path: root/kaldi_io/src/kaldi/matrix/jama-svd.h

// matrix/jama-svd.h

// Copyright 2009-2011 Microsoft Corporation

// See ../../COPYING for clarification regarding multiple authors
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//  http://www.apache.org/licenses/LICENSE-2.0
//
// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
// MERCHANTABLITY OR NON-INFRINGEMENT.
// See the Apache 2 License for the specific language governing permissions and
// limitations under the License.

// This file consists of a port and modification of materials from
//   JAMA: A Java Matrix Package
// under the following notice: This software is a cooperative product of
// The MathWorks and the National Institute of Standards and Technology (NIST)
// which has been released to the public.  This notice and the original code are
// available at http://math.nist.gov/javanumerics/jama/domain.notice


#ifndef KALDI_MATRIX_JAMA_SVD_H_
#define KALDI_MATRIX_JAMA_SVD_H_ 1


#include "matrix/kaldi-matrix.h"
#include "matrix/sp-matrix.h"
#include "matrix/cblas-wrappers.h"

namespace kaldi {

#if defined(HAVE_ATLAS) || defined(USE_KALDI_SVD)
// using ATLAS as our math library, which doesn't have SVD -> need
// to implement it.

// This routine is a modified form of jama_svd.h which is part of the TNT distribution.
// (originally comes from JAMA).

/** Singular Value Decomposition.
 * <P>
 * For an m-by-n matrix A with m >= n, the singular value decomposition is
 * an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
 * an n-by-n orthogonal matrix V so that A = U*S*V'.
 * <P>
 * The singular values, sigma[k] = S(k, k), are ordered so that
 * sigma[0] >= sigma[1] >= ... >= sigma[n-1].
 * <P>
 * The singular value decompostion always exists, so the constructor will
 * never fail.  The matrix condition number and the effective numerical
 * rank can be computed from this decomposition.

 * <p>
 *     (Adapted from JAMA, a Java Matrix Library, developed by jointly
 *     by the Mathworks and NIST; see  http://math.nist.gov/javanumerics/jama).
 */


template<typename Real>
bool MatrixBase<Real>::JamaSvd(VectorBase<Real> *s_in,
                               MatrixBase<Real> *U_in,
                               MatrixBase<Real> *V_in) {  //  Destructive!
  KALDI_ASSERT(s_in != NULL && U_in != this && V_in != this);
  int wantu = (U_in != NULL), wantv = (V_in != NULL);
  Matrix<Real> Utmp, Vtmp;
  MatrixBase<Real> &U = (U_in ? *U_in : Utmp), &V = (V_in ? *V_in : Vtmp);
  VectorBase<Real> &s = *s_in;

  int m = num_rows_, n = num_cols_;
  KALDI_ASSERT(m>=n && m != 0 && n != 0);
  if (wantu) KALDI_ASSERT((int)U.num_rows_ == m && (int)U.num_cols_ == n);
  if (wantv) KALDI_ASSERT((int)V.num_rows_ == n && (int)V.num_cols_ == n);
  KALDI_ASSERT((int)s.Dim() == n);  // n<=m so n is min.

  int nu = n;
  U.SetZero();  // make sure all zero.
  Vector<Real> e(n);
  Vector<Real> work(m);
  MatrixBase<Real> &A(*this);
  Real *adata = A.Data(), *workdata = work.Data(), *edata = e.Data(),
      *udata = U.Data(), *vdata = V.Data();
  int astride = static_cast<int>(A.Stride()),
      ustride = static_cast<int>(U.Stride()),
      vstride = static_cast<int>(V.Stride());
  int i = 0, j = 0, k = 0;

  // Reduce A to bidiagonal form, storing the diagonal elements
  // in s and the super-diagonal elements in e.

  int nct = std::min(m-1, n);
  int nrt = std::max(0, std::min(n-2, m));
  for (k = 0; k < std::max(nct, nrt); k++) {
    if (k < nct) {

      // Compute the transformation for the k-th column and
      // place the k-th diagonal in s(k).
      // Compute 2-norm of k-th column without under/overflow.
      s(k) = 0;
      for (i = k; i < m; i++) {
        s(k) = hypot(s(k), A(i, k));
      }
      if (s(k) != 0.0) {
        if (A(k, k) < 0.0) {
          s(k) = -s(k);
        }
        for (i = k; i < m; i++) {
          A(i, k) /= s(k);
        }
        A(k, k) += 1.0;
      }
      s(k) = -s(k);
    }
    for (j = k+1; j < n; j++) {
      if ((k < nct) && (s(k) != 0.0))  {

        // Apply the transformation.

        Real t = cblas_Xdot(m - k, adata + astride*k + k, astride,
                            adata + astride*k + j, astride);
        /*for (i = k; i < m; i++) {
          t += adata[i*astride + k]*adata[i*astride + j];  //   A(i, k)*A(i, j); // 3
          }*/
        t = -t/A(k, k);
        cblas_Xaxpy(m - k, t, adata + k*astride + k, astride,
                    adata + k*astride + j, astride);
        /*for (i = k; i < m; i++) {
          adata[i*astride + j] += t*adata[i*astride + k];  // A(i, j) += t*A(i, k); // 5
          }*/
      }

      // Place the k-th row of A into e for the
      // subsequent calculation of the row transformation.

      e(j) = A(k, j);
    }
    if (wantu & (k < nct)) {

      // Place the transformation in U for subsequent back
      // multiplication.

      for (i = k; i < m; i++) {
        U(i, k) = A(i, k);
      }
    }
    if (k < nrt) {

      // Compute the k-th row transformation and place the
      // k-th super-diagonal in e(k).
      // Compute 2-norm without under/overflow.
      e(k) = 0;
      for (i = k+1; i < n; i++) {
        e(k) = hypot(e(k), e(i));
      }
      if (e(k) != 0.0) {
        if (e(k+1) < 0.0) {
          e(k) = -e(k);
        }
        for (i = k+1; i < n; i++) {
          e(i) /= e(k);
        }
        e(k+1) += 1.0;
      }
      e(k) = -e(k);
      if ((k+1 < m) & (e(k) != 0.0)) {

        // Apply the transformation.

        for (i = k+1; i < m; i++) {
          work(i) = 0.0;
        }
        for (j = k+1; j < n; j++) {
          for (i = k+1; i < m; i++) {
            workdata[i] += edata[j] * adata[i*astride + j];  // work(i) += e(j)*A(i, j); // 5
          }
        }
        for (j = k+1; j < n; j++) {
          Real t(-e(j)/e(k+1));
          cblas_Xaxpy(m - (k+1), t, workdata + (k+1), 1,
                      adata + (k+1)*astride + j, astride);
          /*
          for (i = k+1; i < m; i++) {
            adata[i*astride + j] += t*workdata[i];  // A(i, j) += t*work(i); // 5
            }*/
        }
      }
      if (wantv) {

        // Place the transformation in V for subsequent
        // back multiplication.

        for (i = k+1; i < n; i++) {
          V(