matrix.java

Jama includes matrix operator class... and linear Algebra... it s cool

            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;
   }


   /** 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 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.");
      }
   }

}