Matrix.html

Matrix.java

package Jama;

import java.text.NumberFormat;
import java.text.DecimalFormat;
import java.text.DecimalFormatSymbols;
import java.util.Locale;
import java.text.FieldPosition;
import java.io.PrintWriter;
import java.io.BufferedReader;
import java.io.StreamTokenizer;
import Jama.util.*;

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., column dimension.


   private int m, n;

/* ------------------------
   Constructors
 * ------------------------ */

Construct an m-by-n matrix of zeros.

Parameters:

m - Number of rows.

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.

Parameters:

m - Number of rows.

n - Number of colums.

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.

See also: constructWithCopy

Throws: IllegalArgumentException All rows must have the same length

Parameters:

A - Two-dimensional array of doubles.



   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.

Parameters:

A - Two-dimensional array of doubles.

m - Number of rows.

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

Throws: IllegalArgumentException Array length must be a multiple of m.

Parameters:

vals - One-dimensional array of doubles, packed by columns (ala Fortran).

m - Number of rows.



   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.

Throws: IllegalArgumentException All rows must have the same length

Parameters:

A - Two-dimensional array of doubles.



   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



   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.

Returns: Pointer to the two-dimensional array of matrix elements.



   public double[][] getArray () {
      return A;
   }

Copy the internal two-dimensional array.

Returns: 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.

Returns: 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.

Returns: 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.

Returns: m, the number of rows.



   public int getRowDimension () {
      return m;
   }

Get column dimension.

Returns: n, the number of columns.



   public int getColumnDimension () {
      return n;
   }

Get a single element.

Throws: ArrayIndexOutOfBoundsException

Returns: A(i,j)

Parameters:

i - Row index.

j - Column index.



   public double get (int i, int j) {
      return A[i][j];
   }

Get a submatrix.

Throws: ArrayIndexOutOfBoundsException Submatrix indices

Returns: A(i0:i1,j0:j1)

Parameters:

i0 - Initial row index

i1 - Final row index

j0 - Initial column index

j1 - Final column index



   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.

Throws: ArrayIndexOutOfBoundsException Submatrix indices

Returns: A(r(:),c(:))

Parameters:

r - Array of row indices.

c - Array of column 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.

Throws: ArrayIndexOutOfBoundsException Submatrix indices

Returns: A(i0:i1,c(:))

Parameters:

i0 - Initial row index

i1 - Final row index

c - Array of column 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.

Throws: ArrayIndexOutOfBoundsException Submatrix indices

Returns: A(r(:),j0:j1)

Parameters:

r - Array of row indices.

i0 - Initial column index

i1 - Final column index



   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.

Throws: ArrayIndexOutOfBoundsException

Parameters:

i - Row index.

j - Column index.

s - A(i,j).



   public void set (int i, int j, double s) {
      A[i][j] = s;
   }

Set a submatrix.

Throws: ArrayIndexOutOfBoundsException Submatrix indices

Parameters:

i0 - Initial row index

i1 - Final row index

j0 - Initial column index

j1 - Final column index

X - A(i0:i1,j0:j1)



   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.

Throws: ArrayIndexOutOfBoundsException Submatrix indices

Parameters:

r - Array of row indices.

c - Array of column indices.

X - A(r(:),c(:))



   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.

Throws: ArrayIndexOutOfBoundsException Submatrix indices

Parameters:

r - Array of row indices.

j0 - Initial column index

j1 - Final column index

X - A(r(:),j0:j1)



   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.

Throws: ArrayIndexOutOfBoundsException Submatrix indices

Parameters:

i0 - Initial row index

i1 - Final row index

c - Array of column indices.

X - A(i0:i1,c(:))



   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.

Returns: 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

Returns: 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

Returns: maximum singular value.



   public double norm2 () {
      return (new SingularValueDecomposition(this).norm2());
   }

Infinity norm

Returns: 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

Returns: 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

Returns: -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

Returns: A + B

Parameters:

B - another matrix



   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

Returns: A + B

Parameters:

B - another matrix



   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

Returns: A - B

Parameters:

B - another matrix



   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

Returns: A - B

Parameters:

B - another matrix



   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

Returns: A.*B

Parameters:

B - another matrix



   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

Returns: A.*B

Parameters:

B - another matrix



   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

Returns: A./B

Parameters:

B - another matrix



   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

Returns: A./B

Parameters:

B - another matrix



   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

Returns: A.\B

Parameters:

B - another matrix



   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

Returns: A.\B

Parameters:

B - another matrix



   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 = sA

Returns: s*A

Parameters:

s - scalar



   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 = sA

Returns: replace A by s*A

Parameters:

s - scalar



   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

Throws: IllegalArgumentException Matrix inner dimensions must agree.

Returns: Matrix product, A * B

Parameters:

B - another matrix



   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

See also: LUDecomposition

Returns: LUDecomposition



   public LUDecomposition lu () {
      return new LUDecomposition(this);
   }

QR Decomposition

See also: QRDecomposition

Returns: QRDecomposition



   public QRDecomposition qr () {
      return new QRDecomposition(this);
   }

Cholesky Decomposition

See also: CholeskyDecomposition

Returns: CholeskyDecomposition



   public CholeskyDecomposition chol () {
      return new CholeskyDecomposition(this);
   }

Singular Value Decomposition

See also: SingularValueDecomposition

Returns: SingularValueDecomposition



   public SingularValueDecomposition svd () {
      return new SingularValueDecomposition(this);
   }

Eigenvalue Decomposition

See also: EigenvalueDecomposition

Returns: EigenvalueDecomposition



   public EigenvalueDecomposition eig () {
      return new EigenvalueDecomposition(this);
   }

Solve AX = B

Returns: solution if A is square, least squares solution otherwise

Parameters:

B - right hand side



   public Matrix solve (Matrix B) {
      return (m == n ? (new LUDecomposition(this)).solve(B) :
                       (new QRDecomposition(this)).solve(B));
   }

Solve XA = B, which is also A'X' = B'

Returns: solution if A is square, least squares solution otherwise.

Parameters:

B - right hand side



   public Matrix solveTranspose (Matrix B) {
      return transpose().solve(B.transpose());
   }

Matrix inverse or pseudoinverse

Returns: inverse(A) if A is square, pseudoinverse otherwise.



   public Matrix inverse () {
      return solve(identity(m,m));
   }

Matrix determinant

Returns: determinant



   public double det () {
      return new LUDecomposition(this).det();
   }

Matrix rank

Returns: effective numerical rank, obtained from SVD.



   public int rank () {
      return new SingularValueDecomposition(this).rank();
   }

Matrix condition (2 norm)

Returns: ratio of largest to smallest singular value.



   public double cond () {
      return new SingularValueDecomposition(this).cond();
   }

Matrix trace.

Returns: 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

Returns: An m-by-n matrix with uniformly distributed random elements.

Parameters:

m - Number of rows.

n - Number of colums.



   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

Returns: An m-by-n matrix with ones on the diagonal and zeros elsewhere.

Parameters:

m - Number of rows.

n - Number of colums.



   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.

Parameters:

w - Column width.

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.

Parameters:

output - Output stream.

w - Column width.

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.

See also: setDecimalFormatSymbols

Parameters:

format - A Formatting object for individual elements.

width - Field width for each column.



   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.

See also: setDecimalFormatSymbols

Parameters:

output - the output stream.

format - A formatting object to format the matrix elements

width - Column width.



   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.

Parameters:

input - the input 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 v = 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 {
         v.addElement(Double.valueOf(tokenizer.sval)); // Read & store 1st row.
      } while (tokenizer.nextToken() == StreamTokenizer.TT_WORD);

      int n = v.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]=((Double)v.elementAt(j)).doubleValue();
      v.removeAllElements();
      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.");
      }
   }

}

This file was generated on Sun Jun 13 10:31:45 PDT 2010 from file Matrix.java
by the ilog.language.tools.Hilite Java tool written by Hassan Aït-Kaci