Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 1 | /* |
| 2 | * Licensed to the Apache Software Foundation (ASF) under one or more |
| 3 | * contributor license agreements. See the NOTICE file distributed with |
| 4 | * this work for additional information regarding copyright ownership. |
| 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 |
| 6 | * (the "License"); you may not use this file except in compliance with |
| 7 | * the License. You may obtain a copy of the License at |
| 8 | * |
| 9 | * http://www.apache.org/licenses/LICENSE-2.0 |
| 10 | * |
| 11 | * Unless required by applicable law or agreed to in writing, software |
| 12 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 14 | * See the License for the specific language governing permissions and |
| 15 | * limitations under the License. |
| 16 | */ |
| 17 | |
| 18 | package org.apache.commons.math.linear; |
| 19 | |
| 20 | |
| 21 | |
| 22 | /** |
| 23 | * An interface to classes that implement an algorithm to calculate the |
| 24 | * Singular Value Decomposition of a real matrix. |
| 25 | * <p> |
| 26 | * The Singular Value Decomposition of matrix A is a set of three matrices: U, |
| 27 | * Σ and V such that A = U × Σ × V<sup>T</sup>. Let A be |
| 28 | * a m × n matrix, then U is a m × p orthogonal matrix, Σ is a |
| 29 | * p × p diagonal matrix with positive or null elements, V is a p × |
| 30 | * n orthogonal matrix (hence V<sup>T</sup> is also orthogonal) where |
| 31 | * p=min(m,n). |
| 32 | * </p> |
| 33 | * <p>This interface is similar to the class with similar name from the |
| 34 | * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the |
| 35 | * following changes:</p> |
| 36 | * <ul> |
| 37 | * <li>the <code>norm2</code> method which has been renamed as {@link #getNorm() |
| 38 | * getNorm},</li> |
| 39 | * <li>the <code>cond</code> method which has been renamed as {@link |
| 40 | * #getConditionNumber() getConditionNumber},</li> |
| 41 | * <li>the <code>rank</code> method which has been renamed as {@link #getRank() |
| 42 | * getRank},</li> |
| 43 | * <li>a {@link #getUT() getUT} method has been added,</li> |
| 44 | * <li>a {@link #getVT() getVT} method has been added,</li> |
| 45 | * <li>a {@link #getSolver() getSolver} method has been added,</li> |
| 46 | * <li>a {@link #getCovariance(double) getCovariance} method has been added.</li> |
| 47 | * </ul> |
| 48 | * @see <a href="http://mathworld.wolfram.com/SingularValueDecomposition.html">MathWorld</a> |
| 49 | * @see <a href="http://en.wikipedia.org/wiki/Singular_value_decomposition">Wikipedia</a> |
| 50 | * @version $Revision: 928081 $ $Date: 2010-03-26 23:36:38 +0100 (ven. 26 mars 2010) $ |
| 51 | * @since 2.0 |
| 52 | */ |
| 53 | public interface SingularValueDecomposition { |
| 54 | |
| 55 | /** |
| 56 | * Returns the matrix U of the decomposition. |
| 57 | * <p>U is an orthogonal matrix, i.e. its transpose is also its inverse.</p> |
| 58 | * @return the U matrix |
| 59 | * @see #getUT() |
| 60 | */ |
| 61 | RealMatrix getU(); |
| 62 | |
| 63 | /** |
| 64 | * Returns the transpose of the matrix U of the decomposition. |
| 65 | * <p>U is an orthogonal matrix, i.e. its transpose is also its inverse.</p> |
| 66 | * @return the U matrix (or null if decomposed matrix is singular) |
| 67 | * @see #getU() |
| 68 | */ |
| 69 | RealMatrix getUT(); |
| 70 | |
| 71 | /** |
| 72 | * Returns the diagonal matrix Σ of the decomposition. |
| 73 | * <p>Σ is a diagonal matrix. The singular values are provided in |
| 74 | * non-increasing order, for compatibility with Jama.</p> |
| 75 | * @return the Σ matrix |
| 76 | */ |
| 77 | RealMatrix getS(); |
| 78 | |
| 79 | /** |
| 80 | * Returns the diagonal elements of the matrix Σ of the decomposition. |
| 81 | * <p>The singular values are provided in non-increasing order, for |
| 82 | * compatibility with Jama.</p> |
| 83 | * @return the diagonal elements of the Σ matrix |
| 84 | */ |
| 85 | double[] getSingularValues(); |
| 86 | |
| 87 | /** |
| 88 | * Returns the matrix V of the decomposition. |
| 89 | * <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p> |
| 90 | * @return the V matrix (or null if decomposed matrix is singular) |
| 91 | * @see #getVT() |
| 92 | */ |
| 93 | RealMatrix getV(); |
| 94 | |
| 95 | /** |
| 96 | * Returns the transpose of the matrix V of the decomposition. |
| 97 | * <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p> |
| 98 | * @return the V matrix (or null if decomposed matrix is singular) |
| 99 | * @see #getV() |
| 100 | */ |
| 101 | RealMatrix getVT(); |
| 102 | |
| 103 | /** |
| 104 | * Returns the n × n covariance matrix. |
| 105 | * <p>The covariance matrix is V × J × V<sup>T</sup> |
| 106 | * where J is the diagonal matrix of the inverse of the squares of |
| 107 | * the singular values.</p> |
| 108 | * @param minSingularValue value below which singular values are ignored |
| 109 | * (a 0 or negative value implies all singular value will be used) |
| 110 | * @return covariance matrix |
| 111 | * @exception IllegalArgumentException if minSingularValue is larger than |
| 112 | * the largest singular value, meaning all singular values are ignored |
| 113 | */ |
| 114 | RealMatrix getCovariance(double minSingularValue) throws IllegalArgumentException; |
| 115 | |
| 116 | /** |
| 117 | * Returns the L<sub>2</sub> norm of the matrix. |
| 118 | * <p>The L<sub>2</sub> norm is max(|A × u|<sub>2</sub> / |
| 119 | * |u|<sub>2</sub>), where |.|<sub>2</sub> denotes the vectorial 2-norm |
| 120 | * (i.e. the traditional euclidian norm).</p> |
| 121 | * @return norm |
| 122 | */ |
| 123 | double getNorm(); |
| 124 | |
| 125 | /** |
| 126 | * Return the condition number of the matrix. |
| 127 | * @return condition number of the matrix |
| 128 | */ |
| 129 | double getConditionNumber(); |
| 130 | |
| 131 | /** |
| 132 | * Return the effective numerical matrix rank. |
| 133 | * <p>The effective numerical rank is the number of non-negligible |
| 134 | * singular values. The threshold used to identify non-negligible |
| 135 | * terms is max(m,n) × ulp(s<sub>1</sub>) where ulp(s<sub>1</sub>) |
| 136 | * is the least significant bit of the largest singular value.</p> |
| 137 | * @return effective numerical matrix rank |
| 138 | */ |
| 139 | int getRank(); |
| 140 | |
| 141 | /** |
| 142 | * Get a solver for finding the A × X = B solution in least square sense. |
| 143 | * @return a solver |
| 144 | */ |
| 145 | DecompositionSolver getSolver(); |
| 146 | |
| 147 | } |