bool qr(const cmat &A, cmat &R)
{
int info;
int m = A.rows();
int n = A.cols();
int lwork = n;
int k = std::min(m, n);
cvec tau(k);
cvec work(lwork);
R = A;
// perform workspace query for optimum lwork value
int lwork_tmp = -1;
zgeqrf_(&m, &n, R._data(), &m, tau._data(), work._data(), &lwork_tmp,
&info);
if (info == 0) {
lwork = static_cast<int>(real(work(0)));
work.set_size(lwork, false);
}
zgeqrf_(&m, &n, R._data(), &m, tau._data(), work._data(), &lwork, &info);
// construct R
for (int i = 0; i < m; i++)
for (int j = 0; j < std::min(i, n); j++)
R(i, j) = 0;
return (info == 0);
}
bool schur(const cmat &A, cmat &U, cmat &T)
{
it_assert_debug(A.rows() == A.cols(), "schur(): Matrix is not square");
char jobvs = 'V';
char sort = 'N';
int info;
int n = A.rows();
int lda = n;
int ldvs = n;
int lwork = 2 * n; // This may be choosen better!
int sdim = 0;
vec rwork(n);
cvec w(n);
cvec work(lwork);
T.set_size(lda, n, false);
U.set_size(ldvs, n, false);
T = A; // The routine overwrites input matrix with eigenvectors
zgees_(&jobvs, &sort, 0, &n, T._data(), &lda, &sdim, w._data(), U._data(),
&ldvs, work._data(), &lwork, rwork._data(), 0, &info);
return (info == 0);
}
bool qr(const cmat &A, cmat &Q, cmat &R, bmat &P)
{
int info;
int m = A.rows();
int n = A.cols();
int lwork = n;
int k = std::min(m, n);
cvec tau(k);
cvec work(lwork);
vec rwork(std::max(1, 2*n));
ivec jpvt(n);
jpvt.zeros();
R = A;
// perform workspace query for optimum lwork value
int lwork_tmp = -1;
zgeqp3_(&m, &n, R._data(), &m, jpvt._data(), tau._data(), work._data(),
&lwork_tmp, rwork._data(), &info);
if (info == 0) {
lwork = static_cast<int>(real(work(0)));
work.set_size(lwork, false);
}
zgeqp3_(&m, &n, R._data(), &m, jpvt._data(), tau._data(), work._data(),
&lwork, rwork._data(), &info);
Q = R;
Q.set_size(m, m, true);
// construct permutation matrix
P = zeros_b(n, n);
for (int j = 0; j < n; j++)
P(jpvt(j) - 1, j) = 1;
// construct R
for (int i = 0; i < m; i++)
for (int j = 0; j < std::min(i, n); j++)
R(i, j) = 0;
// perform workspace query for optimum lwork value
lwork_tmp = -1;
zungqr_(&m, &m, &k, Q._data(), &m, tau._data(), work._data(), &lwork_tmp,
&info);
if (info == 0) {
lwork = static_cast<int>(real(work(0)));
work.set_size(lwork, false);
}
zungqr_(&m, &m, &k, Q._data(), &m, tau._data(), work._data(), &lwork,
&info);
return (info == 0);
}
bool inv(const cmat &X, cmat &Y)
{
// it_assert1(X.rows() == X.cols(), "inv: matrix is not square");
int m = X.rows(), info, lwork;
lwork = m; // may be choosen better
ivec p(m);
Y = X;
cvec work(lwork);
zgetrf_(&m, &m, Y._data(), &m, p._data(), &info); // LU-factorization
if (info!=0)
return false;
zgetri_(&m, Y._data(), &m, p._data(), work._data(), &lwork, &info);
return (info==0);
}
bool svd(const cmat &A, cmat &U, vec &S, cmat &V)
{
char jobu='A', jobvt='A';
int m, n, lda, ldu, ldvt, lwork, info;
m = lda = ldu = A.rows();
n = ldvt = A.cols();
lwork = 2*min(m,n)+max(m,n);
U.set_size(m,m, false);
V.set_size(n,n, false);
S.set_size(min(m,n), false);
cvec work(lwork);
vec rwork(max(1, 5*min(m, n)));
cmat B(A);
zgesvd_(&jobu, &jobvt, &m, &n, B._data(), &lda, S._data(), U._data(), &ldu, V._data(), &ldvt, work._data(), &lwork, rwork._data(), &info);
V = transpose(conj(V)); // This is slow!!!
return (info==0);
}