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opencl_fdfd/main.py
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529
opencl_fdfd/main.py
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import numpy
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from numpy.linalg import norm
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import jinja2
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import pyopencl
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import pyopencl.array
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from pyopencl.elementwise import ElementwiseKernel
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from pyopencl.reduction import ReductionKernel
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import time
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import fdfd_tools.operators
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def type_to_C(float_type: numpy.float32 or numpy.float64) -> str:
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"""
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Returns a string corresponding to the C equivalent of a numpy type.
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:param float_type: numpy type: float32, float64, complex64, complex128
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:return: string containing the corresponding C type (eg. 'double')
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"""
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types = {
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numpy.float32: 'float',
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numpy.float64: 'double',
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numpy.complex64: 'cfloat_t',
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numpy.complex128: 'cdouble_t',
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}
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if float_type not in types:
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raise Exception('Unsupported type')
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return types[float_type]
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def shape_source(shape) -> str:
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"""
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Defines sx, sy, sz C constants specifying the shape of the grid in each of the 3 dimensions.
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:param shape: [sx, sy, sz] values.
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:return: String containing C source.
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"""
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sxyz = """
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// Field sizes
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const int sx = {shape[0]};
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const int sy = {shape[1]};
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const int sz = {shape[2]};
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""".format(shape=shape)
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return sxyz
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# Defines dix, diy, diz constants used for stepping in the x, y, z directions in a linear array
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# (ie, given Ex[i] referring to position (x, y, z), Ex[i+diy] will refer to position (x, y+1, z))
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dixyz_source = """
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// Convert offset in field xyz to linear index offset
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const int dix = 1;
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const int diy = sx;
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const int diz = sx * sy;
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"""
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# Given a linear index i and shape sx, sy, sz, defines x, y, and z
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# as the 3D indices of the current element (i).
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xyz_source = """
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// Convert linear index to field index (xyz)
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const int z = i / (sx * sy);
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const int y = (i - z * sx * sy) / sx;
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const int x = (i - y * sx - z * sx * sy);
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"""
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vec_source = """
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if (i >= sx * sy * sz) {
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PYOPENCL_ELWISE_CONTINUE;
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}
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//Pointers into the components of a vectorized vector-field
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const int XX = 0;
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const int YY = sx * sy * sz;
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const int ZZ = sx * sy * sz * 2;
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"""
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E_ptrs = """
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__global cdouble_t *Ex = E + XX;
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__global cdouble_t *Ey = E + YY;
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__global cdouble_t *Ez = E + ZZ;
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"""
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H_ptrs = """
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__global cdouble_t *Hx = H + XX;
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__global cdouble_t *Hy = H + YY;
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__global cdouble_t *Hz = H + ZZ;
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"""
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# Source code for updating the E field; maxes use of dixyz_source.
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maxwell_E_source = """
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// E update equations
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int imx, imy, imz;
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if ( x == 0 ) {
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imx = i + (sx - 1) * dix;
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} else {
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imx = i - dix;
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}
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if ( y == 0 ) {
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imy = i + (sy - 1) * diy;
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} else {
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imy = i - diy;
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}
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if ( z == 0 ) {
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imz = i + (sz - 1) * diz;
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} else {
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imz = i - diz;
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}
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// E update equations
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{% if pec -%}
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if (pec[XX + i]) {
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Ex[i] = cdouble_new(0.0, 0.0);
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} else
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{%- endif -%}
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{
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cdouble_t tEx = cdouble_mul(Ex[i], oeps[XX + i]);
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cdouble_t Dzy = cdouble_mul(cdouble_sub(Hz[i], Hz[imy]), inv_dhy[y]);
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cdouble_t Dyz = cdouble_mul(cdouble_sub(Hy[i], Hy[imz]), inv_dhz[z]);
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tEx = cdouble_add(tEx, cdouble_sub(Dzy, Dyz));
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Ex[i] = cdouble_mul(tEx, Pl[XX + i]);
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}
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{% if pec -%}
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if (pec[YY + i]) {
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Ey[i] = cdouble_new(0.0, 0.0);
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} else
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{%- endif -%}
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{
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cdouble_t tEy = cdouble_mul(Ey[i], oeps[YY + i]);
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cdouble_t Dxz = cdouble_mul(cdouble_sub(Hx[i], Hx[imz]), inv_dhz[z]);
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cdouble_t Dzx = cdouble_mul(cdouble_sub(Hz[i], Hz[imx]), inv_dhx[x]);
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tEy = cdouble_add(tEy, cdouble_sub(Dxz, Dzx));
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Ey[i] = cdouble_mul(tEy, Pl[YY + i]);
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}
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{% if pec -%}
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if (pec[ZZ + i]) {
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Ez[i] = cdouble_new(0.0, 0.0);
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} else
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{%- endif -%}
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{
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cdouble_t tEz = cdouble_mul(Ez[i], oeps[ZZ + i]);
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cdouble_t Dyx = cdouble_mul(cdouble_sub(Hy[i], Hy[imx]), inv_dhx[x]);
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cdouble_t Dxy = cdouble_mul(cdouble_sub(Hx[i], Hx[imy]), inv_dhy[y]);
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tEz = cdouble_add(tEz, cdouble_sub(Dyx, Dxy));
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Ez[i] = cdouble_mul(tEz, Pl[ZZ + i]);
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}
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"""
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# Source code for updating the H field; maxes use of dixyz_source and assumes mu=0
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maxwell_H_source = """
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// H update equations
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int ipx, ipy, ipz;
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if ( x == sx - 1 ) {
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ipx = i - (sx - 1) * dix;
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} else {
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ipx = i + dix;
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}
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if ( y == sy - 1 ) {
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ipy = i - (sy - 1) * diy;
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} else {
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ipy = i + diy;
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}
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if ( z == sz - 1 ) {
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ipz = i - (sz - 1) * diz;
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} else {
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ipz = i + diz;
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}
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{% if pmc -%}
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if (pmc[XX + i]) {
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Hx[i] = cdouble_new(0.0, 0.0);
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} else
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{%- endif -%}
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{
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cdouble_t Dzy = cdouble_mul(cdouble_sub(Ez[ipy], Ez[i]), inv_dey[y]);
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cdouble_t Dyz = cdouble_mul(cdouble_sub(Ey[ipz], Ey[i]), inv_dez[z]);
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{%- if mu -%}
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Hx[i] = cdouble_mul(inv_mu[XX + i], cdouble_sub(Dzy, Dyz));
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{%- else -%}
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Hx[i] = cdouble_sub(Dzy, Dyz);
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{%- endif %}
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}
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{% if pmc -%}
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if (pmc[YY + i]) {
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Hy[i] = cdouble_new(0.0, 0.0);
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} else
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{%- endif -%}
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{
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cdouble_t Dxz = cdouble_mul(cdouble_sub(Ex[ipz], Ex[i]), inv_dez[z]);
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cdouble_t Dzx = cdouble_mul(cdouble_sub(Ez[ipx], Ez[i]), inv_dex[x]);
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{%- if mu -%}
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Hy[i] = cdouble_mul(inv_mu[YY + i], cdouble_sub(Dxz, Dzx));
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{%- else -%}
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Hy[i] = cdouble_sub(Dxz, Dzx);
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{%- endif %}
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}
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{% if pmc -%}
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if (pmc[XX + i]) {
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Hx[i] = cdouble_new(0.0, 0.0);
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} else
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{%- endif -%}
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{
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cdouble_t Dyx = cdouble_mul(cdouble_sub(Ey[ipx], Ey[i]), inv_dex[x]);
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cdouble_t Dxy = cdouble_mul(cdouble_sub(Ex[ipy], Ex[i]), inv_dey[y]);
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{%- if mu -%}
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Hz[i] = cdouble_mul(inv_mu[ZZ + i], cdouble_sub(Dyx, Dxy));
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{%- else -%}
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Hz[i] = cdouble_sub(Dyx, Dxy);
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{%- endif %}
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}
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"""
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p2e_source = '''
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Ex[i] = cdouble_mul(Pr[XX + i], p[XX + i]);
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Ey[i] = cdouble_mul(Pr[YY + i], p[YY + i]);
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Ez[i] = cdouble_mul(Pr[ZZ + i], p[ZZ + i]);
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'''
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preamble = '''
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#define PYOPENCL_DEFINE_CDOUBLE
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#include <pyopencl-complex.h>
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'''
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ctype = type_to_C(numpy.complex128)
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def ptrs(*args):
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return [ctype + ' *' + s for s in args]
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def create_a(context, shape, mu=False, pec=False, pmc=False):
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dhs = [ctype + ' *inv_dh' + a for a in 'xyz']
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des = [ctype + ' *inv_de' + a for a in 'xyz']
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header = shape_source(shape) + dixyz_source + xyz_source + vec_source + E_ptrs
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P2E_kernel = ElementwiseKernel(context,
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name='P2E',
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preamble=preamble,
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operation=header + p2e_source,
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arguments=', '.join(ptrs('E', 'p', 'Pr')))
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pmc_arg = ['int *pmc']
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e2h_source = header + H_ptrs + jinja2.Template(maxwell_H_source).render(mu=mu, pmc=pmc)
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E2H_kernel = ElementwiseKernel(context,
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name='E2H',
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preamble=preamble,
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operation=e2h_source,
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arguments=', '.join(ptrs('E', 'H', 'inv_mu') + pmc_arg + des))
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pec_arg = ['int *pec']
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h2e_source = header + H_ptrs + jinja2.Template(maxwell_E_source).render(pec=pec)
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H2E_kernel = ElementwiseKernel(context,
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name='H2E',
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preamble=preamble,
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operation=h2e_source,
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arguments=', '.join(ptrs('E', 'H', 'oeps', 'Pl') + pec_arg + dhs))
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def spmv(E, H, p, idxes, oeps, inv_mu, pec, pmc, Pl, Pr, e):
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e2 = P2E_kernel(E, p, Pr, wait_for=e)
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e2 = E2H_kernel(E, H, inv_mu, pmc, *idxes[0], wait_for=[e2])
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e2 = H2E_kernel(E, H, oeps, Pl, pec, *idxes[1], wait_for=[e2])
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return [e2]
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return spmv
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def create_xr_step(context):
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update_xr_source = '''
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x[i] = cdouble_add(x[i], cdouble_mul(alpha, p[i]));
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r[i] = cdouble_sub(r[i], cdouble_mul(alpha, v[i]));
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'''
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xr_args = ', '.join(ptrs('x', 'p', 'r', 'v') + [ctype + ' alpha'])
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xr_kernel = ElementwiseKernel(context,
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name='XR',
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preamble=preamble,
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operation=update_xr_source,
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arguments=xr_args)
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def xr_update(x, p, r, v, alpha, e):
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return [xr_kernel(x, p, r, v, alpha, wait_for=e)]
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return xr_update
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def create_rhoerr_step(context):
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update_ri_source = '''
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(double3)(r[i].real * r[i].real, \
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r[i].real * r[i].imag, \
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r[i].imag * r[i].imag)
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'''
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ri_dtype = pyopencl.array.vec.double3
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ri_kernel = ReductionKernel(context,
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name='RHOERR',
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preamble=preamble,
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dtype_out=ri_dtype,
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neutral='(double3)(0.0, 0.0, 0.0)',
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map_expr=update_ri_source,
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reduce_expr='a+b',
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arguments=ctype + ' *r')
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def ri_update(r, e):
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g = ri_kernel(r, wait_for=e).astype(ri_dtype).get()
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rr, ri, ii = [g[q] for q in 'xyz']
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rho = rr + 2j * ri - ii
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err = rr + ii
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return rho, err
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return ri_update
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def create_p_step(context):
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update_p_source = '''
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p[i] = cdouble_add(r[i], cdouble_mul(beta, p[i]));
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'''
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p_args = ptrs('p', 'r') + [ctype + ' beta']
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p_kernel = ElementwiseKernel(context,
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name='P',
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preamble=preamble,
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operation=update_p_source,
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arguments=', '.join(p_args))
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def p_update(p, r, beta, e):
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return [p_kernel(p, r, beta, wait_for=e)]
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return p_update
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def create_dot(context):
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dot_dtype = numpy.complex128
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dot_kernel = ReductionKernel(context,
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name='dot',
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preamble=preamble,
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dtype_out=dot_dtype,
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neutral='cdouble_new(0.0, 0.0)',
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map_expr='cdouble_mul(p[i], v[i])',
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reduce_expr='cdouble_add(a, b)',
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arguments=ptrs('p', 'v'))
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def ri_update(p, v, e):
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g = dot_kernel(p, v, wait_for=e)
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return g.get()
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return ri_update
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def cg_solver(omega, dxes, J, epsilon, mu=None, pec=None, pmc=None, adjoint=False,
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max_iters=40000, err_thresh=1e-6, context=None, verbose=False):
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start_time = time.perf_counter()
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b = -1j * omega * J
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shape = [d.size for d in dxes[0]]
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'''
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** In this comment, I use the notation M* = conj(M),
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M.T = transpose(M), M' = ctranspose(M), M N = dot(M, N)
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This solver uses a symmetrized wave operator M = (L A R) = (L A R).T
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(where L = inv(R) are diagonal preconditioner matrices) when
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solving the wave equation; therefore, it solves the problem
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M y = d
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=> (L A R) (inv(R) x) = (L b)
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=> A x = b
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with x = R y
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From the fact that M is symmetric, we can write
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(L A R)* = M* = M' = (L A R)' = R' A' L' = R* A' L*
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We obtain M* by conjugating all of our arguments (except J).
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Then we solve
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(R* A' L*) v = (R* b)
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and obtain x:
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x = L* v
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We can accomplish all this simply by conjugating everything (except J) and
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reversing the order of L and R
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'''
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if adjoint:
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# Conjugate everything
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dxes = [[numpy.conj(d) for d in dd] for dd in dxes]
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omega = numpy.conj(omega)
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epsilon = numpy.conj(epsilon)
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if mu is not None:
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mu = numpy.conj(mu)
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L, R = fdfd_tools.operators.e_full_preconditioners(dxes)
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if adjoint:
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b_preconditioned = R @ b
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else:
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b_preconditioned = L @ b
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'''
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Allocate GPU memory and load in data
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'''
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if context is None:
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context = pyopencl.create_some_context(False)
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queue = pyopencl.CommandQueue(context)
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def load_field(v, dtype=numpy.complex128):
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return pyopencl.array.to_device(queue, v.astype(dtype))
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r = load_field(b_preconditioned) # load preconditioned b into r
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H = pyopencl.array.zeros_like(r)
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x = pyopencl.array.zeros_like(r)
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v = pyopencl.array.zeros_like(r)
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p = pyopencl.array.zeros_like(r)
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alpha = 1.0 + 0j
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rho = 1.0 + 0j
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errs = []
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inv_dxes = [[load_field(1 / d) for d in dd] for dd in dxes]
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oeps = load_field(-omega ** 2 * epsilon)
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Pl = load_field(L.diagonal())
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Pr = load_field(R.diagonal())
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mu = numpy.ones_like(epsilon)
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# pec = numpy.zeros_like(epsilon)
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# pmc = numpy.zeros_like(epsilon)
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if mu is None:
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invm = load_field(numpy.array([]))
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else:
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invm = load_field(1 / mu)
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if pec is None:
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gpec = load_field(numpy.array([]), dtype=int)
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else:
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gpec = load_field(pec, dtype=int)
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if pmc is None:
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gpmc = load_field(numpy.array([]), dtype=int)
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else:
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gpmc = load_field(pmc, dtype=int)
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'''
|
||||
Generate OpenCL kernels
|
||||
'''
|
||||
has_mu, has_pec, has_pmc = [q is not None for q in (mu, pec, pmc)]
|
||||
|
||||
a_step_full = create_a(context, shape, has_mu, has_pec, has_pmc)
|
||||
xr_step = create_xr_step(context)
|
||||
rhoerr_step = create_rhoerr_step(context)
|
||||
p_step = create_p_step(context)
|
||||
dot = create_dot(context)
|
||||
|
||||
def a_step(E, H, p, events):
|
||||
return a_step_full(E, H, p, inv_dxes, oeps, invm, gpec, gpmc, Pl, Pr, events)
|
||||
|
||||
'''
|
||||
Start the solve
|
||||
'''
|
||||
start_time2 = time.perf_counter()
|
||||
|
||||
_, err2 = rhoerr_step(r, [])
|
||||
b_norm = numpy.sqrt(err2)
|
||||
print('b_norm check: ', b_norm)
|
||||
|
||||
success = False
|
||||
for k in range(max_iters):
|
||||
if verbose:
|
||||
print('[{:06d}] rho {:.4} alpha {:4.4}'.format(k, rho, alpha), end=' ')
|
||||
|
||||
rho_prev = rho
|
||||
e = xr_step(x, p, r, v, alpha, [])
|
||||
rho, err2 = rhoerr_step(r, e)
|
||||
|
||||
errs += [numpy.sqrt(err2) / b_norm]
|
||||
|
||||
if verbose:
|
||||
print('err', errs[-1])
|
||||
|
||||
if errs[-1] < err_thresh:
|
||||
success = True
|
||||
break
|
||||
|
||||
e = p_step(p, r, rho/rho_prev, [])
|
||||
e = a_step(v, H, p, e)
|
||||
alpha = rho / dot(p, v, e)
|
||||
|
||||
if k % 1000 == 0:
|
||||
print(k)
|
||||
|
||||
'''
|
||||
Done solving
|
||||
'''
|
||||
time_elapsed = time.perf_counter() - start_time
|
||||
|
||||
# Undo preconditioners
|
||||
if adjoint:
|
||||
x = (Pl * x).get()
|
||||
else:
|
||||
x = (Pr * x).get()
|
||||
|
||||
if success:
|
||||
print('Success', end='')
|
||||
else:
|
||||
print('Failure', end=', ')
|
||||
print(', {} iterations in {} sec: {} iterations/sec \
|
||||
'.format(k, time_elapsed, k / time_elapsed))
|
||||
print('final error', errs[-1])
|
||||
print('overhead {} sec'.format(start_time2 - start_time))
|
||||
|
||||
A0 = fdfd_tools.operators.e_full(omega, dxes, epsilon, mu).tocsr()
|
||||
if adjoint:
|
||||
# Remember we conjugated all the contents of A earlier
|
||||
A0 = A0.T
|
||||
print('Post-everything residual:', norm(A0 @ x - b) / norm(b))
|
||||
return x
|
||||
Loading…
Reference in New Issue
Block a user