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Java example source code file (HessenbergTransformer.java)

This example Java source code file (HessenbergTransformer.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

hessenbergtransformer, realmatrix

The HessenbergTransformer.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You 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
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.commons.math3.linear;

import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.Precision;

/**
 * Class transforming a general real matrix to Hessenberg form.
 * <p>A m × m matrix A can be written as the product of three matrices: A = P
 * × H × P<sup>T with P an orthogonal matrix and H a Hessenberg
 * matrix. Both P and H are m × m matrices.</p>
 * <p>Transformation to Hessenberg form is often not a goal by itself, but it is an
 * intermediate step in more general decomposition algorithms like
 * {@link EigenDecomposition eigen decomposition}. This class is therefore
 * intended for internal use by the library and is not public. As a consequence
 * of this explicitly limited scope, many methods directly returns references to
 * internal arrays, not copies.</p>
 * <p>This class is based on the method orthes in class EigenvalueDecomposition
 * from the <a href="http://math.nist.gov/javanumerics/jama/">JAMA library.

* * @see <a href="http://mathworld.wolfram.com/HessenbergDecomposition.html">MathWorld * @see <a href="http://en.wikipedia.org/wiki/Householder_transformation">Householder Transformations * @since 3.1 */ class HessenbergTransformer { /** Householder vectors. */ private final double householderVectors[][]; /** Temporary storage vector. */ private final double ort[]; /** Cached value of P. */ private RealMatrix cachedP; /** Cached value of Pt. */ private RealMatrix cachedPt; /** Cached value of H. */ private RealMatrix cachedH; /** * Build the transformation to Hessenberg form of a general matrix. * * @param matrix matrix to transform * @throws NonSquareMatrixException if the matrix is not square */ HessenbergTransformer(final RealMatrix matrix) { if (!matrix.isSquare()) { throw new NonSquareMatrixException(matrix.getRowDimension(), matrix.getColumnDimension()); } final int m = matrix.getRowDimension(); householderVectors = matrix.getData(); ort = new double[m]; cachedP = null; cachedPt = null; cachedH = null; // transform matrix transform(); } /** * Returns the matrix P of the transform. * <p>P is an orthogonal matrix, i.e. its inverse is also its transpose.

* * @return the P matrix */ public RealMatrix getP() { if (cachedP == null) { final int n = householderVectors.length; final int high = n - 1; final double[][] pa = new double[n][n]; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { pa[i][j] = (i == j) ? 1 : 0; } } for (int m = high - 1; m >= 1; m--) { if (householderVectors[m][m - 1] != 0.0) { for (int i = m + 1; i <= high; i++) { ort[i] = householderVectors[i][m - 1]; } for (int j = m; j <= high; j++) { double g = 0.0; for (int i = m; i <= high; i++) { g += ort[i] * pa[i][j]; } // Double division avoids possible underflow g = (g / ort[m]) / householderVectors[m][m - 1]; for (int i = m; i <= high; i++) { pa[i][j] += g * ort[i]; } } } } cachedP = MatrixUtils.createRealMatrix(pa); } return cachedP; } /** * Returns the transpose of the matrix P of the transform. * <p>P is an orthogonal matrix, i.e. its inverse is also its transpose.

* * @return the transpose of the P matrix */ public RealMatrix getPT() { if (cachedPt == null) { cachedPt = getP().transpose(); } // return the cached matrix return cachedPt; } /** * Returns the Hessenberg matrix H of the transform. * * @return the H matrix */ public RealMatrix getH() { if (cachedH == null) { final int m = householderVectors.length; final double[][] h = new double[m][m]; for (int i = 0; i < m; ++i) { if (i > 0) { // copy the entry of the lower sub-diagonal h[i][i - 1] = householderVectors[i][i - 1]; } // copy upper triangular part of the matrix for (int j = i; j < m; ++j) { h[i][j] = householderVectors[i][j]; } } cachedH = MatrixUtils.createRealMatrix(h); } // return the cached matrix return cachedH; } /** * Get the Householder vectors of the transform. * <p>Note that since this class is only intended for internal use, it returns * directly a reference to its internal arrays, not a copy.</p> * * @return the main diagonal elements of the B matrix */ double[][] getHouseholderVectorsRef() { return householderVectors; } /** * Transform original matrix to Hessenberg form. * <p>Transformation is done using Householder transforms.

*/ private void transform() { final int n = householderVectors.length; final int high = n - 1; for (int m = 1; m <= high - 1; m++) { // Scale column. double scale = 0; for (int i = m; i <= high; i++) { scale += FastMath.abs(householderVectors[i][m - 1]); } if (!Precision.equals(scale, 0)) { // Compute Householder transformation. double h = 0; for (int i = high; i >= m; i--) { ort[i] = householderVectors[i][m - 1] / scale; h += ort[i] * ort[i]; } final double g = (ort[m] > 0) ? -FastMath.sqrt(h) : FastMath.sqrt(h); h -= ort[m] * g; ort[m] -= g; // Apply Householder similarity transformation // H = (I - u*u' / h) * H * (I - u*u' / h) for (int j = m; j < n; j++) { double f = 0; for (int i = high; i >= m; i--) { f += ort[i] * householderVectors[i][j]; } f /= h; for (int i = m; i <= high; i++) { householderVectors[i][j] -= f * ort[i]; } } for (int i = 0; i <= high; i++) { double f = 0; for (int j = high; j >= m; j--) { f += ort[j] * householderVectors[i][j]; } f /= h; for (int j = m; j <= high; j++) { householderVectors[i][j] -= f * ort[j]; } } ort[m] = scale * ort[m]; householderVectors[m][m - 1] = scale * g; } } } }

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