org.apache.commons.math.linear.SingularValueDecomposition Maven / Gradle / Ivy

Go to download
Show more of this group Show more artifacts with this name
Show all versions of commons-math Show documentation
The Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
There is a newer version: 2.2
Show newest version
/*
 * 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.
 * The Singular Value Decomposition of matrix A is a set of three matrices:
 * U, Σ and V such that A = U × Σ × V^T.
 * Let A be an m × n matrix, then U is an m × m orthogonal matrix,
 * Σ is a m × n diagonal matrix with positive diagonal elements,
 * and V is an n × n orthogonal matrix.
 * This interface is similar to the class with similar name from the now defunct
 * JAMA library, with the
 * following changes:
 * 
 *   the norm2 method which has been renamed as {@link #getNorm()
 *   getNorm},
 *   the cond method which has been renamed as {@link
 *   #getConditionNumber() getConditionNumber},
 *   the rank method which has been renamed as {@link #getRank()
 *   getRank},
 *   a {@link #getUT() getUT} method has been added,
 *   a {@link #getVT() getVT} method has been added,
 *   a {@link #getSolver() getSolver} method has been added,
 *   a {@link #getCovariance(double) getCovariance} method has been added.
 * 
 * @see MathWorld
 * @see Wikipedia
 * @version $Revision: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 2009) $
 * @since 2.0
 */
public interface SingularValueDecomposition {

    /**
     * Returns the matrix U of the decomposition. 
     * U is an orthogonal matrix, i.e. its transpose is also its inverse.
     * @return the U matrix
     * @see #getUT()
     */
    RealMatrix getU();

    /**
     * Returns the transpose of the matrix U of the decomposition. 
     * U is an orthogonal matrix, i.e. its transpose is also its inverse.
     * @return the U matrix (or null if decomposed matrix is singular)
     * @see #getU()
     */
    RealMatrix getUT();

    /**
     * Returns the diagonal matrix Σ of the decomposition. 
     * Σ is a diagonal matrix. The singular values are provided in
     * non-increasing order, for compatibility with Jama.
     * @return the Σ matrix
     */
    RealMatrix getS();

    /**
     * Returns the diagonal elements of the matrix Σ of the decomposition.
     * The singular values are provided in non-increasing order, for
     * compatibility with Jama.
     * @return the diagonal elements of the Σ matrix
     */
    double[] getSingularValues();

    /**
     * Returns the matrix V of the decomposition. 
     * V is an orthogonal matrix, i.e. its transpose is also its inverse.
     * @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. 
     * V is an orthogonal matrix, i.e. its transpose is also its inverse.
     * @return the V matrix (or null if decomposed matrix is singular)
     * @see #getV()
     */
    RealMatrix getVT();

    /**
     * Returns the n × n covariance matrix.
     * The covariance matrix is V × J × V^T
     * where J is the diagonal matrix of the inverse of the squares of
     * the singular values.
     * @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 L₂ norm of the matrix.
     * The L₂ norm is max(|A × u|₂ /
     * |u|₂), where |.|₂ denotes the vectorial 2-norm
     * (i.e. the traditional euclidian norm).
     * @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.
     * 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(s₁) where ulp(s₁)
     * is the least significant bit of the largest singular value.
     * @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();

}