void
mvm_uniform_avector(field alpha, bool trans, pcuniform u,
pcavector x, pavector y)
{
avector tmp1, tmp2;
pavector xt, yt;
if (trans) {
xt = init_avector(&tmp1, u->rb->kbranch);
yt = init_avector(&tmp2, u->cb->kbranch);
compress_clusterbasis_avector(u->rb, x, xt);
clear_avector(yt);
mvm_amatrix_avector(alpha, true, &u->S, xt, yt);
expand_clusterbasis_avector(u->cb, yt, y);
uninit_avector(yt);
uninit_avector(xt);
}
else {
xt = init_avector(&tmp1, u->cb->kbranch);
yt = init_avector(&tmp2, u->rb->kbranch);
compress_clusterbasis_avector(u->cb, x, xt);
clear_avector(yt);
mvm_amatrix_avector(alpha, false, &u->S, xt, yt);
expand_clusterbasis_avector(u->rb, yt, y);
uninit_avector(yt);
uninit_avector(xt);
}
}
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;
}
