'.format(
-                indent, text.translate(str.maketrans({'\n': ' ',
-                                                      '[': '\\[',
-                                                      ']': '\\]'})).strip(), value)
-        if type == 'math':
-            return _ToMarkdown.indent(indent,
-                                      '\\[ ' + text.strip() + ' \\]',
-                                      clean_first=True)
-
-        if type == 'versionchanged':
-            title = 'Changed in version: ' + value
-        elif type == 'versionadded':
-            title = 'Added in version: ' + value
-        elif type == 'deprecated' and value:
-            title = 'Deprecated since version: ' + value
-        elif type == 'admonition':
-            title = value
-        elif type.lower() == 'todo':
-            title = 'TODO'
-            text = value + ' ' + text
-        else:
-            title = type.capitalize()
-            if value:
-                title += ': ' + value
-
-        text = _ToMarkdown.indent(indent + '    ', text, clean_first=True)
-        return '{}!!! {} "{}"\n{}\n'.format(indent, type, title, text)
-
-    @staticmethod
-    def admonitions(text, module, limit_types=None):
-        """
-        Process reStructuredText's block directives such as
-        `.. warning::`, `.. deprecated::`, `.. versionadded::`, etc.
-        and turn them into Python-M>arkdown admonitions.
-
-        `limit_types` is optionally a set of directives to limit processing to.
-
-        See: https://python-markdown.github.io/extensions/admonition/
-        """
-        substitute = partial(re.compile(r'^(?P *)\.\. ?(\w+)::(?: *(.*))?'
-                                        r'((?:\n(?:(?P=indent) +.*| *$))*)', re.MULTILINE).sub,
-                             partial(_ToMarkdown._admonition, module=module,
-                                     limit_types=limit_types))
-        # Apply twice for nested (e.g. image inside warning)
-        return substitute(substitute(text))
-
-    @staticmethod
-    def _include_file(indent: str, path: str, options: dict, module: pdoc.Module) -> str:
-        start_line = int(options.get('start-line', 0))
-        end_line = int(options.get('end-line', 0)) or None
-        start_after = options.get('start-after')
-        end_before = options.get('end-before')
-
-        with open(os.path.join(os.path.dirname(module.obj.__file__), path),
-                  encoding='utf-8') as f:
-            text = ''.join(list(f)[start_line:end_line])
-
-        if start_after:
-            text = text[text.index(start_after) + len(start_after):]
-        if end_before:
-            text = text[:text.index(end_before)]
-
-        return _ToMarkdown.indent(indent, text)
-
-    @staticmethod
-    def _directive_opts(text: str) -> dict:
-        return dict(re.findall(r'^ *:([^:]+): *(.*)', text, re.MULTILINE))
-
-    @staticmethod
-    def doctests(text,
-                 _indent_doctests=partial(
-                     re.compile(r'(?:^(?P```|~~~).*\n)?'
-                                r'(?:^>>>.*'
-                                r'(?:\n(?:(?:>>>|\.\.\.).*))*'
-                                r'(?:\n.*)?\n\n?)+'
-                                r'(?P=fence)?', re.MULTILINE).sub,
-                     lambda m: (m.group(0) if m.group('fence') else
-                                ('\n    ' + '\n    '.join(m.group(0).split('\n')) + '\n\n')))):
-        """
-        Indent non-fenced (`~~~`) top-level (0-indented)
-        doctest blocks so they render as code.
-        """
-        if not text.endswith('\n'):  # Needed for the r'(?:\n.*)?\n\n?)+' line (GH-72)
-            text += '\n'
-        return _indent_doctests(text)
-
-    @staticmethod
-    def raw_urls(text):
-        """Wrap URLs in Python-Markdown-compatible ."""
-        return re.sub(r'(?)\s]+)(\s*)', r'\1<\2>\3', text)
-
-
-class _MathPattern(InlineProcessor):
-    NAME = 'pdoc-math'
-    PATTERN = r'(?'):  # CUT was put into its own paragraph
-        toc = toc[:-3].rstrip()
-    return toc
-
-
-def format_git_link(template: str, dobj: pdoc.Doc):
-    """
-    Interpolate `template` as a formatted string literal using values extracted
-    from `dobj` and the working environment.
-    """
-    if not template:
-        return None
-    try:
-        if 'commit' in _str_template_fields(template):
-            commit = _git_head_commit()
-        abs_path = inspect.getfile(inspect.unwrap(dobj.obj))
-        path = _project_relative_path(abs_path)
-        lines, start_line = inspect.getsourcelines(dobj.obj)
-        end_line = start_line + len(lines) - 1
-        url = template.format(**locals())
-        return url
-    except Exception:
-        warn('format_git_link for {} failed:\n{}'.format(dobj.obj, traceback.format_exc()))
-        return None
-
-
-@lru_cache()
-def _git_head_commit():
-    """
-    If the working directory is part of a git repository, return the
-    head git commit hash. Otherwise, raise a CalledProcessError.
-    """
-    process_args = ['git', 'rev-parse', 'HEAD']
-    try:
-        commit = subprocess.check_output(process_args, universal_newlines=True).strip()
-        return commit
-    except OSError as error:
-        warn("git executable not found on system:\n{}".format(error))
-    except subprocess.CalledProcessError as error:
-        warn(
-            "Ensure pdoc is run within a git repository.\n"
-            "`{}` failed with output:\n{}"
-            .format(' '.join(process_args), error.output)
-        )
-    return None
-
-
-@lru_cache()
-def _git_project_root():
-    """
-    Return the path to project root directory or None if indeterminate.
-    """
-    path = None
-    for cmd in (['git', 'rev-parse', '--show-superproject-working-tree'],
-                ['git', 'rev-parse', '--show-toplevel']):
-        try:
-            path = subprocess.check_output(cmd, universal_newlines=True).rstrip('\r\n')
-            if path:
-                break
-        except (subprocess.CalledProcessError, OSError):
-            pass
-    return path
-
-
-@lru_cache()
-def _project_relative_path(absolute_path):
-    """
-    Convert an absolute path of a python source file to a project-relative path.
-    Assumes the project's path is either the current working directory or
-    Python library installation.
-    """
-    from distutils.sysconfig import get_python_lib
-    for prefix_path in (_git_project_root() or os.getcwd(),
-                        get_python_lib()):
-        common_path = os.path.commonpath([prefix_path, absolute_path])
-        if common_path == prefix_path:
-            # absolute_path is a descendant of prefix_path
-            return os.path.relpath(absolute_path, prefix_path)
-    raise RuntimeError(
-        "absolute path {!r} is not a descendant of the current working directory "
-        "or of the system's python library."
-        .format(absolute_path)
-    )
-
-
-@lru_cache()
-def _str_template_fields(template):
-    """
-    Return a list of `str.format` field names in a template string.
-    """
-    from string import Formatter
-    return [
-        field_name
-        for _, field_name, _, _ in Formatter().parse(template)
-        if field_name is not None
-    ]
diff --git a/pdoc_templates/pdf.mako b/pdoc_templates/pdf.mako
deleted file mode 100644
index 50e7989..0000000
--- a/pdoc_templates/pdf.mako
+++ /dev/null
@@ -1,185 +0,0 @@
-<%!
-    import re
-    import pdoc
-    from pdoc.html_helpers import to_markdown, format_git_link
-
-    def link(d, fmt='{}'):
-        name = fmt.format(d.qualname + ('()' if isinstance(d, pdoc.Function) else ''))
-        if isinstance(d, pdoc.External):
-            return name
-        return '[{}](#{})'.format(name, d.refname)
-
-    def _to_md(text, module):
-        text = to_markdown(text, module=module, link=link)
-        # Setext H2 headings to atx H2 headings
-        text = re.sub(r'\n(.+)\n-{3,}\n', r'\n## \1\n\n', text)
-        # Convert admonitions into simpler paragraphs, dedent contents
-        text = re.sub(r'^(?P( *))!!! \w+ \"([^\"]*)\"(.*(?:\n(?P=indent) +.*)*)',
-                      lambda m: '{}**{}:** {}'.format(m.group(2), m.group(3),
-                                                      re.sub('\n {,4}', '\n', m.group(4))),
-                      text, flags=re.MULTILINE)
-        return text
-
-    def subh(text, level=2):
-        # Deepen heading levels so H2 becomes H4 etc.
-        return re.sub(r'\n(#+) +(.+)\n', r'\n%s\1 \2\n' % ('#' * level), text)
-%>
-
-<%def name="title(level, string, id=None)">
-    <% id = ' {#%s}' % id if id is not None else '' %>
-${('#' * level) + ' ' + string + id}
-
-
-<%def name="funcdef(f)">
-    <%
-        returns = show_type_annotations and f.return_annotation() or ''
-        if returns:
-            returns = ' -> ' + returns
-    %>
-> `${f.funcdef()} ${f.name}(${', '.join(f.params(annotate=show_type_annotations))})${returns}`
-
-
-<%def name="classdef(c)">
-> `class ${c.name}(${', '.join(c.params(annotate=show_type_annotations))})`
-
-
-<%def name="show_source(d)">
-  % if (show_source_code or git_link_template) and d.source and d.obj is not getattr(d.inherits, 'obj', None):
-    <% git_link = format_git_link(git_link_template, d) %>
-[[view code]](${git_link})
-  %endif
-
-
----
-description: |
-    API documentation for modules: ${', '.join(m.name for m in modules)}.
-
-lang: en
-
-classoption: oneside
-geometry: margin=1in
-papersize: a4
-
-linkcolor: blue
-links-as-notes: true
-...
-% for module in modules:
-<%
-    submodules = module.submodules()
-    variables = module.variables()
-    functions = module.functions()
-    classes = module.classes()
-
-    def to_md(text):
-        return _to_md(text, module)
-%>
-
--------------------------------------------
-
-${title(1, ('Namespace' if module.is_namespace else 'Module') + ' `%s`' % module.name, module.refname)}
-${module.docstring | to_md}
-
-% if submodules:
-${title(2, 'Sub-modules')}
-    % for m in submodules:
-* [${m.name}](#${m.refname})
-    % endfor
-% endif
-
-% if variables:
-${title(2, 'Variables')}
-    % for v in variables:
-${title(3, 'Variable `%s`' % v.name, v.refname)}
-${show_source(v)}
-${v.docstring | to_md, subh, subh}
-    % endfor
-% endif
-
-% if functions:
-${title(2, 'Functions')}
-    % for f in functions:
-${title(3, 'Function `%s`' % f.name, f.refname)}
-${show_source(f)}
-
-${funcdef(f)}
-
-${f.docstring | to_md, subh, subh}
-    % endfor
-% endif
-
-% if classes:
-${title(2, 'Classes')}
-    % for cls in classes:
-${title(3, 'Class `%s`' % cls.name, cls.refname)}
-${show_source(cls)}
-
-${classdef(cls)}
-
-${cls.docstring | to_md, subh}
-<%
-    class_vars = cls.class_variables(show_inherited_members, sort=sort_identifiers)
-    static_methods = cls.functions(show_inherited_members, sort=sort_identifiers)
-    inst_vars = cls.instance_variables(show_inherited_members, sort=sort_identifiers)
-    methods = cls.methods(show_inherited_members, sort=sort_identifiers)
-    mro = cls.mro()
-    subclasses = cls.subclasses()
-%>
-        % if mro:
-${title(4, 'Ancestors (in MRO)')}
-            % for c in mro:
-* [${c.refname}](#${c.refname})
-            % endfor
-        % endif
-
-        % if subclasses:
-${title(4, 'Descendants')}
-            % for c in subclasses:
-* [${c.refname}](#${c.refname})
-            % endfor
-        % endif
-
-        % if class_vars:
-${title(4, 'Class variables')}
-            % for v in class_vars:
-${title(5, 'Variable `%s`' % v.name, v.refname)}
-${v.docstring | to_md, subh, subh}
-            % endfor
-        % endif
-
-        % if inst_vars:
-${title(4, 'Instance variables')}
-            % for v in inst_vars:
-${title(5, 'Variable `%s`' % v.name, v.refname)}
-${v.docstring | to_md, subh, subh}
-            % endfor
-        % endif
-
-        % if static_methods:
-${title(4, 'Static methods')}
-            % for f in static_methods:
-${title(5, '`Method %s`' % f.name, f.refname)}
-
-${funcdef(f)}
-
-${f.docstring | to_md, subh, subh}
-            % endfor
-        % endif
-
-        % if methods:
-${title(4, 'Methods')}
-            % for f in methods:
-${title(5, 'Method `%s`' % f.name, f.refname)}
-
-${funcdef(f)}
-
-${f.docstring | to_md, subh, subh}
-            % endfor
-        % endif
-    % endfor
-% endif
-
-##\## for module in modules:
-% endfor
-
------
-Generated by *pdoc* ${pdoc.__version__} ().
diff --git a/pdoc_templates/pdoc.css b/pdoc_templates/pdoc.css
deleted file mode 100644
index a563b44..0000000
--- a/pdoc_templates/pdoc.css
+++ /dev/null
@@ -1,381 +0,0 @@
-  .flex {
-    display: flex !important;
-  }
-
-  body {
-    line-height: 1.5em;
-    background: black;
-    color: #DDD;
-    max-width: 140ch;
-  }
-
-  #content {
-    padding: 20px;
-  }
-
-  #sidebar {
-    padding: 30px;
-    overflow: hidden;
-  }
-
-  .http-server-breadcrumbs {
-    font-size: 130%;
-    margin: 0 0 15px 0;
-  }
-
-  #footer {
-    font-size: .75em;
-    padding: 5px 30px;
-    border-top: 1px solid #ddd;
-    text-align: right;
-  }
-    #footer p {
-      margin: 0 0 0 1em;
-      display: inline-block;
-    }
-    #footer p:last-child {
-      margin-right: 30px;
-    }
-
-  h1, h2, h3, h4, h5 {
-    font-weight: 300;
-  }
-  h1 {
-    font-size: 2.5em;
-    line-height: 1.1em;
-    border-top: 20px white;
-  }
-  h2 {
-    font-size: 1.75em;
-    margin: 1em 0 .50em 0;
-  }
-  h3 {
-    font-size: 1.4em;
-    margin: 25px 0 10px 0;
-  }
-  h4 {
-    margin: 0;
-    font-size: 105%;
-  }
-
-  a {
-    color: #999;
-    text-decoration: none;
-    transition: color .3s ease-in-out;
-  }
-  a:hover {
-    color: #18d;
-  }
-
-  .title code {
-    font-weight: bold;
-  }
-  h2[id^="header-"] {
-    margin-top: 2em;
-  }
-  .ident {
-    color: #7ff;
-  }
-
-  pre code {
-    background: transparent;
-    font-size: .8em;
-    line-height: 1.4em;
-  }
-  code {
-    background: #0d0d0e;
-    padding: 1px 4px;
-    overflow-wrap: break-word;
-  }
-  h1 code { background: transparent }
-
-  pre {
-    background: #111;
-    border: 0;
-    border-top: 1px solid #ccc;
-    border-bottom: 1px solid #ccc;
-    margin: 1em 0;
-    padding: 1ex;
-  }
-
-  #http-server-module-list {
-    display: flex;
-    flex-flow: column;
-  }
-    #http-server-module-list div {
-      display: flex;
-    }
-    #http-server-module-list dt {
-      min-width: 10%;
-    }
-    #http-server-module-list p {
-      margin-top: 0;
-    }
-
-  .toc ul,
-  #index {
-    list-style-type: none;
-    margin: 0;
-    padding: 0;
-  }
-    #index code {
-      background: transparent;
-    }
-    #index h3 {
-      border-bottom: 1px solid #ddd;
-    }
-    #index ul {
-      padding: 0;
-    }
-    #index h4 {
-      font-weight: bold;
-    }
-    #index h4 + ul {
-      margin-bottom:.6em;
-    }
-    /* Make TOC lists have 2+ columns when viewport is wide enough.
-       Assuming ~20-character identifiers and ~30% wide sidebar. */
-    @media (min-width: 200ex) { #index .two-column { column-count: 2 } }
-    @media (min-width: 300ex) { #index .two-column { column-count: 3 } }
-
-  dl {
-    margin-bottom: 2em;
-  }
-    dl dl:last-child {
-      margin-bottom: 4em;
-    }
-  dd {
-    margin: 0 0 1em 3em;
-  }
-    #header-classes + dl > dd {
-      margin-bottom: 3em;
-    }
-    dd dd {
-      margin-left: 2em;
-    }
-    dd p {
-      margin: 10px 0;
-    }
-    blockquote code {
-      background: #111;
-      font-weight: bold;
-      font-size: .85em;
-      padding: 5px 10px;
-      display: inline-block;
-      min-width: 40%;
-    }
-      blockquote code:hover {
-        background: #101010;
-      }
-      .name > span:first-child {
-        white-space: nowrap;
-      }
-      .name.class > span:nth-child(2) {
-        margin-left: .4em;
-      }
-    .inherited {
-      color: #777;
-      border-left: 5px solid #eee;
-      padding-left: 1em;
-    }
-    .inheritance em {
-      font-style: normal;
-      font-weight: bold;
-    }
-
-    /* Docstrings titles, e.g. in numpydoc format */
-    .desc h2 {
-      font-weight: 400;
-      font-size: 1.25em;
-    }
-    .desc h3 {
-      font-size: 1em;
-    }
-    .desc dt code {
-      background: inherit;  /* Don't grey-back parameters */
-    }
-
-    .source summary,
-    .git-link-div {
-      color: #aaa;
-      text-align: right;
-      font-weight: 400;
-      font-size: .8em;
-      text-transform: uppercase;
-    }
-      .source summary > * {
-        white-space: nowrap;
-        cursor: pointer;
-      }
-      .git-link {
-        color: inherit;
-        margin-left: 1em;
-      }
-    .source pre {
-      max-height: 500px;
-      overflow: auto;
-      margin: 0;
-    }
-    .source pre code {
-      font-size: 12px;
-      overflow: visible;
-    }
-  .hlist {
-    list-style: none;
-  }
-    .hlist li {
-      display: inline;
-    }
-    .hlist li:after {
-      content: ',\2002';
-    }
-    .hlist li:last-child:after {
-      content: none;
-    }
-    .hlist .hlist {
-      display: inline;
-      padding-left: 1em;
-    }
-
-  img {
-    max-width: 100%;
-  }
-
-  .admonition {
-    padding: .1em .5em;
-    margin-bottom: 1em;
-  }
-    .admonition-title {
-      font-weight: bold;
-    }
-    .admonition.note,
-    .admonition.info,
-    .admonition.important {
-      background: #610;
-    }
-    .admonition.todo,
-    .admonition.versionadded,
-    .admonition.tip,
-    .admonition.hint {
-      background: #202;
-    }
-    .admonition.warning,
-    .admonition.versionchanged,
-    .admonition.deprecated {
-      background: #02b;
-    }
-    .admonition.error,
-    .admonition.danger,
-    .admonition.caution {
-      background: darkpink;
-    }
-
-  @media screen and (min-width: 700px) {
-    #sidebar {
-      width: 30%;
-    }
-    #content {
-      width: 70%;
-      max-width: 100ch;
-      padding: 3em 4em;
-      border-left: 1px solid #ddd;
-    }
-    pre code {
-      font-size: 1em;
-    }
-    .item .name {
-      font-size: 1em;
-    }
-    main {
-      display: flex;
-      flex-direction: row-reverse;
-      justify-content: flex-end;
-    }
-    .toc ul ul,
-    #index ul {
-      padding-left: 1.5em;
-    }
-    .toc > ul > li {
-      margin-top: .5em;
-    }
-  }
-
-@media print {
-  #sidebar h1 {
-    page-break-before: always;
-  }
-  .source {
-    display: none;
-  }
-}
-@media print {
-    * {
-        background: transparent !important;
-        color: #000 !important; /* Black prints faster: h5bp.com/s */
-        box-shadow: none !important;
-        text-shadow: none !important;
-    }
-
-    a[href]:after {
-        content: " (" attr(href) ")";
-        font-size: 90%;
-    }
-    /* Internal, documentation links, recognized by having a title,
-       don't need the URL explicity stated. */
-    a[href][title]:after {
-        content: none;
-    }
-
-    abbr[title]:after {
-        content: " (" attr(title) ")";
-    }
-
-    /*
-     * Don't show links for images, or javascript/internal links
-     */
-
-    .ir a:after,
-    a[href^="javascript:"]:after,
-    a[href^="#"]:after {
-        content: "";
-    }
-
-    pre,
-    blockquote {
-        border: 1px solid #999;
-        page-break-inside: avoid;
-    }
-
-    thead {
-        display: table-header-group; /* h5bp.com/t */
-    }
-
-    tr,
-    img {
-        page-break-inside: avoid;
-    }
-
-    img {
-        max-width: 100% !important;
-    }
-
-    @page {
-        margin: 0.5cm;
-    }
-
-    p,
-    h2,
-    h3 {
-        orphans: 3;
-        widows: 3;
-    }
-
-    h1,
-    h2,
-    h3,
-    h4,
-    h5,
-    h6 {
-        page-break-after: avoid;
-    }
-}
diff --git a/pyproject.toml b/pyproject.toml
index 8b875f3..7f1d6b4 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -39,15 +39,98 @@ include = [
     ]
 dynamic = ["version"]
 dependencies = [
-    "numpy~=1.21",
-    "scipy",
-    ]
+    "gridlock>=2.1",
+    "numpy>=2.0",
+    "scipy~=1.14",
+]
 
 
 [tool.hatch.version]
 path = "meanas/__init__.py"
 
 [project.optional-dependencies]
-dev = ["pytest", "pdoc", "gridlock"]
-examples = ["gridlock"]
-test = ["pytest"]
+dev = [
+    "meanas[test]",
+    "meanas[docs]",
+    "meanas[examples]",
+    "htmlark>=1.0",
+    "ruff>=0.6",
+    ]
+docs = [
+    "mkdocs>=1.6",
+    "mkdocs-material>=9.5",
+    "mkdocstrings[python]>=0.25",
+    "mkdocs-print-site-plugin>=2.3",
+    "pymdown-extensions>=10.7",
+    "htmlark>=1.0",
+    "ruff>=0.6",
+    ]
+examples = [
+    "matplotlib>=3.10.8",
+    "scikit-rf>=1.0",
+]
+test = ["pytest", "coverage"]
+
+
+[tool.ruff]
+exclude = [
+    ".git",
+    "dist",
+    ]
+line-length = 245
+indent-width = 4
+lint.dummy-variable-rgx = "^(_+|(_+[a-zA-Z0-9_]*[a-zA-Z0-9]+?))$"
+lint.select = [
+    "NPY", "E", "F", "W", "B", "ANN", "UP", "SLOT", "SIM", "LOG",
+    "C4", "ISC", "PIE", "PT", "RET", "TCH", "PTH", "INT",
+    "ARG", "PL", "R", "TRY",
+    "G010", "G101", "G201", "G202",
+    "Q002", "Q003", "Q004",
+    ]
+lint.ignore = [
+    #"ANN001",   # No annotation
+    "ANN002",   # *args
+    "ANN003",   # **kwargs
+    "ANN401",   # Any
+    "SIM108",   # single-line if / else assignment
+    "RET504",   # x=y+z; return x
+    "PIE790",   # unnecessary pass
+    "ISC003",   # non-implicit string concatenation
+    "C408",     # dict(x=y) instead of {'x': y}
+    "PLR09",    # Too many xxx
+    "PLR2004",  # magic number
+    "PLC0414",  # import x as x
+    "TRY003",   # Long exception message
+    "TRY002",   # Exception()
+    ]
+
+[tool.ruff.lint.per-file-ignores]
+"meanas/test/**/*.py" = ["ANN", "ARG", "TC006"]
+
+
+[[tool.mypy.overrides]]
+module = [
+    "scipy",
+    "scipy.optimize",
+    "scipy.linalg",
+    "scipy.sparse",
+    "scipy.sparse.linalg",
+    ]
+ignore_missing_imports = true
+
+#[tool.uv.sources]
+#gridlock = { path = "../gridlock", editable = true }
+
+[tool.pytest.ini_options]
+addopts = "-rsXx"
+testpaths = ["meanas"]
+markers = [
+    "complete: slower integration and smoke tests intended for full pre-commit confidence runs",
+]
+
+[tool.coverage.run]
+source = ["meanas"]
+
+[tool.coverage.report]
+show_missing = true
+omit = ["meanas/test/*"]
diff --git a/scripts/configure_docs_url.sh b/scripts/configure_docs_url.sh
new file mode 100755
index 0000000..ceacc18
--- /dev/null
+++ b/scripts/configure_docs_url.sh
@@ -0,0 +1,25 @@
+#!/bin/bash
+
+set -Eeuo pipefail
+
+ROOT="$(git rev-parse --show-toplevel)"
+cd "$ROOT"
+
+if [[ $# -gt 1 ]]; then
+    echo "usage: $0 [docs-site-url]" >&2
+    exit 2
+fi
+
+if [[ $# -eq 1 ]]; then
+    git config meanas.docsSiteUrl "$1"
+    echo "Configured meanas.docsSiteUrl=$1"
+    exit 0
+fi
+
+CURRENT_URL="$(git config --get meanas.docsSiteUrl || true)"
+if [[ -n "$CURRENT_URL" ]]; then
+    echo "$CURRENT_URL"
+else
+    echo "meanas.docsSiteUrl is not configured" >&2
+    exit 1
+fi
diff --git a/scripts/prepare_docs_sources.py b/scripts/prepare_docs_sources.py
new file mode 100644
index 0000000..7e9bcc5
--- /dev/null
+++ b/scripts/prepare_docs_sources.py
@@ -0,0 +1,93 @@
+#!/usr/bin/env python3
+"""Prepare a temporary source tree for docs generation.
+
+The live source keeps readable display-math blocks written as standalone
+`$$ ... $$` docstring sections. MkDocs + mkdocstrings does not consistently
+preserve those blocks as MathJax input when they appear inside API docstrings,
+so the docs build rewrites them in a temporary copy into explicit
+`
...
` containers.
+"""
+
+from __future__ import annotations
+
+from pathlib import Path
+import shutil
+import sys
+
+
+def _rewrite_display_math(text: str) -> str:
+    lines = text.splitlines(keepends=True)
+    output: list[str] = []
+    in_block = False
+    block_indent = ""
+
+    for line in lines:
+        stripped = line.strip()
+        indent = line[: len(line) - len(line.lstrip())]
+
+        if not in_block:
+            if stripped == "$$":
+                block_indent = indent
+                output.append(f'{block_indent}
\\[\n')
+                in_block = True
+                continue
+
+            if stripped.startswith("$$") and stripped.endswith("$$") and stripped != "$$":
+                body = stripped[2:-2].strip()
+                output.append(f'{indent}
\\[ {body} \\]
\n')
+                continue
+
+            if stripped.startswith("$$"):
+                block_indent = indent
+                body = stripped[2:].strip()
+                output.append(f'{block_indent}
\\[\n')
+                if body:
+                    output.append(f"{block_indent}{body}\n")
+                in_block = True
+                continue
+
+            output.append(line)
+            continue
+
+        if stripped == "$$":
+            output.append(f"{block_indent}\\]
\n")
+            in_block = False
+            block_indent = ""
+            continue
+
+        if stripped.endswith("$$"):
+            body = stripped[:-2].rstrip()
+            if body:
+                output.append(f"{block_indent}{body}\n")
+            output.append(f"{block_indent}\\]
\n")
+            in_block = False
+            block_indent = ""
+            continue
+
+        output.append(line)
+
+    if in_block:
+        raise ValueError("unterminated display-math block")
+
+    return "".join(output)
+
+
+def main() -> int:
+    if len(sys.argv) != 3:
+        print("usage: prepare_docs_sources.py  ", file=sys.stderr)
+        return 2
+
+    src_dir = Path(sys.argv[1]).resolve()
+    dst_root = Path(sys.argv[2]).resolve()
+    dst_pkg = dst_root / src_dir.name
+
+    shutil.copytree(src_dir, dst_pkg)
+
+    for path in dst_pkg.rglob("*.py"):
+        path.write_text(_rewrite_display_math(path.read_text()))
+
+    return 0
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())
diff --git a/scripts/publish_docs_branch.sh b/scripts/publish_docs_branch.sh
new file mode 100755
index 0000000..0fe1c4e
--- /dev/null
+++ b/scripts/publish_docs_branch.sh
@@ -0,0 +1,52 @@
+#!/bin/bash
+
+set -Eeuo pipefail
+
+if [[ $# -ne 2 ]]; then
+    echo "usage: $0  " >&2
+    exit 2
+fi
+
+SITE_DIR="$1"
+BRANCH="$2"
+
+if [[ ! -d "$SITE_DIR" ]]; then
+    echo "site directory not found: $SITE_DIR" >&2
+    exit 1
+fi
+
+if ! git rev-parse --git-dir >/dev/null 2>&1; then
+    echo "must be run inside a git repository" >&2
+    exit 1
+fi
+
+TMP_DIR="$(mktemp -d)"
+cleanup() {
+    git worktree remove --force "$TMP_DIR" >/dev/null 2>&1 || true
+}
+trap cleanup EXIT
+
+git fetch origin "$BRANCH" || true
+
+if git show-ref --verify --quiet "refs/remotes/origin/$BRANCH"; then
+    git worktree add --detach "$TMP_DIR" "origin/$BRANCH"
+else
+    git worktree add --detach "$TMP_DIR"
+    git -C "$TMP_DIR" checkout --orphan "$BRANCH"
+fi
+
+find "$TMP_DIR" -mindepth 1 -maxdepth 1 ! -name '.git' -exec rm -rf {} +
+cp -R "$SITE_DIR"/. "$TMP_DIR"/
+touch "$TMP_DIR/.nojekyll"
+
+git -C "$TMP_DIR" config user.name "${GIT_AUTHOR_NAME:-Forgejo Actions}"
+git -C "$TMP_DIR" config user.email "${GIT_AUTHOR_EMAIL:-forgejo-actions@localhost}"
+git -C "$TMP_DIR" add -A
+
+if git -C "$TMP_DIR" diff --cached --quiet; then
+    echo "no docs changes to publish"
+    exit 0
+fi
+
+git -C "$TMP_DIR" commit -m "Publish docs for ${GITHUB_SHA:-local build}"
+git -C "$TMP_DIR" push --force origin "HEAD:${BRANCH}"
diff --git a/scripts/push_with_docs.sh b/scripts/push_with_docs.sh
new file mode 100755
index 0000000..1b6e259
--- /dev/null
+++ b/scripts/push_with_docs.sh
@@ -0,0 +1,68 @@
+#!/bin/bash
+
+set -Eeuo pipefail
+
+ROOT="$(git rev-parse --show-toplevel)"
+cd "$ROOT"
+
+CURRENT_BRANCH="$(git branch --show-current)"
+
+resolve_remote_name() {
+    local branch="$1"
+    shift || true
+
+    for arg in "$@"; do
+        case "$arg" in
+            --)
+                break
+                ;;
+            -*)
+                continue
+                ;;
+            *)
+                if git remote get-url "$arg" >/dev/null 2>&1; then
+                    echo "$arg"
+                    return 0
+                fi
+                ;;
+        esac
+    done
+
+    git config --get "branch.${branch}.pushRemote" \
+        || git config --get remote.pushDefault \
+        || git config --get "branch.${branch}.remote" \
+        || echo origin
+}
+
+REMOTE_NAME="$(resolve_remote_name "$CURRENT_BRANCH" "$@")"
+
+git push "$@"
+
+if [[ "$CURRENT_BRANCH" != "master" ]]; then
+    echo "[meanas docs push] current branch is '${CURRENT_BRANCH:-}' not 'master'; skipping docs publish" >&2
+    exit 0
+fi
+
+if [[ "$REMOTE_NAME" != "origin" ]]; then
+    echo "[meanas docs push] push remote is '${REMOTE_NAME}' not 'origin'; skipping docs publish" >&2
+    exit 0
+fi
+
+if ! command -v mkdocs >/dev/null 2>&1; then
+    echo "[meanas docs push] mkdocs not found; skipping docs publish" >&2
+    exit 0
+fi
+
+DOCS_SITE_URL="${DOCS_SITE_URL:-$(git config --get meanas.docsSiteUrl || true)}"
+export DOCS_SITE_URL
+
+if [[ -n "$DOCS_SITE_URL" ]]; then
+    echo "[meanas docs push] publishing docs for ${DOCS_SITE_URL}" >&2
+else
+    echo "[meanas docs push] DOCS_SITE_URL is unset; building docs with relative site_url" >&2
+fi
+
+echo "[meanas docs push] building docs" >&2
+./make_docs.sh
+echo "[meanas docs push] publishing docs-site branch" >&2
+./scripts/publish_docs_branch.sh site docs-site
diff --git a/uv.lock b/uv.lock
new file mode 100644
index 0000000..08bad0c
--- /dev/null
+++ b/uv.lock
@@ -0,0 +1,1534 @@
+version = 1
+requires-python = ">=3.11"
+resolution-markers = [
+    "python_full_version >= '3.14' and sys_platform == 'win32'",
+    "python_full_version >= '3.14' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.14' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version < '3.14' and sys_platform == 'win32'",
+    "python_full_version < '3.14' and sys_platform == 'emscripten'",
+    "python_full_version < '3.14' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+]
+
+[[package]]
+name = "babel"
+version = "2.18.0"
+source = { registry = "https://pypi.org/simple" }
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