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.
<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 {

/* ------------------------
   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 i0   Initial column index
   @param i1   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++) {