void
basisproduct_clusteroperator(pcclusterbasis cb1, pcclusterbasis cb2,
pclusteroperator pr)
{
pamatrix X, Xt;
amatrix tmp1, tmp2;
uint i;
assert(cb1->t == pr->t);
assert(cb2->t == pr->t);
resize_clusteroperator(pr, cb1->k, cb2->k);
if (pr->sons > 0) {
assert(cb1->sons == pr->sons);
assert(cb2->sons == pr->sons);
for (i = 0; i < pr->sons; i++)
basisproduct_clusteroperator(cb1->son[i], cb2->son[i], pr->son[i]);
clear_amatrix(&pr->C);
for (i = 0; i < pr->sons; i++) {
X = init_amatrix(&tmp1, cb1->son[i]->k, cb2->k);
clear_amatrix(X);
addmul_amatrix(1.0, false, &pr->son[i]->C, false, &cb2->son[i]->E, X);
addmul_amatrix(1.0, true, &cb1->son[i]->E, false, X, &pr->C);
uninit_amatrix(X);
}
}
else {
if (cb1->sons == 0) {
if (cb2->sons == 0) {
clear_amatrix(&pr->C);
addmul_amatrix(1.0, true, &cb1->V, false, &cb2->V, &pr->C);
}
else {
Xt = init_amatrix(&tmp1, cb2->kbranch, cb1->k);
compress_clusterbasis_amatrix(cb2, &cb1->V, Xt);
X = init_sub_amatrix(&tmp2, Xt, cb2->k, 0, cb1->k, 0);
copy_amatrix(true, X, &pr->C);
uninit_amatrix(X);
uninit_amatrix(Xt);
}
}
else {
assert(cb2->sons == 0); /* Could be generalized */
Xt = init_amatrix(&tmp1, cb1->kbranch, cb2->k);
compress_clusterbasis_amatrix(cb1, &cb2->V, Xt);
X = init_sub_amatrix(&tmp2, Xt, cb1->k, 0, cb2->k, 0);
copy_amatrix(false, X, &pr->C);
uninit_amatrix(X);
uninit_amatrix(Xt);
}
}
}
void
clear_hmatrix(phmatrix hm)
{
if (hm->son) {
int rsons = hm->rsons;
int csons = hm->csons;
for (int j=0;j<csons;j++) {
for (int i=0;i<rsons;i++) {
clear_hmatrix(hm->son[i+j*rsons]);
}
}
}
else if(hm->r) {
setrank_rkmatrix(hm->r, 0);
}
else {
assert(hm->f);
clear_amatrix(hm->f);
}
}
void
add_projected_uniform(pcuniform u,
pcclusteroperator ro, pcclusteroperator co,
puniform unew)
{
amatrix tmp;
pamatrix XS;
if (u->rb == unew->rb) {
if (u->cb == unew->cb)
add_amatrix(1.0, false, &u->S, &unew->S);
else {
assert(co->krow == unew->cb->k);
assert(co->kcol == u->cb->k);
addmul_amatrix(1.0, false, &u->S, true, &co->C, &unew->S);
}
}
else {
if (u->cb == unew->cb) {
assert(ro->krow == unew->rb->k);
assert(ro->kcol == u->rb->k);
addmul_amatrix(1.0, false, &ro->C, false, &u->S, &unew->S);
}
else {
assert(ro->krow == unew->rb->k);
assert(ro->kcol == u->rb->k);
assert(co->krow == unew->cb->k);
assert(co->kcol == u->cb->k);
XS = init_amatrix(&tmp, unew->rb->k, u->cb->k);
clear_amatrix(XS);
addmul_amatrix(1.0, false, &ro->C, false, &u->S, XS);
addmul_amatrix(1.0, false, XS, true, &co->C, &unew->S);
uninit_amatrix(XS);
}
}
}
static real
compareweights(pcclusteroperator co1, pcclusteroperator co2, uint level)
{
amatrix tmp;
pamatrix D;
real norm, error, error1;
uint k;
uint i;
k = co1->kcol;
assert(k == co2->kcol);
D = init_amatrix(&tmp, k, k);
clear_amatrix(D);
addmul_amatrix(1.0, true, &co1->C, false, &co1->C, D);
norm = norm2_amatrix(D);
addmul_amatrix(-1.0, true, &co2->C, false, &co2->C, D);
error = norm2_amatrix(D);
uninit_amatrix(D);
if (norm > 0.0)
error /= norm;
if (co1->sons != co2->sons)
printf("Tree mismatch");
else
for (i = 0; i < co1->sons; i++) {
error1 = compareweights(co1->son[i], co2->son[i], level + 1);
if (error1 > error)
error = error1;
}
return error;
}
static void
check_triangularaddmul(bool alower, bool atrans, bool blower, bool btrans)
{
pamatrix a, b, at, bt, x;
amatrix atmp, btmp, attmp, bttmp, xtmp;
real error;
uint dim1, dim2, dim3;
dim1 = 100;
dim2 = 80;
dim3 = 90;
a =
(atrans ? init_amatrix(&atmp, dim2, dim1) :
init_amatrix(&atmp, dim1, dim2));
random_amatrix(a);
b =
(btrans ? init_amatrix(&btmp, dim3, dim2) :
init_amatrix(&btmp, dim2, dim3));
random_amatrix(b);
at = init_amatrix(&attmp, a->rows, a->cols);
if (alower)
copy_lower_amatrix(a, false, at);
else
copy_upper_amatrix(a, false, at);
bt = init_amatrix(&bttmp, b->rows, b->cols);
if (blower)
copy_lower_amatrix(b, false, bt);
else
copy_upper_amatrix(b, false, bt);
x = init_amatrix(&xtmp, dim1, dim3);
clear_amatrix(x);
triangularaddmul_amatrix(1.0, alower, atrans, a, blower, btrans, b, x);
addmul_amatrix(-1.0, atrans, at, btrans, bt, x);
error = norm2_amatrix(x);
(void)
printf
("Checking triangularaddmul(alower=%s, atrans=%s, blower=%s, btrans=%s)\n"
" Accuracy %g, %sokay\n", (alower ? "tr" : "fl"),
(atrans ? "tr" : "fl"), (blower ? "tr" : "fl"), (btrans ? "tr" : "fl"),
error, (error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
uninit_amatrix(x);
uninit_amatrix(bt);
uninit_amatrix(at);
uninit_amatrix(b);
uninit_amatrix(a);
dim1 = 70;
dim2 = 80;
dim3 = 90;
a =
(atrans ? init_amatrix(&atmp, dim2, dim1) :
init_amatrix(&atmp, dim1, dim2));
random_amatrix(a);
b =
(btrans ? init_amatrix(&btmp, dim3, dim2) :
init_amatrix(&btmp, dim2, dim3));
random_amatrix(b);
at = init_amatrix(&attmp, a->rows, a->cols);
if (alower)
copy_lower_amatrix(a, false, at);
else
copy_upper_amatrix(a, false, at);
bt = init_amatrix(&bttmp, b->rows, b->cols);
if (blower)
copy_lower_amatrix(b, false, bt);
else
copy_upper_amatrix(b, false, bt);
x = init_amatrix(&xtmp, dim1, dim3);
clear_amatrix(x);
triangularaddmul_amatrix(1.0, alower, atrans, a, blower, btrans, b, x);
addmul_amatrix(-1.0, atrans, at, btrans, bt, x);
error = norm2_amatrix(x);
(void)
printf
("Checking triangularaddmul(alower=%s, atrans=%s, blower=%s, btrans=%s)\n"
" Accuracy %g, %sokay\n", (alower ? "tr" : "fl"),
(atrans ? "tr" : "fl"), (blower ? "tr" : "fl"), (btrans ? "tr" : "fl"),
error, (error < tolerance ? "" : " NOT "));
if (error >= tolerance)
problems++;
uninit_amatrix(x);
uninit_amatrix(bt);
uninit_amatrix(at);
uninit_amatrix(b);
uninit_amatrix(a);
}
void
project_inplace_uniform(puniform u,
pclusterbasis rb, pcclusteroperator ro,
pclusterbasis cb, pcclusteroperator co)
{
amatrix tmp;
pamatrix X;
if (u->rb == rb) {
if (u->cb == cb) {
/* Nothing to do */
}
else {
assert(co);
assert(co->krow == cb->k);
assert(co->kcol == u->cb->k);
/* Transform coupling matrix */
X = init_amatrix(&tmp, u->rb->k, cb->k);
clear_amatrix(X);
addmul_amatrix(1.0, false, &u->S, true, &co->C, X);
resize_amatrix(&u->S, X->rows, X->cols);
copy_amatrix(false, X, &u->S);
uninit_amatrix(X);
/* Update pointer */
ref_col_uniform(u, cb);
}
}
else {
assert(ro);
assert(ro->krow == rb->k);
assert(ro->kcol == u->rb->k);
if (u->cb == cb) {
/* Transform coupling matrix */
X = init_amatrix(&tmp, rb->k, u->cb->k);
clear_amatrix(X);
addmul_amatrix(1.0, false, &ro->C, false, &u->S, X);
resize_amatrix(&u->S, X->rows, X->cols);
copy_amatrix(false, X, &u->S);
uninit_amatrix(X);
/* Update pointer */
ref_row_uniform(u, rb);
}
else {
assert(co);
assert(co->krow == cb->k);
assert(co->kcol == u->cb->k);
/* Transform coupling matrix for row... */
X = init_amatrix(&tmp, rb->k, u->cb->k);
clear_amatrix(X);
addmul_amatrix(1.0, false, &ro->C, false, &u->S, X);
/* ... and column basis */
resize_amatrix(&u->S, rb->k, cb->k);
clear_amatrix(&u->S);
addmul_amatrix(1.0, false, X, true, &co->C, &u->S);
uninit_amatrix(X);
/* Update pointers */
ref_row_uniform(u, rb);
ref_col_uniform(u, cb);
}
}
}
void
clear_uniform(puniform u)
{
clear_amatrix(&u->S);
}
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;
}
void
coarsen_hmatrix(phmatrix G, ptruncmode tm, real eps, bool recursive)
{
uint rsons = G->rsons;
uint csons = G->csons;
phmatrix son;
prkmatrix R;
pamatrix A, B;
amatrix T, S;
uint i, j, leafs, ranksum, rankoffset, rowoffset, coloffset, rank;
size_t sizeold, sizenew;
leafs = 0;
/* recursion */
if (rsons * csons > 0) {
for (j = 0; j < csons; ++j) {
for (i = 0; i < rsons; ++i) {
son = G->son[i + j * rsons];
if (recursive == true) {
coarsen_hmatrix(son, tm, eps, recursive);
}
leafs += son->rsons * son->csons;
}
}
update_hmatrix(G);
}
else {
/* matrix is a leaf -> northing to do */
return;
}
if (leafs > 0) {
/* matrix has sons which are not leafs -> nothing to do */
return;
}
else {
if (G->rc == G->cc) {
return;
}
/* determine ranksum and size of sons */
ranksum = 0;
sizeold = 0;
for (j = 0; j < csons; ++j) {
for (i = 0; i < rsons; ++i) {
son = G->son[i + j * rsons];
if (son->r) {
ranksum += son->r->k;
sizeold += getsize_rkmatrix(son->r);
}
else {
assert(son->f != NULL);
ranksum += son->f->cols;
sizeold += getsize_amatrix(son->f);
}
}
}
/* new rank-k-matrix */
R = new_rkmatrix(G->rc->size, G->cc->size, ranksum);
A = &R->A;
B = &R->B;
clear_amatrix(A);
clear_amatrix(B);
/* copy sons into a big rank-k-matrix */
rankoffset = 0;
coloffset = 0;
for (j = 0; j < csons; ++j) {
rowoffset = 0;
for (i = 0; i < rsons; ++i) {
son = G->son[i + j * rsons];
rank = son->r ? son->r->k : son->f->cols;
init_sub_amatrix(&T, A, son->rc->size, rowoffset, rank, rankoffset);
init_sub_amatrix(&S, B, son->cc->size, coloffset, rank, rankoffset);
if (son->r) {
copy_amatrix(false, &(son->r->A), &T);
copy_amatrix(false, &(son->r->B), &S);
}
else {
copy_amatrix(false, son->f, &T);
identity_amatrix(&S);
}
rankoffset += rank;
rowoffset += son->rc->size;
uninit_amatrix(&T);
uninit_amatrix(&S);
}
coloffset += G->son[j * rsons]->cc->size;
}
/* compression */
trunc_rkmatrix(tm, eps, R);
sizenew = getsize_rkmatrix(R);
/* use new rank-k-matrix or discard */
if (sizenew < sizeold) {
for (j = 0; j < csons; ++j) {
for (i = 0; i < rsons; ++i) {
unref_hmatrix(G->son[i + j * rsons]);
}
}
G->rsons = 0;
G->csons = 0;
freemem(G->son);
G->son = NULL;
G->f = NULL;
G->r = R;
G->desc = 1;
}
else {
del_rkmatrix(R);
}
}
}
