void blasglue_gemm(char transa, char transb, int m, int n, int k,
real a, scalar *A, int fdA, scalar *B, int fdB,
real b, scalar *C, int fdC)
{
scalar alpha, beta;
if (m*n == 0)
return;
if (k == 0) {
int i, j;
for (i = 0; i < m; ++i)
for (j = 0; j < n; ++j)
ASSIGN_ZERO(C[i*fdC + j]);
return;
}
CHECK(A != C && B != C, "gemm output array must be distinct");
ASSIGN_REAL(alpha,a);
ASSIGN_REAL(beta,b);
F(gemm,GEMM) (&transb, &transa, &n, &m, &k,
&alpha, B, &fdB, A, &fdA, &beta, C, &fdC);
}
static void TEMPLATE (ldl_dsolve)
(
cholmod_factor *L,
cholmod_dense *Y /* nr-by-n with leading dimension nr */
)
{
double d [1] ;
double *Lx, *Yx, *Yz ;
Int *Lp ;
Int n, nrhs, k, p, k1, k2 ;
ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */
ASSERT (L->n == Y->ncol) ; /* dimensions must match */
ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */
ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */
ASSERT (!(L->is_super) && !(L->is_ll)) ; /* L is simplicial LDL' */
nrhs = Y->nrow ;
n = L->n ;
Lp = L->p ;
Lx = L->x ;
Yx = Y->x ;
Yz = Y->z ;
for (k = 0 ; k < n ; k++)
{
k1 = k*nrhs ;
k2 = (k+1)*nrhs ;
ASSIGN_REAL (d,0, Lx,Lp[k]) ;
for (p = k1 ; p < k2 ; p++)
{
DIV_REAL (Yx,Yz,p, Yx,Yz,p, d,0) ;
}
}
}
void blasglue_rscal(int n, real a, scalar *x, int incx)
{
scalar alpha;
ASSIGN_REAL(alpha, a);
F(scal,SCAL) (&n, &alpha, x, &incx);
}
void blasglue_axpy(int n, real a, scalar *x, int incx, scalar *y, int incy)
{
scalar alpha;
ASSIGN_REAL(alpha, a);
F(axpy,AXPY) (&n, &alpha, x, &incx, y, &incy);
}
int main(int argc, char **argv)
{
maxwell_data *mdata;
maxwell_target_data *mtdata = NULL;
int local_N, N_start, alloc_N;
real R[3][3] = { {1,0,0}, {0,0.01,0}, {0,0,0.01} };
real G[3][3] = { {1,0,0}, {0,100,0}, {0,0,100} };
real kvector[3] = {KX,0,0};
evectmatrix H, Hstart, W[NWORK];
real *eigvals;
int i, iters;
int num_iters;
int parity = NO_PARITY;
int nx = NX, ny = NY, nz = NZ;
int num_bands = NUM_BANDS;
real target_freq = 0.0;
int do_target = 0;
evectoperator op;
evectpreconditioner pre_op;
void *op_data, *pre_op_data;
real error_tol = ERROR_TOL;
int mesh_size = MESH_SIZE, mesh[3];
epsilon_data ed;
int stop1 = 0;
int verbose = 0;
int which_preconditioner = 2;
double max_err = 1e20;
srand(time(NULL));
#if defined(DEBUG) && defined(HAVE_FEENABLEEXCEPT)
feenableexcept(FE_INVALID | FE_OVERFLOW); /* crash on NaN/overflow */
#endif
ed.eps_high = EPS_HIGH;
ed.eps_low = EPS_LOW;
ed.eps_high_x = EPS_HIGH_X;
#ifdef HAVE_GETOPT
{
extern char *optarg;
extern int optind;
int c;
while ((c = getopt(argc, argv, "hs:k:b:n:f:x:y:z:emt:c:g:1pvE:"))
!= -1)
switch (c) {
case 'h':
usage();
exit(EXIT_SUCCESS);
break;
case 's':
srand(atoi(optarg));
break;
case 'k':
kvector[0] = atof(optarg);
break;
case 'b':
num_bands = atoi(optarg);
CHECK(num_bands > 0, "num_bands must be positive");
break;
case 'n':
ed.eps_high = atof(optarg);
CHECK(ed.eps_high > 0.0, "index must be positive");
ed.eps_high = ed.eps_high * ed.eps_high;
break;
case 'f':
ed.eps_high_x = atof(optarg);
CHECK(ed.eps_high_x > 0.0, "fill must be positive");
break;
case 'x':
nx = atoi(optarg);
CHECK(nx > 0, "x size must be positive");
break;
case 'y':
ny = atoi(optarg);
CHECK(ny > 0, "y size must be positive");
break;
case 'z':
nz = atoi(optarg);
CHECK(nz > 0, "z size must be positive");
break;
case 'e':
parity = EVEN_Z_PARITY;
break;
case 'm':
parity = ODD_Z_PARITY;
break;
case 't':
target_freq = fabs(atof(optarg));
do_target = 1;
break;
case 'E':
max_err = fabs(atof(optarg));
CHECK(max_err > 0, "maximum error must be positive");
break;
case 'c':
error_tol = fabs(atof(optarg));
break;
case 'g':
mesh_size = atoi(optarg);
CHECK(mesh_size > 0, "mesh size must be positive");
break;
case '1':
stop1 = 1;
break;
case 'p':
which_preconditioner = 1;
break;
case 'v':
verbose = 1;
break;
default:
usage();
exit(EXIT_FAILURE);
}
if (argc != optind) {
usage();
exit(EXIT_FAILURE);
}
}
#endif
#ifdef ENABLE_PROF
stop1 = 1;
#endif
mesh[0] = mesh[1] = mesh[2] = mesh_size;
printf("Creating Maxwell data...\n");
mdata = create_maxwell_data(nx, ny, nz, &local_N, &N_start, &alloc_N,
num_bands, NUM_FFT_BANDS);
CHECK(mdata, "NULL mdata");
set_maxwell_data_parity(mdata, parity);
printf("Setting k vector to (%g, %g, %g)...\n",
kvector[0], kvector[1], kvector[2]);
update_maxwell_data_k(mdata, kvector, G[0], G[1], G[2]);
printf("Initializing dielectric...\n");
/* set up dielectric function (a simple Bragg mirror) */
set_maxwell_dielectric(mdata, mesh, R, G, epsilon, 0, &ed);
if (verbose && ny == 1 && nz == 1) {
printf("dielectric function:\n");
for (i = 0; i < nx; ++i) {
if (mdata->eps_inv[i].m00 == mdata->eps_inv[i].m11)
printf(" eps(%g) = %g\n", i * 1.0 / nx,
1.0/mdata->eps_inv[i].m00);
else
printf(" eps(%g) = x: %g OR y: %g\n", i * 1.0 / nx,
1.0/mdata->eps_inv[i].m00,
1.0/mdata->eps_inv[i].m11);
}
printf("\n");
}
printf("Allocating fields...\n");
H = create_evectmatrix(nx * ny * nz, 2, num_bands,
local_N, N_start, alloc_N);
Hstart = create_evectmatrix(nx * ny * nz, 2, num_bands,
local_N, N_start, alloc_N);
for (i = 0; i < NWORK; ++i)
W[i] = create_evectmatrix(nx * ny * nz, 2, num_bands,
local_N, N_start, alloc_N);
CHK_MALLOC(eigvals, real, num_bands);
for (iters = 0; iters < PROF_ITERS; ++iters) {
printf("Initializing fields...\n");
for (i = 0; i < H.n * H.p; ++i)
ASSIGN_REAL(Hstart.data[i], rand() * 1.0 / RAND_MAX);
/*****************************************/
if (do_target) {
printf("\nSolving for eigenvectors close to %f...\n", target_freq);
mtdata = create_maxwell_target_data(mdata, target_freq);
op = maxwell_target_operator;
if (which_preconditioner == 1)
pre_op = maxwell_target_preconditioner;
else
pre_op = maxwell_target_preconditioner2;
op_data = (void *) mtdata;
pre_op_data = (void *) mtdata;
}
else {
op = maxwell_operator;
if (which_preconditioner == 1)
pre_op = maxwell_preconditioner;
else
pre_op = maxwell_preconditioner2;
op_data = (void *) mdata;
pre_op_data = (void *) mdata;
}
/*****************************************/
printf("\nSolving for eigenvectors with preconditioning...\n");
evectmatrix_copy(H, Hstart);
eigensolver(H, eigvals,
op, op_data, NULL,NULL,
pre_op, pre_op_data,
maxwell_parity_constraint, (void *) mdata,
W, NWORK, error_tol, &num_iters, EIGS_DEFAULT_FLAGS);
if (do_target)
eigensolver_get_eigenvals(H, eigvals, maxwell_operator, mdata,
W[0], W[1]);
printf("Solved for eigenvectors after %d iterations.\n", num_iters);
printf("%15s%15s%15s%15s\n","eigenval", "frequency", "exact freq.",
"error");
for (i = 0; i < num_bands; ++i) {
double err;
real freq = sqrt(eigvals[i]);
real exact_freq = bragg_omega(freq, kvector[0], sqrt(ed.eps_high),
ed.eps_high_x, sqrt(ed.eps_low),
1.0 - ed.eps_high_x, 1.0e-7);
printf("%15f%15f%15f%15e\n", eigvals[i], freq, exact_freq,
err = fabs(freq - exact_freq) / exact_freq);
CHECK(err <= max_err, "error exceeds tolerance");
}
printf("\n");
for (i = 0; i < num_bands; ++i) {
real kdom[3];
real k;
maxwell_dominant_planewave(mdata, H, i + 1, kdom);
if ((i + 1) % 2 == 1)
k = kvector[0] + (i + 1) / 2;
else
k = kvector[0] - (i + 1) / 2;
if (kvector[0] > 0 && kvector[0] < 0.5 && ed.eps_high == 1) {
printf("Expected kdom: %15f%15f%15f\n", k, kvector[1], kvector[2]);
printf("Got kdom: %15f%15f%15f\n", kdom[0], kdom[1], kdom[2]);
CHECK(k == kdom[0] && kvector[1] == kdom[1] && kvector[2] == kdom[2],
"unexpected result from maxwell_dominant_planewave");
}
}
}
if (!stop1) {
/*****************************************/
printf("\nSolving for eigenvectors without preconditioning...\n");
evectmatrix_copy(H, Hstart);
eigensolver(H, eigvals,
op, op_data, NULL,NULL,
NULL, NULL,
maxwell_parity_constraint, (void *) mdata,
W, NWORK, error_tol, &num_iters, EIGS_DEFAULT_FLAGS);
if (do_target)
eigensolver_get_eigenvals(H, eigvals, maxwell_operator, mdata,
W[0], W[1]);
printf("Solved for eigenvectors after %d iterations.\n", num_iters);
printf("%15s%15s%15s%15s\n","eigenval", "frequency", "exact freq.",
"error");
for (i = 0; i < num_bands; ++i) {
double err;
real freq = sqrt(eigvals[i]);
real exact_freq = bragg_omega(freq, kvector[0], sqrt(ed.eps_high),
ed.eps_high_x, sqrt(ed.eps_low),
1.0 - ed.eps_high_x, 1.0e-7);
printf("%15f%15f%15f%15e\n", eigvals[i], freq, exact_freq,
err = fabs(freq - exact_freq) / exact_freq);
CHECK(err <= max_err, "error exceeds tolerance");
}
printf("\n");
/*****************************************/
printf("\nSolving for eigenvectors without conj. grad...\n");
evectmatrix_copy(H, Hstart);
eigensolver(H, eigvals,
op, op_data, NULL,NULL,
pre_op, pre_op_data,
maxwell_parity_constraint, (void *) mdata,
W, NWORK - 1, error_tol, &num_iters, EIGS_DEFAULT_FLAGS);
if (do_target)
eigensolver_get_eigenvals(H, eigvals, maxwell_operator, mdata,
W[0], W[1]);
printf("Solved for eigenvectors after %d iterations.\n", num_iters);
printf("%15s%15s%15s%15s\n","eigenval", "frequency", "exact freq.",
"error");
for (i = 0; i < num_bands; ++i) {
double err;
real freq = sqrt(eigvals[i]);
real exact_freq = bragg_omega(freq, kvector[0], sqrt(ed.eps_high),
ed.eps_high_x, sqrt(ed.eps_low),
1.0 - ed.eps_high_x, 1.0e-7);
printf("%15f%15f%15f%15e\n", eigvals[i], freq, exact_freq,
err = fabs(freq - exact_freq) / exact_freq);
CHECK(err <= max_err, "error exceeds tolerance");
}
printf("\n");
/*****************************************/
printf("\nSolving for eigenvectors without precond. or conj. grad...\n");
evectmatrix_copy(H, Hstart);
eigensolver(H, eigvals,
op, op_data,
NULL, NULL, NULL,NULL,
maxwell_parity_constraint, (void *) mdata,
W, NWORK - 1, error_tol, &num_iters, EIGS_DEFAULT_FLAGS);
if (do_target)
eigensolver_get_eigenvals(H, eigvals, maxwell_operator, mdata,
W[0], W[1]);
printf("Solved for eigenvectors after %d iterations.\n", num_iters);
printf("%15s%15s%15s%15s\n","eigenval", "frequency", "exact freq.",
"error");
for (i = 0; i < num_bands; ++i) {
double err;
real freq = sqrt(eigvals[i]);
real exact_freq = bragg_omega(freq, kvector[0], sqrt(ed.eps_high),
ed.eps_high_x, sqrt(ed.eps_low),
1.0 - ed.eps_high_x, 1.0e-7);
printf("%15f%15f%15f%15e\n", eigvals[i], freq, exact_freq,
err = fabs(freq - exact_freq) / exact_freq);
CHECK(err <= max_err, "error exceeds tolerance");
}
printf("\n");
/*****************************************/
}
destroy_evectmatrix(H);
destroy_evectmatrix(Hstart);
for (i = 0; i < NWORK; ++i)
destroy_evectmatrix(W[i]);
destroy_maxwell_target_data(mtdata);
destroy_maxwell_data(mdata);
free(eigvals);
debug_check_memory_leaks();
return EXIT_SUCCESS;
}
