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diff --git a/src/main/java/org/apache/commons/math/linear/SingularValueDecomposition.java b/src/main/java/org/apache/commons/math/linear/SingularValueDecomposition.java new file mode 100644 index 0000000..5b45cde --- /dev/null +++ b/src/main/java/org/apache/commons/math/linear/SingularValueDecomposition.java @@ -0,0 +1,147 @@ +/* + * 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(); + +} |