| /* |
| * 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; |
| |
| import org.apache.commons.math.FieldElement; |
| |
| /** |
| * An interface to classes that implement an algorithm to calculate the |
| * LU-decomposition of a real matrix. |
| * <p>The LU-decomposition of matrix A is a set of three matrices: P, L and U |
| * such that P×A = L×U. P is a rows permutation matrix that is used |
| * to rearrange the rows of A before so that it can be decomposed. L is a lower |
| * triangular matrix with unit diagonal terms and U is an upper triangular matrix.</p> |
| * <p>This interface is based on the class with similar name from the |
| * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library.</p> |
| * <ul> |
| * <li>a {@link #getP() getP} method has been added,</li> |
| * <li>the <code>det</code> method has been renamed as {@link #getDeterminant() |
| * getDeterminant},</li> |
| * <li>the <code>getDoublePivot</code> method has been removed (but the int based |
| * {@link #getPivot() getPivot} method has been kept),</li> |
| * <li>the <code>solve</code> and <code>isNonSingular</code> methods have been replaced |
| * by a {@link #getSolver() getSolver} method and the equivalent methods provided by |
| * the returned {@link DecompositionSolver}.</li> |
| * </ul> |
| * |
| * @param <T> the type of the field elements |
| * @see <a href="http://mathworld.wolfram.com/LUDecomposition.html">MathWorld</a> |
| * @see <a href="http://en.wikipedia.org/wiki/LU_decomposition">Wikipedia</a> |
| * @version $Revision: 826627 $ $Date: 2009-10-19 12:27:47 +0200 (lun. 19 oct. 2009) $ |
| * @since 2.0 |
| */ |
| public interface FieldLUDecomposition<T extends FieldElement<T>> { |
| |
| /** |
| * Returns the matrix L of the decomposition. |
| * <p>L is an lower-triangular matrix</p> |
| * @return the L matrix (or null if decomposed matrix is singular) |
| */ |
| FieldMatrix<T> getL(); |
| |
| /** |
| * Returns the matrix U of the decomposition. |
| * <p>U is an upper-triangular matrix</p> |
| * @return the U matrix (or null if decomposed matrix is singular) |
| */ |
| FieldMatrix<T> getU(); |
| |
| /** |
| * Returns the P rows permutation matrix. |
| * <p>P is a sparse matrix with exactly one element set to 1.0 in |
| * each row and each column, all other elements being set to 0.0.</p> |
| * <p>The positions of the 1 elements are given by the {@link #getPivot() |
| * pivot permutation vector}.</p> |
| * @return the P rows permutation matrix (or null if decomposed matrix is singular) |
| * @see #getPivot() |
| */ |
| FieldMatrix<T> getP(); |
| |
| /** |
| * Returns the pivot permutation vector. |
| * @return the pivot permutation vector |
| * @see #getP() |
| */ |
| int[] getPivot(); |
| |
| /** |
| * Return the determinant of the matrix |
| * @return determinant of the matrix |
| */ |
| T getDeterminant(); |
| |
| /** |
| * Get a solver for finding the A × X = B solution in exact linear sense. |
| * @return a solver |
| */ |
| FieldDecompositionSolver<T> getSolver(); |
| |
| } |