/*
* GeoTools - The Open Source Java GIS Toolkit
* http://geotools.org
*
* (C) 2001-2008, Open Source Geospatial Foundation (OSGeo)
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation;
* version 2.1 of the License.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*/
package org.geotools.referencing.operation.matrix;
import java.awt.geom.AffineTransform;
import java.text.ParseException;
import java.text.FieldPosition;
import java.text.NumberFormat;
import java.util.Locale;
import java.io.File;
import java.io.FileReader;
import java.io.BufferedReader;
import java.io.IOException;
import javax.vecmath.GMatrix;
import org.opengis.referencing.cs.AxisDirection;
import org.opengis.referencing.operation.Matrix;
import org.opengis.geometry.Envelope;
import org.opengis.geometry.MismatchedDimensionException;
import org.geotools.io.LineFormat;
import org.geotools.io.ContentFormatException;
import org.geotools.util.Utilities;
import org.geotools.resources.XArray;
import org.geotools.resources.i18n.Errors;
import org.geotools.resources.i18n.ErrorKeys;
/**
* A two dimensional array of numbers. Row and column numbering begins with zero.
*
* @since 2.2
*
*
* @source $URL$
* @version $Id$
* @author Martin Desruisseaux (IRD)
* @author Simone Giannecchini
*
* @see javax.vecmath.GMatrix
* @see java.awt.geom.AffineTransform
* @see javax.media.jai.PerspectiveTransform
* @see javax.media.j3d.Transform3D
* @see <A HREF="http://math.nist.gov/javanumerics/jama/">Jama matrix</A>
* @see <A HREF="http://jcp.org/jsr/detail/83.jsp">JSR-83 Multiarray package</A>
*/
public class GeneralMatrix extends GMatrix implements XMatrix {
/**
* Serial number for interoperability with different versions.
*/
private static final long serialVersionUID = 8447482612423035360L;
/**
* Constructs a square identity matrix of size {@code size} × {@code size}.
*
* @param size The number of rows and columns.
*/
public GeneralMatrix(final int size) {
super(size, size);
}
/**
* Creates a matrix of size {@code numRow} × {@code numCol}.
* Elements on the diagonal <var>j==i</var> are set to 1.
*
* @param numRow Number of rows.
* @param numCol Number of columns.
*/
public GeneralMatrix(final int numRow, final int numCol) {
super(numRow, numCol);
}
/**
* Constructs a {@code numRow} × {@code numCol} matrix
* initialized to the values in the {@code matrix} array. The array values
* are copied in one row at a time in row major fashion. The array should be
* exactly <code>numRow*numCol</code> in length. Note that because row and column
* numbering begins with zero, {@code numRow} and {@code numCol} will be
* one larger than the maximum possible matrix index values.
*
* @param numRow Number of rows.
* @param numCol Number of columns.
* @param matrix Initial values.
*/
public GeneralMatrix(final int numRow, final int numCol, final double[] matrix) {
super(numRow, numCol, matrix);
if (numRow*numCol != matrix.length) {
throw new IllegalArgumentException(String.valueOf(matrix.length));
}
}
/**
* Constructs a new matrix from a two-dimensional array of doubles.
*
* @param matrix Array of rows. Each row must have the same length.
* @throws IllegalArgumentException if the specified matrix is not regular
* (i.e. if all rows doesn't have the same length).
*/
public GeneralMatrix(final double[][] matrix) throws IllegalArgumentException {
super(matrix.length, (matrix.length!=0) ? matrix[0].length : 0);
final int numRow = getNumRow();
final int numCol = getNumCol();
for (int j=0; j<numRow; j++) {
if (matrix[j].length!=numCol) {
throw new IllegalArgumentException(Errors.format(ErrorKeys.MATRIX_NOT_REGULAR));
}
setRow(j, matrix[j]);
}
}
/**
* Constructs a new matrix and copies the initial values from the parameter matrix.
*
* @param matrix The matrix to copy.
*/
public GeneralMatrix(final Matrix matrix) {
this(matrix.getNumRow(), matrix.getNumCol());
final int height = getNumRow();
final int width = getNumCol();
for (int j=0; j<height; j++) {
for (int i=0; i<width; i++) {
setElement(j, i, matrix.getElement(j, i));
}
}
}
/**
* Constructs a new matrix and copies the initial values from the parameter matrix.
*
* @param matrix The matrix to copy.
*/
public GeneralMatrix(final GMatrix matrix) {
super(matrix);
}
/**
* Constructs a 3×3 matrix from the specified affine transform.
*
* @param transform The matrix to copy.
*/
public GeneralMatrix(final AffineTransform transform) {
super(3,3, new double[] {
transform.getScaleX(), transform.getShearX(), transform.getTranslateX(),
transform.getShearY(), transform.getScaleY(), transform.getTranslateY(),
0, 0, 1
});
assert isAffine() : this;
}
/**
* Constructs a transform that maps a source region to a destination region.
* Axis order and direction are left unchanged.
*
* <P>If the source dimension is equals to the destination dimension,
* then the transform is affine. However, the following special cases
* are also handled:</P>
*
* <UL>
* <LI>If the target dimension is smaller than the source dimension,
* then extra dimensions are dropped.</LI>
* <LI>If the target dimension is greater than the source dimension,
* then the coordinates in the new dimensions are set to 0.</LI>
* </UL>
*
* @param srcRegion The source region.
* @param dstRegion The destination region.
*/
public GeneralMatrix(final Envelope srcRegion,
final Envelope dstRegion)
{
super(dstRegion.getDimension()+1, srcRegion.getDimension()+1);
// Next lines should be first if only Sun could fix RFE #4093999 (sigh...)
final int srcDim = srcRegion.getDimension();
final int dstDim = dstRegion.getDimension();
for (int i=Math.min(srcDim, dstDim); --i>=0;) {
double scale = dstRegion.getSpan (i) / srcRegion.getSpan (i);
double translate = dstRegion.getMinimum(i) - srcRegion.getMinimum(i)*scale;
setElement(i, i, scale);
setElement(i, srcDim, translate);
}
setElement(dstDim, srcDim, 1);
assert (srcDim != dstDim) || isAffine() : this;
}
/**
* Constructs a transform changing axis order and/or direction.
* For example, the transform may converts (NORTH,WEST) coordinates
* into (EAST,NORTH). Axis direction can be inversed only. For example,
* it is illegal to transform (NORTH,WEST) coordinates into (NORTH,DOWN).
*
* <P>If the source dimension is equals to the destination dimension,
* then the transform is affine. However, the following special cases
* are also handled:</P>
* <BR>
* <UL>
* <LI>If the target dimension is smaller than the source dimension,
* extra axis are dropped. An exception is thrown if the target
* contains some axis not found in the source.</LI>
* </UL>
*
* @param srcAxis The set of axis direction for source coordinate system.
* @param dstAxis The set of axis direction for destination coordinate system.
* @throws IllegalArgumentException If {@code dstAxis} contains some axis
* not found in {@code srcAxis}, or if some colinear axis were found.
*/
public GeneralMatrix(final AxisDirection[] srcAxis,
final AxisDirection[] dstAxis)
{
this(null, srcAxis, null, dstAxis, false);
}
/**
* Constructs a transform mapping a source region to a destination region.
* Axis order and/or direction can be changed during the process.
* For example, the transform may convert (NORTH,WEST) coordinates
* into (EAST,NORTH). Axis direction can be inversed only. For example,
* it is illegal to transform (NORTH,WEST) coordinates into (NORTH,DOWN).
*
* <P>If the source dimension is equals to the destination dimension,
* then the transform is affine. However, the following special cases
* are also handled:</P>
* <BR>
* <UL>
* <LI>If the target dimension is smaller than the source dimension,
* extra axis are dropped. An exception is thrown if the target
* contains some axis not found in the source.</LI>
* </UL>
*
* @param srcRegion The source region.
* @param srcAxis Axis direction for each dimension of the source region.
* @param dstRegion The destination region.
* @param dstAxis Axis direction for each dimension of the destination region.
* @throws MismatchedDimensionException if the envelope dimension doesn't
* matches the axis direction array length.
* @throws IllegalArgumentException If {@code dstAxis} contains some axis
* not found in {@code srcAxis}, or if some colinear axis were found.
*/
public GeneralMatrix(final Envelope srcRegion, final AxisDirection[] srcAxis,
final Envelope dstRegion, final AxisDirection[] dstAxis)
{
this(srcRegion, srcAxis, dstRegion, dstAxis, true);
}
/**
* Implementation of constructors expecting envelope and/or axis directions.
*
* @param validRegions {@code true} if source and destination regions must
* be taken in account. If {@code false}, then source and destination
* regions will be ignored and may be null.
*/
private GeneralMatrix(final Envelope srcRegion, final AxisDirection[] srcAxis,
final Envelope dstRegion, final AxisDirection[] dstAxis,
final boolean validRegions)
{
super(dstAxis.length+1, srcAxis.length+1);
if (validRegions) {
ensureDimensionMatch("srcRegion", srcRegion, srcAxis.length);
ensureDimensionMatch("dstRegion", dstRegion, dstAxis.length);
}
/*
* Map source axis to destination axis. If no axis is moved (for example if the user
* want to transform (NORTH,EAST) to (SOUTH,EAST)), then source and destination index
* will be equal. If some axis are moved (for example if the user want to transform
* (NORTH,EAST) to (EAST,NORTH)), then ordinates at index {@code srcIndex} will
* have to be moved at index {@code dstIndex}.
*/
setZero();
for (int dstIndex=0; dstIndex<dstAxis.length; dstIndex++) {
boolean hasFound = false;
final AxisDirection dstAxe = dstAxis[dstIndex];
final AxisDirection search = dstAxe.absolute();
for (int srcIndex=0; srcIndex<srcAxis.length; srcIndex++) {
final AxisDirection srcAxe = srcAxis[srcIndex];
if (search.equals(srcAxe.absolute())) {
if (hasFound) {
// TODO: Use the localized version of 'getName' in GeoAPI 2.1
throw new IllegalArgumentException(Errors.format(ErrorKeys.COLINEAR_AXIS_$2,
srcAxe.name(), dstAxe.name()));
}
hasFound = true;
/*
* Set the matrix elements. Some matrix elements will never
* be set. They will be left to zero, which is their wanted
* value.
*/
final boolean normal = srcAxe.equals(dstAxe);
double scale = (normal) ? +1 : -1;
double translate = 0;
if (validRegions) {
translate = (normal) ? dstRegion.getMinimum(dstIndex)
: dstRegion.getMaximum(dstIndex);
scale *= dstRegion.getSpan(dstIndex) /
srcRegion.getSpan(srcIndex);
translate -= srcRegion.getMinimum(srcIndex) * scale;
}
setElement(dstIndex, srcIndex, scale);
setElement(dstIndex, srcAxis.length, translate);
}
}
if (!hasFound) {
// TODO: Use the localized version of 'getName' in GeoAPI 2.1
throw new IllegalArgumentException(Errors.format(
ErrorKeys.NO_SOURCE_AXIS_$1, dstAxis[dstIndex].name()));
}
}
setElement(dstAxis.length, srcAxis.length, 1);
assert (srcAxis.length != dstAxis.length) || isAffine() : this;
}
/**
* Convenience method for checking object dimension validity.
* This method is usually invoked for argument checking.
*
* @param name The name of the argument to check.
* @param envelope The envelope to check.
* @param dimension The expected dimension for the object.
* @throws MismatchedDimensionException if the envelope doesn't have the expected dimension.
*/
private static void ensureDimensionMatch(final String name,
final Envelope envelope,
final int dimension)
throws MismatchedDimensionException
{
final int dim = envelope.getDimension();
if (dimension != dim) {
throw new MismatchedDimensionException(Errors.format(
ErrorKeys.MISMATCHED_DIMENSION_$3, name, dim, dimension));
}
}
/**
* Retrieves the specifiable values in the transformation matrix into a
* 2-dimensional array of double precision values. The values are stored
* into the 2-dimensional array using the row index as the first subscript
* and the column index as the second. Values are copied; changes to the
* returned array will not change this matrix.
*
* @param matrix The matrix to extract elements from.
* @return The matrix elements.
*/
public static double[][] getElements(final Matrix matrix) {
if (matrix instanceof GeneralMatrix) {
return ((GeneralMatrix) matrix).getElements();
}
final int numCol = matrix.getNumCol();
final double[][] rows = new double[matrix.getNumRow()][];
for (int j=0; j<rows.length; j++) {
final double[] row;
rows[j] = row = new double[numCol];
for (int i=0; i<row.length; i++) {
row[i] = matrix.getElement(j, i);
}
}
return rows;
}
/**
* Retrieves the specifiable values in the transformation matrix into a
* 2-dimensional array of double precision values. The values are stored
* into the 2-dimensional array using the row index as the first subscript
* and the column index as the second. Values are copied; changes to the
* returned array will not change this matrix.
*
* @return The matrix elements.
*/
public final double[][] getElements() {
final int numCol = getNumCol();
final double[][] rows = new double[getNumRow()][];
for (int j=0; j<rows.length; j++) {
getRow(j, rows[j]=new double[numCol]);
}
return rows;
}
/**
* {@inheritDoc}
*/
public final boolean isAffine() {
int dimension = getNumRow();
if (dimension != getNumCol()) {
return false;
}
dimension--;
for (int i=0; i<=dimension; i++) {
if (getElement(dimension, i) != (i==dimension ? 1 : 0)) {
return false;
}
}
return true;
}
/**
* Returns {@code true} if this matrix is an identity matrix.
*/
public final boolean isIdentity() {
final int numRow = getNumRow();
final int numCol = getNumCol();
if (numRow != numCol) {
return false;
}
for (int j=0; j<numRow; j++) {
for (int i=0; i<numCol; i++) {
if (getElement(j,i) != (i==j ? 1 : 0)) {
return false;
}
}
}
assert isAffine() : this;
assert isIdentity(0) : this;
return true;
}
/**
* {@inheritDoc}
*
* @since 2.3.1
*/
public final boolean isIdentity(double tolerance) {
return isIdentity(this, tolerance);
}
/**
* Returns {@code true} if the matrix is an identity matrix using the provided tolerance.
*/
static boolean isIdentity(final Matrix matrix, double tolerance) {
tolerance = Math.abs(tolerance);
final int numRow = matrix.getNumRow();
final int numCol = matrix.getNumCol();
if (numRow != numCol) {
return false;
}
for (int j=0; j<numRow; j++) {
for (int i=0; i<numCol; i++) {
double e = matrix.getElement(j,i);
if (i == j) {
e--;
}
if (!(Math.abs(e) <= tolerance)) { // Uses '!' in order to catch NaN values.
return false;
}
}
}
// Note: we can't assert matrix.isAffine().
return true;
}
/**
* {@inheritDoc}
*/
public final void multiply(final Matrix matrix) {
final GMatrix m;
if (matrix instanceof GMatrix) {
m = (GMatrix) matrix;
} else {
m = new GeneralMatrix(matrix);
}
mul(m);
}
/**
* {@inheritDoc}
*/
public boolean equals(final Matrix matrix, final double tolerance) {
return epsilonEquals(this, matrix, tolerance);
}
/**
* Compares the element values.
*/
static boolean epsilonEquals(final Matrix m1, final Matrix m2, final double tolerance) {
final int numRow = m1.getNumRow();
if (numRow != m2.getNumRow()) {
return false;
}
final int numCol = m1.getNumCol();
if (numCol != m2.getNumCol()) {
return false;
}
for (int j=0; j<numRow; j++) {
for (int i=0; i<numCol; i++) {
final double v1 = m1.getElement(j, i);
final double v2 = m2.getElement(j, i);
if (!(Math.abs(v1 - v2) <= tolerance)) {
if (Double.doubleToLongBits(v1) == Double.doubleToLongBits(v2)) {
// Special case for NaN and infinite values.
continue;
}
return false;
}
}
}
return true;
}
/**
* Returns an affine transform for this matrix.
* This is a convenience method for interoperability with Java2D.
*
* @return The affine transform for this matrix.
* @throws IllegalStateException if this matrix is not 3×3,
* or if the last row is not {@code [0 0 1]}.
*/
public final AffineTransform toAffineTransform2D() throws IllegalStateException {
int check;
if ((check=getNumRow())!=3 || (check=getNumCol())!=3) {
throw new IllegalStateException(Errors.format(
ErrorKeys.NOT_TWO_DIMENSIONAL_$1, check-1));
}
if (isAffine()) {
return new AffineTransform(getElement(0,0), getElement(1,0),
getElement(0,1), getElement(1,1),
getElement(0,2), getElement(1,2));
}
throw new IllegalStateException(Errors.format(ErrorKeys.NOT_AN_AFFINE_TRANSFORM));
}
/**
* Loads data from the specified file until the first blank line or end of file.
*
* @param file The file to read.
* @return The matrix parsed from the file.
* @throws IOException if an error occured while reading the file.
*
* @since 2.2
*/
public static GeneralMatrix load(final File file) throws IOException {
final BufferedReader in = new BufferedReader(new FileReader(file));
try {
return load(in, Locale.US);
} finally {
in.close();
}
}
/**
* Loads data from the specified streal until the first blank line or end of stream.
*
* @param in The stream to read.
* @param locale The locale for the numbers to be parsed.
* @return The matrix parsed from the stream.
* @throws IOException if an error occured while reading the stream.
*
* @since 2.2
*/
public static GeneralMatrix load(final BufferedReader in, final Locale locale)
throws IOException
{
final LineFormat parser = new LineFormat(locale);
double[] data = null;
double[] row = null;
int numRow = 0;
int numData = 0;
String line;
while ((line=in.readLine()) != null) {
if ((line=line.trim()).length() == 0) {
if (numRow == 0) {
continue;
} else {
break;
}
}
try {
parser.setLine(line);
row = parser.getValues(row);
} catch (ParseException exception) {
throw new ContentFormatException(exception.getLocalizedMessage(), exception);
}
final int upper = numData + row.length;
if (data == null) {
// Assumes a square matrix.
data = new double[numData * numData];
}
if (upper > data.length) {
data = XArray.resize(data, upper*2);
}
System.arraycopy(row, 0, data, numData, row.length);
numData = upper;
numRow++;
assert numData % numRow == 0 : numData;
}
data = (data!=null) ? XArray.resize(data, numData) : new double[0];
return new GeneralMatrix(numRow, numData/numRow, data);
}
/**
* Returns a string representation of this matrix. The returned string is implementation
* dependent. It is usually provided for debugging purposes only.
*/
@Override
public String toString() {
return toString(this);
}
/**
* Returns a string representation of the specified matrix. The returned string is
* implementation dependent. It is usually provided for debugging purposes only.
*/
static String toString(final Matrix matrix) {
final int numRow = matrix.getNumRow();
final int numCol = matrix.getNumCol();
StringBuffer buffer = new StringBuffer();
final int columnWidth = 12;
final String lineSeparator = System.getProperty("line.separator", "\n");
final FieldPosition dummy = new FieldPosition(0);
final NumberFormat format = NumberFormat.getNumberInstance();
format.setGroupingUsed(false);
format.setMinimumFractionDigits(6);
format.setMaximumFractionDigits(6);
for (int j=0; j<numRow; j++) {
for (int i=0; i<numCol; i++) {
final int position = buffer.length();
buffer = format.format(matrix.getElement(j,i), buffer, dummy);
final int spaces = Math.max(columnWidth - (buffer.length() - position), 1);
buffer.insert(position, Utilities.spaces(spaces));
}
buffer.append(lineSeparator);
}
return buffer.toString();
}
/**
* Returns a clone of this matrix.
*/
@Override
public GeneralMatrix clone() {
return (GeneralMatrix) super.clone();
}
}