/* * This software is a cooperative product of The MathWorks and the National * Institute of Standards and Technology (NIST) which has been released to the * public domain. Neither The MathWorks nor NIST assumes any responsibility * whatsoever for its use by other parties, and makes no guarantees, expressed * or implied, about its quality, reliability, or any other characteristic. *//* * Matrix.java * Copyright (C) 1999 The Mathworks and NIST and 2005 University of Waikato, *               Hamilton, New Zealand * */package weka.core.matrix;import weka.core.Utils;import java.io.BufferedReader;import java.io.LineNumberReader;import java.io.PrintWriter;import java.io.Reader;import java.io.Serializable;import java.io.StreamTokenizer;import java.io.StringReader;import java.io.StringWriter;import java.io.Writer;import java.text.DecimalFormat;import java.text.DecimalFormatSymbols;import java.text.NumberFormat;import java.util.Locale;import java.util.StringTokenizer;/*** 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> * <p/> * Adapted from the <a href="http://math.nist.gov/javanumerics/jama/" target="_blank">JAMA</a> package. Additional methods are tagged with the  * <code>@author</code> tag. * * @author The Mathworks and NIST  * @author Fracpete (fracpete at waikato dot ac dot nz) * @version $Revision: 1.5 $*/public class Matrix   implements Cloneable, Serializable {  /**    * Array for internal storage of elements.   * @serial internal array storage.   */  protected double[][] A;  /**    * Row and column dimensions.   * @serial row dimension.   * @serial column dimension.   */  protected int m, n;  /**    * 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];      }    }  }  /**   * Reads a matrix from a reader. The first line in the file should   * contain the number of rows and columns. Subsequent lines   * contain elements of the matrix.   *   * @param     r the reader containing the matrix   * @throws    Exception if an error occurs   * @see       #write(Writer)   * @author    FracPete, taken from old weka.core.Matrix class   */  public Matrix(Reader r) throws Exception {    LineNumberReader lnr = new LineNumberReader(r);    String line;    int currentRow = -1;    while ((line = lnr.readLine()) != null) {      // Comments      if (line.startsWith("%"))          continue;            StringTokenizer st = new StringTokenizer(line);      // Ignore blank lines      if (!st.hasMoreTokens())          continue;      if (currentRow < 0) {        int rows = Integer.parseInt(st.nextToken());        if (!st.hasMoreTokens())          throw new Exception("Line " + lnr.getLineNumber()               + ": expected number of columns");        int cols = Integer.parseInt(st.nextToken());        A = new double[rows][cols];        m = rows;        n = cols;        currentRow++;        continue;      }       else {        if (currentRow == getRowDimension())          throw new Exception("Line " + lnr.getLineNumber()               + ": too many rows provided");        for (int i = 0; i < getColumnDimension(); i++) {          if (!st.hasMoreTokens())            throw new Exception("Line " + lnr.getLineNumber()                 + ": too few matrix elements provided");          set(currentRow, i, Double.valueOf(st.nextToken()).doubleValue());        }        currentRow++;      }    }    if (currentRow == -1)      throw new Exception("Line " + lnr.getLineNumber()           + ": expected number of rows");    else if (currentRow != getRowDimension())      throw new Exception("Line " + lnr.getLineNumber()           + ": too few rows provided");  }  /**    * 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 {