| /* |
| * 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.math.linear; |
| |
| |
| |
| /** |
| * An interface to classes that implement an algorithm to calculate the |
| * Singular Value Decomposition of a real matrix. |
| * <p> |
| * The Singular Value Decomposition of matrix A is a set of three matrices: U, |
| * Σ and V such that A = U × Σ × V<sup>T</sup>. Let A be |
| * a m × n matrix, then U is a m × p orthogonal matrix, Σ is a |
| * p × p diagonal matrix with positive or null elements, V is a p × |
| * n orthogonal matrix (hence V<sup>T</sup> is also orthogonal) where |
| * p=min(m,n). |
| * </p> |
| * <p>This interface is similar to the class with similar name from the |
| * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the |
| * following changes:</p> |
| * <ul> |
| * <li>the <code>norm2</code> method which has been renamed as {@link #getNorm() |
| * getNorm},</li> |
| * <li>the <code>cond</code> method which has been renamed as {@link |
| * #getConditionNumber() getConditionNumber},</li> |
| * <li>the <code>rank</code> method which has been renamed as {@link #getRank() |
| * getRank},</li> |
| * <li>a {@link #getUT() getUT} method has been added,</li> |
| * <li>a {@link #getVT() getVT} method has been added,</li> |
| * <li>a {@link #getSolver() getSolver} method has been added,</li> |
| * <li>a {@link #getCovariance(double) getCovariance} method has been added.</li> |
| * </ul> |
| * @see <a href="http://mathworld.wolfram.com/SingularValueDecomposition.html">MathWorld</a> |
| * @see <a href="http://en.wikipedia.org/wiki/Singular_value_decomposition">Wikipedia</a> |
| * @version $Revision: 928081 $ $Date: 2010-03-26 23:36:38 +0100 (ven. 26 mars 2010) $ |
| * @since 2.0 |
| */ |
| public interface SingularValueDecomposition { |
| |
| /** |
| * Returns the matrix U of the decomposition. |
| * <p>U is an orthogonal matrix, i.e. its transpose is also its inverse.</p> |
| * @return the U matrix |
| * @see #getUT() |
| */ |
| RealMatrix getU(); |
| |
| /** |
| * Returns the transpose of the matrix U of the decomposition. |
| * <p>U is an orthogonal matrix, i.e. its transpose is also its inverse.</p> |
| * @return the U matrix (or null if decomposed matrix is singular) |
| * @see #getU() |
| */ |
| RealMatrix getUT(); |
| |
| /** |
| * Returns the diagonal matrix Σ of the decomposition. |
| * <p>Σ is a diagonal matrix. The singular values are provided in |
| * non-increasing order, for compatibility with Jama.</p> |
| * @return the Σ matrix |
| */ |
| RealMatrix getS(); |
| |
| /** |
| * Returns the diagonal elements of the matrix Σ of the decomposition. |
| * <p>The singular values are provided in non-increasing order, for |
| * compatibility with Jama.</p> |
| * @return the diagonal elements of the Σ matrix |
| */ |
| double[] getSingularValues(); |
| |
| /** |
| * Returns the matrix V of the decomposition. |
| * <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p> |
| * @return the V matrix (or null if decomposed matrix is singular) |
| * @see #getVT() |
| */ |
| RealMatrix getV(); |
| |
| /** |
| * Returns the transpose of the matrix V of the decomposition. |
| * <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p> |
| * @return the V matrix (or null if decomposed matrix is singular) |
| * @see #getV() |
| */ |
| RealMatrix getVT(); |
| |
| /** |
| * Returns the n × n covariance matrix. |
| * <p>The covariance matrix is V × J × V<sup>T</sup> |
| * where J is the diagonal matrix of the inverse of the squares of |
| * the singular values.</p> |
| * @param minSingularValue value below which singular values are ignored |
| * (a 0 or negative value implies all singular value will be used) |
| * @return covariance matrix |
| * @exception IllegalArgumentException if minSingularValue is larger than |
| * the largest singular value, meaning all singular values are ignored |
| */ |
| RealMatrix getCovariance(double minSingularValue) throws IllegalArgumentException; |
| |
| /** |
| * Returns the L<sub>2</sub> norm of the matrix. |
| * <p>The L<sub>2</sub> norm is max(|A × u|<sub>2</sub> / |
| * |u|<sub>2</sub>), where |.|<sub>2</sub> denotes the vectorial 2-norm |
| * (i.e. the traditional euclidian norm).</p> |
| * @return norm |
| */ |
| double getNorm(); |
| |
| /** |
| * Return the condition number of the matrix. |
| * @return condition number of the matrix |
| */ |
| double getConditionNumber(); |
| |
| /** |
| * Return the effective numerical matrix rank. |
| * <p>The effective numerical rank is the number of non-negligible |
| * singular values. The threshold used to identify non-negligible |
| * terms is max(m,n) × ulp(s<sub>1</sub>) where ulp(s<sub>1</sub>) |
| * is the least significant bit of the largest singular value.</p> |
| * @return effective numerical matrix rank |
| */ |
| int getRank(); |
| |
| /** |
| * Get a solver for finding the A × X = B solution in least square sense. |
| * @return a solver |
| */ |
| DecompositionSolver getSolver(); |
| |
| } |