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A Java mapping for the OGC Geography Markup Language (GML)
/*
* gml-objects - A Java mapping for the OGC Geography Markup Language (GML)
* https://github.com/xmlobjects/gml-objects
*
* Copyright 2019-2024 Claus Nagel
*
* Licensed 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.xmlobjects.gml.util.jama;
import java.io.BufferedReader;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.text.DecimalFormat;
import java.text.DecimalFormatSymbols;
import java.text.NumberFormat;
import java.util.Locale;
/**
* Jama = Java Matrix class.
*
* The Java Matrix Class provides the fundamental operations of numerical
* linear algebra. Various constructors create Matrices from two dimensional
* arrays of double precision floating point numbers. Various "gets" and
* "sets" provide access to submatrices and matrix elements. Several methods
* implement basic matrix arithmetic, including matrix addition and
* multiplication, matrix norms, and element-by-element array operations.
* Methods for reading and printing matrices are also included. All the
* operations in this version of the Matrix Class involve real matrices.
* Complex matrices may be handled in a future version.
*
* Five fundamental matrix decompositions, which consist of pairs or triples
* of matrices, permutation vectors, and the like, produce results in five
* decomposition classes. These decompositions are accessed by the Matrix
* class to compute solutions of simultaneous linear equations, determinants,
* inverses and other matrix functions. The five decompositions are:
*
* - Cholesky Decomposition of symmetric, positive definite matrices.
*
- LU Decomposition of rectangular matrices.
*
- QR Decomposition of rectangular matrices.
*
- Singular Value Decomposition of rectangular matrices.
*
- Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.
*
*
* - Example of use:
* - Solve a linear system A x = b and compute the residual norm, ||b - A x||.
*
* double[][] vals = {{1.,2.,3},{4.,5.,6.},{7.,8.,10.}};
* Matrix A = new Matrix(vals);
* Matrix b = Matrix.random(3,1);
* Matrix x = A.solve(b);
* Matrix r = A.times(x).minus(b);
* double rnorm = r.normInf();
*
*
*
* @author The MathWorks, Inc. and the National Institute of Standards and Technology.
* @version 5 August 1998
*/
public class Matrix implements Cloneable, java.io.Serializable {
/* ------------------------
Class variables
* ------------------------ */
/**
* Array for internal storage of elements.
*
* @serial internal array storage.
*/
private double[][] A;
/**
* Row and column dimensions.
*
* @serial row dimension.
* @serial column dimension.
*/
private int m, n;
/* ------------------------
Constructors
* ------------------------ */
/**
* Construct an m-by-n matrix of zeros.
*
* @param m Number of rows.
* @param n Number of colums.
*/
public Matrix(int m, int n) {
this.m = m;
this.n = n;
A = new double[m][n];
}
/**
* Construct an m-by-n constant matrix.
*
* @param m Number of rows.
* @param n Number of colums.
* @param s Fill the matrix with this scalar value.
*/
public Matrix(int m, int n, double s) {
this.m = m;
this.n = n;
A = new double[m][n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
A[i][j] = s;
}
}
}
/**
* Construct a matrix from a 2-D array.
*
* @param A Two-dimensional array of doubles.
* @throws IllegalArgumentException All rows must have the same length
* @see #constructWithCopy
*/
public Matrix(double[][] A) {
m = A.length;
n = A[0].length;
for (int i = 0; i < m; i++) {
if (A[i].length != n) {
throw new IllegalArgumentException("All rows must have the same length.");
}
}
this.A = A;
}
/**
* Construct a matrix quickly without checking arguments.
*
* @param A Two-dimensional array of doubles.
* @param m Number of rows.
* @param n Number of colums.
*/
public Matrix(double[][] A, int m, int n) {
this.A = A;
this.m = m;
this.n = n;
}
/**
* Construct a matrix from a one-dimensional packed array
*
* @param vals One-dimensional array of doubles, packed by columns (ala Fortran).
* @param m Number of rows.
* @throws IllegalArgumentException Array length must be a multiple of m.
*/
public Matrix(double vals[], int m) {
this.m = m;
n = (m != 0 ? vals.length / m : 0);
if (m * n != vals.length) {
throw new IllegalArgumentException("Array length must be a multiple of m.");
}
A = new double[m][n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
A[i][j] = vals[i + j * m];
}
}
}
/* ------------------------
Public Methods
* ------------------------ */
/**
* Construct a matrix from a copy of a 2-D array.
*
* @param A Two-dimensional array of doubles.
* @return copy of A
* @throws IllegalArgumentException All rows must have the same length
*/
public static Matrix constructWithCopy(double[][] A) {
int m = A.length;
int n = A[0].length;
Matrix X = new Matrix(m, n);
double[][] C = X.getArray();
for (int i = 0; i < m; i++) {
if (A[i].length != n) {
throw new IllegalArgumentException
("All rows must have the same length.");
}
for (int j = 0; j < n; j++) {
C[i][j] = A[i][j];
}
}
return X;
}
/**
* Make a deep copy of a matrix
*
* @return deep copy of this matrix
*/
public Matrix copy() {
Matrix X = new Matrix(m, n);
double[][] C = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
C[i][j] = A[i][j];
}
}
return X;
}
/**
* Clone the Matrix object.
*/
public Object clone() {
return this.copy();
}
/**
* Access the internal two-dimensional array.
*
* @return Pointer to the two-dimensional array of matrix elements.
*/
public double[][] getArray() {
return A;
}
/**
* Copy the internal two-dimensional array.
*
* @return Two-dimensional array copy of matrix elements.
*/
public double[][] getArrayCopy() {
double[][] C = new double[m][n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
C[i][j] = A[i][j];
}
}
return C;
}
/**
* Make a one-dimensional column packed copy of the internal array.
*
* @return Matrix elements packed in a one-dimensional array by columns.
*/
public double[] getColumnPackedCopy() {
double[] vals = new double[m * n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
vals[i + j * m] = A[i][j];
}
}
return vals;
}
/**
* Make a one-dimensional row packed copy of the internal array.
*
* @return Matrix elements packed in a one-dimensional array by rows.
*/
public double[] getRowPackedCopy() {
double[] vals = new double[m * n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
vals[i * n + j] = A[i][j];
}
}
return vals;
}
/**
* Get row dimension.
*
* @return m, the number of rows.
*/
public int getRowDimension() {
return m;
}
/**
* Get column dimension.
*
* @return n, the number of columns.
*/
public int getColumnDimension() {
return n;
}
/**
* Get a single element.
*
* @param i Row index.
* @param j Column index.
* @return A(i, j)
* @throws ArrayIndexOutOfBoundsException out of array bounds
*/
public double get(int i, int j) {
return A[i][j];
}
/**
* Get a submatrix.
*
* @param i0 Initial row index
* @param i1 Final row index
* @param j0 Initial column index
* @param j1 Final column index
* @return A(i0 : i1, j0 : j1)
* @throws ArrayIndexOutOfBoundsException Submatrix indices
*/
public Matrix getMatrix(int i0, int i1, int j0, int j1) {
Matrix X = new Matrix(i1 - i0 + 1, j1 - j0 + 1);
double[][] B = X.getArray();
try {
for (int i = i0; i <= i1; i++) {
for (int j = j0; j <= j1; j++) {
B[i - i0][j - j0] = A[i][j];
}
}
} catch (ArrayIndexOutOfBoundsException e) {
throw new ArrayIndexOutOfBoundsException("Submatrix indices");
}
return X;
}
/**
* Get a submatrix.
*
* @param r Array of row indices.
* @param c Array of column indices.
* @return A(r ( :), c(:))
* @throws ArrayIndexOutOfBoundsException Submatrix indices
*/
public Matrix getMatrix(int[] r, int[] c) {
Matrix X = new Matrix(r.length, c.length);
double[][] B = X.getArray();
try {
for (int i = 0; i < r.length; i++) {
for (int j = 0; j < c.length; j++) {
B[i][j] = A[r[i]][c[j]];
}
}
} catch (ArrayIndexOutOfBoundsException e) {
throw new ArrayIndexOutOfBoundsException("Submatrix indices");
}
return X;
}
/**
* Get a submatrix.
*
* @param i0 Initial row index
* @param i1 Final row index
* @param c Array of column indices.
* @return A(i0 : i1, c ( :))
* @throws ArrayIndexOutOfBoundsException Submatrix indices
*/
public Matrix getMatrix(int i0, int i1, int[] c) {
Matrix X = new Matrix(i1 - i0 + 1, c.length);
double[][] B = X.getArray();
try {
for (int i = i0; i <= i1; i++) {
for (int j = 0; j < c.length; j++) {
B[i - i0][j] = A[i][c[j]];
}
}
} catch (ArrayIndexOutOfBoundsException e) {
throw new ArrayIndexOutOfBoundsException("Submatrix indices");
}
return X;
}
/**
* Get a submatrix.
*
* @param r Array of row indices.
* @param j0 Initial column index
* @param j1 Final column index
* @return A(r ( :), j0:j1)
* @throws ArrayIndexOutOfBoundsException Submatrix indices
*/
public Matrix getMatrix(int[] r, int j0, int j1) {
Matrix X = new Matrix(r.length, j1 - j0 + 1);
double[][] B = X.getArray();
try {
for (int i = 0; i < r.length; i++) {
for (int j = j0; j <= j1; j++) {
B[i][j - j0] = A[r[i]][j];
}
}
} catch (ArrayIndexOutOfBoundsException e) {
throw new ArrayIndexOutOfBoundsException("Submatrix indices");
}
return X;
}
/**
* Set a single element.
*
* @param i Row index.
* @param j Column index.
* @param s A(i,j).
* @throws ArrayIndexOutOfBoundsException out of array bounds
*/
public void set(int i, int j, double s) {
A[i][j] = s;
}
/**
* Set a submatrix.
*
* @param i0 Initial row index
* @param i1 Final row index
* @param j0 Initial column index
* @param j1 Final column index
* @param X A(i0:i1,j0:j1)
* @throws ArrayIndexOutOfBoundsException Submatrix indices
*/
public void setMatrix(int i0, int i1, int j0, int j1, Matrix X) {
try {
for (int i = i0; i <= i1; i++) {
for (int j = j0; j <= j1; j++) {
A[i][j] = X.get(i - i0, j - j0);
}
}
} catch (ArrayIndexOutOfBoundsException e) {
throw new ArrayIndexOutOfBoundsException("Submatrix indices");
}
}
/**
* Set a submatrix.
*
* @param r Array of row indices.
* @param c Array of column indices.
* @param X A(r(:),c(:))
* @throws ArrayIndexOutOfBoundsException Submatrix indices
*/
public void setMatrix(int[] r, int[] c, Matrix X) {
try {
for (int i = 0; i < r.length; i++) {
for (int j = 0; j < c.length; j++) {
A[r[i]][c[j]] = X.get(i, j);
}
}
} catch (ArrayIndexOutOfBoundsException e) {
throw new ArrayIndexOutOfBoundsException("Submatrix indices");
}
}
/**
* Set a submatrix.
*
* @param r Array of row indices.
* @param j0 Initial column index
* @param j1 Final column index
* @param X A(r(:),j0:j1)
* @throws ArrayIndexOutOfBoundsException Submatrix indices
*/
public void setMatrix(int[] r, int j0, int j1, Matrix X) {
try {
for (int i = 0; i < r.length; i++) {
for (int j = j0; j <= j1; j++) {
A[r[i]][j] = X.get(i, j - j0);
}
}
} catch (ArrayIndexOutOfBoundsException e) {
throw new ArrayIndexOutOfBoundsException("Submatrix indices");
}
}
/**
* Set a submatrix.
*
* @param i0 Initial row index
* @param i1 Final row index
* @param c Array of column indices.
* @param X A(i0:i1,c(:))
* @throws ArrayIndexOutOfBoundsException Submatrix indices
*/
public void setMatrix(int i0, int i1, int[] c, Matrix X) {
try {
for (int i = i0; i <= i1; i++) {
for (int j = 0; j < c.length; j++) {
A[i][c[j]] = X.get(i - i0, j);
}
}
} catch (ArrayIndexOutOfBoundsException e) {
throw new ArrayIndexOutOfBoundsException("Submatrix indices");
}
}
/**
* Matrix transpose.
*
* @return A'
*/
public Matrix transpose() {
Matrix X = new Matrix(n, m);
double[][] C = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
C[j][i] = A[i][j];
}
}
return X;
}
/**
* One norm
*
* @return maximum column sum.
*/
public double norm1() {
double f = 0;
for (int j = 0; j < n; j++) {
double s = 0;
for (int i = 0; i < m; i++) {
s += Math.abs(A[i][j]);
}
f = Math.max(f, s);
}
return f;
}
/**
* Two norm
*
* @return maximum singular value.
*/
public double norm2() {
return (new SingularValueDecomposition(this).norm2());
}
/**
* Infinity norm
*
* @return maximum row sum.
*/
public double normInf() {
double f = 0;
for (int i = 0; i < m; i++) {
double s = 0;
for (int j = 0; j < n; j++) {
s += Math.abs(A[i][j]);
}
f = Math.max(f, s);
}
return f;
}
/**
* Frobenius norm
*
* @return sqrt of sum of squares of all elements.
*/
public double normF() {
double f = 0;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
f = Maths.hypot(f, A[i][j]);
}
}
return f;
}
/**
* Unary minus
*
* @return -A
*/
public Matrix uminus() {
Matrix X = new Matrix(m, n);
double[][] C = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
C[i][j] = -A[i][j];
}
}
return X;
}
/**
* C = A + B
*
* @param B another matrix
* @return A + B
*/
public Matrix plus(Matrix B) {
checkMatrixDimensions(B);
Matrix X = new Matrix(m, n);
double[][] C = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
C[i][j] = A[i][j] + B.A[i][j];
}
}
return X;
}
/**
* A = A + B
*
* @param B another matrix
* @return A + B
*/
public Matrix plusEquals(Matrix B) {
checkMatrixDimensions(B);
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
A[i][j] = A[i][j] + B.A[i][j];
}
}
return this;
}
/**
* C = A - B
*
* @param B another matrix
* @return A - B
*/
public Matrix minus(Matrix B) {
checkMatrixDimensions(B);
Matrix X = new Matrix(m, n);
double[][] C = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
C[i][j] = A[i][j] - B.A[i][j];
}
}
return X;
}
/**
* A = A - B
*
* @param B another matrix
* @return A - B
*/
public Matrix minusEquals(Matrix B) {
checkMatrixDimensions(B);
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
A[i][j] = A[i][j] - B.A[i][j];
}
}
return this;
}
/**
* Element-by-element multiplication, C = A.*B
*
* @param B another matrix
* @return A.*B
*/
public Matrix arrayTimes(Matrix B) {
checkMatrixDimensions(B);
Matrix X = new Matrix(m, n);
double[][] C = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
C[i][j] = A[i][j] * B.A[i][j];
}
}
return X;
}
/**
* Element-by-element multiplication in place, A = A.*B
*
* @param B another matrix
* @return A.*B
*/
public Matrix arrayTimesEquals(Matrix B) {
checkMatrixDimensions(B);
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
A[i][j] = A[i][j] * B.A[i][j];
}
}
return this;
}
/**
* Element-by-element right division, C = A./B
*
* @param B another matrix
* @return A./B
*/
public Matrix arrayRightDivide(Matrix B) {
checkMatrixDimensions(B);
Matrix X = new Matrix(m, n);
double[][] C = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
C[i][j] = A[i][j] / B.A[i][j];
}
}
return X;
}
/**
* Element-by-element right division in place, A = A./B
*
* @param B another matrix
* @return A./B
*/
public Matrix arrayRightDivideEquals(Matrix B) {
checkMatrixDimensions(B);
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
A[i][j] = A[i][j] / B.A[i][j];
}
}
return this;
}
/**
* Element-by-element left division, C = A.\B
*
* @param B another matrix
* @return A.\B
*/
public Matrix arrayLeftDivide(Matrix B) {
checkMatrixDimensions(B);
Matrix X = new Matrix(m, n);
double[][] C = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
C[i][j] = B.A[i][j] / A[i][j];
}
}
return X;
}
/**
* Element-by-element left division in place, A = A.\B
*
* @param B another matrix
* @return A.\B
*/
public Matrix arrayLeftDivideEquals(Matrix B) {
checkMatrixDimensions(B);
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
A[i][j] = B.A[i][j] / A[i][j];
}
}
return this;
}
/**
* Multiply a matrix by a scalar, C = s*A
*
* @param s scalar
* @return s*A
*/
public Matrix times(double s) {
Matrix X = new Matrix(m, n);
double[][] C = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
C[i][j] = s * A[i][j];
}
}
return X;
}
/**
* Multiply a matrix by a scalar in place, A = s*A
*
* @param s scalar
* @return replace A by s*A
*/
public Matrix timesEquals(double s) {
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
A[i][j] = s * A[i][j];
}
}
return this;
}
/**
* Linear algebraic matrix multiplication, A * B
*
* @param B another matrix
* @return Matrix product, A * B
* @throws IllegalArgumentException Matrix inner dimensions must agree.
*/
public Matrix times(Matrix B) {
if (B.m != n) {
throw new IllegalArgumentException("Matrix inner dimensions must agree.");
}
Matrix X = new Matrix(m, B.n);
double[][] C = X.getArray();
double[] Bcolj = new double[n];
for (int j = 0; j < B.n; j++) {
for (int k = 0; k < n; k++) {
Bcolj[k] = B.A[k][j];
}
for (int i = 0; i < m; i++) {
double[] Arowi = A[i];
double s = 0;
for (int k = 0; k < n; k++) {
s += Arowi[k] * Bcolj[k];
}
C[i][j] = s;
}
}
return X;
}
/**
* LU Decomposition
*
* @return LUDecomposition
* @see LUDecomposition
*/
public LUDecomposition lu() {
return new LUDecomposition(this);
}
/**
* QR Decomposition
*
* @return QRDecomposition
* @see QRDecomposition
*/
public QRDecomposition qr() {
return new QRDecomposition(this);
}
/**
* Cholesky Decomposition
*
* @return CholeskyDecomposition
* @see CholeskyDecomposition
*/
public CholeskyDecomposition chol() {
return new CholeskyDecomposition(this);
}
/**
* Singular Value Decomposition
*
* @return SingularValueDecomposition
* @see SingularValueDecomposition
*/
public SingularValueDecomposition svd() {
return new SingularValueDecomposition(this);
}
/**
* Eigenvalue Decomposition
*
* @return EigenvalueDecomposition
* @see EigenvalueDecomposition
*/
public EigenvalueDecomposition eig() {
return new EigenvalueDecomposition(this);
}
/**
* Solve A*X = B
*
* @param B right hand side
* @return solution if A is square, least squares solution otherwise
*/
public Matrix solve(Matrix B) {
return (m == n ? (new LUDecomposition(this)).solve(B) :
(new QRDecomposition(this)).solve(B));
}
/**
* Solve X*A = B, which is also A'*X' = B'
*
* @param B right hand side
* @return solution if A is square, least squares solution otherwise.
*/
public Matrix solveTranspose(Matrix B) {
return transpose().solve(B.transpose());
}
/**
* Matrix inverse or pseudoinverse
*
* @return inverse(A) if A is square, pseudoinverse otherwise.
*/
public Matrix inverse() {
return solve(identity(m, m));
}
/**
* Matrix determinant
*
* @return determinant
*/
public double det() {
return new LUDecomposition(this).det();
}
/**
* Matrix rank
*
* @return effective numerical rank, obtained from SVD.
*/
public int rank() {
return new SingularValueDecomposition(this).rank();
}
/**
* Matrix condition (2 norm)
*
* @return ratio of largest to smallest singular value.
*/
public double cond() {
return new SingularValueDecomposition(this).cond();
}
/**
* Matrix trace.
*
* @return sum of the diagonal elements.
*/
public double trace() {
double t = 0;
for (int i = 0; i < Math.min(m, n); i++) {
t += A[i][i];
}
return t;
}
/**
* Generate matrix with random elements
*
* @param m Number of rows.
* @param n Number of colums.
* @return An m-by-n matrix with uniformly distributed random elements.
*/
public static Matrix random(int m, int n) {
Matrix A = new Matrix(m, n);
double[][] X = A.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
X[i][j] = Math.random();
}
}
return A;
}
/**
* Generate identity matrix
*
* @param m Number of rows.
* @param n Number of colums.
* @return An m-by-n matrix with ones on the diagonal and zeros elsewhere.
*/
public static Matrix identity(int m, int n) {
Matrix A = new Matrix(m, n);
double[][] X = A.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
X[i][j] = (i == j ? 1.0 : 0.0);
}
}
return A;
}
/**
* Print the matrix to stdout. Line the elements up in columns
* with a Fortran-like 'Fw.d' style format.
*
* @param w Column width.
* @param d Number of digits after the decimal.
*/
public void print(int w, int d) {
print(new PrintWriter(System.out, true), w, d);
}
/**
* Print the matrix to the output stream. Line the elements up in
* columns with a Fortran-like 'Fw.d' style format.
*
* @param output Output stream.
* @param w Column width.
* @param d Number of digits after the decimal.
*/
public void print(PrintWriter output, int w, int d) {
DecimalFormat format = new DecimalFormat();
format.setDecimalFormatSymbols(new DecimalFormatSymbols(Locale.US));
format.setMinimumIntegerDigits(1);
format.setMaximumFractionDigits(d);
format.setMinimumFractionDigits(d);
format.setGroupingUsed(false);
print(output, format, w + 2);
}
/**
* Print the matrix to stdout. Line the elements up in columns.
* Use the format object, and right justify within columns of width
* characters.
* Note that is the matrix is to be read back in, you probably will want
* to use a NumberFormat that is set to US Locale.
*
* @param format A Formatting object for individual elements.
* @param width Field width for each column.
* @see java.text.DecimalFormat#setDecimalFormatSymbols
*/
public void print(NumberFormat format, int width) {
print(new PrintWriter(System.out, true), format, width);
}
// DecimalFormat is a little disappointing coming from Fortran or C's printf.
// Since it doesn't pad on the left, the elements will come out different
// widths. Consequently, we'll pass the desired column width in as an
// argument and do the extra padding ourselves.
/**
* Print the matrix to the output stream. Line the elements up in columns.
* Use the format object, and right justify within columns of width
* characters.
* Note that is the matrix is to be read back in, you probably will want
* to use a NumberFormat that is set to US Locale.
*
* @param output the output stream.
* @param format A formatting object to format the matrix elements
* @param width Column width.
* @see java.text.DecimalFormat#setDecimalFormatSymbols
*/
public void print(PrintWriter output, NumberFormat format, int width) {
output.println(); // start on new line.
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
String s = format.format(A[i][j]); // format the number
int padding = Math.max(1, width - s.length()); // At _least_ 1 space
for (int k = 0; k < padding; k++)
output.print(' ');
output.print(s);
}
output.println();
}
output.println(); // end with blank line.
}
/**
* Read a matrix from a stream. The format is the same the print method,
* so printed matrices can be read back in (provided they were printed using
* US Locale). Elements are separated by
* whitespace, all the elements for each row appear on a single line,
* the last row is followed by a blank line.
*
* @param input the input stream.
* @return matrix
* @throws java.io.IOException failed to read from stream
*/
public static Matrix read(BufferedReader input) throws java.io.IOException {
StreamTokenizer tokenizer = new StreamTokenizer(input);
// Although StreamTokenizer will parse numbers, it doesn't recognize
// scientific notation (E or D); however, Double.valueOf does.
// The strategy here is to disable StreamTokenizer's number parsing.
// We'll only get whitespace delimited words, EOL's and EOF's.
// These words should all be numbers, for Double.valueOf to parse.
tokenizer.resetSyntax();
tokenizer.wordChars(0, 255);
tokenizer.whitespaceChars(0, ' ');
tokenizer.eolIsSignificant(true);
java.util.Vector vD = new java.util.Vector();
// Ignore initial empty lines
while (tokenizer.nextToken() == StreamTokenizer.TT_EOL) ;
if (tokenizer.ttype == StreamTokenizer.TT_EOF)
throw new java.io.IOException("Unexpected EOF on matrix read.");
do {
vD.addElement(Double.valueOf(tokenizer.sval)); // Read & store 1st row.
} while (tokenizer.nextToken() == StreamTokenizer.TT_WORD);
int n = vD.size(); // Now we've got the number of columns!
double row[] = new double[n];
for (int j = 0; j < n; j++) // extract the elements of the 1st row.
row[j] = vD.elementAt(j).doubleValue();
java.util.Vector v = new java.util.Vector();
v.addElement(row); // Start storing rows instead of columns.
while (tokenizer.nextToken() == StreamTokenizer.TT_WORD) {
// While non-empty lines
v.addElement(row = new double[n]);
int j = 0;
do {
if (j >= n) throw new java.io.IOException
("Row " + v.size() + " is too long.");
row[j++] = Double.valueOf(tokenizer.sval).doubleValue();
} while (tokenizer.nextToken() == StreamTokenizer.TT_WORD);
if (j < n) throw new java.io.IOException
("Row " + v.size() + " is too short.");
}
int m = v.size(); // Now we've got the number of rows.
double[][] A = new double[m][];
v.copyInto(A); // copy the rows out of the vector
return new Matrix(A);
}
/* ------------------------
Private Methods
* ------------------------ */
/**
* Check if size(A) == size(B)
**/
private void checkMatrixDimensions(Matrix B) {
if (B.m != m || B.n != n) {
throw new IllegalArgumentException("Matrix dimensions must agree.");
}
}
private static final long serialVersionUID = 1;
}
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