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With inspiration from other libraries
/*
* 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 java.io.IOException;
import java.io.ObjectInputStream;
import java.io.ObjectOutputStream;
import java.util.Arrays;
import org.apache.commons.math3.Field;
import org.apache.commons.math3.FieldElement;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.ZeroException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.fraction.BigFraction;
import org.apache.commons.math3.fraction.Fraction;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathArrays;
import org.apache.commons.math3.util.MathUtils;
import org.apache.commons.math3.util.Precision;
/**
* A collection of static methods that operate on or return matrices.
*
*/
public class MatrixUtils {
/**
* The default format for {@link RealMatrix} objects.
* @since 3.1
*/
public static final RealMatrixFormat DEFAULT_FORMAT = RealMatrixFormat.getInstance();
/**
* A format for {@link RealMatrix} objects compatible with octave.
* @since 3.1
*/
public static final RealMatrixFormat OCTAVE_FORMAT = new RealMatrixFormat("[", "]", "", "", "; ", ", ");
/**
* Private constructor.
*/
private MatrixUtils() {
super();
}
/**
* Returns a {@link RealMatrix} with specified dimensions.
* The type of matrix returned depends on the dimension. Below
* 212 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.
* The matrix elements are all set to 0.0.
* @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.
* The type of matrix returned depends on the dimension. Below
* 212 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.
* The matrix elements are all set to field.getZero().
* @param 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 > FieldMatrix createFieldMatrix(final Field field,
final int rows,
final int columns) {
return (rows * columns <= 4096) ?
new Array2DRowFieldMatrix(field, rows, columns) : new BlockFieldMatrix(field, rows, columns);
}
/**
* Returns a {@link RealMatrix} whose entries are the the values in the
* the input array.
* The type of matrix returned depends on the dimension. Below
* 212 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.
* The input array is copied, not referenced.
*
* @param data input array
* @return RealMatrix containing the values of the array
* @throws org.apache.commons.math3.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}.
* @throws DimensionMismatchException if {@code data} is not rectangular.
* @see #createRealMatrix(int, int)
*/
public static RealMatrix createRealMatrix(double[][] data)
throws NullArgumentException, DimensionMismatchException,
NoDataException {
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.
* The type of matrix returned depends on the dimension. Below
* 212 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.
* The input array is copied, not referenced.
* @param the type of the field elements
* @param data input array
* @return a matrix containing the values of the array.
* @throws org.apache.commons.math3.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 > FieldMatrix createFieldMatrix(T[][] data)
throws DimensionMismatchException, NoDataException, NullArgumentException {
if (data == null ||
data[0] == null) {
throw new NullArgumentException();
}
return (data.length * data[0].length <= 4096) ?
new Array2DRowFieldMatrix(data) : new BlockFieldMatrix(data);
}
/**
* Returns dimension x dimension 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 dimension x dimension identity matrix.
*
* @param 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 > FieldMatrix
createFieldIdentityMatrix(final Field field, final int dimension) {
final T zero = field.getZero();
final T one = field.getOne();
final T[][] d = MathArrays.buildArray(field, dimension, dimension);
for (int row = 0; row < dimension; row++) {
final T[] dRow = d[row];
Arrays.fill(dRow, zero);
dRow[row] = one;
}
return new Array2DRowFieldMatrix(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 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 > FieldMatrix
createFieldDiagonalMatrix(final T[] diagonal) {
final FieldMatrix 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)
throws NoDataException, NullArgumentException {
if (data == null) {
throw new NullArgumentException();
}
return new ArrayRealVector(data, true);
}
/**
* Creates a {@link FieldVector} using the data from the input array.
*
* @param 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 > FieldVector createFieldVector(final T[] data)
throws NoDataException, NullArgumentException, ZeroException {
if (data == null) {
throw new NullArgumentException();
}
if (data.length == 0) {
throw new ZeroException(LocalizedFormats.VECTOR_MUST_HAVE_AT_LEAST_ONE_ELEMENT);
}
return new ArrayFieldVector(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)
throws NoDataException, NullArgumentException {
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 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 > FieldMatrix
createRowFieldMatrix(final T[] rowData)
throws NoDataException, NullArgumentException {
if (rowData == null) {
throw new NullArgumentException();
}
final int nCols = rowData.length;
if (nCols == 0) {
throw new NoDataException(LocalizedFormats.AT_LEAST_ONE_COLUMN);
}
final FieldMatrix 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)
throws NoDataException, NullArgumentException {
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 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 > FieldMatrix
createColumnFieldMatrix(final T[] columnData)
throws NoDataException, NullArgumentException {
if (columnData == null) {
throw new NullArgumentException();
}
final int nRows = columnData.length;
if (nRows == 0) {
throw new NoDataException(LocalizedFormats.AT_LEAST_ONE_ROW);
}
final FieldMatrix m = createFieldMatrix(columnData[0].getField(), nRows, 1);
for (int i = 0; i < nRows; ++i) {
m.setEntry(i, 0, columnData[i]);
}
return m;
}
/**
* Checks whether a matrix is symmetric, within a given relative tolerance.
*
* @param matrix Matrix to check.
* @param relativeTolerance Tolerance of the symmetry check.
* @param raiseException If {@code true}, an exception will be raised if
* the matrix is not symmetric.
* @return {@code true} if {@code matrix} is symmetric.
* @throws NonSquareMatrixException if the matrix is not square.
* @throws NonSymmetricMatrixException if the matrix is not symmetric.
*/
private static boolean isSymmetricInternal(RealMatrix matrix,
double relativeTolerance,
boolean raiseException) {
final int rows = matrix.getRowDimension();
if (rows != matrix.getColumnDimension()) {
if (raiseException) {
throw new NonSquareMatrixException(rows, matrix.getColumnDimension());
} else {
return false;
}
}
for (int i = 0; i < rows; i++) {
for (int j = i + 1; j < rows; j++) {
final double mij = matrix.getEntry(i, j);
final double mji = matrix.getEntry(j, i);
if (FastMath.abs(mij - mji) >
FastMath.max(FastMath.abs(mij), FastMath.abs(mji)) * relativeTolerance) {
if (raiseException) {
throw new NonSymmetricMatrixException(i, j, relativeTolerance);
} else {
return false;
}
}
}
}
return true;
}
/**
* Checks whether a matrix is symmetric.
*
* @param matrix Matrix to check.
* @param eps Relative tolerance.
* @throws NonSquareMatrixException if the matrix is not square.
* @throws NonSymmetricMatrixException if the matrix is not symmetric.
* @since 3.1
*/
public static void checkSymmetric(RealMatrix matrix,
double eps) {
isSymmetricInternal(matrix, eps, true);
}
/**
* Checks whether a matrix is symmetric.
*
* @param matrix Matrix to check.
* @param eps Relative tolerance.
* @return {@code true} if {@code matrix} is symmetric.
* @since 3.1
*/
public static boolean isSymmetric(RealMatrix matrix,
double eps) {
return isSymmetricInternal(matrix, eps, false);
}
/**
* 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)
throws OutOfRangeException {
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)
throws OutOfRangeException {
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)
throws OutOfRangeException {
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)
throws NumberIsTooSmallException, OutOfRangeException {
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)
throws NoDataException, NullArgumentException, OutOfRangeException {
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)
throws MatrixDimensionMismatchException {
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)
throws MatrixDimensionMismatchException {
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)
throws DimensionMismatchException {
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 m) {
final FractionMatrixConverter converter = new FractionMatrixConverter();
m.walkInOptimizedOrder(converter);
return converter.getConvertedMatrix();
}
/** Converter for {@link FieldMatrix}/{@link Fraction}. */
private static class FractionMatrixConverter extends DefaultFieldMatrixPreservingVisitor {
/** Converted array. */
private double[][] data;
/** Simple constructor. */
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 m) {
final BigFractionMatrixConverter converter = new BigFractionMatrixConverter();
m.walkInOptimizedOrder(converter);
return converter.getConvertedMatrix();
}
/** Converter for {@link FieldMatrix}/{@link BigFraction}. */
private static class BigFractionMatrixConverter extends DefaultFieldMatrixPreservingVisitor {
/** Converted array. */
private double[][] data;
/** Simple constructor. */
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}.
*
* This method is intended to be called from within a private
* writeObject method (after a call to
* oos.defaultWriteObject()) in a class that has a
* {@link RealVector} field, which should be declared transient.
* 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.
*
*
* The following example shows how a simple class with a name and a real vector
* should be written:
*
* 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);
* }
*
* }
*
*
*
* @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.
*
* This method is intended to be called from within a private
* readObject method (after a call to
* ois.defaultReadObject()) in a class that has a
* {@link RealVector} field, which should be declared transient.
* 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.
*
* @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}.
*
* This method is intended to be called from within a private
* writeObject method (after a call to
* oos.defaultWriteObject()) in a class that has a
* {@link RealMatrix} field, which should be declared transient.
* 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.
*
*
* The following example shows how a simple class with a name and a real matrix
* should be written:
*
* 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);
* }
*
* }
*
*
*
* @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.
*
* This method is intended to be called from within a private
* readObject method (after a call to
* ois.defaultReadObject()) in a class that has a
* {@link RealMatrix} field, which should be declared transient.
* 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.
*
* @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;
}
}
/**Solve a system of composed of a Lower Triangular Matrix
* {@link RealMatrix}.
*
* This method is called to solve systems of equations which are
* of the lower triangular form. The matrix {@link RealMatrix}
* is assumed, though not checked, to be in lower triangular form.
* The vector {@link RealVector} is overwritten with the solution.
* The matrix is checked that it is square and its dimensions match
* the length of the vector.
*
* @param rm RealMatrix which is lower triangular
* @param b RealVector this is overwritten
* @throws DimensionMismatchException if the matrix and vector are not
* conformable
* @throws NonSquareMatrixException if the matrix {@code rm} is not square
* @throws MathArithmeticException if the absolute value of one of the diagonal
* coefficient of {@code rm} is lower than {@link Precision#SAFE_MIN}
*/
public static void solveLowerTriangularSystem(RealMatrix rm, RealVector b)
throws DimensionMismatchException, MathArithmeticException,
NonSquareMatrixException {
if ((rm == null) || (b == null) || ( rm.getRowDimension() != b.getDimension())) {
throw new DimensionMismatchException(
(rm == null) ? 0 : rm.getRowDimension(),
(b == null) ? 0 : b.getDimension());
}
if( rm.getColumnDimension() != rm.getRowDimension() ){
throw new NonSquareMatrixException(rm.getRowDimension(),
rm.getColumnDimension());
}
int rows = rm.getRowDimension();
for( int i = 0 ; i < rows ; i++ ){
double diag = rm.getEntry(i, i);
if( FastMath.abs(diag) < Precision.SAFE_MIN ){
throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR);
}
double bi = b.getEntry(i)/diag;
b.setEntry(i, bi );
for( int j = i+1; j< rows; j++ ){
b.setEntry(j, b.getEntry(j)-bi*rm.getEntry(j,i) );
}
}
}
/** Solver a system composed of an Upper Triangular Matrix
* {@link RealMatrix}.
*
* This method is called to solve systems of equations which are
* of the lower triangular form. The matrix {@link RealMatrix}
* is assumed, though not checked, to be in upper triangular form.
* The vector {@link RealVector} is overwritten with the solution.
* The matrix is checked that it is square and its dimensions match
* the length of the vector.
*
* @param rm RealMatrix which is upper triangular
* @param b RealVector this is overwritten
* @throws DimensionMismatchException if the matrix and vector are not
* conformable
* @throws NonSquareMatrixException if the matrix {@code rm} is not
* square
* @throws MathArithmeticException if the absolute value of one of the diagonal
* coefficient of {@code rm} is lower than {@link Precision#SAFE_MIN}
*/
public static void solveUpperTriangularSystem(RealMatrix rm, RealVector b)
throws DimensionMismatchException, MathArithmeticException,
NonSquareMatrixException {
if ((rm == null) || (b == null) || ( rm.getRowDimension() != b.getDimension())) {
throw new DimensionMismatchException(
(rm == null) ? 0 : rm.getRowDimension(),
(b == null) ? 0 : b.getDimension());
}
if( rm.getColumnDimension() != rm.getRowDimension() ){
throw new NonSquareMatrixException(rm.getRowDimension(),
rm.getColumnDimension());
}
int rows = rm.getRowDimension();
for( int i = rows-1 ; i >-1 ; i-- ){
double diag = rm.getEntry(i, i);
if( FastMath.abs(diag) < Precision.SAFE_MIN ){
throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR);
}
double bi = b.getEntry(i)/diag;
b.setEntry(i, bi );
for( int j = i-1; j>-1; j-- ){
b.setEntry(j, b.getEntry(j)-bi*rm.getEntry(j,i) );
}
}
}
/**
* Computes the inverse of the given matrix by splitting it into
* 4 sub-matrices.
*
* @param m Matrix whose inverse must be computed.
* @param splitIndex Index that determines the "split" line and
* column.
* The element corresponding to this index will part of the
* upper-left sub-matrix.
* @return the inverse of {@code m}.
* @throws NonSquareMatrixException if {@code m} is not square.
*/
public static RealMatrix blockInverse(RealMatrix m,
int splitIndex) {
final int n = m.getRowDimension();
if (m.getColumnDimension() != n) {
throw new NonSquareMatrixException(m.getRowDimension(),
m.getColumnDimension());
}
final int splitIndex1 = splitIndex + 1;
final RealMatrix a = m.getSubMatrix(0, splitIndex, 0, splitIndex);
final RealMatrix b = m.getSubMatrix(0, splitIndex, splitIndex1, n - 1);
final RealMatrix c = m.getSubMatrix(splitIndex1, n - 1, 0, splitIndex);
final RealMatrix d = m.getSubMatrix(splitIndex1, n - 1, splitIndex1, n - 1);
final SingularValueDecomposition aDec = new SingularValueDecomposition(a);
final DecompositionSolver aSolver = aDec.getSolver();
if (!aSolver.isNonSingular()) {
throw new SingularMatrixException();
}
final RealMatrix aInv = aSolver.getInverse();
final SingularValueDecomposition dDec = new SingularValueDecomposition(d);
final DecompositionSolver dSolver = dDec.getSolver();
if (!dSolver.isNonSingular()) {
throw new SingularMatrixException();
}
final RealMatrix dInv = dSolver.getInverse();
final RealMatrix tmp1 = a.subtract(b.multiply(dInv).multiply(c));
final SingularValueDecomposition tmp1Dec = new SingularValueDecomposition(tmp1);
final DecompositionSolver tmp1Solver = tmp1Dec.getSolver();
if (!tmp1Solver.isNonSingular()) {
throw new SingularMatrixException();
}
final RealMatrix result00 = tmp1Solver.getInverse();
final RealMatrix tmp2 = d.subtract(c.multiply(aInv).multiply(b));
final SingularValueDecomposition tmp2Dec = new SingularValueDecomposition(tmp2);
final DecompositionSolver tmp2Solver = tmp2Dec.getSolver();
if (!tmp2Solver.isNonSingular()) {
throw new SingularMatrixException();
}
final RealMatrix result11 = tmp2Solver.getInverse();
final RealMatrix result01 = aInv.multiply(b).multiply(result11).scalarMultiply(-1);
final RealMatrix result10 = dInv.multiply(c).multiply(result00).scalarMultiply(-1);
final RealMatrix result = new Array2DRowRealMatrix(n, n);
result.setSubMatrix(result00.getData(), 0, 0);
result.setSubMatrix(result01.getData(), 0, splitIndex1);
result.setSubMatrix(result10.getData(), splitIndex1, 0);
result.setSubMatrix(result11.getData(), splitIndex1, splitIndex1);
return result;
}
/**
* Computes the inverse of the given matrix.
*
* By default, the inverse of the matrix is computed using the QR-decomposition,
* unless a more efficient method can be determined for the input matrix.
*
* Note: this method will use a singularity threshold of 0,
* use {@link #inverse(RealMatrix, double)} if a different threshold is needed.
*
* @param matrix Matrix whose inverse shall be computed
* @return the inverse of {@code matrix}
* @throws NullArgumentException if {@code matrix} is {@code null}
* @throws SingularMatrixException if m is singular
* @throws NonSquareMatrixException if matrix is not square
* @since 3.3
*/
public static RealMatrix inverse(RealMatrix matrix)
throws NullArgumentException, SingularMatrixException, NonSquareMatrixException {
return inverse(matrix, 0);
}
/**
* Computes the inverse of the given matrix.
*
* By default, the inverse of the matrix is computed using the QR-decomposition,
* unless a more efficient method can be determined for the input matrix.
*
* @param matrix Matrix whose inverse shall be computed
* @param threshold Singularity threshold
* @return the inverse of {@code m}
* @throws NullArgumentException if {@code matrix} is {@code null}
* @throws SingularMatrixException if matrix is singular
* @throws NonSquareMatrixException if matrix is not square
* @since 3.3
*/
public static RealMatrix inverse(RealMatrix matrix, double threshold)
throws NullArgumentException, SingularMatrixException, NonSquareMatrixException {
MathUtils.checkNotNull(matrix);
if (!matrix.isSquare()) {
throw new NonSquareMatrixException(matrix.getRowDimension(),
matrix.getColumnDimension());
}
if (matrix instanceof DiagonalMatrix) {
return ((DiagonalMatrix) matrix).inverse(threshold);
} else {
QRDecomposition decomposition = new QRDecomposition(matrix, threshold);
return decomposition.getSolver().getInverse();
}
}
}