svd.cpp

强大的C++库

/*!
 * \file
 * \brief Implementation of Singular Value Decompositions
 * \author Tony Ottosson, Simon Wood and Adam Piatyszek
 *
 * -------------------------------------------------------------------------
 *
 * IT++ - C++ library of mathematical, signal processing, speech processing,
 *        and communications classes and functions
 *
 * Copyright (C) 1995-2008  (see AUTHORS file for a list of contributors)
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
 *
 * -------------------------------------------------------------------------
 */

#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