| /* |
| * 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 java.lang.reflect.Array; |
| |
| import org.apache.commons.math.Field; |
| import org.apache.commons.math.FieldElement; |
| import org.apache.commons.math.MathRuntimeException; |
| import org.apache.commons.math.exception.util.LocalizedFormats; |
| |
| /** |
| * 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: PA = LU, L is lower triangular, and U is |
| * upper triangular and P is a permutation matrix. All matrices are |
| * m×m.</p> |
| * <p>Since {@link FieldElement field elements} do not provide an ordering |
| * operator, the permutation matrix is computed here only in order to avoid |
| * a zero pivot element, no attempt is done to get the largest pivot element.</p> |
| * |
| * @param <T> the type of the field elements |
| * @version $Revision: 983921 $ $Date: 2010-08-10 12:46:06 +0200 (mar. 10 août 2010) $ |
| * @since 2.0 |
| */ |
| public class FieldLUDecompositionImpl<T extends FieldElement<T>> implements FieldLUDecomposition<T> { |
| |
| /** Field to which the elements belong. */ |
| private final Field<T> field; |
| |
| /** Entries of LU decomposition. */ |
| private T lu[][]; |
| |
| /** Pivot permutation associated with LU decomposition */ |
| private int[] pivot; |
| |
| /** Parity of the permutation associated with the LU decomposition */ |
| private boolean even; |
| |
| /** Singularity indicator. */ |
| private boolean singular; |
| |
| /** Cached value of L. */ |
| private FieldMatrix<T> cachedL; |
| |
| /** Cached value of U. */ |
| private FieldMatrix<T> cachedU; |
| |
| /** Cached value of P. */ |
| private FieldMatrix<T> cachedP; |
| |
| /** |
| * Calculates the LU-decomposition of the given matrix. |
| * @param matrix The matrix to decompose. |
| * @exception NonSquareMatrixException if matrix is not square |
| */ |
| public FieldLUDecompositionImpl(FieldMatrix<T> matrix) |
| throws NonSquareMatrixException { |
| |
| if (!matrix.isSquare()) { |
| throw new NonSquareMatrixException(matrix.getRowDimension(), matrix.getColumnDimension()); |
| } |
| |
| final int m = matrix.getColumnDimension(); |
| field = matrix.getField(); |
| 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++) { |
| |
| T sum = field.getZero(); |
| |
| // upper |
| for (int row = 0; row < col; row++) { |
| final T[] luRow = lu[row]; |
| sum = luRow[col]; |
| for (int i = 0; i < row; i++) { |
| sum = sum.subtract(luRow[i].multiply(lu[i][col])); |
| } |
| luRow[col] = sum; |
| } |
| |
| // lower |
| int nonZero = col; // permutation row |
| for (int row = col; row < m; row++) { |
| final T[] luRow = lu[row]; |
| sum = luRow[col]; |
| for (int i = 0; i < col; i++) { |
| sum = sum.subtract(luRow[i].multiply(lu[i][col])); |
| } |
| luRow[col] = sum; |
| |
| if (lu[nonZero][col].equals(field.getZero())) { |
| // try to select a better permutation choice |
| ++nonZero; |
| } |
| } |
| |
| // Singularity check |
| if (nonZero >= m) { |
| singular = true; |
| return; |
| } |
| |
| // Pivot if necessary |
| if (nonZero != col) { |
| T tmp = field.getZero(); |
| for (int i = 0; i < m; i++) { |
| tmp = lu[nonZero][i]; |
| lu[nonZero][i] = lu[col][i]; |
| lu[col][i] = tmp; |
| } |
| int temp = pivot[nonZero]; |
| pivot[nonZero] = pivot[col]; |
| pivot[col] = temp; |
| even = !even; |
| } |
| |
| // Divide the lower elements by the "winning" diagonal elt. |
| final T luDiag = lu[col][col]; |
| for (int row = col + 1; row < m; row++) { |
| final T[] luRow = lu[row]; |
| luRow[col] = luRow[col].divide(luDiag); |
| } |
| } |
| |
| } |
| |
| /** {@inheritDoc} */ |
| public FieldMatrix<T> getL() { |
| if ((cachedL == null) && !singular) { |
| final int m = pivot.length; |
| cachedL = new Array2DRowFieldMatrix<T>(field, m, m); |
| for (int i = 0; i < m; ++i) { |
| final T[] luI = lu[i]; |
| for (int j = 0; j < i; ++j) { |
| cachedL.setEntry(i, j, luI[j]); |
| } |
| cachedL.setEntry(i, i, field.getOne()); |
| } |
| } |
| return cachedL; |
| } |
| |
| /** {@inheritDoc} */ |
| public FieldMatrix<T> getU() { |
| if ((cachedU == null) && !singular) { |
| final int m = pivot.length; |
| cachedU = new Array2DRowFieldMatrix<T>(field, m, m); |
| for (int i = 0; i < m; ++i) { |
| final T[] luI = lu[i]; |
| for (int j = i; j < m; ++j) { |
| cachedU.setEntry(i, j, luI[j]); |
| } |
| } |
| } |
| return cachedU; |
| } |
| |
| /** {@inheritDoc} */ |
| public FieldMatrix<T> getP() { |
| if ((cachedP == null) && !singular) { |
| final int m = pivot.length; |
| cachedP = new Array2DRowFieldMatrix<T>(field, m, m); |
| for (int i = 0; i < m; ++i) { |
| cachedP.setEntry(i, pivot[i], field.getOne()); |
| } |
| } |
| return cachedP; |
| } |
| |
| /** {@inheritDoc} */ |
| public int[] getPivot() { |
| return pivot.clone(); |
| } |
| |
| /** {@inheritDoc} */ |
| public T getDeterminant() { |
| if (singular) { |
| return field.getZero(); |
| } else { |
| final int m = pivot.length; |
| T determinant = even ? field.getOne() : field.getZero().subtract(field.getOne()); |
| for (int i = 0; i < m; i++) { |
| determinant = determinant.multiply(lu[i][i]); |
| } |
| return determinant; |
| } |
| } |
| |
| /** {@inheritDoc} */ |
| public FieldDecompositionSolver<T> getSolver() { |
| return new Solver<T>(field, lu, pivot, singular); |
| } |
| |
| /** Specialized solver. */ |
| private static class Solver<T extends FieldElement<T>> implements FieldDecompositionSolver<T> { |
| |
| /** Serializable version identifier. */ |
| private static final long serialVersionUID = -6353105415121373022L; |
| |
| /** Field to which the elements belong. */ |
| private final Field<T> field; |
| |
| /** Entries of LU decomposition. */ |
| private final T lu[][]; |
| |
| /** Pivot permutation associated with LU decomposition. */ |
| private final int[] pivot; |
| |
| /** Singularity indicator. */ |
| private final boolean singular; |
| |
| /** |
| * Build a solver from decomposed matrix. |
| * @param field field to which the matrix elements belong |
| * @param lu entries of LU decomposition |
| * @param pivot pivot permutation associated with LU decomposition |
| * @param singular singularity indicator |
| */ |
| private Solver(final Field<T> field, final T[][] lu, |
| final int[] pivot, final boolean singular) { |
| this.field = field; |
| this.lu = lu; |
| this.pivot = pivot; |
| this.singular = singular; |
| } |
| |
| /** {@inheritDoc} */ |
| public boolean isNonSingular() { |
| return !singular; |
| } |
| |
| /** {@inheritDoc} */ |
| public T[] solve(T[] b) |
| throws IllegalArgumentException, InvalidMatrixException { |
| |
| final int m = pivot.length; |
| if (b.length != m) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.VECTOR_LENGTH_MISMATCH, |
| b.length, m); |
| } |
| if (singular) { |
| throw new SingularMatrixException(); |
| } |
| |
| @SuppressWarnings("unchecked") // field is of type T |
| final T[] bp = (T[]) Array.newInstance(field.getZero().getClass(), m); |
| |
| // Apply permutations to b |
| for (int row = 0; row < m; row++) { |
| bp[row] = b[pivot[row]]; |
| } |
| |
| // Solve LY = b |
| for (int col = 0; col < m; col++) { |
| final T bpCol = bp[col]; |
| for (int i = col + 1; i < m; i++) { |
| bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col])); |
| } |
| } |
| |
| // Solve UX = Y |
| for (int col = m - 1; col >= 0; col--) { |
| bp[col] = bp[col].divide(lu[col][col]); |
| final T bpCol = bp[col]; |
| for (int i = 0; i < col; i++) { |
| bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col])); |
| } |
| } |
| |
| return bp; |
| |
| } |
| |
| /** {@inheritDoc} */ |
| public FieldVector<T> solve(FieldVector<T> b) |
| throws IllegalArgumentException, InvalidMatrixException { |
| try { |
| return solve((ArrayFieldVector<T>) b); |
| } catch (ClassCastException cce) { |
| |
| final int m = pivot.length; |
| if (b.getDimension() != m) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.VECTOR_LENGTH_MISMATCH, |
| b.getDimension(), m); |
| } |
| if (singular) { |
| throw new SingularMatrixException(); |
| } |
| |
| @SuppressWarnings("unchecked") // field is of type T |
| final T[] bp = (T[]) Array.newInstance(field.getZero().getClass(), 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 T bpCol = bp[col]; |
| for (int i = col + 1; i < m; i++) { |
| bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col])); |
| } |
| } |
| |
| // Solve UX = Y |
| for (int col = m - 1; col >= 0; col--) { |
| bp[col] = bp[col].divide(lu[col][col]); |
| final T bpCol = bp[col]; |
| for (int i = 0; i < col; i++) { |
| bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col])); |
| } |
| } |
| |
| return new ArrayFieldVector<T>(bp, false); |
| |
| } |
| } |
| |
| /** Solve the linear equation A × X = B. |
| * <p>The A matrix is implicit here. It is </p> |
| * @param b right-hand side of the equation A × X = B |
| * @return a vector X such that A × X = B |
| * @exception IllegalArgumentException if matrices dimensions don't match |
| * @exception InvalidMatrixException if decomposed matrix is singular |
| */ |
| public ArrayFieldVector<T> solve(ArrayFieldVector<T> b) |
| throws IllegalArgumentException, InvalidMatrixException { |
| return new ArrayFieldVector<T>(solve(b.getDataRef()), false); |
| } |
| |
| /** {@inheritDoc} */ |
| public FieldMatrix<T> solve(FieldMatrix<T> b) |
| throws IllegalArgumentException, InvalidMatrixException { |
| |
| final int m = pivot.length; |
| if (b.getRowDimension() != m) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.DIMENSIONS_MISMATCH_2x2, |
| b.getRowDimension(), b.getColumnDimension(), m, "n"); |
| } |
| if (singular) { |
| throw new SingularMatrixException(); |
| } |
| |
| final int nColB = b.getColumnDimension(); |
| |
| // Apply permutations to b |
| @SuppressWarnings("unchecked") // field is of type T |
| final T[][] bp = (T[][]) Array.newInstance(field.getZero().getClass(), new int[] { m, nColB }); |
| for (int row = 0; row < m; row++) { |
| final T[] 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 T[] bpCol = bp[col]; |
| for (int i = col + 1; i < m; i++) { |
| final T[] bpI = bp[i]; |
| final T luICol = lu[i][col]; |
| for (int j = 0; j < nColB; j++) { |
| bpI[j] = bpI[j].subtract(bpCol[j].multiply(luICol)); |
| } |
| } |
| } |
| |
| // Solve UX = Y |
| for (int col = m - 1; col >= 0; col--) { |
| final T[] bpCol = bp[col]; |
| final T luDiag = lu[col][col]; |
| for (int j = 0; j < nColB; j++) { |
| bpCol[j] = bpCol[j].divide(luDiag); |
| } |
| for (int i = 0; i < col; i++) { |
| final T[] bpI = bp[i]; |
| final T luICol = lu[i][col]; |
| for (int j = 0; j < nColB; j++) { |
| bpI[j] = bpI[j].subtract(bpCol[j].multiply(luICol)); |
| } |
| } |
| } |
| |
| return new Array2DRowFieldMatrix<T>(bp, false); |
| |
| } |
| |
| /** {@inheritDoc} */ |
| public FieldMatrix<T> getInverse() throws InvalidMatrixException { |
| final int m = pivot.length; |
| final T one = field.getOne(); |
| FieldMatrix<T> identity = new Array2DRowFieldMatrix<T>(field, m, m); |
| for (int i = 0; i < m; ++i) { |
| identity.setEntry(i, i, one); |
| } |
| return solve(identity); |
| } |
| |
| } |
| |
| } |