/*
 *                    BioJava development code
 *
 * This code may be freely distributed and modified under the
 * terms of the GNU Lesser General Public Licence.  This should
 * be distributed with the code.  If you do not have a copy,
 * see:
 *
 *      http://www.gnu.org/copyleft/lesser.html
 *
 * Copyright for this code is held jointly by the individual
 * authors.  These should be listed in @author doc comments.
 *
 * For more information on the BioJava project and its aims,
 * or to join the biojava-l mailing list, visit the home page
 * at:
 *
 *      http://www.biojava.org/
 *
 */
/* Derived from the MathWorks and NIST implementation, which was released into
 * the public domain.
 *
 * http://math.nist.gov/javanumerics/jama/
 */
package org.biojava.nbio.structure.jama;

import java.io.BufferedReader;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.io.StringWriter;
import java.text.DecimalFormat;
import java.text.DecimalFormatSymbols;
import java.text.NumberFormat;
import java.util.Locale;


/**
 *      Jama = Java Matrix class.
 * <P>
 *      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.
 * <P>
 *      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:
 * <P><UL>
 *      <LI>Cholesky Decomposition of symmetric, positive definite matrices.
 *      <LI>LU Decomposition of rectangular matrices.
 *      <LI>QR Decomposition of rectangular matrices.
 *      <LI>Singular Value Decomposition of rectangular matrices.
 *      <LI>Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.
 * </UL>
 * <DL>
 * <DT><B>Example of use:</B></DT>
 * <P>
 * <DD>Solve a linear system A x = b and compute the residual norm, ||b - A x||.
 * <P><PRE>
 *              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();
 * </PRE></DD>
 * </DL>
 *
 * @author The MathWorks, Inc. and the National Institute of Standards and Technology.
 * @version 5 August 1998
 */

public class Matrix implements Cloneable, java.io.Serializable {

         static final long serialVersionUID = 8492558293015348719l;


/* ------------------------
        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.
        @exception  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.
        @exception  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.
        @exception  IllegalArgumentException All rows must have the same length
        @return a Matrix
        */

        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 a identical copy of the 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.
        */

        @Override
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)
        @exception  ArrayIndexOutOfBoundsException
        */

        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)
        @exception  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(:))
        @exception  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(:))
        @exception  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)
        @exception  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).
        @exception  ArrayIndexOutOfBoundsException
        */

        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)
        @exception  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(:))
        @exception  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)
        @exception  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(:))
        @exception  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
        @exception  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;
        }

        @Override
public String toString(){
                StringWriter writer = new StringWriter();
                PrintWriter printWriter = new PrintWriter(writer);
                print(printWriter,getColumnDimension(),3);
                return writer.toString();
        }


        /** 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 a Matrix
        @throws java.io.IOException
        */

        @SuppressWarnings({ "rawtypes", "unchecked" })
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.");
                }
        }

}