Add solvers submodule and clean up examples.

Solvers submodule includes a generic solver in case you already have a
sparse matrix solver, or in case you have no solver at all.

Example file now uses alternate solvers if available, and has a nicer
way of picking which solver gets used.
This commit is contained in:
jan 2016-08-04 22:46:02 -07:00
parent 85880c859e
commit ec674fe3f4
3 changed files with 153 additions and 16 deletions

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@ -1,18 +1,22 @@
import importlib
import numpy
from numpy.linalg import norm
from fdfd_tools import vec, unvec, waveguide_mode
import fdfd_tools, fdfd_tools.functional, fdfd_tools.grid
import fdfd_tools
import fdfd_tools.functional
import fdfd_tools.grid
from fdfd_tools.solvers import generic as generic_solver
import gridlock
from matplotlib import pyplot
#import magma_fdfd
from opencl_fdfd import cg_solver, csr
__author__ = 'Jan Petykiewicz'
def test0():
def test0(solver=generic_solver):
dx = 50 # discretization (nm/cell)
pml_thickness = 10 # (number of cells)
@ -59,21 +63,27 @@ def test0():
J = [numpy.zeros_like(grid.grids[0], dtype=complex) for _ in range(3)]
J[1][15, grid.shape[1]//2, grid.shape[2]//2] = 1e5
'''
Solve!
'''
x = solver(J=vec(J), **sim_args)
A = fdfd_tools.functional.e_full(omega, dxes, vec(grid.grids)).tocsr()
b = -1j * omega * vec(J)
print('Norm of the residual is ', norm(A @ x - b))
x = solve_A(A, b)
E = unvec(x, grid.shape)
print('Norm of the residual is {}'.format(numpy.linalg.norm(A.dot(x) - b)/numpy.linalg.norm(b)))
'''
Plot results
'''
pyplot.figure()
pyplot.pcolor(numpy.real(E[1][:, :, grid.shape[2]//2]), cmap='seismic')
pyplot.axis('equal')
pyplot.show()
def test1():
def test1(solver=generic_solver):
dx = 40 # discretization (nm/cell)
pml_thickness = 10 # (number of cells)
@ -142,17 +152,14 @@ def test1():
'pmc': vec(pmcg.grids),
}
x = solver(J=vec(J), **sim_args)
b = -1j * omega * vec(J)
A = fdfd_tools.operators.e_full(**sim_args).tocsr()
# x = magma_fdfd.solve_A(A, b)
# x = csr.cg_solver(J=vec(J), **sim_args)
x = cg_solver(J=vec(J), **sim_args)
print('Norm of the residual is ', norm(A @ x - b))
E = unvec(x, grid.shape)
print('Norm of the residual is ', numpy.linalg.norm(A @ x - b))
'''
Plot results
'''
@ -197,6 +204,22 @@ def test1():
pyplot.show()
print('Average overlap with mode:', sum(q)/len(q))
def module_available(name):
return importlib.util.find_spec(name) is not None
if __name__ == '__main__':
# test0()
test1()
if module_available('opencl_fdfd'):
from opencl_fdfd import cg_solver as opencl_solver
test1(opencl_solver)
# from opencl_fdfd.csr import fdfd_cg_solver as opencl_csr_solver
# test1(opencl_csr_solver)
# elif module_available('magma_fdfd'):
# from magma_fdfd import solver as magma_solver
# test1(magma_solver)
else:
test1()

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@ -22,4 +22,4 @@ Dependencies:
from .vectorization import vec, unvec, field_t, vfield_t
from .grid import dx_lists_t
__author__ = 'Jan Petykiewicz'
__author__ = 'Jan Petykiewicz'

114
fdfd_tools/solvers.py Normal file
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@ -0,0 +1,114 @@
"""
Solvers for FDFD problems.
"""
from typing import List, Callable, Dict, Any
import numpy
from numpy.linalg import norm
import scipy.sparse.linalg
from . import operators
def _scipy_qmr(A: scipy.sparse.csr_matrix,
b: numpy.ndarray,
**kwargs
) -> numpy.ndarray:
"""
Wrapper for scipy.sparse.linalg.qmr
:param A: Sparse matrix
:param b: Right-hand-side vector
:param kwargs: Passed as **kwargs to the wrapped function
:return: Guess for solution (returned even if didn't converge)
"""
'''
Report on our progress
'''
iter = 0
def print_residual(xk):
nonlocal iter
iter += 1
if iter % 100 == 0:
print('Solver residual at iteration', iter, ':', norm(A @ xk - b))
if 'callback' in kwargs:
def augmented_callback(xk):
print_residual(xk)
kwargs['callback'](xk)
kwargs['callback'] = augmented_callback
else:
kwargs['callback'] = print_residual
'''
Run the actual solve
'''
x, _ = scipy.sparse.linalg.qmr(A, b, **kwargs)
return x
def generic(omega: complex,
dxes: List[List[numpy.ndarray]],
J: numpy.ndarray,
epsilon: numpy.ndarray,
mu: numpy.ndarray = None,
pec: numpy.ndarray = None,
pmc: numpy.ndarray = None,
adjoint: bool = False,
matrix_solver: Callable[..., numpy.ndarray] = _scipy_qmr,
matrix_solver_opts: Dict[str, Any] = None,
) -> numpy.ndarray:
"""
Conjugate gradient FDFD solver using CSR sparse matrices.
All ndarray arguments should be 1D array, as returned by fdfd_tools.vec().
:param omega: Complex frequency to solve at.
:param dxes: [[dx_e, dy_e, dz_e], [dx_h, dy_h, dz_h]] (complex cell sizes)
:param J: Electric current distribution (at E-field locations)
:param epsilon: Dielectric constant distribution (at E-field locations)
:param mu: Magnetic permeability distribution (at H-field locations)
:param pec: Perfect electric conductor distribution
(at E-field locations; non-zero value indicates PEC is present)
:param pmc: Perfect magnetic conductor distribution
(at H-field locations; non-zero value indicates PMC is present)
:param adjoint: If true, solves the adjoint problem.
:param matrix_solver: Called as matrix_solver(A, b, **matrix_solver_opts) -> x
Where A: scipy.sparse.csr_matrix
b: numpy.ndarray
x: numpy.ndarray
Default is a wrapped version of scipy.sparse.linalg.qmr()
which doesn't return convergence info and prints the residual
every 100 iterations.
:param matrix_solver_opts: Passed as kwargs to matrix_solver(...)
:return: E-field which solves the system.
"""
if matrix_solver_opts is None:
matrix_solver_opts = dict()
b0 = -1j * omega * J
A0 = operators.e_full(omega, dxes, epsilon=epsilon, mu=mu, pec=pec, pmc=pmc)
Pl, Pr = operators.e_full_preconditioners(dxes)
if adjoint:
A = (Pl @ A0 @ Pr).H
b = Pr.H @ b0
else:
A = Pl @ A0 @ Pr
b = Pl @ b0
x = matrix_solver(A.tocsr(), b, **matrix_solver_opts)
if adjoint:
x0 = Pl.H @ x
else:
x0 = Pr @ x
return x0