Merge pull request #2 from yimmon/master

remove needless files

1 files changed, 0 insertions, 924 deletions

diff --git a/kaldi_io/src/kaldi/matrix/jama-eig.h b/kaldi_io/src/kaldi/matrix/jama-eig.h
deleted file mode 100644
index c7278bc..0000000
--- a/kaldi_io/src/kaldi/matrix/jama-eig.h
+++ /dev/null
@@ -1,924 +0,0 @@
-// matrix/jama-eig.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_EIG_H_
-#define KALDI_MATRIX_JAMA_EIG_H_ 1
-
-#include "matrix/kaldi-matrix.h"
-
-namespace kaldi {
-
-// This class is not to be used externally.  See the Eig function in the Matrix
-// class in kaldi-matrix.h.  This is the external interface.
-
-template<typename Real> class EigenvalueDecomposition {
-  // This class is based on the EigenvalueDecomposition class from the JAMA
-  // library (version 1.0.2).
- public:
-  EigenvalueDecomposition(const MatrixBase<Real> &A);
-
-  ~EigenvalueDecomposition();  // free memory.
-
-  void GetV(MatrixBase<Real> *V_out) {  // V is what we call P externally; it's the matrix of
-    // eigenvectors.
-    KALDI_ASSERT(V_out->NumRows() == static_cast<MatrixIndexT>(n_)
-                 && V_out->NumCols() == static_cast<MatrixIndexT>(n_));
-    for (int i = 0; i < n_; i++)
-      for (int j = 0; j < n_; j++)
-        (*V_out)(i, j) = V(i, j);  // V(i, j) is member function.
-  }
-  void GetRealEigenvalues(VectorBase<Real> *r_out) {
-    // returns real part of eigenvalues.
-    KALDI_ASSERT(r_out->Dim() == static_cast<MatrixIndexT>(n_));
-    for (int i = 0; i < n_; i++)
-      (*r_out)(i) = d_[i];
-  }
-  void GetImagEigenvalues(VectorBase<Real> *i_out) {
-    // returns imaginary part of eigenvalues.
-    KALDI_ASSERT(i_out->Dim() == static_cast<MatrixIndexT>(n_));
-    for (int i = 0; i < n_; i++)
-      (*i_out)(i) = e_[i];
-  }
- private:
-
-  inline Real &H(int r, int c) { return H_[r*n_ + c]; }
-  inline Real &V(int r, int c) { return V_[r*n_ + c]; }
-
-  // complex division
-  inline static void cdiv(Real xr, Real xi, Real yr, Real yi, Real *cdivr, Real *cdivi) {
-    Real r, d;
-    if (std::abs(yr) > std::abs(yi)) {
-      r = yi/yr;
-      d = yr + r*yi;
-      *cdivr = (xr + r*xi)/d;
-      *cdivi = (xi - r*xr)/d;
-    } else {
-      r = yr/yi;
-      d = yi + r*yr;
-      *cdivr = (r*xr + xi)/d;
-      *cdivi = (r*xi - xr)/d;
-    }
-  }
-
-  // Nonsymmetric reduction from Hessenberg to real Schur form.
-  void Hqr2 ();
-
-
-  int n_;  // matrix dimension.
-
-  Real *d_, *e_;  // real and imaginary parts of eigenvalues.
-  Real *V_;  // the eigenvectors (P in our external notation)
-  Real *H_;  // the nonsymmetric Hessenberg form.
-  Real *ort_;  // working storage for nonsymmetric algorithm.
-
-  // Symmetric Householder reduction to tridiagonal form.
-  void Tred2 ();
-
-  // Symmetric tridiagonal QL algorithm.
-  void Tql2 ();
-
-  // Nonsymmetric reduction to Hessenberg form.
-  void Orthes ();
-
-};
-
-template class EigenvalueDecomposition<float>;  // force instantiation.
-template class EigenvalueDecomposition<double>;  // force instantiation.
-
-template<typename Real> void  EigenvalueDecomposition<Real>::Tred2() {
-  //  This is derived from the Algol procedures tred2 by
-  //  Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
-  //  Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
-  //  Fortran subroutine in EISPACK.
-
-  for (int j = 0; j < n_; j++) {
-    d_[j] = V(n_-1, j);
-  }
-
-  // Householder reduction to tridiagonal form.
-
-  for (int i = n_-1; i > 0; i--) {
-
-    // Scale to avoid under/overflow.
-
-    Real scale = 0.0;
-    Real h = 0.0;
-    for (int k = 0; k < i; k++) {
-      scale = scale + std::abs(d_[k]);
-    }
-    if (scale == 0.0) {
-      e_[i] = d_[i-1];
-      for (int j = 0; j < i; j++) {
-        d_[j] = V(i-1, j);
-        V(i, j) = 0.0;
-        V(j, i) = 0.0;
-      }
-    } else {
-
-      // Generate Householder vector.
-
-      for (int k = 0; k < i; k++) {
-        d_[k] /= scale;
-        h += d_[k] * d_[k];
-      }
-      Real f = d_[i-1];
-      Real g = std::sqrt(h);
-      if (f > 0) {
-        g = -g;
-      }
-      e_[i] = scale * g;
-      h = h - f * g;
-      d_[i-1] = f - g;
-      for (int j = 0; j < i; j++) {
-        e_[j] = 0.0;
-      }
-
-      // Apply similarity transformation to remaining columns.
-
-      for (int j = 0; j < i; j++) {
-        f = d_[j];
-        V(j, i) = f;
-        g =e_[j] + V(j, j) * f;
-        for (int k = j+1; k <= i-1; k++) {
-          g += V(k, j) * d_[k];
-          e_[k] += V(k, j) * f;
-        }
-        e_[j] = g;
-      }
-      f = 0.0;
-      for (int j = 0; j < i; j++) {
-        e_[j] /= h;
-        f += e_[j] * d_[j];
-      }
-      Real hh = f / (h + h);
-      for (int j = 0; j < i; j++) {
-        e_[j] -= hh * d_[j];
-      }
-      for (int j = 0; j < i; j++) {
-        f = d_[j];
-        g = e_[j];
-        for (int k = j; k <= i-1; k++) {
-          V(k, j) -= (f * e_[k] + g * d_[k]);
-        }
-        d_[j] = V(i-1, j);
-        V(i, j) = 0.0;
-      }
-    }
-    d_[i] = h;
-  }
-
-  // Accumulate transformations.
-
-  for (int i = 0; i < n_-1; i++) {
-    V(n_-1, i) = V(i, i);
-    V(i, i) = 1.0;
-    Real h = d_[i+1];
-    if (h != 0.0) {
-      for (int k = 0; k <= i; k++) {
-        d_[k] = V(k, i+1) / h;
-      }
-      for (int j = 0; j <= i; j++) {
-        Real g = 0.0;
-        for (int k = 0; k <= i; k++) {
-          g += V(k, i+1) * V(k, j);
-        }
-        for (int k = 0; k <= i; k++) {
-          V(k, j) -= g * d_[k];
-        }
-      }
-    }
-    for (int k = 0; k <= i; k++) {
-      V(k, i+1) = 0.0;
-    }
-  }
-  for (int j = 0; j < n_; j++) {
-    d_[j] = V(n_-1, j);
-    V(n_-1, j) = 0.0;
-  }
-  V(n_-1, n_-1) = 1.0;
-   e_[0] = 0.0;
-}
-
-template<typename Real> void EigenvalueDecomposition<Real>::Tql2() {
-  //  This is derived from the Algol procedures tql2, by
-  //  Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
-  //  Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
-  //  Fortran subroutine in EISPACK.
-
-  for (int i = 1; i < n_; i++) {
-     e_[i-1] = e_[i];
-  }
-   e_[n_-1] = 0.0;
-
-  Real f = 0.0;
-  Real tst1 = 0.0;
-  Real eps = std::numeric_limits<Real>::epsilon();
-  for (int l = 0; l < n_; l++) {
-
-    // Find small subdiagonal element
-
-    tst1 = std::max(tst1, std::abs(d_[l]) + std::abs(e_[l]));
-    int m = l;
-    while (m < n_) {
-      if (std::abs(e_[m]) <= eps*tst1) {
-        break;
-      }
-      m++;
-    }
-
-    // If m == l, d_[l] is an eigenvalue,
-    // otherwise, iterate.
-
-    if (m > l) {
-      int iter = 0;
-      do {
-        iter = iter + 1;  // (Could check iteration count here.)
-
-        // Compute implicit shift
-
-        Real g = d_[l];
-        Real p = (d_[l+1] - g) / (2.0 *e_[l]);
-        Real r = Hypot(p, static_cast<Real>(1.0));  // This is a Kaldi version of hypot that works with templates.
-        if (p < 0) {
-          r = -r;
-        }
-        d_[l] =e_[l] / (p + r);
-        d_[l+1] =e_[l] * (p + r);
-        Real dl1 = d_[l+1];
-        Real h = g - d_[l];
-        for (int i = l+2; i < n_; i++) {
-          d_[i] -= h;
-        }
-        f = f + h;
-
-        // Implicit QL transformation.
-
-        p = d_[m];
-        Real c = 1.0;
-        Real c2 = c;
-        Real c3 = c;
-        Real el1 =e_[l+1];
-        Real s = 0.0;
-        Real s2 = 0.0;
-        for (int i = m-1; i >= l; i--) {
-          c3 = c2;
-          c2 = c;
-          s2 = s;
-          g = c *e_[i];
-          h = c * p;
-          r = Hypot(p, e_[i]);  // This is a Kaldi version of Hypot that works with templates.
-          e_[i+1] = s * r;
-          s =e_[i] / r;
-          c = p / r;
-          p = c * d_[i] - s * g;
-          d_[i+1] = h + s * (c * g + s * d_[i]);
-
-          // Accumulate transformation.
-
-          for (int k = 0; k < n_; k++) {
-            h = V(k, i+1);
-            V(k, i+1) = s * V(k, i) + c * h;
-            V(k, i) = c * V(k, i) - s * h;
-          }
-        }
-        p = -s * s2 * c3 * el1 *e_[l] / dl1;
-        e_[l] = s * p;
-        d_[l] = c * p;
-
-        // Check for convergence.
-
-      } while (std::abs(e_[l]) > eps*tst1);
-    }
-    d_[l] = d_[l] + f;
-    e_[l] = 0.0;
-  }
-
-  // Sort eigenvalues and corresponding vectors.
-
-  for (int i = 0; i < n_-1; i++) {
-    int k = i;
-    Real p = d_[i];
-    for (int j = i+1; j < n_; j++) {
-      if (d_[j] < p) {
-        k = j;
-        p = d_[j];
-      }
-    }
-    if (k != i) {
-      d_[k] = d_[i];
-      d_[i] = p;
-      for (int j = 0; j < n_; j++) {
-        p = V(j, i);
-        V(j, i) = V(j, k);
-        V(j, k) = p;
-      }
-    }
-  }
-}
-
-template<typename Real>
-void EigenvalueDecomposition<Real>::Orthes() {
-
-  //  This is derived from the Algol procedures orthes and ortran,
-  //  by Martin and Wilkinson, Handbook for Auto. Comp.,
-  //  Vol.ii-Linear Algebra, and the corresponding
-  //  Fortran subroutines in EISPACK.
-
-  int low = 0;
-  int high = n_-1;
-
-  for (int m = low+1; m <= high-1; m++) {
-
-    // Scale column.
-
-    Real scale = 0.0;
-    for (int i = m; i <= high; i++) {
-      scale = scale + std::abs(H(i, m-1));
-    }
-    if (scale != 0.0) {
-
-      // Compute Householder transformation.
-
-      Real h = 0.0;
-      for (int i = high; i >= m; i--) {
-        ort_[i] = H(i, m-1)/scale;
-        h += ort_[i] * ort_[i];
-      }
-      Real g = std::sqrt(h);
-      if (ort_[m] > 0) {
-        g = -g;
-      }
-      h = h - ort_[m] * g;
-      ort_[m] = ort_[m] - g;
-
-      // Apply Householder similarity transformation
-      // H = (I-u*u'/h)*H*(I-u*u')/h)
-
-      for (int j = m; j < n_; j++) {
-        Real f = 0.0;
-        for (int i = high; i >= m; i--) {
-          f += ort_[i]*H(i, j);
-        }
-        f = f/h;
-        for (int i = m; i <= high; i++) {
-          H(i, j) -= f*ort_[i];
-        }
-      }
-
-      for (int i = 0; i <= high; i++) {
-        Real f = 0.0;
-        for (int j = high; j >= m; j--) {
-          f += ort_[j]*H(i, j);
-        }
-        f = f/h;
-        for (int j = m; j <= high; j++) {
-          H(i, j) -= f*ort_[j];
-        }
-      }
-      ort_[m] = scale*ort_[m];
-      H(m, m-1) = scale*g;
-    }
-  }
-
-  // Accumulate transformations (Algol's ortran).
-
-  for (int i = 0; i < n_; i++) {
-    for (int j = 0; j < n_; j++) {
-      V(i, j) = (i == j ? 1.0 : 0.0);
-    }
-  }
-
-  for (int m = high-1; m >= low+1; m--) {
-    if (H(m, m-1) != 0.0) {
-      for (int i = m+1; i <= high; i++) {
-        ort_[i] = H(i, m-1);
-      }
-      for (int j = m; j <= high; j++) {
-        Real g = 0.0;
-        for (int i = m; i <= high; i++) {
-          g += ort_[i] * V(i, j);
-        }
-        // Double division avoids possible underflow
-        g = (g / ort_[m]) / H(m, m-1);
-        for (int i = m; i <= high; i++) {
-          V(i, j) += g * ort_[i];
-        }
-      }
-    }
-  }
-}
-
-template<typename Real> void  EigenvalueDecomposition<Real>::Hqr2() {
-  //  This is derived from the Algol procedure hqr2,
-  //  by Martin and Wilkinson, Handbook for Auto. Comp.,
-  //  Vol.ii-Linear Algebra, and the corresponding
-  //  Fortran subroutine in EISPACK.
-
-  int nn = n_;
-  int n = nn-1;
-  int low = 0;
-  int high = nn-1;
-  Real eps = std::numeric_limits<Real>::epsilon();
-  Real exshift = 0.0;
-  Real p = 0, q = 0, r = 0, s = 0, z=0, t, w, x, y;
-
-  // Store roots isolated by balanc and compute matrix norm
-
-  Real norm = 0.0;
-  for (int i = 0; i < nn; i++) {
-    if (i < low || i > high) {
-      d_[i] = H(i, i);
-      e_[i] = 0.0;
-    }
-    for (int j = std::max(i-1, 0); j < nn; j++) {
-      norm = norm + std::abs(H(i, j));
-    }
-  }
-
-  // Outer loop over eigenvalue index
-
-  int iter = 0;
-  while (n >= low) {
-
-    // Look for single small sub-diagonal element
-
-    int l = n;
-    while (l > low) {
-      s = std::abs(H(l-1, l-1)) + std::abs(H(l, l));
-      if (s == 0.0) {
-        s = norm;
-      }
-      if (std::abs(H(l, l-1)) < eps * s) {
-        break;
-      }
-      l--;
-    }
-
-    // Check for convergence
-    // One root found
-
-    if (l == n) {
-      H(n, n) = H(n, n) + exshift;
-      d_[n] = H(n, n);
-      e_[n] = 0.0;
-      n--;
-      iter = 0;
-
-      // Two roots found
-
-    } else if (l == n-1) {
-      w = H(n, n-1) * H(n-1, n);
-      p = (H(n-1, n-1) - H(n, n)) / 2.0;
-      q = p * p + w;
-      z = std::sqrt(std::abs(q));
-      H(n, n) = H(n, n) + exshift;
-      H(n-1, n-1) = H(n-1, n-1) + exshift;
-      x = H(n, n);
-
-      // Real pair
-
-      if (q >= 0) {
-        if (p >= 0) {
-          z = p + z;
-        } else {
-          z = p - z;
-        }
-        d_[n-1] = x + z;
-        d_[n] = d_[n-1];
-        if (z != 0.0) {
-          d_[n] = x - w / z;
-        }
-        e_[n-1] = 0.0;
-        e_[n] = 0.0;
-        x = H(n, n-1);
-        s = std::abs(x) + std::abs(z);
-        p = x / s;
-        q = z / s;
-        r = std::sqrt(p * p+q * q);
-        p = p / r;
-        q = q / r;
-
-        // Row modification
-
-        for (int j = n-1; j < nn; j++) {
-          z = H(n-1, j);
-          H(n-1, j) = q * z + p * H(n, j);
-          H(n, j) = q * H(n, j) - p * z;
-        }
-
-        // Column modification
-
-        for (int i = 0; i <= n; i++) {
-          z = H(i, n-1);
-          H(i, n-1) = q * z + p * H(i, n);
-          H(i, n) = q * H(i, n) - p * z;
-        }
-
-        // Accumulate transformations
-
-        for (int i = low; i <= high; i++) {
-          z = V(i, n-1);
-          V(i, n-1) = q * z + p * V(i, n);
-          V(i, n) = q * V(i, n) - p * z;
-        }
-
-        // Complex pair
-
-      } else {
-        d_[n-1] = x + p;
-        d_[n] = x + p;
-        e_[n-1] = z;
-        e_[n] = -z;
-      }
-      n = n - 2;
-      iter = 0;
-
-      // No convergence yet
-
-    } else {
-
-      // Form shift
-
-      x = H(n, n);
-      y = 0.0;
-      w = 0.0;
-      if (l < n) {
-        y = H(n-1, n-1);
-        w = H(n, n-1) * H(n-1, n);
-      }
-
-      // Wilkinson's original ad hoc shift
-
-      if (iter == 10) {
-        exshift += x;
-        for (int i = low; i <= n; i++) {
-          H(i, i) -= x;
-        }
-        s = std::abs(H(n, n-1)) + std::abs(H(n-1, n-2));
-        x = y = 0.75 * s;
-        w = -0.4375 * s * s;
-      }
-
-      // MATLAB's new ad hoc shift
-
-      if (iter == 30) {
-        s = (y - x) / 2.0;
-        s = s * s + w;
-        if (s > 0) {
-          s = std::sqrt(s);
-          if (y < x) {
-            s = -s;
-          }
-          s = x - w / ((y - x) / 2.0 + s);
-          for (int i = low; i <= n; i++) {
-            H(i, i) -= s;
-          }
-          exshift += s;
-          x = y = w = 0.964;
-        }
-      }
-
-      iter = iter + 1;   // (Could check iteration count here.)
-
-      // Look for two consecutive small sub-diagonal elements
-
-      int m = n-2;
-      while (m >= l) {
-        z = H(m, m);
-        r = x - z;
-        s = y - z;
-        p = (r * s - w) / H(m+1, m) + H(m, m+1);
-        q = H(m+1, m+1) - z - r - s;
-        r = H(m+2, m+1);
-        s = std::abs(p) + std::abs(q) + std::abs(r);
-        p = p / s;
-        q = q / s;
-        r = r / s;
-        if (m == l) {
-          break;
-        }
-        if (std::abs(H(m, m-1)) * (std::abs(q) + std::abs(r)) <
-            eps * (std::abs(p) * (std::abs(H(m-1, m-1)) + std::abs(z) +
-                                  std::abs(H(m+1, m+1))))) {
-          break;
-        }
-        m--;
-      }
-
-      for (int i = m+2; i <= n; i++) {
-        H(i, i-2) = 0.0;
-        if (i > m+2) {
-          H(i, i-3) = 0.0;
-        }
-      }
-
-      // Double QR step involving rows l:n and columns m:n
-
-      for (int k = m; k <= n-1; k++) {
-        bool notlast = (k != n-1);
-        if (k != m) {
-          p = H(k, k-1);
-          q = H(k+1, k-1);
-          r = (notlast ? H(k+2, k-1) : 0.0);
-          x = std::abs(p) + std::abs(q) + std::abs(r);
-          if (x != 0.0) {
-            p = p / x;
-            q = q / x;
-            r = r / x;
-          }
-        }
-        if (x == 0.0) {
-          break;
-        }
-        s = std::sqrt(p * p + q * q + r * r);
-        if (p < 0) {
-          s = -s;
-        }
-        if (s != 0) {
-          if (k != m) {
-            H(k, k-1) = -s * x;
-          } else if (l != m) {
-            H(k, k-1) = -H(k, k-1);
-          }
-          p = p + s;
-          x = p / s;
-          y = q / s;
-          z = r / s;
-          q = q / p;
-          r = r / p;
-
-          // Row modification
-
-          for (int j = k; j < nn; j++) {
-            p = H(k, j) + q * H(k+1, j);
-            if (notlast) {
-              p = p + r * H(k+2, j);
-              H(k+2, j) = H(k+2, j) - p * z;
-            }
-            H(k, j) = H(k, j) - p * x;
-            H(k+1, j) = H(k+1, j) - p * y;
-          }
-
-          // Column modification
-
-          for (int i = 0; i <= std::min(n, k+3); i++) {
-            p = x * H(i, k) + y * H(i, k+1);
-            if (notlast) {
-              p = p + z * H(i, k+2);
-              H(i, k+2) = H(i, k+2) - p * r;
-            }
-            H(i, k) = H(i, k) - p;
-            H(i, k+1) = H(i, k+1) - p * q;
-          }
-
-          // Accumulate transformations
-
-          for (int i = low; i <= high; i++) {
-            p = x * V(i, k) + y * V(i, k+1);
-            if (notlast) {
-              p = p + z * V(i, k+2);
-              V(i, k+2) = V(i, k+2) - p * r;
-            }
-            V(i, k) = V(i, k) - p;
-            V(i, k+1) = V(i, k+1) - p * q;
-          }
-        }  // (s != 0)
-      }  // k loop
-    }  // check convergence
-  }  // while (n >= low)
-
-  // Backsubstitute to find vectors of upper triangular form
-
-  if (norm == 0.0) {
-    return;
-  }
-
-  for (n = nn-1; n >= 0; n--) {
-    p = d_[n];
-    q = e_[n];
-
-    // Real vector
-
-    if (q == 0) {
-      int l = n;
-      H(n, n) = 1.0;
-      for (int i = n-1; i >= 0; i--) {
-        w = H(i, i) - p;
-        r = 0.0;
-        for (int j = l; j <= n; j++) {
-          r = r + H(i, j) * H(j, n);
-        }
-        if (e_[i] < 0.0) {
-          z = w;
-          s = r;
-        } else {
-          l = i;
-          if (e_[i] == 0.0) {
-            if (w != 0.0) {
-              H(i, n) = -r / w;
-            } else {
-              H(i, n) = -r / (eps * norm);
-            }
-
-            // Solve real equations
-
-          } else {
-            x = H(i, i+1);
-            y = H(i+1, i);
-            q = (d_[i] - p) * (d_[i] - p) +e_[i] *e_[i];
-            t = (x * s - z * r) / q;
-            H(i, n) = t;
-            if (std::abs(x) > std::abs(z)) {
-              H(i+1, n) = (-r - w * t) / x;
-            } else {
-              H(i+1, n) = (-s - y * t) / z;
-            }
-          }
-
-          // Overflow control
-
-          t = std::abs(H(i, n));
-          if ((eps * t) * t > 1) {
-            for (int j = i; j <= n; j++) {
-              H(j, n) = H(j, n) / t;
-            }
-          }
-        }
-      }
-
-      // Complex vector
-
-    } else if (q < 0) {
-      int l = n-1;
-
-      // Last vector component imaginary so matrix is triangular
-
-      if (std::abs(H(n, n-1)) > std::abs(H(n-1, n))) {
-        H(n-1, n-1) = q / H(n, n-1);
-        H(n-1, n) = -(H(n, n) - p) / H(n, n-1);
-      } else {
-        Real cdivr, cdivi;
-        cdiv(0.0, -H(n-1, n), H(n-1, n-1)-p, q, &cdivr, &cdivi);
-        H(n-1, n-1) = cdivr;
-        H(n-1, n) = cdivi;
-      }
-      H(n, n-1) = 0.0;
-      H(n, n) = 1.0;
-      for (int i = n-2; i >= 0; i--) {
-        Real ra, sa, vr, vi;
-        ra = 0.0;
-        sa = 0.0;
-        for (int j = l; j <= n; j++) {
-          ra = ra + H(i, j) * H(j, n-1);
-          sa = sa + H(i, j) * H(j, n);
-        }
-        w = H(i, i) - p;
-
-        if (e_[i] < 0.0) {
-          z = w;
-          r = ra;
-          s = sa;
-        } else {
-          l = i;
-          if (e_[i] == 0) {
-            Real cdivr, cdivi;
-            cdiv(-ra, -sa, w, q, &cdivr, &cdivi);
-            H(i, n-1) = cdivr;
-            H(i, n) = cdivi;
-          } else {
-            Real cdivr, cdivi;
-            // Solve complex equations
-
-            x = H(i, i+1);
-            y = H(i+1, i);
-            vr = (d_[i] - p) * (d_[i] - p) +e_[i] *e_[i] - q * q;
-            vi = (d_[i] - p) * 2.0 * q;
-            if (vr == 0.0 && vi == 0.0) {
-              vr = eps * norm * (std::abs(w) + std::abs(q) +
-                                 std::abs(x) + std::abs(y) + std::abs(z));
-            }
-            cdiv(x*r-z*ra+q*sa, x*s-z*sa-q*ra, vr, vi, &cdivr, &cdivi);
-            H(i, n-1) = cdivr;
-            H(i, n) = cdivi;
-            if (std::abs(x) > (std::abs(z) + std::abs(q))) {
-              H(i+1, n-1) = (-ra - w * H(i, n-1) + q * H(i, n)) / x;
-              H(i+1, n) = (-sa - w * H(i, n) - q * H(i, n-1)) / x;
-            } else {
-              cdiv(-r-y*H(i, n-1), -s-y*H(i, n), z, q, &cdivr, &cdivi);
-              H(i+1, n-1) = cdivr;
-              H(i+1, n) = cdivi;
-            }
-          }
-
-          // Overflow control
-
-          t = std::max(std::abs(H(i, n-1)), std::abs(H(i, n)));
-          if ((eps * t) * t > 1) {
-            for (int j = i; j <= n; j++) {
-              H(j, n-1) = H(j, n-1) / t;
-              H(j, n) = H(j, n) / t;
-            }
-          }
-        }
-      }
-    }
-  }
-
-  // Vectors of isolated roots
-
-  for (int i = 0; i < nn; i++) {
-    if (i < low || i > high) {
-      for (int j = i; j < nn; j++) {
-        V(i, j) = H(i, j);
-      }
-    }
-  }
-
-  // Back transformation to get eigenvectors of original matrix
-
-  for (int j = nn-1; j >= low; j--) {
-    for (int i = low; i <= high; i++) {
-      z = 0.0;
-      for (int k = low; k <= std::min(j, high); k++) {
-        z = z + V(i, k) * H(k, j);
-      }
-      V(i, j) = z;
-    }
-  }
-}
-
-template<typename Real>
-EigenvalueDecomposition<Real>::EigenvalueDecomposition(const MatrixBase<Real> &A) {
-  KALDI_ASSERT(A.NumCols() == A.NumRows() && A.NumCols() >= 1);
-  n_ = A.NumRows();
-  V_ = new Real[n_*n_];
-  d_ = new Real[n_];
-  e_ = new Real[n_];
-  H_ = NULL;
-  ort_ = NULL;
-  if (A.IsSymmetric(0.0)) {
-
-    for (int i = 0; i < n_; i++)
-      for (int j = 0; j < n_; j++)
-        V(i, j) = A(i, j);  // Note that V(i, j) is a member function; A(i, j) is an operator
-    // of the matrix A.
-    // Tridiagonalize.
-    Tred2();
-
-    // Diagonalize.
-    Tql2();
-  } else {
-    H_ = new Real[n_*n_];
-    ort_ = new Real[n_];
-    for (int i = 0; i < n_; i++)
-      for (int j = 0; j < n_; j++)
-        H(i, j) = A(i, j);  // as before: H is member function, A(i, j) is operator of matrix.
-
-    // Reduce to Hessenberg form.
-    Orthes();
-
-    // Reduce Hessenberg to real Schur form.
-    Hqr2();
-  }
-}
-
-template<typename Real>
-EigenvalueDecomposition<Real>::~EigenvalueDecomposition() {
-  delete [] d_;
-  delete [] e_;
-  delete [] V_;
-  if (H_) delete [] H_;
-  if (ort_) delete [] ort_;
-}
-
-// see function MatrixBase<Real>::Eig in kaldi-matrix.cc
-
-
-} // namespace kaldi
-
-#endif // KALDI_MATRIX_JAMA_EIG_H_