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);
}
void Matlab_Engine::get(cmat &m, const char *name){
mxArray *T;
if((T = engGetArray(e, name)) == NULL)
cout << "No variable with the given name exists in the Matlab workspace!\n";
else{
if(mxGetNumberOfDimensions(T)==2){
double *pt_r = (double*) mxGetPr(T);
double *pt_i = (double*) mxGetPi(T);
const int *dims = mxGetDimensions(T);
m.set_size(dims[0], dims[1], false);
if(mxIsComplex(T)) // Copy both real and imaginary part.
for(int row=0; row<dims[0]; row++){
for(int col=0; col<dims[1]; col++){
complex<double> value(*pt_r++, *pt_i++);
m(row, col) = value;
}
}
else // Copy only the real part.
for(int row=0; row<dims[0]; row++){
for(int col=0; col<dims[1]; col++){
complex<double> value(*pt_r++, 0);
m(row, col) = value;
}
}
}
else
cout << "The requested variable is not a matrix!\n";
}
}
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 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);
}
bool qr(const cmat &A, cmat &Q, 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);
Q = R;
Q.set_size(m, m, true);
// 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);
}