void
uninit_hmatrix(phmatrix hm)
{
int rsons = hm->rsons;
int csons = hm->csons;
assert(hm->refs == 0);
if (hm->son) {
for (int j=0;j<csons;j++) {
for (int i=0;i<rsons;i++) {
unref_hmatrix(hm->son[i+j*rsons]);
}
}
delete [] hm->son;
}
if (hm->f) {
del_amatrix(hm->f);
}
if (hm->r) {
del_rkmatrix(hm->r);
}
}
/* Simple convenience wrapper for GMRES solver */
static void
solve_gmres_bem3d(matrixtype type, void *A, pavector b, pavector x,
real accuracy, uint steps)
{
addeval_t addevalA;
pavector rhat, q, tau;
pamatrix qr;
uint i, j, n, kk, kmax;
real norm;
addevalA = (addeval_t) addeval_A;
kmax = 500;
n = b->dim;
assert(x->dim == n);
qr = new_zero_amatrix(n, kmax);
rhat = new_avector(n);
q = new_avector(n);
tau = new_avector(kmax);
clear_avector(x);
init_gmres(addevalA, A, b, x, rhat, q, &kk, qr, tau);
for (i = 0; i < steps; i += kmax) {
for (j = 0; j < kmax && i + j < steps; ++j) {
step_gmres(addevalA, A, b, x, rhat, q, &kk, qr, tau);
norm = residualnorm_gmres(rhat, kk);
#ifndef NDEBUG
printf(" Residual: %.5e\t Iterations: %u\r", norm, j + i);
fflush(stdout);
#endif
if (norm <= accuracy) {
finish_gmres(addevalA, A, b, x, rhat, q, &kk, qr, tau);
break;
}
}
if (norm <= accuracy) {
break;
}
else {
finish_gmres(addevalA, A, b, x, rhat, q, &kk, qr, tau);
}
}
printf("\n");
del_avector(rhat);
del_avector(q);
del_avector(tau);
del_amatrix(qr);
}
int
main()
{
pamatrix a, acopy, l, ld, r, q, qr;
pavector x, b, tau;
uint rows, cols;
real error;
rows = 8;
cols = 5;
(void) printf("----------------------------------------\n"
"Check random %u x %u Cholesky factorization\n", rows, rows);
(void) printf("Creating random self-adjoint positive definite matrix\n");
a = new_amatrix(rows, rows);
random_spd_amatrix(a, 1.0);
(void) printf("Creating random solution and right-hand side\n");
x = new_avector(rows);
random_avector(x);
b = new_avector(rows);
clear_avector(b);
mvm_amatrix_avector(1.0, false, a, x, b);
(void) printf("Copying matrix\n");
acopy = new_amatrix(rows, rows);
copy_amatrix(false, a, acopy);
(void) printf("Computing Cholesky factorization\n");
choldecomp_amatrix(a);
(void) printf("Solving\n");
cholsolve_amatrix_avector(a, b);
add_avector(-1.0, x, b);
error = norm2_avector(b);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
(void) printf("Building triangular factor\n");
l = new_amatrix(rows, rows);
copy_lower_amatrix(a, false, l);
(void) printf("Checking factorization\n");
copy_amatrix(false, acopy, a);
addmul_amatrix(-1.0, false, l, true, l, a);
error = normfrob_amatrix(a);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
del_amatrix(l);
del_amatrix(acopy);
del_avector(b);
del_avector(x);
del_amatrix(a);
(void) printf("----------------------------------------\n"
"Check random %u x %u LDL^T factorization\n", rows, rows);
(void) printf("Creating random self-adjoint positive definite matrix\n");
a = new_amatrix(rows, rows);
random_spd_amatrix(a, 1.0);
(void) printf("Creating random solution and right-hand side\n");
x = new_avector(rows);
random_avector(x);
b = new_avector(rows);
clear_avector(b);
mvm_amatrix_avector(1.0, false, a, x, b);
(void) printf("Copying matrix\n");
acopy = new_amatrix(rows, rows);
copy_amatrix(false, a, acopy);
(void) printf("Computing LDL^T factorization\n");
ldltdecomp_amatrix(a);
(void) printf("Solving\n");
ldltsolve_amatrix_avector(a, b);
add_avector(-1.0, x, b);
error = norm2_avector(b);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
(void) printf("Building triangular factor\n");
l = new_amatrix(rows, rows);
copy_lower_amatrix(a, true, l);
(void) printf("Multiplying by diagonal\n");
ld = new_amatrix(rows, rows);
copy_amatrix(false, l, ld);
diageval_amatrix(true, a, true, ld);
(void) printf("Checking factorization\n");
copy_amatrix(false, acopy, a);
addmul_amatrix(-1.0, false, ld, true, l, a);
error = normfrob_amatrix(a);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
del_amatrix(ld);
del_amatrix(l);
del_amatrix(acopy);
del_avector(b);
del_avector(x);
del_amatrix(a);
(void) printf("----------------------------------------\n"
"Check random %u x %u LR factorization\n", rows, rows);
(void) printf("Creating random invertible matrix\n");
a = new_amatrix(rows, rows);
random_invertible_amatrix(a, 1.0);
(void) printf("Creating random solution and right-hand side\n");
x = new_avector(rows);
random_avector(x);
b = new_avector(rows);
clear_avector(b);
mvm_amatrix_avector(1.0, false, a, x, b);
(void) printf("Copying matrix\n");
acopy = new_amatrix(rows, rows);
copy_amatrix(false, a, acopy);
(void) printf("Computing LR factorization\n");
lrdecomp_amatrix(a);
(void) printf("Solving\n");
lrsolve_amatrix_avector(a, b);
add_avector(-1.0, x, b);
error = norm2_avector(b);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
(void) printf("Building triangular factors\n");
l = new_amatrix(rows, rows);
r = new_amatrix(rows, rows);
copy_lower_amatrix(a, true, l);
copy_upper_amatrix(a, false, r);
(void) printf("Checking factorization\n");
copy_amatrix(false, acopy, a);
addmul_amatrix(-1.0, false, l, false, r, a);
error = normfrob_amatrix(a);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
/* Check forward/backward substitution */
(void) printf("----------------------------------------\n");
check_triangularsolve(true, true, false, l, false);
check_triangularsolve(true, true, false, l, true);
check_triangularsolve(true, true, true, l, false);
check_triangularsolve(true, true, true, l, true);
check_triangularsolve(true, false, false, l, false);
check_triangularsolve(true, false, false, l, true);
check_triangularsolve(true, false, true, l, false);
check_triangularsolve(true, false, true, l, true);
check_triangularsolve(false, false, false, r, false);
check_triangularsolve(false, false, false, r, true);
check_triangularsolve(false, false, true, r, false);
check_triangularsolve(false, false, true, r, true);
set_unit(r);
check_triangularsolve(false, true, false, r, false);
check_triangularsolve(false, true, false, r, true);
check_triangularsolve(false, true, true, r, false);
check_triangularsolve(false, true, true, r, true);
/* Intermediate clean-up */
(void) printf("Cleaning up\n");
del_amatrix(r);
del_amatrix(l);
/* Check triangular matrix multiplication */
(void) printf("----------------------------------------\n");
check_triangularaddmul(false, false, false, false);
check_triangularaddmul(true, false, false, false);
check_triangularaddmul(false, true, false, false);
check_triangularaddmul(true, true, false, false);
check_triangularaddmul(false, false, true, false);
check_triangularaddmul(true, false, true, false);
check_triangularaddmul(false, true, true, false);
check_triangularaddmul(true, true, true, false);
check_triangularaddmul(false, false, false, true);
check_triangularaddmul(true, false, false, true);
check_triangularaddmul(false, true, false, true);
check_triangularaddmul(true, true, false, true);
check_triangularaddmul(false, false, true, true);
check_triangularaddmul(true, false, true, true);
check_triangularaddmul(false, true, true, true);
check_triangularaddmul(true, true, true, true);
/* Checking QR factorization */
(void) printf("----------------------------------------\n"
"Check square QR factorization\n");
copy_amatrix(false, acopy, a);
random_avector(x);
clear_avector(b);
mvm_amatrix_avector(1.0, false, a, x, b);
tau = new_avector(rows);
qrdecomp_amatrix(a, tau);
(void) printf("Solving\n");
qrsolve_amatrix_avector(a, tau, b);
add_avector(-1.0, x, b);
error = norm2_avector(b);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
q = new_amatrix(rows, rows);
qrexpand_amatrix(a, tau, q);
(void) printf("Checking factorization\n");
r = new_amatrix(rows, rows);
copy_upper_amatrix(a, false, r);
qr = new_amatrix(rows, rows);
copy_amatrix(false, acopy, qr);
addmul_amatrix(-1.0, false, q, false, r, qr);
error = normfrob_amatrix(qr);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
(void) printf("Checking inverse\n");
copy_amatrix(false, acopy, a);
qrinvert_amatrix(a);
identity_amatrix(qr);
addmul_amatrix(-1.0, false, acopy, false, a, qr);
error = normfrob_amatrix(qr);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
/* Intermediate clean-up */
(void) printf("Cleaning up\n");
del_amatrix(qr);
del_amatrix(r);
del_amatrix(q);
del_avector(tau);
del_avector(b);
del_avector(x);
del_amatrix(acopy);
del_amatrix(a);
/* Check forward/backward evaluation */
(void) printf("----------------------------------------\n");
a = new_amatrix(rows, cols);
random_amatrix(a);
check_lowereval(false, false, a, false);
check_lowereval(false, false, a, true);
check_lowereval(false, true, a, false);
check_lowereval(false, true, a, true);
check_uppereval(false, false, a, false);
check_uppereval(false, false, a, true);
check_uppereval(false, true, a, false);
check_uppereval(false, true, a, true);
set_unit(a);
check_lowereval(true, false, a, false);
check_lowereval(true, false, a, true);
check_lowereval(true, true, a, false);
check_lowereval(true, true, a, true);
check_uppereval(true, false, a, false);
check_uppereval(true, false, a, true);
check_uppereval(true, true, a, false);
check_uppereval(true, true, a, true);
(void) printf("Cleaning up\n");
del_amatrix(a);
a = new_amatrix(cols, rows);
random_amatrix(a);
check_lowereval(false, false, a, false);
check_lowereval(false, false, a, true);
check_lowereval(false, true, a, false);
check_lowereval(false, true, a, true);
check_uppereval(false, false, a, false);
check_uppereval(false, false, a, true);
check_uppereval(false, true, a, false);
check_uppereval(false, true, a, true);
set_unit(a);
check_lowereval(true, false, a, false);
check_lowereval(true, false, a, true);
check_lowereval(true, true, a, false);
check_lowereval(true, true, a, true);
check_uppereval(true, false, a, false);
check_uppereval(true, false, a, true);
check_uppereval(true, true, a, false);
check_uppereval(true, true, a, true);
(void) printf("Cleaning up\n");
del_amatrix(a);
/* Test random QR factorizations */
(void) printf("----------------------------------------\n"
"Check full rectangular QR factorization\n");
a = new_amatrix(rows, cols);
random_amatrix(a);
acopy = new_amatrix(rows, cols);
copy_amatrix(false, a, acopy);
tau = new_avector(rows);
qrdecomp_amatrix(a, tau);
q = new_amatrix(rows, rows);
r = new_amatrix(rows, cols);
qrexpand_amatrix(a, tau, q);
copy_upper_amatrix(a, false, r);
qr = new_amatrix(rows, cols);
copy_amatrix(false, acopy, qr);
addmul_amatrix(-1.0, false, q, false, r, qr);
error = normfrob_amatrix(qr);
printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
del_amatrix(r);
del_amatrix(q);
(void) printf("Check skinny QR factorization\n");
q = new_amatrix(rows, cols);
r = new_amatrix(cols, cols);
qrexpand_amatrix(a, tau, q);
copy_upper_amatrix(a, false, r);
copy_amatrix(false, acopy, qr);
addmul_amatrix(-1.0, false, q, false, r, qr);
error = normfrob_amatrix(qr);
printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
/* Final clean-up */
(void) printf("Cleaning up\n");
del_amatrix(qr);
del_amatrix(r);
del_amatrix(q);
del_avector(tau);
del_amatrix(acopy);
del_amatrix(a);
(void) printf("----------------------------------------\n"
" %u matrices and\n"
" %u vectors still active\n"
" %u errors found\n", getactives_amatrix(),
getactives_avector(), problems);
return problems;
}
int
main(int argc, char **argv)
{
pcurve2d gr;
pamatrix Vfull, KMfull;
pbem2d bem_slp, bem_dlp;
pcluster root;
pblock block;
phmatrix V, KM;
pclusterbasis Vrb, Vcb, KMrb, KMcb;
ph2matrix V2, KM2;
uint n, q, clf, m, l;
real eta, delta, eps_aca;
init_h2lib(&argc, &argv);
n = 579;
q = 2;
clf = 16;
eta = 1.0;
gr = new_circle_curve2d(n, 0.333);
bem_slp = new_slp_laplace_bem2d(gr, q, BASIS_CONSTANT_BEM2D);
bem_dlp = new_dlp_laplace_bem2d(gr, q, BASIS_CONSTANT_BEM2D,
BASIS_CONSTANT_BEM2D, 0.5);
root = build_bem2d_cluster(bem_slp, clf, BASIS_CONSTANT_BEM2D);
block = build_nonstrict_block(root, root, &eta, admissible_max_cluster);
Vfull = new_amatrix(n, n);
KMfull = new_amatrix(n, n);
bem_slp->nearfield(NULL, NULL, bem_slp, false, Vfull);
bem_dlp->nearfield(NULL, NULL, bem_dlp, false, KMfull);
V = build_from_block_hmatrix(block, 0);
KM = build_from_block_hmatrix(block, 0);
printf("----------------------------------------\n");
printf("Testing inner Boundary integral equations:\n");
printf("----------------------------------------\n\n");
/*
* Test Interpolation
*/
m = 9;
setup_hmatrix_aprx_inter_row_bem2d(bem_slp, root, root, block, m);
setup_hmatrix_aprx_inter_row_bem2d(bem_dlp, root, root, block, m);
test_hmatrix_system("Interpolation row", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false);
setup_hmatrix_aprx_inter_col_bem2d(bem_slp, root, root, block, m);
setup_hmatrix_aprx_inter_col_bem2d(bem_dlp, root, root, block, m);
test_hmatrix_system("Interpolation column", Vfull, KMfull, block, bem_slp,
V, bem_dlp, KM, false);
setup_hmatrix_aprx_inter_mixed_bem2d(bem_slp, root, root, block, m);
setup_hmatrix_aprx_inter_mixed_bem2d(bem_dlp, root, root, block, m);
test_hmatrix_system("Interpolation mixed", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false);
/*
* Test Green
*/
m = 10;
l = 2;
delta = 0.5;
setup_hmatrix_aprx_green_row_bem2d(bem_slp, root, root, block, m, l, delta,
build_bem2d_rect_quadpoints);
setup_hmatrix_aprx_green_row_bem2d(bem_dlp, root, root, block, m, l, delta,
build_bem2d_rect_quadpoints);
test_hmatrix_system("Green row", Vfull, KMfull, block, bem_slp, V, bem_dlp,
KM, false);
setup_hmatrix_aprx_green_col_bem2d(bem_slp, root, root, block, m, l, delta,
build_bem2d_rect_quadpoints);
setup_hmatrix_aprx_green_col_bem2d(bem_dlp, root, root, block, m, l, delta,
build_bem2d_rect_quadpoints);
test_hmatrix_system("Green column", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false);
setup_hmatrix_aprx_green_mixed_bem2d(bem_slp, root, root, block, m, l,
delta, build_bem2d_rect_quadpoints);
setup_hmatrix_aprx_green_mixed_bem2d(bem_dlp, root, root, block, m, l,
delta, build_bem2d_rect_quadpoints);
test_hmatrix_system("Green mixed", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false);
/*
* Test Greenhybrid
*/
m = 3;
l = 1;
delta = 1.0;
eps_aca = 1.0e-7;
setup_hmatrix_aprx_greenhybrid_row_bem2d(bem_slp, root, root, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
setup_hmatrix_aprx_greenhybrid_row_bem2d(bem_dlp, root, root, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
test_hmatrix_system("Greenhybrid row", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false);
setup_hmatrix_aprx_greenhybrid_col_bem2d(bem_slp, root, root, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
setup_hmatrix_aprx_greenhybrid_col_bem2d(bem_dlp, root, root, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
test_hmatrix_system("Greenhybrid column", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false);
setup_hmatrix_aprx_greenhybrid_mixed_bem2d(bem_slp, root, root, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
setup_hmatrix_aprx_greenhybrid_mixed_bem2d(bem_dlp, root, root, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
test_hmatrix_system("Greenhybrid mixed", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false);
/*
* Test ACA / PACA / HCA
*/
m = 4;
eps_aca = 1.0e-6;
setup_hmatrix_aprx_aca_bem2d(bem_slp, root, root, block, eps_aca);
setup_hmatrix_aprx_aca_bem2d(bem_dlp, root, root, block, eps_aca);
test_hmatrix_system("ACA full pivoting", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false);
setup_hmatrix_aprx_paca_bem2d(bem_slp, root, root, block, eps_aca);
setup_hmatrix_aprx_paca_bem2d(bem_dlp, root, root, block, eps_aca);
test_hmatrix_system("ACA partial pivoting", Vfull, KMfull, block, bem_slp,
V, bem_dlp, KM, false);
setup_hmatrix_aprx_hca_bem2d(bem_slp, root, root, block, m, eps_aca);
setup_hmatrix_aprx_hca_bem2d(bem_dlp, root, root, block, m, eps_aca);
test_hmatrix_system("HCA2", Vfull, KMfull, block, bem_slp, V, bem_dlp, KM,
false);
/*
* H2-matrix
*/
del_hmatrix(V);
del_hmatrix(KM);
del_block(block);
block = build_strict_block(root, root, &eta, admissible_max_cluster);
Vrb = build_from_cluster_clusterbasis(root);
Vcb = build_from_cluster_clusterbasis(root);
KMrb = build_from_cluster_clusterbasis(root);
KMcb = build_from_cluster_clusterbasis(root);
V2 = build_from_block_h2matrix(block, Vrb, Vcb);
KM2 = build_from_block_h2matrix(block, KMrb, KMcb);
/*
* Test Interpolation
*/
m = 9;
setup_h2matrix_aprx_inter_bem2d(bem_slp, Vrb, Vcb, block, m);
setup_h2matrix_aprx_inter_bem2d(bem_dlp, KMrb, KMcb, block, m);
test_h2matrix_system("Interpolation", Vfull, KMfull, block, bem_slp, V2,
bem_dlp, KM2, false);
/*
* Test Greenhybrid
*/
m = 3;
l = 1;
delta = 1.0;
eps_aca = 1.0e-7;
setup_h2matrix_aprx_greenhybrid_bem2d(bem_slp, Vrb, Vcb, block, m, l, delta,
eps_aca, build_bem2d_rect_quadpoints);
setup_h2matrix_aprx_greenhybrid_bem2d(bem_dlp, KMrb, KMcb, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
test_h2matrix_system("Greenhybrid", Vfull, KMfull, block, bem_slp, V2,
bem_dlp, KM2, false);
setup_h2matrix_aprx_greenhybrid_ortho_bem2d(bem_slp, Vrb, Vcb, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
setup_h2matrix_aprx_greenhybrid_ortho_bem2d(bem_dlp, KMrb, KMcb, block, m,
l, delta, eps_aca,
build_bem2d_rect_quadpoints);
test_h2matrix_system("Greenhybrid ortho", Vfull, KMfull, block, bem_slp, V2,
bem_dlp, KM2, false);
del_h2matrix(V2);
del_h2matrix(KM2);
del_block(block);
del_bem2d(bem_dlp);
printf("----------------------------------------\n");
printf("Testing outer Boundary integral equations:\n");
printf("----------------------------------------\n\n");
bem_dlp = new_dlp_laplace_bem2d(gr, q, BASIS_CONSTANT_BEM2D,
BASIS_CONSTANT_BEM2D, -0.5);
block = build_nonstrict_block(root, root, &eta, admissible_max_cluster);
bem_dlp->nearfield(NULL, NULL, bem_dlp, false, KMfull);
V = build_from_block_hmatrix(block, 0);
KM = build_from_block_hmatrix(block, 0);
/*
* Test Interpolation
*/
m = 9;
setup_hmatrix_aprx_inter_row_bem2d(bem_slp, root, root, block, m);
setup_hmatrix_aprx_inter_row_bem2d(bem_dlp, root, root, block, m);
test_hmatrix_system("Interpolation row", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, true);
setup_hmatrix_aprx_inter_col_bem2d(bem_slp, root, root, block, m);
setup_hmatrix_aprx_inter_col_bem2d(bem_dlp, root, root, block, m);
test_hmatrix_system("Interpolation column", Vfull, KMfull, block, bem_slp,
V, bem_dlp, KM, true);
setup_hmatrix_aprx_inter_mixed_bem2d(bem_slp, root, root, block, m);
setup_hmatrix_aprx_inter_mixed_bem2d(bem_dlp, root, root, block, m);
test_hmatrix_system("Interpolation mixed", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, true);
/*
* Test Green
*/
m = 10;
l = 2;
delta = 0.5;
setup_hmatrix_aprx_green_row_bem2d(bem_slp, root, root, block, m, l, delta,
build_bem2d_rect_quadpoints);
setup_hmatrix_aprx_green_row_bem2d(bem_dlp, root, root, block, m, l, delta,
build_bem2d_rect_quadpoints);
test_hmatrix_system("Green row", Vfull, KMfull, block, bem_slp, V, bem_dlp,
KM, true);
setup_hmatrix_aprx_green_col_bem2d(bem_slp, root, root, block, m, l, delta,
build_bem2d_rect_quadpoints);
setup_hmatrix_aprx_green_col_bem2d(bem_dlp, root, root, block, m, l, delta,
build_bem2d_rect_quadpoints);
test_hmatrix_system("Green column", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, true);
setup_hmatrix_aprx_green_mixed_bem2d(bem_slp, root, root, block, m, l,
delta, build_bem2d_rect_quadpoints);
setup_hmatrix_aprx_green_mixed_bem2d(bem_dlp, root, root, block, m, l,
delta, build_bem2d_rect_quadpoints);
test_hmatrix_system("Green mixed", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, true);
/*
* Test Greenhybrid
*/
m = 3;
l = 1;
delta = 1.0;
eps_aca = 1.0e-7;
setup_hmatrix_aprx_greenhybrid_row_bem2d(bem_slp, root, root, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
setup_hmatrix_aprx_greenhybrid_row_bem2d(bem_dlp, root, root, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
test_hmatrix_system("Greenhybrid row", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, true);
setup_hmatrix_aprx_greenhybrid_col_bem2d(bem_slp, root, root, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
setup_hmatrix_aprx_greenhybrid_col_bem2d(bem_dlp, root, root, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
test_hmatrix_system("Greenhybrid column", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, true);
setup_hmatrix_aprx_greenhybrid_mixed_bem2d(bem_slp, root, root, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
setup_hmatrix_aprx_greenhybrid_mixed_bem2d(bem_dlp, root, root, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
test_hmatrix_system("Greenhybrid mixed", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, true);
/*
* Test ACA / PACA / HCA
*/
m = 4;
eps_aca = 1.0e-6;
setup_hmatrix_aprx_aca_bem2d(bem_slp, root, root, block, eps_aca);
setup_hmatrix_aprx_aca_bem2d(bem_dlp, root, root, block, eps_aca);
test_hmatrix_system("ACA full pivoting", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, true);
setup_hmatrix_aprx_paca_bem2d(bem_slp, root, root, block, eps_aca);
setup_hmatrix_aprx_paca_bem2d(bem_dlp, root, root, block, eps_aca);
test_hmatrix_system("ACA partial pivoting", Vfull, KMfull, block, bem_slp,
V, bem_dlp, KM, true);
setup_hmatrix_aprx_hca_bem2d(bem_slp, root, root, block, m, eps_aca);
setup_hmatrix_aprx_hca_bem2d(bem_dlp, root, root, block, m, eps_aca);
test_hmatrix_system("HCA2", Vfull, KMfull, block, bem_slp, V, bem_dlp, KM,
true);
/*
* H2-matrix
*/
del_hmatrix(V);
del_hmatrix(KM);
del_block(block);
block = build_strict_block(root, root, &eta, admissible_max_cluster);
Vrb = build_from_cluster_clusterbasis(root);
Vcb = build_from_cluster_clusterbasis(root);
KMrb = build_from_cluster_clusterbasis(root);
KMcb = build_from_cluster_clusterbasis(root);
V2 = build_from_block_h2matrix(block, Vrb, Vcb);
KM2 = build_from_block_h2matrix(block, KMrb, KMcb);
/*
* Test Interpolation
*/
m = 9;
setup_h2matrix_aprx_inter_bem2d(bem_slp, Vrb, Vcb, block, m);
setup_h2matrix_aprx_inter_bem2d(bem_dlp, KMrb, KMcb, block, m);
test_h2matrix_system("Interpolation", Vfull, KMfull, block, bem_slp, V2,
bem_dlp, KM2, true);
/*
* Test Greenhybrid
*/
m = 3;
l = 1;
delta = 1.0;
eps_aca = 1.0e-7;
setup_h2matrix_aprx_greenhybrid_bem2d(bem_slp, Vrb, Vcb, block, m, l, delta,
eps_aca, build_bem2d_rect_quadpoints);
setup_h2matrix_aprx_greenhybrid_bem2d(bem_dlp, KMrb, KMcb, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
test_h2matrix_system("Greenhybrid", Vfull, KMfull, block, bem_slp, V2,
bem_dlp, KM2, true);
setup_h2matrix_aprx_greenhybrid_ortho_bem2d(bem_slp, Vrb, Vcb, block, m, l,
delta, eps_aca,
build_bem2d_rect_quadpoints);
setup_h2matrix_aprx_greenhybrid_ortho_bem2d(bem_dlp, KMrb, KMcb, block, m,
l, delta, eps_aca,
build_bem2d_rect_quadpoints);
test_h2matrix_system("Greenhybrid Ortho", Vfull, KMfull, block, bem_slp, V2,
bem_dlp, KM2, true);
del_h2matrix(V2);
del_h2matrix(KM2);
del_block(block);
freemem(root->idx);
del_cluster(root);
del_bem2d(bem_slp);
del_bem2d(bem_dlp);
del_amatrix(Vfull);
del_amatrix(KMfull);
del_curve2d(gr);
(void) printf("----------------------------------------\n"
" %u matrices and\n"
" %u vectors still active\n"
" %u errors found\n", getactives_amatrix(),
getactives_avector(), problems);
uninit_h2lib();
return problems;
}
int
main(int argc, char **argv)
{
pmacrosurface3d mg;
psurface3d gr;
pamatrix Vfull, KMfull;
pbem3d bem_slp, bem_dlp;
pcluster root;
pblock block;
phmatrix V, KM;
pclusterbasis Vrb, Vcb, KMrb, KMcb;
ph2matrix V2, KM2;
uint n, q, clf, m, l;
real eta, delta, eps_aca;
field kvec[3];
cl_device_id *devices;
cl_uint ndevices;
uint *idx;
uint i;
init_h2lib(&argc, &argv);
get_opencl_devices(&devices, &ndevices);
ndevices = 1;
set_opencl_devices(devices, ndevices, 2);
kvec[0] = 2.0, kvec[1] = 0.0, kvec[2] = 0.0;
n = 512;
q = 2;
clf = 16;
eta = 1.0;
mg = new_sphere_macrosurface3d();
gr = build_from_macrosurface3d_surface3d(mg, REAL_SQRT(n * 0.125));
n = gr->triangles;
printf("Testing unit sphere with %d triangles\n", n);
bem_slp = new_slp_helmholtz_ocl_bem3d(kvec, gr, q, q + 2,
BASIS_CONSTANT_BEM3D);
bem_dlp = new_dlp_helmholtz_ocl_bem3d(kvec, gr, q, q + 2,
BASIS_CONSTANT_BEM3D,
BASIS_CONSTANT_BEM3D, 0.5);
root = build_bem3d_cluster(bem_slp, clf, BASIS_CONSTANT_BEM3D);
block = build_nonstrict_block(root, root, &eta, admissible_max_cluster);
max_pardepth = 0;
Vfull = new_amatrix(n, n);
KMfull = new_amatrix(n, n);
idx = allocuint(n);
for (i = 0; i < n; ++i) {
idx[i] = i;
}
SCHEDULE_OPENCL(0, 1, bem_slp->nearfield, idx, idx, bem_slp, false, Vfull);
SCHEDULE_OPENCL(0, 1, bem_dlp->nearfield, idx, idx, bem_dlp, false, KMfull);
V = build_from_block_hmatrix(block, 0);
KM = build_from_block_hmatrix(block, 0);
printf("----------------------------------------\n");
printf("Testing outer Boundary integral equations:\n");
printf("----------------------------------------\n\n");
/*
* Test Interpolation
*/
m = 4;
setup_hmatrix_aprx_inter_row_bem3d(bem_slp, root, root, block, m);
setup_hmatrix_aprx_inter_row_bem3d(bem_dlp, root, root, block, m);
test_hmatrix_system("Interpolation row", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_inter_col_bem3d(bem_slp, root, root, block, m);
setup_hmatrix_aprx_inter_col_bem3d(bem_dlp, root, root, block, m);
test_hmatrix_system("Interpolation column", Vfull, KMfull, block, bem_slp,
V, bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_inter_mixed_bem3d(bem_slp, root, root, block, m);
setup_hmatrix_aprx_inter_mixed_bem3d(bem_dlp, root, root, block, m);
test_hmatrix_system("Interpolation mixed", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
/*
* Test Green
*/
m = 5;
l = 1;
delta = 0.5;
setup_hmatrix_aprx_green_row_bem3d(bem_slp, root, root, block, m, l, delta,
build_bem3d_cube_quadpoints);
setup_hmatrix_aprx_green_row_bem3d(bem_dlp, root, root, block, m, l, delta,
build_bem3d_cube_quadpoints);
test_hmatrix_system("Green row", Vfull, KMfull, block, bem_slp, V, bem_dlp,
KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_green_col_bem3d(bem_slp, root, root, block, m, l, delta,
build_bem3d_cube_quadpoints);
setup_hmatrix_aprx_green_col_bem3d(bem_dlp, root, root, block, m, l, delta,
build_bem3d_cube_quadpoints);
test_hmatrix_system("Green column", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_green_mixed_bem3d(bem_slp, root, root, block, m, l,
delta, build_bem3d_cube_quadpoints);
setup_hmatrix_aprx_green_mixed_bem3d(bem_dlp, root, root, block, m, l,
delta, build_bem3d_cube_quadpoints);
test_hmatrix_system("Green mixed", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
/*
* Test Greenhybrid
*/
m = 2;
l = 1;
delta = 1.0;
eps_aca = 2.0e-2;
setup_hmatrix_aprx_greenhybrid_row_bem3d(bem_slp, root, root, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
setup_hmatrix_aprx_greenhybrid_row_bem3d(bem_dlp, root, root, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
test_hmatrix_system("Greenhybrid row", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_greenhybrid_col_bem3d(bem_slp, root, root, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
setup_hmatrix_aprx_greenhybrid_col_bem3d(bem_dlp, root, root, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
test_hmatrix_system("Greenhybrid column", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_greenhybrid_mixed_bem3d(bem_slp, root, root, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
setup_hmatrix_aprx_greenhybrid_mixed_bem3d(bem_dlp, root, root, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
test_hmatrix_system("Greenhybrid mixed", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
/*
* Test ACA / PACA / HCA
*/
m = 2;
eps_aca = 1.0e-2;
/* Nearfield computation on GPU not applicable here yet! */
// setup_hmatrix_aprx_aca_bem3d(bem_slp, root, root, block, eps_aca);
// setup_hmatrix_aprx_aca_bem3d(bem_dlp, root, root, block, eps_aca);
// test_hmatrix_system("ACA full pivoting", Vfull, KMfull, block, bem_slp, V,
// bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
//
// setup_hmatrix_aprx_paca_bem3d(bem_slp, root, root, block, eps_aca);
// setup_hmatrix_aprx_paca_bem3d(bem_slp, root, root, block, eps_aca);
// test_hmatrix_system("ACA partial pivoting", Vfull, KMfull, block, bem_slp, V,
// bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_hca_bem3d(bem_slp, root, root, block, m, eps_aca);
setup_hmatrix_aprx_hca_bem3d(bem_slp, root, root, block, m, eps_aca);
test_hmatrix_system("HCA2", Vfull, KMfull, block, bem_slp, V, bem_dlp, KM,
false, true, 1.0e-3, 2.0e-3);
del_hmatrix(V);
del_hmatrix(KM);
del_block(block);
/*
* H2-matrix
*/
block = build_strict_block(root, root, &eta, admissible_max_cluster);
Vrb = build_from_cluster_clusterbasis(root);
Vcb = build_from_cluster_clusterbasis(root);
KMrb = build_from_cluster_clusterbasis(root);
KMcb = build_from_cluster_clusterbasis(root);
V2 = build_from_block_h2matrix(block, Vrb, Vcb);
KM2 = build_from_block_h2matrix(block, KMrb, KMcb);
/*
* Test Interpolation
*/
m = 3;
setup_h2matrix_aprx_inter_bem3d(bem_slp, Vrb, Vcb, block, m);
setup_h2matrix_aprx_inter_bem3d(bem_dlp, KMrb, KMcb, block, m);
test_h2matrix_system("Interpolation", Vfull, KMfull, block, bem_slp, V2,
bem_dlp, KM2, false, true, 1.0e-3, 2.0e-3);
/*
* Test Greenhybrid
*/
m = 2;
l = 1;
delta = 1.0;
eps_aca = 2.0e-2;
setup_h2matrix_aprx_greenhybrid_bem3d(bem_slp, Vrb, Vcb, block, m, l, delta,
eps_aca, build_bem3d_cube_quadpoints);
setup_h2matrix_aprx_greenhybrid_bem3d(bem_dlp, KMrb, KMcb, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
test_h2matrix_system("Greenhybrid", Vfull, KMfull, block, bem_slp, V2,
bem_dlp, KM2, false, true, 1.0e-3, 2.0e-3);
/* Nearfield computation on GPU not applicable here yet! */
// setup_h2matrix_aprx_greenhybrid_ortho_bem3d(bem_slp, Vrb, Vcb, block, m, l,
// delta, eps_aca, build_bem3d_cube_quadpoints);
// setup_h2matrix_aprx_greenhybrid_ortho_bem3d(bem_dlp, KMrb, KMcb, block, m, l,
// delta, eps_aca, build_bem3d_cube_quadpoints);
// test_h2matrix_system("Greenhybrid ortho", Vfull, KMfull, block, bem_slp, V2,
// bem_dlp, KM2, false, true, 1.0e-3, 2.0e-3);
del_h2matrix(V2);
del_h2matrix(KM2);
del_block(block);
freemem(root->idx);
del_cluster(root);
del_helmholtz_ocl_bem3d(bem_slp);
del_helmholtz_ocl_bem3d(bem_dlp);
del_amatrix(Vfull);
del_amatrix(KMfull);
del_surface3d(gr);
del_macrosurface3d(mg);
freemem(idx);
(void) printf("----------------------------------------\n"
" %u matrices and\n"
" %u vectors still active\n"
" %u errors found\n", getactives_amatrix(),
getactives_avector(), problems);
uninit_h2lib();
return problems;
}
int
main()
{
ptridiag T, Tcopy;
pamatrix A, Acopy, Q, U, Vt;
pavector work;
prealavector sigma, lambda;
real error;
uint rows, cols, mid;
uint i, n, iter;
int info;
/* ------------------------------------------------------------
* Testing symmetric tridiagonal eigenvalue solver
* ------------------------------------------------------------ */
n = 6;
/* Testing symmetric tridiagonal eigenvalue solver */
(void) printf("==================================================\n"
"Testing symmetric tridiagonal eigenvalue solver\n"
"==================================================\n"
"Setting up %u x %u tridiagonal matrix\n", n, n);
T = new_tridiag(n);
for (i = 0; i < n; i++)
T->d[i] = 2.0;
for (i = 0; i < n - 1; i++)
T->l[i] = T->u[i] = -1.0;
Tcopy = new_tridiag(n);
copy_tridiag(T, Tcopy);
A = new_amatrix(n, n);
clear_amatrix(A);
for (i = 0; i < n; i++)
A->a[i + i * A->ld] = T->d[i];
for (i = 0; i < n - 1; i++) {
A->a[(i + 1) + i * A->ld] = T->l[i];
A->a[i + (i + 1) * A->ld] = T->u[i];
}
Acopy = clone_amatrix(A);
Q = new_identity_amatrix(n, n);
U = new_amatrix(n, n);
(void) printf("Performing self-made implicit QR iteration\n");
iter = sb_muleig_tridiag(T, Q, 8 * n);
(void) printf(" %u iterations\n", iter);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, Q);
(void) printf(" Orthogonality Q %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
copy_amatrix(false, Q, U);
diageval_tridiag_amatrix(1.0, true, T, true, U);
addmul_amatrix(-1.0, false, U, true, Q, A);
error = normfrob_amatrix(A);
(void) printf(" Accuracy %g. %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
(void) printf("Performing default implicit QR iteration\n");
identity_amatrix(Q);
i = muleig_tridiag(Tcopy, Q);
if (i == 0)
(void) printf(" Success\n");
else {
(void) printf(" Failure\n");
problems++;
}
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, Q);
(void) printf(" Orthogonality Q %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
copy_amatrix(false, Q, U);
diageval_tridiag_amatrix(1.0, true, Tcopy, true, U);
addmul_amatrix(-1.0, false, U, true, Q, Acopy);
error = normfrob_amatrix(Acopy);
(void) printf(" Accuracy %g. %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
del_amatrix(U);
del_amatrix(Q);
del_amatrix(Acopy);
del_amatrix(A);
del_tridiag(Tcopy);
del_tridiag(T);
(void) printf("--------------------------------------------------\n"
"Setting up random %u x %u tridiagonal matrix\n", n, n);
T = new_tridiag(n);
for (i = 0; i < n; i++)
T->d[i] = 2.0 * rand() / RAND_MAX - 1.0;
for (i = 0; i < n - 1; i++) {
T->l[i] = 2.0 * rand() / RAND_MAX - 1.0;
T->u[i] = CONJ(T->l[i]);
}
A = new_amatrix(n, n);
clear_amatrix(A);
for (i = 0; i < n; i++)
A->a[i + i * A->ld] = T->d[i];
for (i = 0; i < n - 1; i++) {
A->a[(i + 1) + i * A->ld] = T->l[i];
A->a[i + (i + 1) * A->ld] = T->u[i];
}
Tcopy = new_tridiag(n);
copy_tridiag(T, Tcopy);
Acopy = clone_amatrix(A);
Q = new_identity_amatrix(n, n);
U = new_amatrix(n, n);
(void) printf("Performing implicit QR iteration\n");
iter = sb_muleig_tridiag(T, Q, 8 * n);
(void) printf(" %u iterations\n", iter);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, Q);
(void) printf(" Orthogonality Q %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
copy_amatrix(false, Q, U);
diageval_tridiag_amatrix(1.0, true, T, true, U);
addmul_amatrix(-1.0, false, U, true, Q, A);
error = normfrob_amatrix(A);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
(void) printf("Using default eigenvalue solver\n");
identity_amatrix(Q);
muleig_tridiag(Tcopy, Q);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, Q);
(void) printf(" Orthogonality Q %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
copy_amatrix(false, Q, U);
diageval_tridiag_amatrix(1.0, true, Tcopy, true, U);
addmul_amatrix(-1.0, false, U, true, Q, Acopy);
error = normfrob_amatrix(Acopy);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
del_amatrix(U);
del_amatrix(Q);
del_amatrix(Acopy);
del_amatrix(A);
del_tridiag(Tcopy);
del_tridiag(T);
/* ------------------------------------------------------------
* Testing self-adjoint matrix eigenvalue solver
* ------------------------------------------------------------ */
(void) printf("==================================================\n"
"Testing self-adjoint matrix eigenvalue solver\n"
"==================================================\n"
"Setting up random %u x %u self-adjoint matrix\n", n, n);
A = new_amatrix(n, n);
random_selfadjoint_amatrix(A);
Acopy = new_amatrix(n, n);
copy_amatrix(false, A, Acopy);
lambda = new_realavector(n);
Q = new_identity_amatrix(n, n);
(void) printf("Performing implicit QR iteration\n");
iter = sb_eig_amatrix(A, lambda, Q, 8 * n);
(void) printf(" %u iterations\n", iter);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, Q);
(void) printf(" Orthogonality Q %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
U = new_amatrix(n, n);
copy_amatrix(false, Q, U);
copy_amatrix(false, Acopy, A);
diageval_realavector_amatrix(1.0, true, lambda, true, U);
addmul_amatrix(-1.0, false, U, true, Q, A);
error = normfrob_amatrix(A);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
(void) printf("Using default eigenvalue solver\n");
copy_amatrix(false, Acopy, A);
info = eig_amatrix(A, lambda, Q);
assert(info == 0);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, Q);
(void) printf(" Orthogonality Q %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
copy_amatrix(false, Q, U);
diageval_realavector_amatrix(1.0, true, lambda, true, U);
addmul_amatrix(-1.0, false, U, true, Q, Acopy);
error = normfrob_amatrix(Acopy);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
del_amatrix(U);
del_amatrix(Q);
del_realavector(lambda);
del_amatrix(Acopy);
del_amatrix(A);
/* ------------------------------------------------------------
* Testing bidiagonal SVD solver
* ------------------------------------------------------------ */
(void) printf("==================================================\n"
"Testing bidiagonal SVD solver\n"
"==================================================\n"
"Setting up bidiagonal %u x %u matrix\n", n, n);
T = new_tridiag(n);
for (i = 0; i < n; i++)
T->d[i] = i + 1.0;
for (i = 0; i < n - 1; i++) {
T->l[i] = 1.0;
T->u[i] = 0.0;
}
A = new_amatrix(n, n);
clear_amatrix(A);
for (i = 0; i < n; i++)
A->a[i + i * A->ld] = T->d[i];
for (i = 0; i < n - 1; i++)
A->a[(i + 1) + i * A->ld] = T->l[i];
Tcopy = new_tridiag(n);
copy_tridiag(T, Tcopy);
Acopy = new_amatrix(n, n);
copy_amatrix(false, A, Acopy);
U = new_identity_amatrix(n, n);
Vt = new_identity_amatrix(n, n);
(void) printf("Performing self-made implicit SVD iteration\n");
iter = sb_mulsvd_tridiag(T, U, Vt, 8 * n);
(void) printf(" %u iterations\n", iter);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
diageval_tridiag_amatrix(1.0, true, T, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, A);
error = normfrob_amatrix(A);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
(void) printf("Using default SVD solver\n");
copy_tridiag(Tcopy, T);
identity_amatrix(U);
identity_amatrix(Vt);
mulsvd_tridiag(T, U, Vt);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
copy_amatrix(false, Acopy, A);
diageval_tridiag_amatrix(1.0, true, T, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, A);
error = normfrob_amatrix(A);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
del_amatrix(Vt);
del_amatrix(U);
del_amatrix(Acopy);
del_tridiag(Tcopy);
del_amatrix(A);
del_tridiag(T);
(void) printf("--------------------------------------------------\n"
"Setting up random bidiagonal %u x %u matrix\n", n, n);
T = new_tridiag(n);
for (i = 0; i < n; i++) {
T->d[i] = 2.0 * rand() / RAND_MAX - 1.0;
}
for (i = 0; i < n - 1; i++) {
T->l[i] = 2.0 * rand() / RAND_MAX - 1.0;
T->u[i] = 0.0;
}
A = new_amatrix(n, n);
clear_amatrix(A);
for (i = 0; i < n; i++)
A->a[i + i * A->ld] = T->d[i];
for (i = 0; i < n - 1; i++)
A->a[(i + 1) + i * A->ld] = T->l[i];
Tcopy = new_tridiag(n);
copy_tridiag(T, Tcopy);
Acopy = clone_amatrix(A);
U = new_identity_amatrix(n, n);
Vt = new_identity_amatrix(n, n);
(void) printf("Performing implicit SVD iteration\n");
iter = sb_mulsvd_tridiag(T, U, Vt, 8 * n);
(void) printf(" %u iterations\n", iter);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
diageval_tridiag_amatrix(1.0, true, T, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, A);
error = normfrob_amatrix(A);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
(void) printf("Using default SVD solver\n");
copy_tridiag(Tcopy, T);
copy_amatrix(false, Acopy, A);
identity_amatrix(U);
identity_amatrix(Vt);
mulsvd_tridiag(T, U, Vt);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
diageval_tridiag_amatrix(1.0, true, T, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, A);
error = normfrob_amatrix(A);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
del_amatrix(Vt);
del_amatrix(U);
del_amatrix(Acopy);
del_tridiag(Tcopy);
del_amatrix(A);
del_tridiag(T);
/* ------------------------------------------------------------
* Testing Golub-Kahan bidiagonalization
* ------------------------------------------------------------ */
rows = 10;
cols = 7;
mid = UINT_MIN(rows, cols);
(void) printf("==================================================\n"
"Testing Golub-Kahan bidiagonalization\n"
"==================================================\n"
"Setting up random %u x %u matrix\n", rows, cols);
A = new_amatrix(rows, cols);
random_amatrix(A);
Acopy = new_amatrix(rows, cols);
copy_amatrix(false, A, Acopy);
U = new_amatrix(rows, mid);
Vt = new_amatrix(mid, cols);
T = new_tridiag(mid);
(void) printf("Bidiagonalizing\n");
bidiagonalize_amatrix(A, T, U, Vt);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
lowereval_tridiag_amatrix(1.0, true, T, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, Acopy);
error = normfrob_amatrix(Acopy);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
del_tridiag(T);
del_amatrix(Vt);
del_amatrix(U);
del_amatrix(Acopy);
del_amatrix(A);
rows = 8;
cols = 15;
mid = UINT_MIN(rows, cols);
(void) printf("--------------------------------------------------\n"
"Setting up %u x %u matrix\n", rows, cols);
A = new_amatrix(rows, cols);
random_amatrix(A);
Acopy = new_amatrix(rows, cols);
copy_amatrix(false, A, Acopy);
U = new_amatrix(rows, mid);
Vt = new_amatrix(mid, cols);
T = new_tridiag(mid);
(void) printf("Bidiagonalizing\n");
bidiagonalize_amatrix(A, T, U, Vt);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
lowereval_tridiag_amatrix(1.0, true, T, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, Acopy);
error = normfrob_amatrix(Acopy);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
del_tridiag(T);
del_amatrix(Vt);
del_amatrix(U);
del_amatrix(Acopy);
del_amatrix(A);
/* ------------------------------------------------------------
* Testing general SVD solver
* ------------------------------------------------------------ */
(void) printf("==================================================\n"
"Testing general SVD solver\n"
"==================================================\n"
"Setting up 3 x 4 matrix\n");
A = new_amatrix(3, 4);
setentry_amatrix(A, 0, 0, 1.0);
setentry_amatrix(A, 1, 0, 2.0);
setentry_amatrix(A, 2, 0, 3.0);
setentry_amatrix(A, 0, 1, 2.0);
setentry_amatrix(A, 1, 1, 4.0);
setentry_amatrix(A, 2, 1, 6.0);
setentry_amatrix(A, 0, 2, 2.0);
setentry_amatrix(A, 1, 2, 5.0);
setentry_amatrix(A, 2, 2, 8.0);
setentry_amatrix(A, 0, 3, 1.0);
setentry_amatrix(A, 1, 3, 4.0);
setentry_amatrix(A, 2, 3, 7.0);
Acopy = new_amatrix(A->rows, A->cols);
copy_amatrix(false, A, Acopy);
U = new_identity_amatrix(3, 3);
Vt = new_identity_amatrix(3, 4);
sigma = new_realavector(3);
work = new_avector(3 * 3);
(void) printf("Running self-made SVD solver\n");
iter = sb_svd_amatrix(A, sigma, U, Vt, 24);
(void) printf(" %u iterations\n", iter);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
diageval_realavector_amatrix(1.0, true, sigma, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, Acopy);
error = normfrob_amatrix(Acopy);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
del_avector(work);
del_realavector(sigma);
del_amatrix(Vt);
del_amatrix(U);
del_amatrix(Acopy);
del_amatrix(A);
(void) printf("--------------------------------------------------\n"
"Setting up 4 x 3 matrix\n");
A = new_amatrix(4, 3);
setentry_amatrix(A, 0, 0, 1.0);
setentry_amatrix(A, 0, 1, 2.0);
setentry_amatrix(A, 0, 2, 3.0);
setentry_amatrix(A, 1, 0, 2.0);
setentry_amatrix(A, 1, 1, 4.0);
setentry_amatrix(A, 1, 2, 6.0);
setentry_amatrix(A, 2, 0, 2.0);
setentry_amatrix(A, 2, 1, 5.0);
setentry_amatrix(A, 2, 2, 8.0);
setentry_amatrix(A, 3, 0, 1.0);
setentry_amatrix(A, 3, 1, 4.0);
setentry_amatrix(A, 3, 2, 7.0);
Acopy = new_amatrix(A->rows, A->cols);
copy_amatrix(false, A, Acopy);
U = new_amatrix(4, 3);
Vt = new_amatrix(3, 3);
sigma = new_realavector(3);
work = new_avector(3 * 3);
(void) printf("Running self-made SVD solver\n");
iter = sb_svd_amatrix(A, sigma, U, Vt, 24);
(void) printf(" %u iterations\n", iter);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality V %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
diageval_realavector_amatrix(1.0, true, sigma, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, Acopy);
error = normfrob_amatrix(Acopy);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
del_avector(work);
del_realavector(sigma);
del_amatrix(Vt);
del_amatrix(U);
del_amatrix(Acopy);
del_amatrix(A);
(void) printf("--------------------------------------------------\n"
"Setting up 4 x 3 matrix\n");
A = new_amatrix(4, 3);
setentry_amatrix(A, 0, 0, 1.0);
setentry_amatrix(A, 0, 1, 2.0);
setentry_amatrix(A, 0, 2, 3.0);
setentry_amatrix(A, 1, 0, 2.0);
setentry_amatrix(A, 1, 1, 4.0);
setentry_amatrix(A, 1, 2, 6.0);
setentry_amatrix(A, 2, 0, 2.0);
setentry_amatrix(A, 2, 1, 5.0);
setentry_amatrix(A, 2, 2, 8.0);
setentry_amatrix(A, 3, 0, 1.0);
setentry_amatrix(A, 3, 1, 4.0);
setentry_amatrix(A, 3, 2, 7.0);
Acopy = clone_amatrix(A);
U = new_amatrix(4, 3);
Vt = new_amatrix(3, 3);
sigma = new_realavector(3);
work = new_avector(3 * 3);
(void) printf("Running self-made SVD solver\n");
iter = sb_svd_amatrix(A, sigma, U, Vt, 24);
(void) printf(" %u iterations\n", iter);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
diageval_realavector_amatrix(1.0, true, sigma, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, Acopy);
error = normfrob_amatrix(Acopy);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
del_avector(work);
del_realavector(sigma);
del_amatrix(Vt);
del_amatrix(U);
del_amatrix(Acopy);
del_amatrix(A);
rows = 9;
cols = 7;
mid = UINT_MIN(rows, cols);
(void) printf("--------------------------------------------------\n"
"Setting up random %u x %u matrix\n", rows, cols);
A = new_amatrix(rows, cols);
random_amatrix(A);
Acopy = new_amatrix(A->rows, A->cols);
copy_amatrix(false, A, Acopy);
U = new_amatrix(rows, mid);
Vt = new_amatrix(mid, cols);
sigma = new_realavector(mid);
work = new_avector(3 * mid);
(void) printf("Running self-made SVD solver\n");
iter = sb_svd_amatrix(A, sigma, U, Vt, 10 * mid);
(void) printf(" %u iterations\n", iter);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
diageval_realavector_amatrix(1.0, true, sigma, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, Acopy);
error = normfrob_amatrix(Acopy);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
del_avector(work);
del_realavector(sigma);
del_amatrix(Vt);
del_amatrix(U);
del_amatrix(Acopy);
del_amatrix(A);
rows = 10;
cols = 6;
mid = UINT_MIN(rows, cols);
(void) printf("--------------------------------------------------\n"
"Setting up random %u x %u matrix\n", rows, cols);
A = new_amatrix(rows, cols);
random_amatrix(A);
Acopy = new_amatrix(A->rows, A->cols);
copy_amatrix(false, A, Acopy);
U = new_amatrix(rows, mid);
Vt = new_amatrix(mid, cols);
sigma = new_realavector(mid);
work = new_avector(3 * mid);
(void) printf("Running self-made SVD solver\n");
iter = sb_svd_amatrix(A, sigma, U, Vt, 10 * mid);
(void) printf(" %u iterations\n", iter);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
copy_amatrix(false, Acopy, A);
diageval_realavector_amatrix(1.0, true, sigma, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, A);
error = normfrob_amatrix(A);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
(void) printf("Running default SVD solver\n");
copy_amatrix(false, Acopy, A);
svd_amatrix(A, sigma, U, Vt);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
copy_amatrix(false, Acopy, A);
diageval_realavector_amatrix(1.0, true, sigma, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, A);
error = normfrob_amatrix(A);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
del_avector(work);
del_realavector(sigma);
del_amatrix(Vt);
del_amatrix(U);
del_amatrix(Acopy);
del_amatrix(A);
rows = 7;
cols = 13;
mid = UINT_MIN(rows, cols);
(void) printf("--------------------------------------------------\n"
"Setting up random %u x %u matrix\n", rows, cols);
A = new_amatrix(rows, cols);
random_amatrix(A);
Acopy = new_amatrix(A->rows, A->cols);
copy_amatrix(false, A, Acopy);
U = new_amatrix(rows, mid);
Vt = new_amatrix(mid, cols);
sigma = new_realavector(mid);
work = new_avector(3 * mid);
(void) printf("Running self-made SVD solver\n");
iter = sb_svd_amatrix(A, sigma, U, Vt, 10 * mid);
(void) printf(" %u iterations\n", iter);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
copy_amatrix(false, Acopy, A);
diageval_realavector_amatrix(1.0, true, sigma, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, A);
error = normfrob_amatrix(A);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
(void) printf("Running default SVD solver\n");
copy_amatrix(false, Acopy, A);
svd_amatrix(A, sigma, U, Vt);
(void) printf("Checking accuracy\n");
error = check_ortho_amatrix(false, U);
(void) printf(" Orthogonality U %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
error = check_ortho_amatrix(true, Vt);
(void) printf(" Orthogonality Vt %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
copy_amatrix(false, Acopy, A);
diageval_realavector_amatrix(1.0, true, sigma, true, U);
addmul_amatrix(-1.0, false, U, false, Vt, A);
error = normfrob_amatrix(A);
(void) printf(" Accuracy %g, %sokay\n", error,
(error < tolerance ? "" : "NOT "));
if (error >= tolerance)
problems++;
del_avector(work);
del_realavector(sigma);
del_amatrix(Vt);
del_amatrix(U);
del_amatrix(Acopy);
del_amatrix(A);
printf("----------------------------------------\n"
" %u matrices and\n"
" %u vectors still active\n"
" %u errors found\n", getactives_amatrix(), getactives_avector(),
problems);
return problems;
}
pcluster
build_pca_cluster(pclustergeometry cf, uint size, uint * idx, uint clf)
{
const uint dim = cf->dim;
pamatrix C, Q;
pavector v;
prealavector lambda;
real *x, *y;
real w;
uint i, j, k, size0, size1;
pcluster t;
assert(size > 0);
size0 = 0;
size1 = 0;
if (size > clf) {
x = allocreal(dim);
y = allocreal(dim);
/* determine weight of current cluster */
w = 0.0;
for (i = 0; i < size; ++i) {
w += cf->w[idx[i]];
}
w = 1.0 / w;
for (j = 0; j < dim; ++j) {
x[j] = 0.0;
}
/* determine center of mass */
for (i = 0; i < size; ++i) {
for (j = 0; j < dim; ++j) {
x[j] += cf->w[idx[i]] * cf->x[idx[i]][j];
}
}
for (j = 0; j < dim; ++j) {
x[j] *= w;
}
C = new_zero_amatrix(dim, dim);
Q = new_zero_amatrix(dim, dim);
lambda = new_realavector(dim);
/* setup covariance matrix */
for (i = 0; i < size; ++i) {
for (j = 0; j < dim; ++j) {
y[j] = cf->x[idx[i]][j] - x[j];
}
for (j = 0; j < dim; ++j) {
for (k = 0; k < dim; ++k) {
C->a[j + k * C->ld] += cf->w[idx[i]] * y[j] * y[k];
}
}
}
/* get eigenvalues and eigenvectors of covariance matrix */
eig_amatrix(C, lambda, Q);
/* get eigenvector from largest eigenvalue */
v = new_avector(0);
init_column_avector(v, Q, dim - 1);
/* separate cluster with v as separation-plane */
for (i = 0; i < size; ++i) {
/* x_i - X */
for (j = 0; j < dim; ++j) {
y[j] = cf->x[idx[i]][j] - x[j];
}
/* <y,v> */
w = 0.0;
for (j = 0; j < dim; ++j) {
w += y[j] * v->v[j];
}
if (w >= 0.0) {
j = idx[i];
idx[i] = idx[size0];
idx[size0] = j;
size0++;
}
else {
size1++;
}
}
assert(size0 + size1 == size);
del_amatrix(Q);
del_amatrix(C);
del_realavector(lambda);
del_avector(v);
freemem(x);
freemem(y);
/* recursion */
if (size0 > 0) {
if (size1 > 0) {
t = new_cluster(size, idx, 2, cf->dim);
t->son[0] = build_pca_cluster(cf, size0, idx, clf);
t->son[1] = build_pca_cluster(cf, size1, idx + size0, clf);
update_bbox_cluster(t);
}
else {
t = new_cluster(size, idx, 1, cf->dim);
t->son[0] = build_pca_cluster(cf, size0, idx, clf);
update_bbox_cluster(t);
}
}
else {
assert(size1 > 0);
t = new_cluster(size, idx, 1, cf->dim);
t->son[0] = build_pca_cluster(cf, size1, idx, clf);
update_bbox_cluster(t);
}
}
else {
t = new_cluster(size, idx, 0, cf->dim);
update_support_bbox_cluster(cf, t);
}
update_cluster(t);
return t;
}
