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);
}
cmat operator-(const double &s, const cmat &m)
{
it_assert_debug(m.rows() > 0 && m.cols() > 0, "operator-(): Matrix of zero length");
cmat temp(m.rows(), m.cols());
for (int i = 0;i < m._datasize();i++) {
temp._data()[i] = std::complex<double>((double)s - m(i).real(), -m(i).imag());
}
return temp;
}
static
void assert_cmat(const cmat &ref, const cmat &act)
{
ASSERT_EQ(ref.rows(), act.rows());
ASSERT_EQ(ref.cols(), act.cols());
for (int n = 0; n < ref.rows(); ++n) {
for (int k = 0; k < ref.cols(); ++k) {
ASSERT_NEAR(ref(n,k).real(), act(n,k).real(), tol);
ASSERT_NEAR(ref(n,k).imag(), act(n,k).imag(), tol);
}
}
}
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);
}
cmat operator/(const cmat &m, const double &s)
{
it_assert_debug(m.rows() > 0 && m.cols() > 0, "operator/(): Matrix of zero length");
cmat temp = m;
for (int i = 0;i < m._datasize();i++) {
temp._data()[i] /= (double)s;
}
return temp;
}
// Perform LTE ratematching for convolutionally encoded bits d to fit
// an e vector of length n_e.
cvec lte_conv_ratematch(
const cmat & d,
const uint32 & n_e
) {
const uint8 n_c=32;
const uint32 n_r=ceil((double)d.cols()/n_c);
ASSERT(d.rows()==3);
// Subblock interleaving
const static int perm_pattern_c[]={1,17,9,25,5,21,13,29,3,19,11,27,7,23,15,31,0,16,8,24,4,20,12,28,2,18,10,26,6,22,14,30};
const ivec perm_pattern(perm_pattern_c,32);
cmat v(3,n_r*n_c);
#ifndef NDEBUG
v=NAN;
#endif
for (uint8 t=0;t<3;t++) {
cvec temp_row=d.get_row(t);
cvec temp_nan(n_r*n_c-d.cols());
temp_nan=NAN;
temp_row=concat(temp_nan,temp_row);
cmat y=transpose(reshape(temp_row,n_c,n_r));
// Permute the columns
cmat y_perm(n_r,n_c);
#ifndef NDEBUG
y_perm=NAN;
#endif
for (uint8 k=0;k<32;k++) {
y_perm.set_col(k,y.get_col(perm_pattern(k)));
}
// Assign
v.set_row(t,cvectorize(y_perm));
}
// Bit collection
cvec w=cvectorize(transpose(v));
// Selection
cvec e(n_e);
#ifndef NDEBUG
e=NAN;
#endif
uint32 k=0;
uint32 j=0;
while (k<n_e) {
if (isfinite(w(j).real())) {
e(k)=w(j);
k++;
}
j=mod(j+1,3*n_r*n_c);
}
return e;
}
cmat operator+(const mat &a, const cmat &b)
{
it_assert_debug(a.cols() == b.cols() && a.rows() == b.rows(), "operator+(): sizes does not match");
cmat temp(b);
for (int i = 0;i < a.rows();i++) {
for (int j = 0;j < a.cols();j++) {
temp(i, j) += std::complex<double>(static_cast<double>(a(i, j)), 0.0);
}
}
return temp;
}
cmat operator+(const smat &a, const cmat &b)
{
it_assert_debug(a.cols() == b.cols() && a.rows() == b.rows(), "operator+(): sizes does not match");
cmat temp(b);
for (int i = 0;i < a.rows();i++) {
for (int j = 0;j < a.cols();j++) {
temp(i, j) += (double)a(i, j);
}
}
return temp;
}
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);
}
void Matlab_Engine::put(const cmat &m, const char *name){
const int rows = m.rows();
const int cols = m.cols();
mxArray *T;
if((T = mxCreateDoubleMatrix(rows, cols, mxCOMPLEX)) == NULL)
cout << "Unable to allocate Matlab matrix. Out of memory?\n";
mxSetName(T, name);
double *pt_r = (double*) mxGetPr(T);
double *pt_i = (double*) mxGetPi(T);
for(int row=0; row<rows; row++){
for(int col=0; col<cols; col++){
*pt_r++ = real(m(row, col));
*pt_i++ = imag(m(row, col));
}
}
if(engPutArray(e, T))
cout << "Unable to put it++ matrix to Matlab workspace!\n";
}
bool svd(const cmat &A, vec &S)
{
char jobu='N', jobvt='N';
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);
cvec U, V;
//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);
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);
}
/* Determinant of complex square matrix.
Calculate determinant of inmatrix (Uses LU-factorisation)
(See Theorem 3.2.1 p. 97 in Golub & van Loan, "Matrix Computations").
det(X) = det(P')*det(L)*det(U) = det(P')*1*prod(diag(U))
Needs LU-factorization of complex matrices (LAPACK)
*/
double_complex det(const cmat &X)
{
// it_assert1(X.rows()==X.cols(),"det : Only square matrices");
int i;
cmat L, U;
ivec p;
double s=1.0;
lu(X,L,U,p); // calculate LU-factorisation
double_complex temp=U(0,0);
for (i=1;i<X.rows();i++) {
temp*=U(i,i);
}
// Calculate det(P´). Equal to (-1)^(no row changes)
for (i=0; i<p.size(); i++)
if (i != p(i))
s *=-1.0;
return temp*s;
}
void DiagonalResponse::solve(cmat& res, const cmat& M) const {
// TODO make sure this is optimal
assert( diag.size() == M.rows() );
assert( &res != &M );
res = (M.transpose() * diag.asDiagonal() ).transpose();
}