diff options
author | Determinant <[email protected]> | 2015-08-14 11:51:42 +0800 |
---|---|---|
committer | Determinant <[email protected]> | 2015-08-14 11:51:42 +0800 |
commit | 96a32415ab43377cf1575bd3f4f2980f58028209 (patch) | |
tree | 30a2d92d73e8f40ac87b79f6f56e227bfc4eea6e /kaldi_io/src/kaldi/matrix/jama-eig.h | |
parent | c177a7549bd90670af4b29fa813ddea32cfe0f78 (diff) |
add implementation for kaldi io (by ymz)
Diffstat (limited to 'kaldi_io/src/kaldi/matrix/jama-eig.h')
-rw-r--r-- | kaldi_io/src/kaldi/matrix/jama-eig.h | 924 |
1 files changed, 924 insertions, 0 deletions
diff --git a/kaldi_io/src/kaldi/matrix/jama-eig.h b/kaldi_io/src/kaldi/matrix/jama-eig.h new file mode 100644 index 0000000..c7278bc --- /dev/null +++ b/kaldi_io/src/kaldi/matrix/jama-eig.h @@ -0,0 +1,924 @@ +// 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_ |