/*
* 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.Serializable;
import java.math.BigDecimal;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.exception.util.LocalizedFormats;
/**
* Implementation of {@link BigMatrix} using a BigDecimal[][] array to store entries
* and <a href="http://www.math.gatech.edu/~bourbaki/math2601/Web-notes/2num.pdf">
* LU decompostion</a> to support linear system
* solution and inverse.
* <p>
* The LU decompostion is performed as needed, to support the following operations: <ul>
* <li>solve</li>
* <li>isSingular</li>
* <li>getDeterminant</li>
* <li>inverse</li> </ul></p>
* <p>
* <strong>Usage notes</strong>:<br>
* <ul><li>
* The LU decomposition is stored and reused on subsequent calls. If matrix
* data are modified using any of the public setXxx methods, the saved
* decomposition is discarded. If data are modified via references to the
* underlying array obtained using <code>getDataRef()</code>, then the stored
* LU decomposition will not be discarded. In this case, you need to
* explicitly invoke <code>LUDecompose()</code> to recompute the decomposition
* before using any of the methods above.</li>
* <li>
* As specified in the {@link BigMatrix} interface, matrix element indexing
* is 0-based -- e.g., <code>getEntry(0, 0)</code>
* returns the element in the first row, first column of the matrix.</li></ul></p>
*
* @deprecated as of 2.0, replaced by {@link Array2DRowFieldMatrix} with a {@link
* org.apache.commons.math.util.BigReal} parameter
* @version $Revision: 1042376 $ $Date: 2010-12-05 16:54:55 +0100 (dim. 05 déc. 2010) $
*/
@Deprecated
public class BigMatrixImpl implements BigMatrix, Serializable {
/** BigDecimal 0 */
static final BigDecimal ZERO = new BigDecimal(0);
/** BigDecimal 1 */
static final BigDecimal ONE = new BigDecimal(1);
/** Bound to determine effective singularity in LU decomposition */
private static final BigDecimal TOO_SMALL = new BigDecimal(10E-12);
/** Serialization id */
private static final long serialVersionUID = -1011428905656140431L;
/** Entries of the matrix */
protected BigDecimal data[][] = null;
/** Entries of cached LU decomposition.
* All updates to data (other than luDecompose()) *must* set this to null
*/
protected BigDecimal lu[][] = null;
/** Permutation associated with LU decomposition */
protected int[] permutation = null;
/** Parity of the permutation associated with the LU decomposition */
protected int parity = 1;
/** Rounding mode for divisions **/
private int roundingMode = BigDecimal.ROUND_HALF_UP;
/*** BigDecimal scale ***/
private int scale = 64;
/**
* Creates a matrix with no data
*/
public BigMatrixImpl() {
}
/**
* Create a new BigMatrix with the supplied row and column dimensions.
*
* @param rowDimension the number of rows in the new matrix
* @param columnDimension the number of columns in the new matrix
* @throws IllegalArgumentException if row or column dimension is not
* positive
*/
public BigMatrixImpl(int rowDimension, int columnDimension) {
if (rowDimension < 1 ) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.INSUFFICIENT_DIMENSION, rowDimension, 1);
}
if (columnDimension < 1) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.INSUFFICIENT_DIMENSION, columnDimension, 1);
}
data = new BigDecimal[rowDimension][columnDimension];
lu = null;
}
/**
* Create a new BigMatrix using <code>d</code> as the underlying
* data array.
* <p>The input array is copied, not referenced. This constructor has
* the same effect as calling {@link #BigMatrixImpl(BigDecimal[][], boolean)}
* with the second argument set to <code>true</code>.</p>
*
* @param d data for new matrix
* @throws IllegalArgumentException if <code>d</code> is not rectangular
* (not all rows have the same length) or empty
* @throws NullPointerException if <code>d</code> is null
*/
public BigMatrixImpl(BigDecimal[][] d) {
this.copyIn(d);
lu = null;
}
/**
* Create a new BigMatrix using the input array as the underlying
* data array.
* <p>If an array is built specially in order to be embedded in a
* BigMatrix and not used directly, the <code>copyArray</code> may be
* set to <code>false</code. This will prevent the copying and improve
* performance as no new array will be built and no data will be copied.</p>
* @param d data for new matrix
* @param copyArray if true, the input array will be copied, otherwise
* it will be referenced
* @throws IllegalArgumentException if <code>d</code> is not rectangular
* (not all rows have the same length) or empty
* @throws NullPointerException if <code>d</code> is null
* @see #BigMatrixImpl(BigDecimal[][])
*/
public BigMatrixImpl(BigDecimal[][] d, boolean copyArray) {
if (copyArray) {
copyIn(d);
} else {
if (d == null) {
throw new NullPointerException();
}
final int nRows = d.length;
if (nRows == 0) {
throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_ROW);
}
final int nCols = d[0].length;
if (nCols == 0) {
throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_COLUMN);
}
for (int r = 1; r < nRows; r++) {
if (d[r].length != nCols) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.DIFFERENT_ROWS_LENGTHS,
nCols, d[r].length);
}
}
data = d;
}
lu = null;
}
/**
* Create a new BigMatrix using <code>d</code> as the underlying
* data array.
* <p>Since the underlying array will hold <code>BigDecimal</code>
* instances, it will be created.</p>
*
* @param d data for new matrix
* @throws IllegalArgumentException if <code>d</code> is not rectangular
* (not all rows have the same length) or empty
* @throws NullPointerException if <code>d</code> is null
*/
public BigMatrixImpl(double[][] d) {
final int nRows = d.length;
if (nRows == 0) {
throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_ROW);
}
final int nCols = d[0].length;
if (nCols == 0) {
throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_COLUMN);
}
for (int row = 1; row < nRows; row++) {
if (d[row].length != nCols) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.DIFFERENT_ROWS_LENGTHS,
nCols, d[row].length);
}
}
this.copyIn(d);
lu = null;
}
/**
* Create a new BigMatrix using the values represented by the strings in
* <code>d</code> as the underlying data array.
*
* @param d data for new matrix
* @throws IllegalArgumentException if <code>d</code> is not rectangular
* (not all rows have the same length) or empty
* @throws NullPointerException if <code>d</code> is null
*/
public BigMatrixImpl(String[][] d) {
final int nRows = d.length;
if (nRows == 0) {
throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_ROW);
}
final int nCols = d[0].length;
if (nCols == 0) {
throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_COLUMN);
}
for (int row = 1; row < nRows; row++) {
if (d[row].length != nCols) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.DIFFERENT_ROWS_LENGTHS,
nCols, d[row].length);
}
}
this.copyIn(d);
lu = null;
}
/**
* Create a new (column) BigMatrix using <code>v</code> as the
* data for the unique column of the <code>v.length x 1</code> matrix
* created.
* <p>
* The input array is copied, not referenced.</p>
*
* @param v column vector holding data for new matrix
*/
public BigMatrixImpl(BigDecimal[] v) {
final int nRows = v.length;
data = new BigDecimal[nRows][1];
for (int row = 0; row < nRows; row++) {
data[row][0] = v[row];
}
}
/**
* Create a new BigMatrix which is a copy of this.
*
* @return the cloned matrix
*/
public BigMatrix copy() {
return new BigMatrixImpl(this.copyOut(), false);
}
/**
* Compute the sum of this and <code>m</code>.
*
* @param m matrix to be added
* @return this + m
* @throws IllegalArgumentException if m is not the same size as this
*/
public BigMatrix add(BigMatrix m) throws IllegalArgumentException {
try {
return add((BigMatrixImpl) m);
} catch (ClassCastException cce) {
// safety check
MatrixUtils.checkAdditionCompatible(this, m);
final int rowCount = getRowDimension();
final int columnCount = getColumnDimension();
final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount];
for (int row = 0; row < rowCount; row++) {
final BigDecimal[] dataRow = data[row];
final BigDecimal[] outDataRow = outData[row];
for (int col = 0; col < columnCount; col++) {
outDataRow[col] = dataRow[col].add(m.getEntry(row, col));
}
}
return new BigMatrixImpl(outData, false);
}
}
/**
* Compute the sum of this and <code>m</code>.
*
* @param m matrix to be added
* @return this + m
* @throws IllegalArgumentException if m is not the same size as this
*/
public BigMatrixImpl add(BigMatrixImpl m) throws IllegalArgumentException {
// safety check
MatrixUtils.checkAdditionCompatible(this, m);
final int rowCount = getRowDimension();
final int columnCount = getColumnDimension();
final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount];
for (int row = 0; row < rowCount; row++) {
final BigDecimal[] dataRow = data[row];
final BigDecimal[] mRow = m.data[row];
final BigDecimal[] outDataRow = outData[row];
for (int col = 0; col < columnCount; col++) {
outDataRow[col] = dataRow[col].add(mRow[col]);
}
}
return new BigMatrixImpl(outData, false);
}
/**
* Compute this minus <code>m</code>.
*
* @param m matrix to be subtracted
* @return this + m
* @throws IllegalArgumentException if m is not the same size as this
*/
public BigMatrix subtract(BigMatrix m) throws IllegalArgumentException {
try {
return subtract((BigMatrixImpl) m);
} catch (ClassCastException cce) {
// safety check
MatrixUtils.checkSubtractionCompatible(this, m);
final int rowCount = getRowDimension();
final int columnCount = getColumnDimension();
final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount];
for (int row = 0; row < rowCount; row++) {
final BigDecimal[] dataRow = data[row];
final BigDecimal[] outDataRow = outData[row];
for (int col = 0; col < columnCount; col++) {
outDataRow[col] = dataRow[col].subtract(getEntry(row, col));
}
}
return new BigMatrixImpl(outData, false);
}
}
/**
* Compute this minus <code>m</code>.
*
* @param m matrix to be subtracted
* @return this + m
* @throws IllegalArgumentException if m is not the same size as this
*/
public BigMatrixImpl subtract(BigMatrixImpl m) throws IllegalArgumentException {
// safety check
MatrixUtils.checkSubtractionCompatible(this, m);
final int rowCount = getRowDimension();
final int columnCount = getColumnDimension();
final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount];
for (int row = 0; row < rowCount; row++) {
final BigDecimal[] dataRow = data[row];
final BigDecimal[] mRow = m.data[row];
final BigDecimal[] outDataRow = outData[row];
for (int col = 0; col < columnCount; col++) {
outDataRow[col] = dataRow[col].subtract(mRow[col]);
}
}
return new BigMatrixImpl(outData, false);
}
/**
* Returns the result of adding d to each entry of this.
*
* @param d value to be added to each entry
* @return d + this
*/
public BigMatrix scalarAdd(BigDecimal d) {
final int rowCount = getRowDimension();
final int columnCount = getColumnDimension();
final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount];
for (int row = 0; row < rowCount; row++) {
final BigDecimal[] dataRow = data[row];
final BigDecimal[] outDataRow = outData[row];
for (int col = 0; col < columnCount; col++) {
outDataRow[col] = dataRow[col].add(d);
}
}
return new BigMatrixImpl(outData, false);
}
/**
* Returns the result of multiplying each entry of this by <code>d</code>
* @param d value to multiply all entries by
* @return d * this
*/
public BigMatrix scalarMultiply(BigDecimal d) {
final int rowCount = getRowDimension();
final int columnCount = getColumnDimension();
final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount];
for (int row = 0; row < rowCount; row++) {
final BigDecimal[] dataRow = data[row];
final BigDecimal[] outDataRow = outData[row];
for (int col = 0; col < columnCount; col++) {
outDataRow[col] = dataRow[col].multiply(d);
}
}
return new BigMatrixImpl(outData, false);
}
/**
* Returns the result of postmultiplying this by <code>m</code>.
* @param m matrix to postmultiply by
* @return this*m
* @throws IllegalArgumentException
* if columnDimension(this) != rowDimension(m)
*/
public BigMatrix multiply(BigMatrix m) throws IllegalArgumentException {
try {
return multiply((BigMatrixImpl) m);
} catch (ClassCastException cce) {
// safety check
MatrixUtils.checkMultiplicationCompatible(this, m);
final int nRows = this.getRowDimension();
final int nCols = m.getColumnDimension();
final int nSum = this.getColumnDimension();
final BigDecimal[][] outData = new BigDecimal[nRows][nCols];
for (int row = 0; row < nRows; row++) {
final BigDecimal[] dataRow = data[row];
final BigDecimal[] outDataRow = outData[row];
for (int col = 0; col < nCols; col++) {
BigDecimal sum = ZERO;
for (int i = 0; i < nSum; i++) {
sum = sum.add(dataRow[i].multiply(m.getEntry(i, col)));
}
outDataRow[col] = sum;
}
}
return new BigMatrixImpl(outData, false);
}
}
/**
* Returns the result of postmultiplying this by <code>m</code>.
* @param m matrix to postmultiply by
* @return this*m
* @throws IllegalArgumentException
* if columnDimension(this) != rowDimension(m)
*/
public BigMatrixImpl multiply(BigMatrixImpl m) throws IllegalArgumentException {
// safety check
MatrixUtils.checkMultiplicationCompatible(this, m);
final int nRows = this.getRowDimension();
final int nCols = m.getColumnDimension();
final int nSum = this.getColumnDimension();
final BigDecimal[][] outData = new BigDecimal[nRows][nCols];
for (int row = 0; row < nRows; row++) {
final BigDecimal[] dataRow = data[row];
final BigDecimal[] outDataRow = outData[row];
for (int col = 0; col < nCols; col++) {
BigDecimal sum = ZERO;
for (int i = 0; i < nSum; i++) {
sum = sum.add(dataRow[i].multiply(m.data[i][col]));
}
outDataRow[col] = sum;
}
}
return new BigMatrixImpl(outData, false);
}
/**
* Returns the result premultiplying this by <code>m</code>.
* @param m matrix to premultiply by
* @return m * this
* @throws IllegalArgumentException
* if rowDimension(this) != columnDimension(m)
*/
public BigMatrix preMultiply(BigMatrix m) throws IllegalArgumentException {
return m.multiply(this);
}
/**
* Returns matrix entries as a two-dimensional array.
* <p>
* Makes a fresh copy of the underlying data.</p>
*
* @return 2-dimensional array of entries
*/
public BigDecimal[][] getData() {
return copyOut();
}
/**
* Returns matrix entries as a two-dimensional array.
* <p>
* Makes a fresh copy of the underlying data converted to
* <code>double</code> values.</p>
*
* @return 2-dimensional array of entries
*/
public double[][] getDataAsDoubleArray() {
final int nRows = getRowDimension();
final int nCols = getColumnDimension();
final double d[][] = new double[nRows][nCols];
for (int i = 0; i < nRows; i++) {
for (int j = 0; j < nCols; j++) {
d[i][j] = data[i][j].doubleValue();
}
}
return d;
}
/**
* Returns a reference to the underlying data array.
* <p>
* Does not make a fresh copy of the underlying data.</p>
*
* @return 2-dimensional array of entries
*/
public BigDecimal[][] getDataRef() {
return data;
}
/***
* Gets the rounding mode for division operations
* The default is {@link java.math.BigDecimal#ROUND_HALF_UP}
* @see BigDecimal
* @return the rounding mode.
*/
public int getRoundingMode() {
return roundingMode;
}
/***
* Sets the rounding mode for decimal divisions.
* @see BigDecimal
* @param roundingMode rounding mode for decimal divisions
*/
public void setRoundingMode(int roundingMode) {
this.roundingMode = roundingMode;
}
/***
* Sets the scale for division operations.
* The default is 64
* @see BigDecimal
* @return the scale
*/
public int getScale() {
return scale;
}
/***
* Sets the scale for division operations.
* @see BigDecimal
* @param scale scale for division operations
*/
public void setScale(int scale) {
this.scale = scale;
}
/**
* Returns the <a href="http://mathworld.wolfram.com/MaximumAbsoluteRowSumNorm.html">
* maximum absolute row sum norm</a> of the matrix.
*
* @return norm
*/
public BigDecimal getNorm() {
BigDecimal maxColSum = ZERO;
for (int col = 0; col < this.getColumnDimension(); col++) {
BigDecimal sum = ZERO;
for (int row = 0; row < this.getRowDimension(); row++) {
sum = sum.add(data[row][col].abs());
}
maxColSum = maxColSum.max(sum);
}
return maxColSum;
}
/**
* Gets a submatrix. Rows and columns are indicated
* counting from 0 to n-1.
*
* @param startRow Initial row index
* @param endRow Final row index
* @param startColumn Initial column index
* @param endColumn Final column index
* @return The subMatrix containing the data of the
* specified rows and columns
* @exception MatrixIndexException if row or column selections are not valid
*/
public BigMatrix getSubMatrix(int startRow, int endRow,
int startColumn, int endColumn)
throws MatrixIndexException {
MatrixUtils.checkRowIndex(this, startRow);
MatrixUtils.checkRowIndex(this, endRow);
if (startRow > endRow) {
throw new MatrixIndexException(LocalizedFormats.INITIAL_ROW_AFTER_FINAL_ROW,
startRow, endRow);
}
MatrixUtils.checkColumnIndex(this, startColumn);
MatrixUtils.checkColumnIndex(this, endColumn);
if (startColumn > endColumn) {
throw new MatrixIndexException(LocalizedFormats.INITIAL_COLUMN_AFTER_FINAL_COLUMN,
startColumn, endColumn);
}
final BigDecimal[][] subMatrixData =
new BigDecimal[endRow - startRow + 1][endColumn - startColumn + 1];
for (int i = startRow; i <= endRow; i++) {
System.arraycopy(data[i], startColumn,
subMatrixData[i - startRow], 0,
endColumn - startColumn + 1);
}
return new BigMatrixImpl(subMatrixData, false);
}
/**
* Gets a submatrix. Rows and columns are indicated
* counting from 0 to n-1.
*
* @param selectedRows Array of row indices must be non-empty
* @param selectedColumns Array of column indices must be non-empty
* @return The subMatrix containing the data in the
* specified rows and columns
* @exception MatrixIndexException if supplied row or column index arrays
* are not valid
*/
public BigMatrix getSubMatrix(int[] selectedRows, int[] selectedColumns)
throws MatrixIndexException {
if (selectedRows.length * selectedColumns.length == 0) {
if (selectedRows.length == 0) {
throw new MatrixIndexException(LocalizedFormats.EMPTY_SELECTED_ROW_INDEX_ARRAY);
}
throw new MatrixIndexException(LocalizedFormats.EMPTY_SELECTED_COLUMN_INDEX_ARRAY);
}
final BigDecimal[][] subMatrixData =
new BigDecimal[selectedRows.length][selectedColumns.length];
try {
for (int i = 0; i < selectedRows.length; i++) {
final BigDecimal[] subI = subMatrixData[i];
final BigDecimal[] dataSelectedI = data[selectedRows[i]];
for (int j = 0; j < selectedColumns.length; j++) {
subI[j] = dataSelectedI[selectedColumns[j]];
}
}
} catch (ArrayIndexOutOfBoundsException e) {
// we redo the loop with checks enabled
// in order to generate an appropriate message
for (final int row : selectedRows) {
MatrixUtils.checkRowIndex(this, row);
}
for (final int column : selectedColumns) {
MatrixUtils.checkColumnIndex(this, column);
}
}
return new BigMatrixImpl(subMatrixData, false);
}
/**
* Replace the submatrix starting at <code>row, column</code> using data in
* the input <code>subMatrix</code> array. Indexes are 0-based.
* <p>
* Example:<br>
* Starting with <pre>
* 1 2 3 4
* 5 6 7 8
* 9 0 1 2
* </pre>
* and <code>subMatrix = {{3, 4} {5,6}}</code>, invoking
* <code>setSubMatrix(subMatrix,1,1))</code> will result in <pre>
* 1 2 3 4
* 5 3 4 8
* 9 5 6 2
* </pre></p>
*
* @param subMatrix array containing the submatrix replacement data
* @param row row coordinate of the top, left element to be replaced
* @param column column coordinate of the top, left element to be replaced
* @throws MatrixIndexException if subMatrix does not fit into this
* matrix from element in (row, column)
* @throws IllegalArgumentException if <code>subMatrix</code> is not rectangular
* (not all rows have the same length) or empty
* @throws NullPointerException if <code>subMatrix</code> is null
* @since 1.1
*/
public void setSubMatrix(BigDecimal[][] subMatrix, int row, int column)
throws MatrixIndexException {
final int nRows = subMatrix.length;
if (nRows == 0) {
throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_ROW);
}
final int nCols = subMatrix[0].length;
if (nCols == 0) {
throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_COLUMN);
}
for (int r = 1; r < nRows; r++) {
if (subMatrix[r].length != nCols) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.DIFFERENT_ROWS_LENGTHS,
nCols, subMatrix[r].length);
}
}
if (data == null) {
if (row > 0) {
throw MathRuntimeException.createIllegalStateException(
LocalizedFormats.FIRST_ROWS_NOT_INITIALIZED_YET,
row);
}
if (column > 0) {
throw MathRuntimeException.createIllegalStateException(
LocalizedFormats.FIRST_COLUMNS_NOT_INITIALIZED_YET,
column);
}
data = new BigDecimal[nRows][nCols];
System.arraycopy(subMatrix, 0, data, 0, subMatrix.length);
} else {
MatrixUtils.checkRowIndex(this, row);
MatrixUtils.checkColumnIndex(this, column);
MatrixUtils.checkRowIndex(this, nRows + row - 1);
MatrixUtils.checkColumnIndex(this, nCols + column - 1);
}
for (int i = 0; i < nRows; i++) {
System.arraycopy(subMatrix[i], 0, data[row + i], column, nCols);
}
lu = null;
}
/**
* Returns the entries in row number <code>row</code>
* as a row matrix. Row indices start at 0.
*
* @param row the row to be fetched
* @return row matrix
* @throws MatrixIndexException if the specified row index is invalid
*/
public BigMatrix getRowMatrix(int row) throws MatrixIndexException {
MatrixUtils.checkRowIndex(this, row);
final int ncols = this.getColumnDimension();
final BigDecimal[][] out = new BigDecimal[1][ncols];
System.arraycopy(data[row], 0, out[0], 0, ncols);
return new BigMatrixImpl(out, false);
}
/**
* Returns the entries in column number <code>column</code>
* as a column matrix. Column indices start at 0.
*
* @param column the column to be fetched
* @return column matrix
* @throws MatrixIndexException if the specified column index is invalid
*/
public BigMatrix getColumnMatrix(int column) throws MatrixIndexException {
MatrixUtils.checkColumnIndex(this, column);
final int nRows = this.getRowDimension();
final BigDecimal[][] out = new BigDecimal[nRows][1];
for (int row = 0; row < nRows; row++) {
out[row][0] = data[row][column];
}
return new BigMatrixImpl(out, false);
}
/**
* Returns the entries in row number <code>row</code> as an array.
* <p>
* Row indices start at 0. A <code>MatrixIndexException</code> is thrown
* unless <code>0 <= row < rowDimension.</code></p>
*
* @param row the row to be fetched
* @return array of entries in the row
* @throws MatrixIndexException if the specified row index is not valid
*/
public BigDecimal[] getRow(int row) throws MatrixIndexException {
MatrixUtils.checkRowIndex(this, row);
final int ncols = this.getColumnDimension();
final BigDecimal[] out = new BigDecimal[ncols];
System.arraycopy(data[row], 0, out, 0, ncols);
return out;
}
/**
* Returns the entries in row number <code>row</code> as an array
* of double values.
* <p>
* Row indices start at 0. A <code>MatrixIndexException</code> is thrown
* unless <code>0 <= row < rowDimension.</code></p>
*
* @param row the row to be fetched
* @return array of entries in the row
* @throws MatrixIndexException if the specified row index is not valid
*/
public double[] getRowAsDoubleArray(int row) throws MatrixIndexException {
MatrixUtils.checkRowIndex(this, row);
final int ncols = this.getColumnDimension();
final double[] out = new double[ncols];
for (int i=0;i<ncols;i++) {
out[i] = data[row][i].doubleValue();
}
return out;
}
/**
* Returns the entries in column number <code>col</code> as an array.
* <p>
* Column indices start at 0. A <code>MatrixIndexException</code> is thrown
* unless <code>0 <= column < columnDimension.</code></p>
*
* @param col the column to be fetched
* @return array of entries in the column
* @throws MatrixIndexException if the specified column index is not valid
*/
public BigDecimal[] getColumn(int col) throws MatrixIndexException {
MatrixUtils.checkColumnIndex(this, col);
final int nRows = this.getRowDimension();
final BigDecimal[] out = new BigDecimal[nRows];
for (int i = 0; i < nRows; i++) {
out[i] = data[i][col];
}
return out;
}
/**
* Returns the entries in column number <code>col</code> as an array
* of double values.
* <p>
* Column indices start at 0. A <code>MatrixIndexException</code> is thrown
* unless <code>0 <= column < columnDimension.</code></p>
*
* @param col the column to be fetched
* @return array of entries in the column
* @throws MatrixIndexException if the specified column index is not valid
*/
public double[] getColumnAsDoubleArray(int col) throws MatrixIndexException {
MatrixUtils.checkColumnIndex(this, col);
final int nrows = this.getRowDimension();
final double[] out = new double[nrows];
for (int i=0;i<nrows;i++) {
out[i] = data[i][col].doubleValue();
}
return out;
}
/**
* Returns the entry in the specified row and column.
* <p>
* Row and column indices start at 0 and must satisfy
* <ul>
* <li><code>0 <= row < rowDimension</code></li>
* <li><code> 0 <= column < columnDimension</code></li>
* </ul>
* otherwise a <code>MatrixIndexException</code> is thrown.</p>
*
* @param row row location of entry to be fetched
* @param column column location of entry to be fetched
* @return matrix entry in row,column
* @throws MatrixIndexException if the row or column index is not valid
*/
public BigDecimal getEntry(int row, int column)
throws MatrixIndexException {
try {
return data[row][column];
} catch (ArrayIndexOutOfBoundsException e) {
throw new MatrixIndexException(
LocalizedFormats.NO_SUCH_MATRIX_ENTRY,
row, column, getRowDimension(), getColumnDimension());
}
}
/**
* Returns the entry in the specified row and column as a double.
* <p>
* Row and column indices start at 0 and must satisfy
* <ul>
* <li><code>0 <= row < rowDimension</code></li>
* <li><code> 0 <= column < columnDimension</code></li>
* </ul>
* otherwise a <code>MatrixIndexException</code> is thrown.</p>
*
* @param row row location of entry to be fetched
* @param column column location of entry to be fetched
* @return matrix entry in row,column
* @throws MatrixIndexException if the row
* or column index is not valid
*/
public double getEntryAsDouble(int row, int column) throws MatrixIndexException {
return getEntry(row,column).doubleValue();
}
/**
* Returns the transpose matrix.
*
* @return transpose matrix
*/
public BigMatrix transpose() {
final int nRows = this.getRowDimension();
final int nCols = this.getColumnDimension();
final BigDecimal[][] outData = new BigDecimal[nCols][nRows];
for (int row = 0; row < nRows; row++) {
final BigDecimal[] dataRow = data[row];
for (int col = 0; col < nCols; col++) {
outData[col][row] = dataRow[col];
}
}
return new BigMatrixImpl(outData, false);
}
/**
* Returns the inverse matrix if this matrix is invertible.
*
* @return inverse matrix
* @throws InvalidMatrixException if this is not invertible
*/
public BigMatrix inverse() throws InvalidMatrixException {
return solve(MatrixUtils.createBigIdentityMatrix(getRowDimension()));
}
/**
* Returns the determinant of this matrix.
*
* @return determinant
* @throws InvalidMatrixException if matrix is not square
*/
public BigDecimal getDeterminant() throws InvalidMatrixException {
if (!isSquare()) {
throw new NonSquareMatrixException(getRowDimension(), getColumnDimension());
}
if (isSingular()) { // note: this has side effect of attempting LU decomp if lu == null
return ZERO;
} else {
BigDecimal det = (parity == 1) ? ONE : ONE.negate();
for (int i = 0; i < getRowDimension(); i++) {
det = det.multiply(lu[i][i]);
}
return det;
}
}
/**
* Is this a square matrix?
* @return true if the matrix is square (rowDimension = columnDimension)
*/
public boolean isSquare() {
return getColumnDimension() == getRowDimension();
}
/**
* Is this a singular matrix?
* @return true if the matrix is singular
*/
public boolean isSingular() {
if (lu == null) {
try {
luDecompose();
return false;
} catch (InvalidMatrixException ex) {
return true;
}
} else { // LU decomp must have been successfully performed
return false; // so the matrix is not singular
}
}
/**
* Returns the number of rows in the matrix.
*
* @return rowDimension
*/
public int getRowDimension() {
return data.length;
}
/**
* Returns the number of columns in the matrix.
*
* @return columnDimension
*/
public int getColumnDimension() {
return data[0].length;
}
/**
* Returns the <a href="http://mathworld.wolfram.com/MatrixTrace.html">
* trace</a> of the matrix (the sum of the elements on the main diagonal).
*
* @return trace
*
* @throws IllegalArgumentException if this matrix is not square.
*/
public BigDecimal getTrace() throws IllegalArgumentException {
if (!isSquare()) {
throw new NonSquareMatrixException(getRowDimension(), getColumnDimension());
}
BigDecimal trace = data[0][0];
for (int i = 1; i < this.getRowDimension(); i++) {
trace = trace.add(data[i][i]);
}
return trace;
}
/**
* Returns the result of multiplying this by the vector <code>v</code>.
*
* @param v the vector to operate on
* @return this*v
* @throws IllegalArgumentException if columnDimension != v.size()
*/
public BigDecimal[] operate(BigDecimal[] v) throws IllegalArgumentException {
if (v.length != getColumnDimension()) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.VECTOR_LENGTH_MISMATCH,
v.length, getColumnDimension() );
}
final int nRows = this.getRowDimension();
final int nCols = this.getColumnDimension();
final BigDecimal[] out = new BigDecimal[nRows];
for (int row = 0; row < nRows; row++) {
BigDecimal sum = ZERO;
for (int i = 0; i < nCols; i++) {
sum = sum.add(data[row][i].multiply(v[i]));
}
out[row] = sum;
}
return out;
}
/**
* Returns the result of multiplying this by the vector <code>v</code>.
*
* @param v the vector to operate on
* @return this*v
* @throws IllegalArgumentException if columnDimension != v.size()
*/
public BigDecimal[] operate(double[] v) throws IllegalArgumentException {
final BigDecimal bd[] = new BigDecimal[v.length];
for (int i = 0; i < bd.length; i++) {
bd[i] = new BigDecimal(v[i]);
}
return operate(bd);
}
/**
* Returns the (row) vector result of premultiplying this by the vector <code>v</code>.
*
* @param v the row vector to premultiply by
* @return v*this
* @throws IllegalArgumentException if rowDimension != v.size()
*/
public BigDecimal[] preMultiply(BigDecimal[] v) throws IllegalArgumentException {
final int nRows = this.getRowDimension();
if (v.length != nRows) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.VECTOR_LENGTH_MISMATCH,
v.length, nRows );
}
final int nCols = this.getColumnDimension();
final BigDecimal[] out = new BigDecimal[nCols];
for (int col = 0; col < nCols; col++) {
BigDecimal sum = ZERO;
for (int i = 0; i < nRows; i++) {
sum = sum.add(data[i][col].multiply(v[i]));
}
out[col] = sum;
}
return out;
}
/**
* Returns a matrix of (column) solution vectors for linear systems with
* coefficient matrix = this and constant vectors = columns of
* <code>b</code>.
*
* @param b array of constants forming RHS of linear systems to
* to solve
* @return solution array
* @throws IllegalArgumentException if this.rowDimension != row dimension
* @throws InvalidMatrixException if this matrix is not square or is singular
*/
public BigDecimal[] solve(BigDecimal[] b) throws IllegalArgumentException, InvalidMatrixException {
final int nRows = this.getRowDimension();
if (b.length != nRows) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.VECTOR_LENGTH_MISMATCH,
b.length, nRows);
}
final BigMatrix bMatrix = new BigMatrixImpl(b);
final BigDecimal[][] solution = ((BigMatrixImpl) (solve(bMatrix))).getDataRef();
final BigDecimal[] out = new BigDecimal[nRows];
for (int row = 0; row < nRows; row++) {
out[row] = solution[row][0];
}
return out;
}
/**
* Returns a matrix of (column) solution vectors for linear systems with
* coefficient matrix = this and constant vectors = columns of
* <code>b</code>.
*
* @param b array of constants forming RHS of linear systems to
* to solve
* @return solution array
* @throws IllegalArgumentException if this.rowDimension != row dimension
* @throws InvalidMatrixException if this matrix is not square or is singular
*/
public BigDecimal[] solve(double[] b) throws IllegalArgumentException, InvalidMatrixException {
final BigDecimal bd[] = new BigDecimal[b.length];
for (int i = 0; i < bd.length; i++) {
bd[i] = new BigDecimal(b[i]);
}
return solve(bd);
}
/**
* Returns a matrix of (column) solution vectors for linear systems with
* coefficient matrix = this and constant vectors = columns of
* <code>b</code>.
*
* @param b matrix of constant vectors forming RHS of linear systems to
* to solve
* @return matrix of solution vectors
* @throws IllegalArgumentException if this.rowDimension != row dimension
* @throws InvalidMatrixException if this matrix is not square or is singular
*/
public BigMatrix solve(BigMatrix b) throws IllegalArgumentException, InvalidMatrixException {
if (b.getRowDimension() != getRowDimension()) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.DIMENSIONS_MISMATCH_2x2,
b.getRowDimension(), b.getColumnDimension(), getRowDimension(), "n");
}
if (!isSquare()) {
throw new NonSquareMatrixException(getRowDimension(), getColumnDimension());
}
if (this.isSingular()) { // side effect: compute LU decomp
throw new SingularMatrixException();
}
final int nCol = this.getColumnDimension();
final int nColB = b.getColumnDimension();
final int nRowB = b.getRowDimension();
// Apply permutations to b
final BigDecimal[][] bp = new BigDecimal[nRowB][nColB];
for (int row = 0; row < nRowB; row++) {
final BigDecimal[] bpRow = bp[row];
for (int col = 0; col < nColB; col++) {
bpRow[col] = b.getEntry(permutation[row], col);
}
}
// Solve LY = b
for (int col = 0; col < nCol; col++) {
for (int i = col + 1; i < nCol; i++) {
final BigDecimal[] bpI = bp[i];
final BigDecimal[] luI = lu[i];
for (int j = 0; j < nColB; j++) {
bpI[j] = bpI[j].subtract(bp[col][j].multiply(luI[col]));
}
}
}
// Solve UX = Y
for (int col = nCol - 1; col >= 0; col--) {
final BigDecimal[] bpCol = bp[col];
final BigDecimal luDiag = lu[col][col];
for (int j = 0; j < nColB; j++) {
bpCol[j] = bpCol[j].divide(luDiag, scale, roundingMode);
}
for (int i = 0; i < col; i++) {
final BigDecimal[] bpI = bp[i];
final BigDecimal[] luI = lu[i];
for (int j = 0; j < nColB; j++) {
bpI[j] = bpI[j].subtract(bp[col][j].multiply(luI[col]));
}
}
}
return new BigMatrixImpl(bp, false);
}
/**
* Computes a new
* <a href="http://www.math.gatech.edu/~bourbaki/math2601/Web-notes/2num.pdf">
* LU decompostion</a> for this matrix, storing the result for use by other methods.
* <p>
* <strong>Implementation Note</strong>:<br>
* Uses <a href="http://www.damtp.cam.ac.uk/user/fdl/people/sd/lectures/nummeth98/linear.htm">
* Crout's algortithm</a>, with partial pivoting.</p>
* <p>
* <strong>Usage Note</strong>:<br>
* This method should rarely be invoked directly. Its only use is
* to force recomputation of the LU decomposition when changes have been
* made to the underlying data using direct array references. Changes
* made using setXxx methods will trigger recomputation when needed
* automatically.</p>
*
* @throws InvalidMatrixException if the matrix is non-square or singular.
*/
public void luDecompose() throws InvalidMatrixException {
final int nRows = this.getRowDimension();
final int nCols = this.getColumnDimension();
if (nRows != nCols) {
throw new NonSquareMatrixException(getRowDimension(), getColumnDimension());
}
lu = this.getData();
// Initialize permutation array and parity
permutation = new int[nRows];
for (int row = 0; row < nRows; row++) {
permutation[row] = row;
}
parity = 1;
// Loop over columns
for (int col = 0; col < nCols; col++) {
BigDecimal sum = ZERO;
// upper
for (int row = 0; row < col; row++) {
final BigDecimal[] 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 max = col; // permutation row
BigDecimal largest = ZERO;
for (int row = col; row < nRows; row++) {
final BigDecimal[] 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;
// maintain best permutation choice
if (sum.abs().compareTo(largest) == 1) {
largest = sum.abs();
max = row;
}
}
// Singularity check
if (lu[max][col].abs().compareTo(TOO_SMALL) <= 0) {
lu = null;
throw new SingularMatrixException();
}
// Pivot if necessary
if (max != col) {
BigDecimal tmp = ZERO;
for (int i = 0; i < nCols; i++) {
tmp = lu[max][i];
lu[max][i] = lu[col][i];
lu[col][i] = tmp;
}
int temp = permutation[max];
permutation[max] = permutation[col];
permutation[col] = temp;
parity = -parity;
}
// Divide the lower elements by the "winning" diagonal elt.
final BigDecimal luDiag = lu[col][col];
for (int row = col + 1; row < nRows; row++) {
final BigDecimal[] luRow = lu[row];
luRow[col] = luRow[col].divide(luDiag, scale, roundingMode);
}
}
}
/**
* Get a string representation for this matrix.
* @return a string representation for this matrix
*/
@Override
public String toString() {
StringBuilder res = new StringBuilder();
res.append("BigMatrixImpl{");
if (data != null) {
for (int i = 0; i < data.length; i++) {
if (i > 0) {
res.append(",");
}
res.append("{");
for (int j = 0; j < data[0].length; j++) {
if (j > 0) {
res.append(",");
}
res.append(data[i][j]);
}
res.append("}");
}
}
res.append("}");
return res.toString();
}
/**
* Returns true iff <code>object</code> is a
* <code>BigMatrixImpl</code> instance with the same dimensions as this
* and all corresponding matrix entries are equal. BigDecimal.equals
* is used to compare corresponding entries.
*
* @param object the object to test equality against.
* @return true if object equals this
*/
@Override
public boolean equals(Object object) {
if (object == this ) {
return true;
}
if (object instanceof BigMatrixImpl == false) {
return false;
}
final BigMatrix m = (BigMatrix) object;
final int nRows = getRowDimension();
final int nCols = getColumnDimension();
if (m.getColumnDimension() != nCols || m.getRowDimension() != nRows) {
return false;
}
for (int row = 0; row < nRows; row++) {
final BigDecimal[] dataRow = data[row];
for (int col = 0; col < nCols; col++) {
if (!dataRow[col].equals(m.getEntry(row, col))) {
return false;
}
}
}
return true;
}
/**
* Computes a hashcode for the matrix.
*
* @return hashcode for matrix
*/
@Override
public int hashCode() {
int ret = 7;
final int nRows = getRowDimension();
final int nCols = getColumnDimension();
ret = ret * 31 + nRows;
ret = ret * 31 + nCols;
for (int row = 0; row < nRows; row++) {
final BigDecimal[] dataRow = data[row];
for (int col = 0; col < nCols; col++) {
ret = ret * 31 + (11 * (row+1) + 17 * (col+1)) *
dataRow[col].hashCode();
}
}
return ret;
}
//------------------------ Protected methods
/**
* Returns the LU decomposition as a BigMatrix.
* Returns a fresh copy of the cached LU matrix if this has been computed;
* otherwise the composition is computed and cached for use by other methods.
* Since a copy is returned in either case, changes to the returned matrix do not
* affect the LU decomposition property.
* <p>
* The matrix returned is a compact representation of the LU decomposition.
* Elements below the main diagonal correspond to entries of the "L" matrix;
* elements on and above the main diagonal correspond to entries of the "U"
* matrix.</p>
* <p>
* Example: <pre>
*
* Returned matrix L U
* 2 3 1 1 0 0 2 3 1
* 5 4 6 5 1 0 0 4 6
* 1 7 8 1 7 1 0 0 8
* </pre>
*
* The L and U matrices satisfy the matrix equation LU = permuteRows(this), <br>
* where permuteRows reorders the rows of the matrix to follow the order determined
* by the <a href=#getPermutation()>permutation</a> property.</p>
*
* @return LU decomposition matrix
* @throws InvalidMatrixException if the matrix is non-square or singular.
*/
protected BigMatrix getLUMatrix() throws InvalidMatrixException {
if (lu == null) {
luDecompose();
}
return new BigMatrixImpl(lu);
}
/**
* Returns the permutation associated with the lu decomposition.
* The entries of the array represent a permutation of the numbers 0, ... , nRows - 1.
* <p>
* Example:
* permutation = [1, 2, 0] means current 2nd row is first, current third row is second
* and current first row is last.</p>
* <p>
* Returns a fresh copy of the array.</p>
*
* @return the permutation
*/
protected int[] getPermutation() {
final int[] out = new int[permutation.length];
System.arraycopy(permutation, 0, out, 0, permutation.length);
return out;
}
//------------------------ Private methods
/**
* Returns a fresh copy of the underlying data array.
*
* @return a copy of the underlying data array.
*/
private BigDecimal[][] copyOut() {
final int nRows = this.getRowDimension();
final BigDecimal[][] out = new BigDecimal[nRows][this.getColumnDimension()];
// can't copy 2-d array in one shot, otherwise get row references
for (int i = 0; i < nRows; i++) {
System.arraycopy(data[i], 0, out[i], 0, data[i].length);
}
return out;
}
/**
* Replaces data with a fresh copy of the input array.
* <p>
* Verifies that the input array is rectangular and non-empty.</p>
*
* @param in data to copy in
* @throws IllegalArgumentException if input array is emtpy or not
* rectangular
* @throws NullPointerException if input array is null
*/
private void copyIn(BigDecimal[][] in) {
setSubMatrix(in,0,0);
}
/**
* Replaces data with a fresh copy of the input array.
*
* @param in data to copy in
*/
private void copyIn(double[][] in) {
final int nRows = in.length;
final int nCols = in[0].length;
data = new BigDecimal[nRows][nCols];
for (int i = 0; i < nRows; i++) {
final BigDecimal[] dataI = data[i];
final double[] inI = in[i];
for (int j = 0; j < nCols; j++) {
dataI[j] = new BigDecimal(inI[j]);
}
}
lu = null;
}
/**
* Replaces data with BigDecimals represented by the strings in the input
* array.
*
* @param in data to copy in
*/
private void copyIn(String[][] in) {
final int nRows = in.length;
final int nCols = in[0].length;
data = new BigDecimal[nRows][nCols];
for (int i = 0; i < nRows; i++) {
final BigDecimal[] dataI = data[i];
final String[] inI = in[i];
for (int j = 0; j < nCols; j++) {
dataI[j] = new BigDecimal(inI[j]);
}
}
lu = null;
}
}