1dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/* 2dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Licensed to the Apache Software Foundation (ASF) under one or more 3dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * contributor license agreements. See the NOTICE file distributed with 4dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * this work for additional information regarding copyright ownership. 5dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The ASF licenses this file to You under the Apache License, Version 2.0 6dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * (the "License"); you may not use this file except in compliance with 7dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * the License. You may obtain a copy of the License at 8dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 9dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * http://www.apache.org/licenses/LICENSE-2.0 10dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 11dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Unless required by applicable law or agreed to in writing, software 12dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * distributed under the License is distributed on an "AS IS" BASIS, 13dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * See the License for the specific language governing permissions and 15dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * limitations under the License. 16dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 17dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 18dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpackage org.apache.commons.math.linear; 19dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 20dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport java.lang.reflect.Array; 21dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 22dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.Field; 23dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.FieldElement; 24dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.MathRuntimeException; 25dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.exception.util.LocalizedFormats; 26dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 27dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/** 28dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Calculates the LUP-decomposition of a square matrix. 29dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p>The LUP-decomposition of a matrix A consists of three matrices 30dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * L, U and P that satisfy: PA = LU, L is lower triangular, and U is 31dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * upper triangular and P is a permutation matrix. All matrices are 32dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * m×m.</p> 33dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p>Since {@link FieldElement field elements} do not provide an ordering 34dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * operator, the permutation matrix is computed here only in order to avoid 35dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * a zero pivot element, no attempt is done to get the largest pivot element.</p> 36dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 37dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param <T> the type of the field elements 38dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @version $Revision: 983921 $ $Date: 2010-08-10 12:46:06 +0200 (mar. 10 août 2010) $ 39dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @since 2.0 40dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 41dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpublic class FieldLUDecompositionImpl<T extends FieldElement<T>> implements FieldLUDecomposition<T> { 42dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 43dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Field to which the elements belong. */ 44dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private final Field<T> field; 45dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 46dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Entries of LU decomposition. */ 47dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private T lu[][]; 48dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 49dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Pivot permutation associated with LU decomposition */ 50dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private int[] pivot; 51dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 52dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Parity of the permutation associated with the LU decomposition */ 53dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private boolean even; 54dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 55dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Singularity indicator. */ 56dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private boolean singular; 57dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 58dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Cached value of L. */ 59dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private FieldMatrix<T> cachedL; 60dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 61dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Cached value of U. */ 62dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private FieldMatrix<T> cachedU; 63dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 64dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Cached value of P. */ 65dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private FieldMatrix<T> cachedP; 66dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 67dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 68dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Calculates the LU-decomposition of the given matrix. 69dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param matrix The matrix to decompose. 70dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @exception NonSquareMatrixException if matrix is not square 71dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 72dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public FieldLUDecompositionImpl(FieldMatrix<T> matrix) 73dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throws NonSquareMatrixException { 74dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 75dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (!matrix.isSquare()) { 76dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw new NonSquareMatrixException(matrix.getRowDimension(), matrix.getColumnDimension()); 77dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 78dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 79dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int m = matrix.getColumnDimension(); 80dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond field = matrix.getField(); 81dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond lu = matrix.getData(); 82dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond pivot = new int[m]; 83dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond cachedL = null; 84dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond cachedU = null; 85dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond cachedP = null; 86dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 87dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Initialize permutation array and parity 88dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int row = 0; row < m; row++) { 89dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond pivot[row] = row; 90dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 91dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond even = true; 92dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond singular = false; 93dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 94dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Loop over columns 95dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int col = 0; col < m; col++) { 96dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 97dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond T sum = field.getZero(); 98dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 99dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // upper 100dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int row = 0; row < col; row++) { 101dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[] luRow = lu[row]; 102dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond sum = luRow[col]; 103dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < row; i++) { 104dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond sum = sum.subtract(luRow[i].multiply(lu[i][col])); 105dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 106dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond luRow[col] = sum; 107dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 108dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 109dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // lower 110dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond int nonZero = col; // permutation row 111dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int row = col; row < m; row++) { 112dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[] luRow = lu[row]; 113dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond sum = luRow[col]; 114dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < col; i++) { 115dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond sum = sum.subtract(luRow[i].multiply(lu[i][col])); 116dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 117dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond luRow[col] = sum; 118dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 119dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (lu[nonZero][col].equals(field.getZero())) { 120dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // try to select a better permutation choice 121dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond ++nonZero; 122dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 123dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 124dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 125dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Singularity check 126dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (nonZero >= m) { 127dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond singular = true; 128dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return; 129dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 130dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 131dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Pivot if necessary 132dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (nonZero != col) { 133dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond T tmp = field.getZero(); 134dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < m; i++) { 135dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond tmp = lu[nonZero][i]; 136dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond lu[nonZero][i] = lu[col][i]; 137dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond lu[col][i] = tmp; 138dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 139dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond int temp = pivot[nonZero]; 140dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond pivot[nonZero] = pivot[col]; 141dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond pivot[col] = temp; 142dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond even = !even; 143dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 144dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 145dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Divide the lower elements by the "winning" diagonal elt. 146dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T luDiag = lu[col][col]; 147dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int row = col + 1; row < m; row++) { 148dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[] luRow = lu[row]; 149dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond luRow[col] = luRow[col].divide(luDiag); 150dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 151dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 152dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 153dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 154dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 155dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 156dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public FieldMatrix<T> getL() { 157dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if ((cachedL == null) && !singular) { 158dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int m = pivot.length; 159dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond cachedL = new Array2DRowFieldMatrix<T>(field, m, m); 160dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < m; ++i) { 161dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[] luI = lu[i]; 162dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int j = 0; j < i; ++j) { 163dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond cachedL.setEntry(i, j, luI[j]); 164dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 165dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond cachedL.setEntry(i, i, field.getOne()); 166dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 167dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 168dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return cachedL; 169dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 170dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 171dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 172dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public FieldMatrix<T> getU() { 173dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if ((cachedU == null) && !singular) { 174dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int m = pivot.length; 175dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond cachedU = new Array2DRowFieldMatrix<T>(field, m, m); 176dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < m; ++i) { 177dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[] luI = lu[i]; 178dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int j = i; j < m; ++j) { 179dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond cachedU.setEntry(i, j, luI[j]); 180dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 181dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 182dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 183dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return cachedU; 184dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 185dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 186dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 187dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public FieldMatrix<T> getP() { 188dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if ((cachedP == null) && !singular) { 189dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int m = pivot.length; 190dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond cachedP = new Array2DRowFieldMatrix<T>(field, m, m); 191dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < m; ++i) { 192dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond cachedP.setEntry(i, pivot[i], field.getOne()); 193dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 194dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 195dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return cachedP; 196dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 197dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 198dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 199dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public int[] getPivot() { 200dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return pivot.clone(); 201dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 202dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 203dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 204dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public T getDeterminant() { 205dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (singular) { 206dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return field.getZero(); 207dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } else { 208dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int m = pivot.length; 209dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond T determinant = even ? field.getOne() : field.getZero().subtract(field.getOne()); 210dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < m; i++) { 211dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond determinant = determinant.multiply(lu[i][i]); 212dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 213dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return determinant; 214dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 215dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 216dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 217dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 218dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public FieldDecompositionSolver<T> getSolver() { 219dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return new Solver<T>(field, lu, pivot, singular); 220dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 221dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 222dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Specialized solver. */ 223dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static class Solver<T extends FieldElement<T>> implements FieldDecompositionSolver<T> { 224dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 225dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Serializable version identifier. */ 226dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final long serialVersionUID = -6353105415121373022L; 227dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 228dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Field to which the elements belong. */ 229dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private final Field<T> field; 230dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 231dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Entries of LU decomposition. */ 232dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private final T lu[][]; 233dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 234dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Pivot permutation associated with LU decomposition. */ 235dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private final int[] pivot; 236dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 237dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Singularity indicator. */ 238dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private final boolean singular; 239dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 240dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 241dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Build a solver from decomposed matrix. 242dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param field field to which the matrix elements belong 243dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param lu entries of LU decomposition 244dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param pivot pivot permutation associated with LU decomposition 245dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param singular singularity indicator 246dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 247dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private Solver(final Field<T> field, final T[][] lu, 248dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int[] pivot, final boolean singular) { 249dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond this.field = field; 250dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond this.lu = lu; 251dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond this.pivot = pivot; 252dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond this.singular = singular; 253dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 254dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 255dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 256dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public boolean isNonSingular() { 257dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return !singular; 258dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 259dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 260dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 261dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public T[] solve(T[] b) 262dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throws IllegalArgumentException, InvalidMatrixException { 263dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 264dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int m = pivot.length; 265dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (b.length != m) { 266dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw MathRuntimeException.createIllegalArgumentException( 267dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond LocalizedFormats.VECTOR_LENGTH_MISMATCH, 268dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond b.length, m); 269dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 270dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (singular) { 271dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw new SingularMatrixException(); 272dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 273dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 274dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @SuppressWarnings("unchecked") // field is of type T 275dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[] bp = (T[]) Array.newInstance(field.getZero().getClass(), m); 276dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 277dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Apply permutations to b 278dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int row = 0; row < m; row++) { 279dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond bp[row] = b[pivot[row]]; 280dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 281dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 282dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Solve LY = b 283dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int col = 0; col < m; col++) { 284dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T bpCol = bp[col]; 285dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = col + 1; i < m; i++) { 286dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col])); 287dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 288dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 289dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 290dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Solve UX = Y 291dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int col = m - 1; col >= 0; col--) { 292dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond bp[col] = bp[col].divide(lu[col][col]); 293dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T bpCol = bp[col]; 294dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < col; i++) { 295dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col])); 296dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 297dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 298dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 299dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return bp; 300dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 301dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 302dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 303dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 304dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public FieldVector<T> solve(FieldVector<T> b) 305dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throws IllegalArgumentException, InvalidMatrixException { 306dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond try { 307dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return solve((ArrayFieldVector<T>) b); 308dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } catch (ClassCastException cce) { 309dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 310dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int m = pivot.length; 311dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (b.getDimension() != m) { 312dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw MathRuntimeException.createIllegalArgumentException( 313dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond LocalizedFormats.VECTOR_LENGTH_MISMATCH, 314dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond b.getDimension(), m); 315dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 316dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (singular) { 317dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw new SingularMatrixException(); 318dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 319dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 320dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @SuppressWarnings("unchecked") // field is of type T 321dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[] bp = (T[]) Array.newInstance(field.getZero().getClass(), m); 322dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 323dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Apply permutations to b 324dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int row = 0; row < m; row++) { 325dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond bp[row] = b.getEntry(pivot[row]); 326dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 327dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 328dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Solve LY = b 329dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int col = 0; col < m; col++) { 330dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T bpCol = bp[col]; 331dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = col + 1; i < m; i++) { 332dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col])); 333dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 334dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 335dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 336dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Solve UX = Y 337dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int col = m - 1; col >= 0; col--) { 338dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond bp[col] = bp[col].divide(lu[col][col]); 339dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T bpCol = bp[col]; 340dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < col; i++) { 341dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col])); 342dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 343dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 344dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 345dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return new ArrayFieldVector<T>(bp, false); 346dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 347dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 348dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 349dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 350dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Solve the linear equation A × X = B. 351dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p>The A matrix is implicit here. It is </p> 352dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param b right-hand side of the equation A × X = B 353dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @return a vector X such that A × X = B 354dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @exception IllegalArgumentException if matrices dimensions don't match 355dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @exception InvalidMatrixException if decomposed matrix is singular 356dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 357dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public ArrayFieldVector<T> solve(ArrayFieldVector<T> b) 358dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throws IllegalArgumentException, InvalidMatrixException { 359dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return new ArrayFieldVector<T>(solve(b.getDataRef()), false); 360dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 361dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 362dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 363dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public FieldMatrix<T> solve(FieldMatrix<T> b) 364dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throws IllegalArgumentException, InvalidMatrixException { 365dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 366dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int m = pivot.length; 367dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (b.getRowDimension() != m) { 368dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw MathRuntimeException.createIllegalArgumentException( 369dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond LocalizedFormats.DIMENSIONS_MISMATCH_2x2, 370dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond b.getRowDimension(), b.getColumnDimension(), m, "n"); 371dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 372dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (singular) { 373dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw new SingularMatrixException(); 374dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 375dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 376dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int nColB = b.getColumnDimension(); 377dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 378dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Apply permutations to b 379dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @SuppressWarnings("unchecked") // field is of type T 380dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[][] bp = (T[][]) Array.newInstance(field.getZero().getClass(), new int[] { m, nColB }); 381dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int row = 0; row < m; row++) { 382dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[] bpRow = bp[row]; 383dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int pRow = pivot[row]; 384dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int col = 0; col < nColB; col++) { 385dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond bpRow[col] = b.getEntry(pRow, col); 386dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 387dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 388dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 389dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Solve LY = b 390dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int col = 0; col < m; col++) { 391dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[] bpCol = bp[col]; 392dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = col + 1; i < m; i++) { 393dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[] bpI = bp[i]; 394dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T luICol = lu[i][col]; 395dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int j = 0; j < nColB; j++) { 396dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond bpI[j] = bpI[j].subtract(bpCol[j].multiply(luICol)); 397dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 398dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 399dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 400dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 401dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Solve UX = Y 402dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int col = m - 1; col >= 0; col--) { 403dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[] bpCol = bp[col]; 404dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T luDiag = lu[col][col]; 405dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int j = 0; j < nColB; j++) { 406dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond bpCol[j] = bpCol[j].divide(luDiag); 407dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 408dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < col; i++) { 409dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T[] bpI = bp[i]; 410dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T luICol = lu[i][col]; 411dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int j = 0; j < nColB; j++) { 412dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond bpI[j] = bpI[j].subtract(bpCol[j].multiply(luICol)); 413dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 414dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 415dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 416dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 417dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return new Array2DRowFieldMatrix<T>(bp, false); 418dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 419dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 420dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 421dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 422dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public FieldMatrix<T> getInverse() throws InvalidMatrixException { 423dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int m = pivot.length; 424dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final T one = field.getOne(); 425dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond FieldMatrix<T> identity = new Array2DRowFieldMatrix<T>(field, m, m); 426dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < m; ++i) { 427dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond identity.setEntry(i, i, one); 428dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 429dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return solve(identity); 430dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 431dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 432dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 433dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 434dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond} 435