/* * 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.io.IOException; import java.io.ObjectInputStream; import java.io.ObjectOutputStream; import java.lang.reflect.Array; import java.util.Arrays; import org.apache.commons.math.Field; import org.apache.commons.math.FieldElement; import org.apache.commons.math.exception.OutOfRangeException; import org.apache.commons.math.exception.NoDataException; import org.apache.commons.math.exception.NumberIsTooSmallException; import org.apache.commons.math.exception.NullArgumentException; import org.apache.commons.math.exception.DimensionMismatchException; import org.apache.commons.math.exception.ZeroException; import org.apache.commons.math.exception.util.LocalizedFormats; import org.apache.commons.math.fraction.BigFraction; import org.apache.commons.math.fraction.Fraction; /** * A collection of static methods that operate on or return matrices. * * @version $Id: MatrixUtils.java 1131229 2011-06-03 20:49:25Z luc $ */ public class MatrixUtils { /** * Private constructor. */ private MatrixUtils() { super(); } /** * Returns a {@link RealMatrix} with specified dimensions. * <p>The type of matrix returned depends on the dimension. Below * 2<sup>12</sup> elements (i.e. 4096 elements or 64×64 for a * square matrix) which can be stored in a 32kB array, a {@link * Array2DRowRealMatrix} instance is built. Above this threshold a {@link * BlockRealMatrix} instance is built.</p> * <p>The matrix elements are all set to 0.0.</p> * @param rows number of rows of the matrix * @param columns number of columns of the matrix * @return RealMatrix with specified dimensions * @see #createRealMatrix(double[][]) */ public static RealMatrix createRealMatrix(final int rows, final int columns) { return (rows * columns <= 4096) ? new Array2DRowRealMatrix(rows, columns) : new BlockRealMatrix(rows, columns); } /** * Returns a {@link FieldMatrix} with specified dimensions. * <p>The type of matrix returned depends on the dimension. Below * 2<sup>12</sup> elements (i.e. 4096 elements or 64×64 for a * square matrix), a {@link FieldMatrix} instance is built. Above * this threshold a {@link BlockFieldMatrix} instance is built.</p> * <p>The matrix elements are all set to field.getZero().</p> * @param <T> the type of the field elements * @param field field to which the matrix elements belong * @param rows number of rows of the matrix * @param columns number of columns of the matrix * @return FieldMatrix with specified dimensions * @see #createFieldMatrix(FieldElement[][]) * @since 2.0 */ public static <T extends FieldElement<T>> FieldMatrix<T> createFieldMatrix(final Field<T> field, final int rows, final int columns) { return (rows * columns <= 4096) ? new Array2DRowFieldMatrix<T>(field, rows, columns) : new BlockFieldMatrix<T>(field, rows, columns); } /** * Returns a {@link RealMatrix} whose entries are the the values in the * the input array. * <p>The type of matrix returned depends on the dimension. Below * 2<sup>12</sup> elements (i.e. 4096 elements or 64×64 for a * square matrix) which can be stored in a 32kB array, a {@link * Array2DRowRealMatrix} instance is built. Above this threshold a {@link * BlockRealMatrix} instance is built.</p> * <p>The input array is copied, not referenced.</p> * * @param data input array * @return RealMatrix containing the values of the array * @throws org.apache.commons.math.exception.DimensionMismatchException * if {@code data} is not rectangular (not all rows have the same length). * @throws NoDataException if a row or column is empty. * @throws NullArgumentException if either {@code data} or {@code data[0]} * is {@code null}. * @see #createRealMatrix(int, int) */ public static RealMatrix createRealMatrix(double[][] data) { if (data == null || data[0] == null) { throw new NullArgumentException(); } return (data.length * data[0].length <= 4096) ? new Array2DRowRealMatrix(data) : new BlockRealMatrix(data); } /** * Returns a {@link FieldMatrix} whose entries are the the values in the * the input array. * <p>The type of matrix returned depends on the dimension. Below * 2<sup>12</sup> elements (i.e. 4096 elements or 64×64 for a * square matrix), a {@link FieldMatrix} instance is built. Above * this threshold a {@link BlockFieldMatrix} instance is built.</p> * <p>The input array is copied, not referenced.</p> * @param <T> the type of the field elements * @param data input array * @return a matrix containing the values of the array. * @throws org.apache.commons.math.exception.DimensionMismatchException * if {@code data} is not rectangular (not all rows have the same length). * @throws NoDataException if a row or column is empty. * @throws NullArgumentException if either {@code data} or {@code data[0]} * is {@code null}. * @see #createFieldMatrix(Field, int, int) * @since 2.0 */ public static <T extends FieldElement<T>> FieldMatrix<T> createFieldMatrix(T[][] data) { if (data == null || data[0] == null) { throw new NullArgumentException(); } return (data.length * data[0].length <= 4096) ? new Array2DRowFieldMatrix<T>(data) : new BlockFieldMatrix<T>(data); } /** * Returns <code>dimension x dimension</code> identity matrix. * * @param dimension dimension of identity matrix to generate * @return identity matrix * @throws IllegalArgumentException if dimension is not positive * @since 1.1 */ public static RealMatrix createRealIdentityMatrix(int dimension) { final RealMatrix m = createRealMatrix(dimension, dimension); for (int i = 0; i < dimension; ++i) { m.setEntry(i, i, 1.0); } return m; } /** * Returns <code>dimension x dimension</code> identity matrix. * * @param <T> the type of the field elements * @param field field to which the elements belong * @param dimension dimension of identity matrix to generate * @return identity matrix * @throws IllegalArgumentException if dimension is not positive * @since 2.0 */ public static <T extends FieldElement<T>> FieldMatrix<T> createFieldIdentityMatrix(final Field<T> field, final int dimension) { final T zero = field.getZero(); final T one = field.getOne(); @SuppressWarnings("unchecked") // zero is type T final T[][] d = (T[][]) Array.newInstance(zero.getClass(), new int[] { dimension, dimension }); for (int row = 0; row < dimension; row++) { final T[] dRow = d[row]; Arrays.fill(dRow, zero); dRow[row] = one; } return new Array2DRowFieldMatrix<T>(field, d, false); } /** * Returns a diagonal matrix with specified elements. * * @param diagonal diagonal elements of the matrix (the array elements * will be copied) * @return diagonal matrix * @since 2.0 */ public static RealMatrix createRealDiagonalMatrix(final double[] diagonal) { final RealMatrix m = createRealMatrix(diagonal.length, diagonal.length); for (int i = 0; i < diagonal.length; ++i) { m.setEntry(i, i, diagonal[i]); } return m; } /** * Returns a diagonal matrix with specified elements. * * @param <T> the type of the field elements * @param diagonal diagonal elements of the matrix (the array elements * will be copied) * @return diagonal matrix * @since 2.0 */ public static <T extends FieldElement<T>> FieldMatrix<T> createFieldDiagonalMatrix(final T[] diagonal) { final FieldMatrix<T> m = createFieldMatrix(diagonal[0].getField(), diagonal.length, diagonal.length); for (int i = 0; i < diagonal.length; ++i) { m.setEntry(i, i, diagonal[i]); } return m; } /** * Creates a {@link RealVector} using the data from the input array. * * @param data the input data * @return a data.length RealVector * @throws NoDataException if {@code data} is empty. * @throws NullArgumentException if {@code data} is {@code null}. */ public static RealVector createRealVector(double[] data) { if (data == null) { throw new NullArgumentException(); } return new ArrayRealVector(data, true); } /** * Creates a {@link FieldVector} using the data from the input array. * * @param <T> the type of the field elements * @param data the input data * @return a data.length FieldVector * @throws NoDataException if {@code data} is empty. * @throws NullArgumentException if {@code data} is {@code null}. * @throws ZeroException if {@code data} has 0 elements */ public static <T extends FieldElement<T>> FieldVector<T> createFieldVector(final T[] data) { if (data == null) { throw new NullArgumentException(); } if (data.length == 0) { throw new ZeroException(LocalizedFormats.VECTOR_MUST_HAVE_AT_LEAST_ONE_ELEMENT); } return new ArrayFieldVector<T>(data[0].getField(), data, true); } /** * Create a row {@link RealMatrix} using the data from the input * array. * * @param rowData the input row data * @return a 1 x rowData.length RealMatrix * @throws NoDataException if {@code rowData} is empty. * @throws NullArgumentException if {@code rowData} is {@code null}. */ public static RealMatrix createRowRealMatrix(double[] rowData) { if (rowData == null) { throw new NullArgumentException(); } final int nCols = rowData.length; final RealMatrix m = createRealMatrix(1, nCols); for (int i = 0; i < nCols; ++i) { m.setEntry(0, i, rowData[i]); } return m; } /** * Create a row {@link FieldMatrix} using the data from the input * array. * * @param <T> the type of the field elements * @param rowData the input row data * @return a 1 x rowData.length FieldMatrix * @throws NoDataException if {@code rowData} is empty. * @throws NullArgumentException if {@code rowData} is {@code null}. */ public static <T extends FieldElement<T>> FieldMatrix<T> createRowFieldMatrix(final T[] rowData) { if (rowData == null) { throw new NullArgumentException(); } final int nCols = rowData.length; if (nCols == 0) { throw new NoDataException(LocalizedFormats.AT_LEAST_ONE_COLUMN); } final FieldMatrix<T> m = createFieldMatrix(rowData[0].getField(), 1, nCols); for (int i = 0; i < nCols; ++i) { m.setEntry(0, i, rowData[i]); } return m; } /** * Creates a column {@link RealMatrix} using the data from the input * array. * * @param columnData the input column data * @return a columnData x 1 RealMatrix * @throws NoDataException if {@code columnData} is empty. * @throws NullArgumentException if {@code columnData} is {@code null}. */ public static RealMatrix createColumnRealMatrix(double[] columnData) { if (columnData == null) { throw new NullArgumentException(); } final int nRows = columnData.length; final RealMatrix m = createRealMatrix(nRows, 1); for (int i = 0; i < nRows; ++i) { m.setEntry(i, 0, columnData[i]); } return m; } /** * Creates a column {@link FieldMatrix} using the data from the input * array. * * @param <T> the type of the field elements * @param columnData the input column data * @return a columnData x 1 FieldMatrix * @throws NoDataException if {@code data} is empty. * @throws NullArgumentException if {@code columnData} is {@code null}. */ public static <T extends FieldElement<T>> FieldMatrix<T> createColumnFieldMatrix(final T[] columnData) { if (columnData == null) { throw new NullArgumentException(); } final int nRows = columnData.length; if (nRows == 0) { throw new NoDataException(LocalizedFormats.AT_LEAST_ONE_ROW); } final FieldMatrix<T> m = createFieldMatrix(columnData[0].getField(), nRows, 1); for (int i = 0; i < nRows; ++i) { m.setEntry(i, 0, columnData[i]); } return m; } /** * Check if matrix indices are valid. * * @param m Matrix. * @param row Row index to check. * @param column Column index to check. * @throws OutOfRangeException if {@code row} or {@code column} is not * a valid index. */ public static void checkMatrixIndex(final AnyMatrix m, final int row, final int column) { checkRowIndex(m, row); checkColumnIndex(m, column); } /** * Check if a row index is valid. * * @param m Matrix. * @param row Row index to check. * @throws OutOfRangeException if {@code row} is not a valid index. */ public static void checkRowIndex(final AnyMatrix m, final int row) { if (row < 0 || row >= m.getRowDimension()) { throw new OutOfRangeException(LocalizedFormats.ROW_INDEX, row, 0, m.getRowDimension() - 1); } } /** * Check if a column index is valid. * * @param m Matrix. * @param column Column index to check. * @throws OutOfRangeException if {@code column} is not a valid index. */ public static void checkColumnIndex(final AnyMatrix m, final int column) { if (column < 0 || column >= m.getColumnDimension()) { throw new OutOfRangeException(LocalizedFormats.COLUMN_INDEX, column, 0, m.getColumnDimension() - 1); } } /** * Check if submatrix ranges indices are valid. * Rows and columns are indicated counting from 0 to {@code n - 1}. * * @param m Matrix. * @param startRow Initial row index. * @param endRow Final row index. * @param startColumn Initial column index. * @param endColumn Final column index. * @throws OutOfRangeException if the indices are invalid. * @throws NumberIsTooSmallException if {@code endRow < startRow} or * {@code endColumn < startColumn}. */ public static void checkSubMatrixIndex(final AnyMatrix m, final int startRow, final int endRow, final int startColumn, final int endColumn) { checkRowIndex(m, startRow); checkRowIndex(m, endRow); if (endRow < startRow) { throw new NumberIsTooSmallException(LocalizedFormats.INITIAL_ROW_AFTER_FINAL_ROW, endRow, startRow, false); } checkColumnIndex(m, startColumn); checkColumnIndex(m, endColumn); if (endColumn < startColumn) { throw new NumberIsTooSmallException(LocalizedFormats.INITIAL_COLUMN_AFTER_FINAL_COLUMN, endColumn, startColumn, false); } } /** * Check if submatrix ranges indices are valid. * Rows and columns are indicated counting from 0 to n-1. * * @param m Matrix. * @param selectedRows Array of row indices. * @param selectedColumns Array of column indices. * @throws NullArgumentException if {@code selectedRows} or * {@code selectedColumns} are {@code null}. * @throws NoDataException if the row or column selections are empty (zero * length). * @throws OutOfRangeException if row or column selections are not valid. */ public static void checkSubMatrixIndex(final AnyMatrix m, final int[] selectedRows, final int[] selectedColumns) { if (selectedRows == null) { throw new NullArgumentException(); } if (selectedColumns == null) { throw new NullArgumentException(); } if (selectedRows.length == 0) { throw new NoDataException(LocalizedFormats.EMPTY_SELECTED_ROW_INDEX_ARRAY); } if (selectedColumns.length == 0) { throw new NoDataException(LocalizedFormats.EMPTY_SELECTED_COLUMN_INDEX_ARRAY); } for (final int row : selectedRows) { checkRowIndex(m, row); } for (final int column : selectedColumns) { checkColumnIndex(m, column); } } /** * Check if matrices are addition compatible. * * @param left Left hand side matrix. * @param right Right hand side matrix. * @throws MatrixDimensionMismatchException if the matrices are not addition compatible. */ public static void checkAdditionCompatible(final AnyMatrix left, final AnyMatrix right) { if ((left.getRowDimension() != right.getRowDimension()) || (left.getColumnDimension() != right.getColumnDimension())) { throw new MatrixDimensionMismatchException(left.getRowDimension(), left.getColumnDimension(), right.getRowDimension(), right.getColumnDimension()); } } /** * Check if matrices are subtraction compatible * * @param left Left hand side matrix. * @param right Right hand side matrix. * @throws MatrixDimensionMismatchException if the matrices are not addition compatible. */ public static void checkSubtractionCompatible(final AnyMatrix left, final AnyMatrix right) { if ((left.getRowDimension() != right.getRowDimension()) || (left.getColumnDimension() != right.getColumnDimension())) { throw new MatrixDimensionMismatchException(left.getRowDimension(), left.getColumnDimension(), right.getRowDimension(), right.getColumnDimension()); } } /** * Check if matrices are multiplication compatible * * @param left Left hand side matrix. * @param right Right hand side matrix. * @throws DimensionMismatchException if matrices are not multiplication compatible. */ public static void checkMultiplicationCompatible(final AnyMatrix left, final AnyMatrix right) { if (left.getColumnDimension() != right.getRowDimension()) { throw new DimensionMismatchException(left.getColumnDimension(), right.getRowDimension()); } } /** * Convert a {@link FieldMatrix}/{@link Fraction} matrix to a {@link RealMatrix}. * @param m Matrix to convert. * @return the converted matrix. */ public static Array2DRowRealMatrix fractionMatrixToRealMatrix(final FieldMatrix<Fraction> m) { final FractionMatrixConverter converter = new FractionMatrixConverter(); m.walkInOptimizedOrder(converter); return converter.getConvertedMatrix(); } /** Converter for {@link FieldMatrix}/{@link Fraction}. */ private static class FractionMatrixConverter extends DefaultFieldMatrixPreservingVisitor<Fraction> { /** Converted array. */ private double[][] data; /** Simple constructor. */ public FractionMatrixConverter() { super(Fraction.ZERO); } /** {@inheritDoc} */ @Override public void start(int rows, int columns, int startRow, int endRow, int startColumn, int endColumn) { data = new double[rows][columns]; } /** {@inheritDoc} */ @Override public void visit(int row, int column, Fraction value) { data[row][column] = value.doubleValue(); } /** * Get the converted matrix. * * @return the converted matrix. */ Array2DRowRealMatrix getConvertedMatrix() { return new Array2DRowRealMatrix(data, false); } } /** * Convert a {@link FieldMatrix}/{@link BigFraction} matrix to a {@link RealMatrix}. * * @param m Matrix to convert. * @return the converted matrix. */ public static Array2DRowRealMatrix bigFractionMatrixToRealMatrix(final FieldMatrix<BigFraction> m) { final BigFractionMatrixConverter converter = new BigFractionMatrixConverter(); m.walkInOptimizedOrder(converter); return converter.getConvertedMatrix(); } /** Converter for {@link FieldMatrix}/{@link BigFraction}. */ private static class BigFractionMatrixConverter extends DefaultFieldMatrixPreservingVisitor<BigFraction> { /** Converted array. */ private double[][] data; /** Simple constructor. */ public BigFractionMatrixConverter() { super(BigFraction.ZERO); } /** {@inheritDoc} */ @Override public void start(int rows, int columns, int startRow, int endRow, int startColumn, int endColumn) { data = new double[rows][columns]; } /** {@inheritDoc} */ @Override public void visit(int row, int column, BigFraction value) { data[row][column] = value.doubleValue(); } /** * Get the converted matrix. * * @return the converted matrix. */ Array2DRowRealMatrix getConvertedMatrix() { return new Array2DRowRealMatrix(data, false); } } /** Serialize a {@link RealVector}. * <p> * This method is intended to be called from within a private * <code>writeObject</code> method (after a call to * <code>oos.defaultWriteObject()</code>) in a class that has a * {@link RealVector} field, which should be declared <code>transient</code>. * This way, the default handling does not serialize the vector (the {@link * RealVector} interface is not serializable by default) but this method does * serialize it specifically. * </p> * <p> * The following example shows how a simple class with a name and a real vector * should be written: * <pre><code> * public class NamedVector implements Serializable { * * private final String name; * private final transient RealVector coefficients; * * // omitted constructors, getters ... * * private void writeObject(ObjectOutputStream oos) throws IOException { * oos.defaultWriteObject(); // takes care of name field * MatrixUtils.serializeRealVector(coefficients, oos); * } * * private void readObject(ObjectInputStream ois) throws ClassNotFoundException, IOException { * ois.defaultReadObject(); // takes care of name field * MatrixUtils.deserializeRealVector(this, "coefficients", ois); * } * * } * </code></pre> * </p> * * @param vector real vector to serialize * @param oos stream where the real vector should be written * @exception IOException if object cannot be written to stream * @see #deserializeRealVector(Object, String, ObjectInputStream) */ public static void serializeRealVector(final RealVector vector, final ObjectOutputStream oos) throws IOException { final int n = vector.getDimension(); oos.writeInt(n); for (int i = 0; i < n; ++i) { oos.writeDouble(vector.getEntry(i)); } } /** Deserialize a {@link RealVector} field in a class. * <p> * This method is intended to be called from within a private * <code>readObject</code> method (after a call to * <code>ois.defaultReadObject()</code>) in a class that has a * {@link RealVector} field, which should be declared <code>transient</code>. * This way, the default handling does not deserialize the vector (the {@link * RealVector} interface is not serializable by default) but this method does * deserialize it specifically. * </p> * @param instance instance in which the field must be set up * @param fieldName name of the field within the class (may be private and final) * @param ois stream from which the real vector should be read * @exception ClassNotFoundException if a class in the stream cannot be found * @exception IOException if object cannot be read from the stream * @see #serializeRealVector(RealVector, ObjectOutputStream) */ public static void deserializeRealVector(final Object instance, final String fieldName, final ObjectInputStream ois) throws ClassNotFoundException, IOException { try { // read the vector data final int n = ois.readInt(); final double[] data = new double[n]; for (int i = 0; i < n; ++i) { data[i] = ois.readDouble(); } // create the instance final RealVector vector = new ArrayRealVector(data, false); // set up the field final java.lang.reflect.Field f = instance.getClass().getDeclaredField(fieldName); f.setAccessible(true); f.set(instance, vector); } catch (NoSuchFieldException nsfe) { IOException ioe = new IOException(); ioe.initCause(nsfe); throw ioe; } catch (IllegalAccessException iae) { IOException ioe = new IOException(); ioe.initCause(iae); throw ioe; } } /** Serialize a {@link RealMatrix}. * <p> * This method is intended to be called from within a private * <code>writeObject</code> method (after a call to * <code>oos.defaultWriteObject()</code>) in a class that has a * {@link RealMatrix} field, which should be declared <code>transient</code>. * This way, the default handling does not serialize the matrix (the {@link * RealMatrix} interface is not serializable by default) but this method does * serialize it specifically. * </p> * <p> * The following example shows how a simple class with a name and a real matrix * should be written: * <pre><code> * public class NamedMatrix implements Serializable { * * private final String name; * private final transient RealMatrix coefficients; * * // omitted constructors, getters ... * * private void writeObject(ObjectOutputStream oos) throws IOException { * oos.defaultWriteObject(); // takes care of name field * MatrixUtils.serializeRealMatrix(coefficients, oos); * } * * private void readObject(ObjectInputStream ois) throws ClassNotFoundException, IOException { * ois.defaultReadObject(); // takes care of name field * MatrixUtils.deserializeRealMatrix(this, "coefficients", ois); * } * * } * </code></pre> * </p> * * @param matrix real matrix to serialize * @param oos stream where the real matrix should be written * @exception IOException if object cannot be written to stream * @see #deserializeRealMatrix(Object, String, ObjectInputStream) */ public static void serializeRealMatrix(final RealMatrix matrix, final ObjectOutputStream oos) throws IOException { final int n = matrix.getRowDimension(); final int m = matrix.getColumnDimension(); oos.writeInt(n); oos.writeInt(m); for (int i = 0; i < n; ++i) { for (int j = 0; j < m; ++j) { oos.writeDouble(matrix.getEntry(i, j)); } } } /** Deserialize a {@link RealMatrix} field in a class. * <p> * This method is intended to be called from within a private * <code>readObject</code> method (after a call to * <code>ois.defaultReadObject()</code>) in a class that has a * {@link RealMatrix} field, which should be declared <code>transient</code>. * This way, the default handling does not deserialize the matrix (the {@link * RealMatrix} interface is not serializable by default) but this method does * deserialize it specifically. * </p> * @param instance instance in which the field must be set up * @param fieldName name of the field within the class (may be private and final) * @param ois stream from which the real matrix should be read * @exception ClassNotFoundException if a class in the stream cannot be found * @exception IOException if object cannot be read from the stream * @see #serializeRealMatrix(RealMatrix, ObjectOutputStream) */ public static void deserializeRealMatrix(final Object instance, final String fieldName, final ObjectInputStream ois) throws ClassNotFoundException, IOException { try { // read the matrix data final int n = ois.readInt(); final int m = ois.readInt(); final double[][] data = new double[n][m]; for (int i = 0; i < n; ++i) { final double[] dataI = data[i]; for (int j = 0; j < m; ++j) { dataI[j] = ois.readDouble(); } } // create the instance final RealMatrix matrix = new Array2DRowRealMatrix(data, false); // set up the field final java.lang.reflect.Field f = instance.getClass().getDeclaredField(fieldName); f.setAccessible(true); f.set(instance, matrix); } catch (NoSuchFieldException nsfe) { IOException ioe = new IOException(); ioe.initCause(nsfe); throw ioe; } catch (IllegalAccessException iae) { IOException ioe = new IOException(); ioe.initCause(iae); throw ioe; } } }