    001    /*
    002     * Licensed to the Apache Software Foundation (ASF) under one or more
    003     * contributor license agreements.  See the NOTICE file distributed with
    004     * this work for additional information regarding copyright ownership.
    005     * The ASF licenses this file to You under the Apache License, Version 2.0
    006     * (the "License"); you may not use this file except in compliance with
    007     * the License.  You may obtain a copy of the License at
    008     *
    009     *      http://www.apache.org/licenses/LICENSE-2.0
    010     *
    011     * Unless required by applicable law or agreed to in writing, software
    012     * distributed under the License is distributed on an "AS IS" BASIS,
    013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    014     * See the License for the specific language governing permissions and
    015     * limitations under the License.
    016     */
    017
    018    package org.apache.commons.math.linear;
    019
    020    import org.apache.commons.math.FieldElement;
    021
    022    /**
    023     * An interface to classes that implement an algorithm to calculate the
    024     * LU-decomposition of a real matrix.
    025     * <p>The LU-decomposition of matrix A is a set of three matrices: P, L and U
    026     * such that P&times;A = L&times;U. P is a rows permutation matrix that is used
    027     * to rearrange the rows of A before so that it can be decomposed. L is a lower
    028     * triangular matrix with unit diagonal terms and U is an upper triangular matrix.</p>
    029     * <p>This interface is based on the class with similar name from the
    030     * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library.</p>
    031     * <ul>
    032     *   <li>a {@link #getP() getP} method has been added,</li>
    033     *   <li>the <code>det</code> method has been renamed as {@link #getDeterminant()
    034     *   getDeterminant},</li>
    035     *   <li>the <code>getDoublePivot</code> method has been removed (but the int based
    036     *   {@link #getPivot() getPivot} method has been kept),</li>
    037     *   <li>the <code>solve</code> and <code>isNonSingular</code> methods have been replaced
    038     *   by a {@link #getSolver() getSolver} method and the equivalent methods provided by
    039     *   the returned {@link DecompositionSolver}.</li>
    040     * </ul>
    041     *
    042     * @param <T> the type of the field elements
    043     * @see <a href="http://mathworld.wolfram.com/LUDecomposition.html">MathWorld</a>
    044     * @see <a href="http://en.wikipedia.org/wiki/LU_decomposition">Wikipedia</a>
    045     * @version $Revision: 826627 $ $Date: 2009-10-19 12:27:47 +0200 (lun. 19 oct. 2009) $
    046     * @since 2.0
    047     */
    048    public interface FieldLUDecomposition<T extends FieldElement<T>> {
    049
    050        /**
    051         * Returns the matrix L of the decomposition.
    052         * <p>L is an lower-triangular matrix</p>
    053         * @return the L matrix (or null if decomposed matrix is singular)
    054         */
    055        FieldMatrix<T> getL();
    056
    057        /**
    058         * Returns the matrix U of the decomposition.
    059         * <p>U is an upper-triangular matrix</p>
    060         * @return the U matrix (or null if decomposed matrix is singular)
    061         */
    062        FieldMatrix<T> getU();
    063
    064        /**
    065         * Returns the P rows permutation matrix.
    066         * <p>P is a sparse matrix with exactly one element set to 1.0 in
    067         * each row and each column, all other elements being set to 0.0.</p>
    068         * <p>The positions of the 1 elements are given by the {@link #getPivot()
    069         * pivot permutation vector}.</p>
    070         * @return the P rows permutation matrix (or null if decomposed matrix is singular)
    071         * @see #getPivot()
    072         */
    073        FieldMatrix<T> getP();
    074
    075        /**
    076         * Returns the pivot permutation vector.
    077         * @return the pivot permutation vector
    078         * @see #getP()
    079         */
    080        int[] getPivot();
    081
    082        /**
    083         * Return the determinant of the matrix
    084         * @return determinant of the matrix
    085         */
    086        T getDeterminant();
    087
    088        /**
    089         * Get a solver for finding the A &times; X = B solution in exact linear sense.
    090         * @return a solver
    091         */
    092        FieldDecompositionSolver<T> getSolver();
    093
    094    }