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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.Serializable;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathUtils;
import org.apache.commons.math3.util.Precision;
/**
* Implementation of a diagonal matrix.
*
* @since 3.1.1
*/
public class DiagonalMatrix extends AbstractRealMatrix
implements Serializable {
/** Serializable version identifier. */
private static final long serialVersionUID = 20121229L;
/** Entries of the diagonal. */
private final double[] data;
/**
* Creates a matrix with the supplied dimension.
*
* @param dimension Number of rows and columns in the new matrix.
* @throws NotStrictlyPositiveException if the dimension is
* not positive.
*/
public DiagonalMatrix(final int dimension)
throws NotStrictlyPositiveException {
super(dimension, dimension);
data = new double[dimension];
}
/**
* Creates a matrix using the input array as the underlying data.
*
* The input array is copied, not referenced.
*
* @param d Data for the new matrix.
*/
public DiagonalMatrix(final double[] d) {
this(d, true);
}
/**
* Creates a matrix using the input array as the underlying data.
*
* If an array is created specially in order to be embedded in a
* this instance and not used directly, the {@code copyArray} may be
* set to {@code false}.
* This will prevent the copying and improve performance as no new
* array will be built and no data will be copied.
*
* @param d Data for new matrix.
* @param copyArray if {@code true}, the input array will be copied,
* otherwise it will be referenced.
* @exception NullArgumentException if d is null
*/
public DiagonalMatrix(final double[] d, final boolean copyArray)
throws NullArgumentException {
MathUtils.checkNotNull(d);
data = copyArray ? d.clone() : d;
}
/**
* {@inheritDoc}
*
* @throws DimensionMismatchException if the requested dimensions are not equal.
*/
@Override
public RealMatrix createMatrix(final int rowDimension,
final int columnDimension)
throws NotStrictlyPositiveException,
DimensionMismatchException {
if (rowDimension != columnDimension) {
throw new DimensionMismatchException(rowDimension, columnDimension);
}
return new DiagonalMatrix(rowDimension);
}
/** {@inheritDoc} */
@Override
public RealMatrix copy() {
return new DiagonalMatrix(data);
}
/**
* Compute the sum of {@code this} and {@code m}.
*
* @param m Matrix to be added.
* @return {@code this + m}.
* @throws MatrixDimensionMismatchException if {@code m} is not the same
* size as {@code this}.
*/
public DiagonalMatrix add(final DiagonalMatrix m)
throws MatrixDimensionMismatchException {
// Safety check.
MatrixUtils.checkAdditionCompatible(this, m);
final int dim = getRowDimension();
final double[] outData = new double[dim];
for (int i = 0; i < dim; i++) {
outData[i] = data[i] + m.data[i];
}
return new DiagonalMatrix(outData, false);
}
/**
* Returns {@code this} minus {@code m}.
*
* @param m Matrix to be subtracted.
* @return {@code this - m}
* @throws MatrixDimensionMismatchException if {@code m} is not the same
* size as {@code this}.
*/
public DiagonalMatrix subtract(final DiagonalMatrix m)
throws MatrixDimensionMismatchException {
MatrixUtils.checkSubtractionCompatible(this, m);
final int dim = getRowDimension();
final double[] outData = new double[dim];
for (int i = 0; i < dim; i++) {
outData[i] = data[i] - m.data[i];
}
return new DiagonalMatrix(outData, false);
}
/**
* Returns the result of postmultiplying {@code this} by {@code m}.
*
* @param m matrix to postmultiply by
* @return {@code this * m}
* @throws DimensionMismatchException if
* {@code columnDimension(this) != rowDimension(m)}
*/
public DiagonalMatrix multiply(final DiagonalMatrix m)
throws DimensionMismatchException {
MatrixUtils.checkMultiplicationCompatible(this, m);
final int dim = getRowDimension();
final double[] outData = new double[dim];
for (int i = 0; i < dim; i++) {
outData[i] = data[i] * m.data[i];
}
return new DiagonalMatrix(outData, false);
}
/**
* Returns the result of postmultiplying {@code this} by {@code m}.
*
* @param m matrix to postmultiply by
* @return {@code this * m}
* @throws DimensionMismatchException if
* {@code columnDimension(this) != rowDimension(m)}
*/
@Override
public RealMatrix multiply(final RealMatrix m)
throws DimensionMismatchException {
if (m instanceof DiagonalMatrix) {
return multiply((DiagonalMatrix) m);
} else {
MatrixUtils.checkMultiplicationCompatible(this, m);
final int nRows = m.getRowDimension();
final int nCols = m.getColumnDimension();
final double[][] product = new double[nRows][nCols];
for (int r = 0; r < nRows; r++) {
for (int c = 0; c < nCols; c++) {
product[r][c] = data[r] * m.getEntry(r, c);
}
}
return new Array2DRowRealMatrix(product, false);
}
}
/** {@inheritDoc} */
@Override
public double[][] getData() {
final int dim = getRowDimension();
final double[][] out = new double[dim][dim];
for (int i = 0; i < dim; i++) {
out[i][i] = data[i];
}
return out;
}
/**
* Gets a reference to the underlying data array.
*
* @return 1-dimensional array of entries.
*/
public double[] getDataRef() {
return data;
}
/** {@inheritDoc} */
@Override
public double getEntry(final int row, final int column)
throws OutOfRangeException {
MatrixUtils.checkMatrixIndex(this, row, column);
return row == column ? data[row] : 0;
}
/** {@inheritDoc}
* @throws NumberIsTooLargeException if {@code row != column} and value is non-zero.
*/
@Override
public void setEntry(final int row, final int column, final double value)
throws OutOfRangeException, NumberIsTooLargeException {
if (row == column) {
MatrixUtils.checkRowIndex(this, row);
data[row] = value;
} else {
ensureZero(value);
}
}
/** {@inheritDoc}
* @throws NumberIsTooLargeException if {@code row != column} and increment is non-zero.
*/
@Override
public void addToEntry(final int row,
final int column,
final double increment)
throws OutOfRangeException, NumberIsTooLargeException {
if (row == column) {
MatrixUtils.checkRowIndex(this, row);
data[row] += increment;
} else {
ensureZero(increment);
}
}
/** {@inheritDoc} */
@Override
public void multiplyEntry(final int row,
final int column,
final double factor)
throws OutOfRangeException {
// we don't care about non-diagonal elements for multiplication
if (row == column) {
MatrixUtils.checkRowIndex(this, row);
data[row] *= factor;
}
}
/** {@inheritDoc} */
@Override
public int getRowDimension() {
return data.length;
}
/** {@inheritDoc} */
@Override
public int getColumnDimension() {
return data.length;
}
/** {@inheritDoc} */
@Override
public double[] operate(final double[] v)
throws DimensionMismatchException {
return multiply(new DiagonalMatrix(v, false)).getDataRef();
}
/** {@inheritDoc} */
@Override
public double[] preMultiply(final double[] v)
throws DimensionMismatchException {
return operate(v);
}
/** {@inheritDoc} */
@Override
public RealVector preMultiply(final RealVector v) throws DimensionMismatchException {
final double[] vectorData;
if (v instanceof ArrayRealVector) {
vectorData = ((ArrayRealVector) v).getDataRef();
} else {
vectorData = v.toArray();
}
return MatrixUtils.createRealVector(preMultiply(vectorData));
}
/** Ensure a value is zero.
* @param value value to check
* @exception NumberIsTooLargeException if value is not zero
*/
private void ensureZero(final double value) throws NumberIsTooLargeException {
if (!Precision.equals(0.0, value, 1)) {
throw new NumberIsTooLargeException(FastMath.abs(value), 0, true);
}
}
/**
* Computes the inverse of this diagonal matrix.
*
* Note: this method will use a singularity threshold of 0,
* use {@link #inverse(double)} if a different threshold is needed.
*
* @return the inverse of {@code m}
* @throws SingularMatrixException if the matrix is singular
* @since 3.3
*/
public DiagonalMatrix inverse() throws SingularMatrixException {
return inverse(0);
}
/**
* Computes the inverse of this diagonal matrix.
*
* @param threshold Singularity threshold.
* @return the inverse of {@code m}
* @throws SingularMatrixException if the matrix is singular
* @since 3.3
*/
public DiagonalMatrix inverse(double threshold) throws SingularMatrixException {
if (isSingular(threshold)) {
throw new SingularMatrixException();
}
final double[] result = new double[data.length];
for (int i = 0; i < data.length; i++) {
result[i] = 1.0 / data[i];
}
return new DiagonalMatrix(result, false);
}
/** Returns whether this diagonal matrix is singular, i.e. any diagonal entry
* is equal to {@code 0} within the given threshold.
*
* @param threshold Singularity threshold.
* @return {@code true} if the matrix is singular, {@code false} otherwise
* @since 3.3
*/
public boolean isSingular(double threshold) {
for (int i = 0; i < data.length; i++) {
if (Precision.equals(data[i], 0.0, threshold)) {
return true;
}
}
return false;
}
}