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diff --git a/src/main/java/org/apache/commons/math3/linear/LUDecomposition.java b/src/main/java/org/apache/commons/math3/linear/LUDecomposition.java new file mode 100644 index 0000000..798bb61 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/linear/LUDecomposition.java @@ -0,0 +1,409 @@ +/* + * 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.math3.linear; + +import org.apache.commons.math3.exception.DimensionMismatchException; +import org.apache.commons.math3.util.FastMath; + +/** + * Calculates the LUP-decomposition of a square matrix. + * + * <p>The LUP-decomposition of a matrix A consists of three matrices L, U and P that satisfy: + * P×A = L×U. L is lower triangular (with unit diagonal terms), U is upper triangular + * and P is a permutation matrix. All matrices are m×m. + * + * <p>As shown by the presence of the P matrix, this decomposition is implemented using partial + * pivoting. + * + * <p>This class is based on the class with similar name from the <a + * href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library. + * + * <ul> + * <li>a {@link #getP() getP} method has been added, + * <li>the {@code det} method has been renamed as {@link #getDeterminant() getDeterminant}, + * <li>the {@code getDoublePivot} method has been removed (but the int based {@link #getPivot() + * getPivot} method has been kept), + * <li>the {@code solve} and {@code isNonSingular} methods have been replaced by a {@link + * #getSolver() getSolver} method and the equivalent methods provided by the returned {@link + * DecompositionSolver}. + * </ul> + * + * @see <a href="http://mathworld.wolfram.com/LUDecomposition.html">MathWorld</a> + * @see <a href="http://en.wikipedia.org/wiki/LU_decomposition">Wikipedia</a> + * @since 2.0 (changed to concrete class in 3.0) + */ +public class LUDecomposition { + /** Default bound to determine effective singularity in LU decomposition. */ + private static final double DEFAULT_TOO_SMALL = 1e-11; + + /** Entries of LU decomposition. */ + private final double[][] lu; + + /** Pivot permutation associated with LU decomposition. */ + private final int[] pivot; + + /** Parity of the permutation associated with the LU decomposition. */ + private boolean even; + + /** Singularity indicator. */ + private boolean singular; + + /** Cached value of L. */ + private RealMatrix cachedL; + + /** Cached value of U. */ + private RealMatrix cachedU; + + /** Cached value of P. */ + private RealMatrix cachedP; + + /** + * Calculates the LU-decomposition of the given matrix. This constructor uses 1e-11 as default + * value for the singularity threshold. + * + * @param matrix Matrix to decompose. + * @throws NonSquareMatrixException if matrix is not square. + */ + public LUDecomposition(RealMatrix matrix) { + this(matrix, DEFAULT_TOO_SMALL); + } + + /** + * Calculates the LU-decomposition of the given matrix. + * + * @param matrix The matrix to decompose. + * @param singularityThreshold threshold (based on partial row norm) under which a matrix is + * considered singular + * @throws NonSquareMatrixException if matrix is not square + */ + public LUDecomposition(RealMatrix matrix, double singularityThreshold) { + if (!matrix.isSquare()) { + throw new NonSquareMatrixException( + matrix.getRowDimension(), matrix.getColumnDimension()); + } + + final int m = matrix.getColumnDimension(); + lu = matrix.getData(); + pivot = new int[m]; + cachedL = null; + cachedU = null; + cachedP = null; + + // Initialize permutation array and parity + for (int row = 0; row < m; row++) { + pivot[row] = row; + } + even = true; + singular = false; + + // Loop over columns + for (int col = 0; col < m; col++) { + + // upper + for (int row = 0; row < col; row++) { + final double[] luRow = lu[row]; + double sum = luRow[col]; + for (int i = 0; i < row; i++) { + sum -= luRow[i] * lu[i][col]; + } + luRow[col] = sum; + } + + // lower + int max = col; // permutation row + double largest = Double.NEGATIVE_INFINITY; + for (int row = col; row < m; row++) { + final double[] luRow = lu[row]; + double sum = luRow[col]; + for (int i = 0; i < col; i++) { + sum -= luRow[i] * lu[i][col]; + } + luRow[col] = sum; + + // maintain best permutation choice + if (FastMath.abs(sum) > largest) { + largest = FastMath.abs(sum); + max = row; + } + } + + // Singularity check + if (FastMath.abs(lu[max][col]) < singularityThreshold) { + singular = true; + return; + } + + // Pivot if necessary + if (max != col) { + double tmp = 0; + final double[] luMax = lu[max]; + final double[] luCol = lu[col]; + for (int i = 0; i < m; i++) { + tmp = luMax[i]; + luMax[i] = luCol[i]; + luCol[i] = tmp; + } + int temp = pivot[max]; + pivot[max] = pivot[col]; + pivot[col] = temp; + even = !even; + } + + // Divide the lower elements by the "winning" diagonal elt. + final double luDiag = lu[col][col]; + for (int row = col + 1; row < m; row++) { + lu[row][col] /= luDiag; + } + } + } + + /** + * Returns the matrix L of the decomposition. + * + * <p>L is a lower-triangular matrix + * + * @return the L matrix (or null if decomposed matrix is singular) + */ + public RealMatrix getL() { + if ((cachedL == null) && !singular) { + final int m = pivot.length; + cachedL = MatrixUtils.createRealMatrix(m, m); + for (int i = 0; i < m; ++i) { + final double[] luI = lu[i]; + for (int j = 0; j < i; ++j) { + cachedL.setEntry(i, j, luI[j]); + } + cachedL.setEntry(i, i, 1.0); + } + } + return cachedL; + } + + /** + * Returns the matrix U of the decomposition. + * + * <p>U is an upper-triangular matrix + * + * @return the U matrix (or null if decomposed matrix is singular) + */ + public RealMatrix getU() { + if ((cachedU == null) && !singular) { + final int m = pivot.length; + cachedU = MatrixUtils.createRealMatrix(m, m); + for (int i = 0; i < m; ++i) { + final double[] luI = lu[i]; + for (int j = i; j < m; ++j) { + cachedU.setEntry(i, j, luI[j]); + } + } + } + return cachedU; + } + + /** + * 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>The positions of the 1 elements are given by the {@link #getPivot() pivot permutation + * vector}. + * + * @return the P rows permutation matrix (or null if decomposed matrix is singular) + * @see #getPivot() + */ + public RealMatrix getP() { + if ((cachedP == null) && !singular) { + final int m = pivot.length; + cachedP = MatrixUtils.createRealMatrix(m, m); + for (int i = 0; i < m; ++i) { + cachedP.setEntry(i, pivot[i], 1.0); + } + } + return cachedP; + } + + /** + * Returns the pivot permutation vector. + * + * @return the pivot permutation vector + * @see #getP() + */ + public int[] getPivot() { + return pivot.clone(); + } + + /** + * Return the determinant of the matrix + * + * @return determinant of the matrix + */ + public double getDeterminant() { + if (singular) { + return 0; + } else { + final int m = pivot.length; + double determinant = even ? 1 : -1; + for (int i = 0; i < m; i++) { + determinant *= lu[i][i]; + } + return determinant; + } + } + + /** + * Get a solver for finding the A × X = B solution in exact linear sense. + * + * @return a solver + */ + public DecompositionSolver getSolver() { + return new Solver(lu, pivot, singular); + } + + /** Specialized solver. */ + private static class Solver implements DecompositionSolver { + + /** Entries of LU decomposition. */ + private final double[][] lu; + + /** Pivot permutation associated with LU decomposition. */ + private final int[] pivot; + + /** Singularity indicator. */ + private final boolean singular; + + /** + * Build a solver from decomposed matrix. + * + * @param lu entries of LU decomposition + * @param pivot pivot permutation associated with LU decomposition + * @param singular singularity indicator + */ + private Solver(final double[][] lu, final int[] pivot, final boolean singular) { + this.lu = lu; + this.pivot = pivot; + this.singular = singular; + } + + /** {@inheritDoc} */ + public boolean isNonSingular() { + return !singular; + } + + /** {@inheritDoc} */ + public RealVector solve(RealVector b) { + final int m = pivot.length; + if (b.getDimension() != m) { + throw new DimensionMismatchException(b.getDimension(), m); + } + if (singular) { + throw new SingularMatrixException(); + } + + final double[] bp = new double[m]; + + // Apply permutations to b + for (int row = 0; row < m; row++) { + bp[row] = b.getEntry(pivot[row]); + } + + // Solve LY = b + for (int col = 0; col < m; col++) { + final double bpCol = bp[col]; + for (int i = col + 1; i < m; i++) { + bp[i] -= bpCol * lu[i][col]; + } + } + + // Solve UX = Y + for (int col = m - 1; col >= 0; col--) { + bp[col] /= lu[col][col]; + final double bpCol = bp[col]; + for (int i = 0; i < col; i++) { + bp[i] -= bpCol * lu[i][col]; + } + } + + return new ArrayRealVector(bp, false); + } + + /** {@inheritDoc} */ + public RealMatrix solve(RealMatrix b) { + + final int m = pivot.length; + if (b.getRowDimension() != m) { + throw new DimensionMismatchException(b.getRowDimension(), m); + } + if (singular) { + throw new SingularMatrixException(); + } + + final int nColB = b.getColumnDimension(); + + // Apply permutations to b + final double[][] bp = new double[m][nColB]; + for (int row = 0; row < m; row++) { + final double[] bpRow = bp[row]; + final int pRow = pivot[row]; + for (int col = 0; col < nColB; col++) { + bpRow[col] = b.getEntry(pRow, col); + } + } + + // Solve LY = b + for (int col = 0; col < m; col++) { + final double[] bpCol = bp[col]; + for (int i = col + 1; i < m; i++) { + final double[] bpI = bp[i]; + final double luICol = lu[i][col]; + for (int j = 0; j < nColB; j++) { + bpI[j] -= bpCol[j] * luICol; + } + } + } + + // Solve UX = Y + for (int col = m - 1; col >= 0; col--) { + final double[] bpCol = bp[col]; + final double luDiag = lu[col][col]; + for (int j = 0; j < nColB; j++) { + bpCol[j] /= luDiag; + } + for (int i = 0; i < col; i++) { + final double[] bpI = bp[i]; + final double luICol = lu[i][col]; + for (int j = 0; j < nColB; j++) { + bpI[j] -= bpCol[j] * luICol; + } + } + } + + return new Array2DRowRealMatrix(bp, false); + } + + /** + * Get the inverse of the decomposed matrix. + * + * @return the inverse matrix. + * @throws SingularMatrixException if the decomposed matrix is singular. + */ + public RealMatrix getInverse() { + return solve(MatrixUtils.createRealIdentityMatrix(pivot.length)); + } + } +} |