svd.cpp

Go to the documentation of this file.

#ifndef _MSC_VER
#  include <itpp/config.h>
#else
#  include <itpp/config_msvc.h>
#endif

#if defined(HAVE_LAPACK)
#  include <itpp/base/algebra/lapack.h>
#endif

#include <itpp/base/algebra/svd.h>


namespace itpp
{

#if defined(HAVE_LAPACK)

bool svd(const mat &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 = std::max(3 * std::min(m, n) + std::max(m, n), 5 * std::min(m, n));

  mat U, V;
  S.set_size(std::min(m, n), false);
  vec work(lwork);

  mat B(A);

  // The theoretical calculation of lwork above results in the minimum size
  // needed for dgesvd_ to run to completion without having memory errors.
  // For speed improvement it is best to set lwork=-1 and have dgesvd_
  // calculate the best workspace requirement.
  int lwork_tmp = -1;
  dgesvd_(&jobu, &jobvt, &m, &n, B._data(), &lda, S._data(), U._data(), &ldu,
          V._data(), &ldvt, work._data(), &lwork_tmp, &info);
  if (info == 0) {
    lwork = static_cast<int>(work(0));
    work.set_size(lwork, false);
  }

  dgesvd_(&jobu, &jobvt, &m, &n, B._data(), &lda, S._data(), U._data(), &ldu,
          V._data(), &ldvt, work._data(), &lwork, &info);

  return (info == 0);
}

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 * std::min(m, n) + std::max(m, n);

  cvec U, V;
  S.set_size(std::min(m, n), false);
  cvec work(lwork);
  vec rwork(5*std::min(m, n));

  cmat B(A);

  // The theoretical calculation of lwork above results in the minimum size
  // needed for zgesvd_ to run to completion without having memory errors.
  // For speed improvement it is best to set lwork=-1 and have zgesvd_
  // calculate the best workspace requirement.
  int lwork_tmp = -1;
  zgesvd_(&jobu, &jobvt, &m, &n, B._data(), &lda, S._data(), U._data(), &ldu,
          V._data(), &ldvt, work._data(), &lwork_tmp, rwork._data(), &info);
  if (info == 0) {
    lwork = static_cast<int>(real(work(0)));
    work.set_size(lwork, false);
  }

  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 mat &A, mat &U, vec &S, mat &V)
{
  char jobu = 'A', jobvt = 'A';
  int m, n, lda, ldu, ldvt, lwork, info;
  m = lda = ldu = A.rows();
  n = ldvt = A.cols();
  lwork = std::max(3 * std::min(m, n) + std::max(m, n), 5 * std::min(m, n));

  U.set_size(m, m, false);
  V.set_size(n, n, false);
  S.set_size(std::min(m, n), false);
  vec work(lwork);

  mat B(A);

  // The theoretical calculation of lwork above results in the minimum size
  // needed for dgesvd_ to run to completion without having memory errors.
  // For speed improvement it is best to set lwork=-1 and have dgesvd_
  // calculate the best workspace requirement.
  int lwork_tmp = -1;
  dgesvd_(&jobu, &jobvt, &m, &n, B._data(), &lda, S._data(), U._data(), &ldu,
          V._data(), &ldvt, work._data(), &lwork_tmp, &info);
  if (info == 0) {
    lwork = static_cast<int>(work(0));
    work.set_size(lwork, false);
  }

  dgesvd_(&jobu, &jobvt, &m, &n, B._data(), &lda, S._data(), U._data(), &ldu,
          V._data(), &ldvt, work._data(), &lwork, &info);

  V = V.T(); // This is probably slow!!!

  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 * std::min(m, n) + std::max(m, n);

  U.set_size(m, m, false);
  V.set_size(n, n, false);
  S.set_size(std::min(m, n), false);
  cvec work(lwork);
  vec rwork(5 * std::min(m, n));

  cmat B(A);

  // The theoretical calculation of lwork above results in the minimum size
  // needed for zgesvd_ to run to completion without having memory errors.
  // For speed improvement it is best to set lwork=-1 and have zgesvd_
  // calculate the best workspace requirement.
  int lwork_tmp = -1;
  zgesvd_(&jobu, &jobvt, &m, &n, B._data(), &lda, S._data(), U._data(), &ldu,
          V._data(), &ldvt, work._data(), &lwork_tmp, rwork._data(), &info);
  if (info == 0) {
    lwork = static_cast<int>(real(work(0)));
    work.set_size(lwork, false);
  }

  zgesvd_(&jobu, &jobvt, &m, &n, B._data(), &lda, S._data(), U._data(), &ldu,
          V._data(), &ldvt, work._data(), &lwork, rwork._data(), &info);

  V = V.H(); // This is slow!!!

  return (info == 0);
}

#else

bool svd(const mat &A, vec &S)
{
  it_error("LAPACK library is needed to use svd() function");
  return false;
}

bool svd(const cmat &A, vec &S)
{
  it_error("LAPACK library is needed to use svd() function");
  return false;
}

bool svd(const mat &A, mat &U, vec &S, mat &V)
{
  it_error("LAPACK library is needed to use svd() function");
  return false;
}

bool svd(const cmat &A, cmat &U, vec &S, cmat &V)
{
  it_error("LAPACK library is needed to use svd() function");
  return false;
}

#endif // HAVE_LAPACK

vec svd(const mat &A)
{
  vec S;
  svd(A, S);
  return S;
}

vec svd(const cmat &A)
{
  vec S;
  svd(A, S);
  return S;
}

} //namespace itpp