package edu.claflin.finder.algo.clustering.struct.leading_eigenvector_struct;

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.
	
	This is a reduced version of JAMA, a public domain linear algebra package for Java.
	I trimmed it to only keep EigenvalueDecomposition since that's all I needed for
	the leading eigenvector algorithm. I added the source files instead of using the .jar
	due to issues registering dependencies with Ant. 
	   
	For the full source code, jar, documentation, examples, etc. visit:
	https://math.nist.gov/javanumerics/jama/
	
	@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.
   @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
   */

   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.
   @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;
   }

   /** 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;
   }
   
   /** 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.
   */

   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<Double> vD = new java.util.Vector<Double>();

      // 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<double[]> v = new java.util.Vector<double[]>();
      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;
}
