weka.core.matrix

## Class Matrix

- java.lang.Object
- - weka.core.matrix.Matrix

- All Implemented Interfaces:
    java.io.Serializable, java.lang.Cloneable, RevisionHandler
  Direct Known Subclasses:
    ConfusionMatrix

      public class Matrix
      extends java.lang.Object
      implements java.lang.Cloneable, java.io.Serializable, RevisionHandler

  Jama = Java Matrix class.

  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.

  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:

  - Cholesky Decomposition of symmetric, positive definite matrices.
  - LU Decomposition of rectangular matrices.
  - QR Decomposition of rectangular matrices.
  - Singular Value Decomposition of rectangular matrices.
  - Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.
  Example of use:

    Solve a linear system A x = b and compute the residual norm, ||b - A x||.

         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();

  Adapted from the JAMA package. Additional methods are tagged with the `@author` tag.
  Version:
    $Revision: 10203 $
  Author:
    The Mathworks and NIST, Fracpete (fracpete at waikato dot ac dot nz)
  See Also:
    Serialized Form

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `Matrix(double[][] A)` Construct a matrix from a 2-D array.
    `Matrix(double[][] A, int m, int n)` Construct a matrix quickly without checking arguments.
    `Matrix(double[] vals, int m)` Construct a matrix from a one-dimensional packed array
    `Matrix(int m, int n)` Construct an m-by-n matrix of zeros.
    `Matrix(int m, int n, double s)` Construct an m-by-n constant matrix.
    `Matrix(java.io.Reader r)` Reads a matrix from a reader.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `Matrix` | `arrayLeftDivide(Matrix B)` Element-by-element left division, C = A.\B
    `Matrix` | `arrayLeftDivideEquals(Matrix B)` Element-by-element left division in place, A = A.\B
    `Matrix` | `arrayRightDivide(Matrix B)` Element-by-element right division, C = A./B
    `Matrix` | `arrayRightDivideEquals(Matrix B)` Element-by-element right division in place, A = A./B
    `Matrix` | `arrayTimes(Matrix B)` Element-by-element multiplication, C = A.*B
    `Matrix` | `arrayTimesEquals(Matrix B)` Element-by-element multiplication in place, A = A.*B
    `CholeskyDecomposition` | `chol()` Cholesky Decomposition
    `java.lang.Object` | `clone()` Clone the Matrix object.
    `double` | `cond()` Matrix condition (2 norm)
    `static Matrix` | `constructWithCopy(double[][] A)` Construct a matrix from a copy of a 2-D array.
    `Matrix` | `copy()` Make a deep copy of a matrix
    `double` | `det()` Matrix determinant
    `EigenvalueDecomposition` | `eig()` Eigenvalue Decomposition
    `double` | `get(int i, int j)` Get a single element.
    `double[][]` | `getArray()` Access the internal two-dimensional array.
    `double[][]` | `getArrayCopy()` Copy the internal two-dimensional array.
    `int` | `getColumnDimension()` Get column dimension.
    `double[]` | `getColumnPackedCopy()` Make a one-dimensional column packed copy of the internal array.
    `Matrix` | `getMatrix(int[] r, int[] c)` Get a submatrix.
    `Matrix` | `getMatrix(int[] r, int j0, int j1)` Get a submatrix.
    `Matrix` | `getMatrix(int i0, int i1, int[] c)` Get a submatrix.
    `Matrix` | `getMatrix(int i0, int i1, int j0, int j1)` Get a submatrix.
    `java.lang.String` | `getRevision()` Returns the revision string.
    `int` | `getRowDimension()` Get row dimension.
    `double[]` | `getRowPackedCopy()` Make a one-dimensional row packed copy of the internal array.
    `static Matrix` | `identity(int m, int n)` Generate identity matrix
    `Matrix` | `inverse()` Matrix inverse or pseudoinverse
    `boolean` | `isSquare()` returns whether the matrix is a square matrix or not.
    `boolean` | `isSymmetric()` Returns true if the matrix is symmetric.
    `LUDecomposition` | `lu()` LU Decomposition
    `static void` | `main(java.lang.String[] args)` Main method for testing this class.
    `Matrix` | `minus(Matrix B)` C = A - B
    `Matrix` | `minusEquals(Matrix B)` A = A - B
    `double` | `norm1()` One norm
    `double` | `norm2()` Two norm
    `double` | `normF()` Frobenius norm
    `double` | `normInf()` Infinity norm
    `static Matrix` | `parseMatlab(java.lang.String matlab)` creates a matrix from the given Matlab string.
    `Matrix` | `plus(Matrix B)` C = A + B
    `Matrix` | `plusEquals(Matrix B)` A = A + B
    `void` | `print(int w, int d)` Print the matrix to stdout.
    `void` | `print(java.text.NumberFormat format, int width)` Print the matrix to stdout.
    `void` | `print(java.io.PrintWriter output, int w, int d)` Print the matrix to the output stream.
    `void` | `print(java.io.PrintWriter output, java.text.NumberFormat format, int width)` Print the matrix to the output stream.
    `QRDecomposition` | `qr()` QR Decomposition
    `static Matrix` | `random(int m, int n)` Generate matrix with random elements
    `int` | `rank()` Matrix rank
    `static Matrix` | `read(java.io.BufferedReader input)` Read a matrix from a stream.
    `LinearRegression` | `regression(Matrix y, double ridge)` Performs a (ridged) linear regression.
    `LinearRegression` | `regression(Matrix y, double[] w, double ridge)` Performs a weighted (ridged) linear regression.
    `void` | `set(int i, int j, double s)` Set a single element.
    `void` | `setMatrix(int[] r, int[] c, Matrix X)` Set a submatrix.
    `void` | `setMatrix(int[] r, int j0, int j1, Matrix X)` Set a submatrix.
    `void` | `setMatrix(int i0, int i1, int[] c, Matrix X)` Set a submatrix.
    `void` | `setMatrix(int i0, int i1, int j0, int j1, Matrix X)` Set a submatrix.
    `Matrix` | `solve(Matrix B)` Solve A*X = B
    `Matrix` | `solveTranspose(Matrix B)` Solve X*A = B, which is also A'*X' = B'
    `Matrix` | `sqrt()` returns the square root of the matrix, i.e., X from the equation X*X = A. Steps in the Calculation (see `sqrtm` in Matlab): perform eigenvalue decomposition [V,D]=eig(A) take the square root of all elements in D (only the ones with positive sign are considered for further computation) S=sqrt(D) calculate the root X=V*S/V, which can be also written as X=(V'\(V*S)')' Note: since this method uses other high-level methods, it generates several instances of matrices.
    `SingularValueDecomposition` | `svd()` Singular Value Decomposition
    `Matrix` | `times(double s)` Multiply a matrix by a scalar, C = s*A
    `Matrix` | `times(Matrix B)` Linear algebraic matrix multiplication, A * B
    `Matrix` | `timesEquals(double s)` Multiply a matrix by a scalar in place, A = s*A
    `java.lang.String` | `toMatlab()` converts the Matrix into a single line Matlab string: matrix is enclosed by parentheses, rows are separated by semicolon and single cells by blanks, e.g., [1 2; 3 4].
    `java.lang.String` | `toString()` Converts a matrix to a string.
    `double` | `trace()` Matrix trace.
    `Matrix` | `transpose()` Matrix transpose.
    `Matrix` | `uminus()` Unary minus
    `void` | `write(java.io.Writer w)` Writes out a matrix.

    - ### Methods inherited from class java.lang.Object

      `equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`

- - ### Constructor Detail

    - #### Matrix

          public Matrix(int m,
                int n)

      Construct an m-by-n matrix of zeros.
      Parameters:
        `m` - Number of rows.
        `n` - Number of colums.

    - #### Matrix

          public Matrix(int m,
                int n,
                double s)

      Construct an m-by-n constant matrix.
      Parameters:
        `m` - Number of rows.
        `n` - Number of colums.
        `s` - Fill the matrix with this scalar value.

    - #### Matrix

          public Matrix(double[][] A)

      Construct a matrix from a 2-D array.
      Parameters:
        `A` - Two-dimensional array of doubles.
      Throws:
        `java.lang.IllegalArgumentException` - All rows must have the same length
      See Also:
        `constructWithCopy(double[][])`

    - #### Matrix

          public Matrix(double[][] A,
                int m,
                int n)

      Construct a matrix quickly without checking arguments.
      Parameters:
        `A` - Two-dimensional array of doubles.
        `m` - Number of rows.
        `n` - Number of colums.

    - #### Matrix

          public Matrix(double[] vals,
                int m)

      Construct a matrix from a one-dimensional packed array
      Parameters:
        `vals` - One-dimensional array of doubles, packed by columns (ala Fortran).
        `m` - Number of rows.
      Throws:
        `java.lang.IllegalArgumentException` - Array length must be a multiple of m.

    - #### Matrix

          public Matrix(java.io.Reader r)
                 throws java.lang.Exception

      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. (FracPete: taken from old weka.core.Matrix class)
      Parameters:
        `r` - the reader containing the matrix
      Throws:
        `java.lang.Exception` - if an error occurs
      See Also:
        `write(Writer)`

  - ### Method Detail

    - #### constructWithCopy

          public static Matrix constructWithCopy(double[][] A)

      Construct a matrix from a copy of a 2-D array.
      Parameters:
        `A` - Two-dimensional array of doubles.
      Throws:
        `java.lang.IllegalArgumentException` - All rows must have the same length

    - #### copy

          public Matrix copy()

      Make a deep copy of a matrix

    - #### clone

          public java.lang.Object clone()

      Clone the Matrix object.
      Overrides:
        `clone` in class `java.lang.Object`

    - #### getArray

          public double[][] getArray()

      Access the internal two-dimensional array.
      Returns:
        Pointer to the two-dimensional array of matrix elements.

    - #### getArrayCopy

          public double[][] getArrayCopy()

      Copy the internal two-dimensional array.
      Returns:
        Two-dimensional array copy of matrix elements.

    - #### getColumnPackedCopy

          public double[] getColumnPackedCopy()

      Make a one-dimensional column packed copy of the internal array.
      Returns:
        Matrix elements packed in a one-dimensional array by columns.

    - #### getRowPackedCopy

          public double[] getRowPackedCopy()

      Make a one-dimensional row packed copy of the internal array.
      Returns:
        Matrix elements packed in a one-dimensional array by rows.

    - #### getRowDimension

          public int getRowDimension()

      Get row dimension.
      Returns:
        m, the number of rows.

    - #### getColumnDimension

          public int getColumnDimension()

      Get column dimension.
      Returns:
        n, the number of columns.

    - #### get

          public double get(int i,
                   int j)

      Get a single element.
      Parameters:
        `i` - Row index.
        `j` - Column index.
      Returns:
        A(i,j)
      Throws:
        `java.lang.ArrayIndexOutOfBoundsException`

    - #### getMatrix

          public Matrix getMatrix(int i0,
                         int i1,
                         int j0,
                         int j1)

      Get a submatrix.
      Parameters:
        `i0` - Initial row index
        `i1` - Final row index
        `j0` - Initial column index
        `j1` - Final column index
      Returns:
        A(i0:i1,j0:j1)
      Throws:
        `java.lang.ArrayIndexOutOfBoundsException` - Submatrix indices

    - #### getMatrix

          public Matrix getMatrix(int[] r,
                         int[] c)

      Get a submatrix.
      Parameters:
        `r` - Array of row indices.
        `c` - Array of column indices.
      Returns:
        A(r(:),c(:))
      Throws:
        `java.lang.ArrayIndexOutOfBoundsException` - Submatrix indices

    - #### getMatrix

          public Matrix getMatrix(int i0,
                         int i1,
                         int[] c)

      Get a submatrix.
      Parameters:
        `i0` - Initial row index
        `i1` - Final row index
        `c` - Array of column indices.
      Returns:
        A(i0:i1,c(:))
      Throws:
        `java.lang.ArrayIndexOutOfBoundsException` - Submatrix indices

    - #### getMatrix

          public Matrix getMatrix(int[] r,
                         int j0,
                         int j1)

      Get a submatrix.
      Parameters:
        `r` - Array of row indices.
        `j0` - Initial column index
        `j1` - Final column index
      Returns:
        A(r(:),j0:j1)
      Throws:
        `java.lang.ArrayIndexOutOfBoundsException` - Submatrix indices

    - #### set

          public void set(int i,
                 int j,
                 double s)

      Set a single element.
      Parameters:
        `i` - Row index.
        `j` - Column index.
        `s` - A(i,j).
      Throws:
        `java.lang.ArrayIndexOutOfBoundsException`

    - #### setMatrix

          public void setMatrix(int i0,
                       int i1,
                       int j0,
                       int j1,
                       Matrix X)

      Set a submatrix.
      Parameters:
        `i0` - Initial row index
        `i1` - Final row index
        `j0` - Initial column index
        `j1` - Final column index
        `X` - A(i0:i1,j0:j1)
      Throws:
        `java.lang.ArrayIndexOutOfBoundsException` - Submatrix indices

    - #### setMatrix

          public void setMatrix(int[] r,
                       int[] c,
                       Matrix X)

      Set a submatrix.
      Parameters:
        `r` - Array of row indices.
        `c` - Array of column indices.
        `X` - A(r(:),c(:))
      Throws:
        `java.lang.ArrayIndexOutOfBoundsException` - Submatrix indices

    - #### setMatrix

          public void setMatrix(int[] r,
                       int j0,
                       int j1,
                       Matrix X)

      Set a submatrix.
      Parameters:
        `r` - Array of row indices.
        `j0` - Initial column index
        `j1` - Final column index
        `X` - A(r(:),j0:j1)
      Throws:
        `java.lang.ArrayIndexOutOfBoundsException` - Submatrix indices

    - #### setMatrix

          public void setMatrix(int i0,
                       int i1,
                       int[] c,
                       Matrix X)

      Set a submatrix.
      Parameters:
        `i0` - Initial row index
        `i1` - Final row index
        `c` - Array of column indices.
        `X` - A(i0:i1,c(:))
      Throws:
        `java.lang.ArrayIndexOutOfBoundsException` - Submatrix indices

    - #### isSymmetric

          public boolean isSymmetric()

      Returns true if the matrix is symmetric. (FracPete: taken from old weka.core.Matrix class)
      Returns:
        boolean true if matrix is symmetric.

    - #### isSquare

          public boolean isSquare()

      returns whether the matrix is a square matrix or not.
      Returns:
        true if the matrix is a square matrix

    - #### transpose

          public Matrix transpose()

      Matrix transpose.
      Returns:
        A'

    - #### norm1

          public double norm1()

      One norm
      Returns:
        maximum column sum.

    - #### norm2

          public double norm2()

      Two norm
      Returns:
        maximum singular value.

    - #### normInf

          public double normInf()

      Infinity norm
      Returns:
        maximum row sum.

    - #### normF

          public double normF()

      Frobenius norm
      Returns:
        sqrt of sum of squares of all elements.

    - #### uminus

          public Matrix uminus()

      Unary minus
      Returns:
        -A

    - #### plus

          public Matrix plus(Matrix B)

      C = A + B
      Parameters:
        `B` - another matrix
      Returns:
        A + B

    - #### plusEquals

          public Matrix plusEquals(Matrix B)

      A = A + B
      Parameters:
        `B` - another matrix
      Returns:
        A + B

    - #### minus

          public Matrix minus(Matrix B)

      C = A - B
      Parameters:
        `B` - another matrix
      Returns:
        A - B

    - #### minusEquals

          public Matrix minusEquals(Matrix B)

      A = A - B
      Parameters:
        `B` - another matrix
      Returns:
        A - B

    - #### arrayTimes

          public Matrix arrayTimes(Matrix B)

      Element-by-element multiplication, C = A.*B
      Parameters:
        `B` - another matrix
      Returns:
        A.*B

    - #### arrayTimesEquals

          public Matrix arrayTimesEquals(Matrix B)

      Element-by-element multiplication in place, A = A.*B
      Parameters:
        `B` - another matrix
      Returns:
        A.*B

    - #### arrayRightDivide

          public Matrix arrayRightDivide(Matrix B)

      Element-by-element right division, C = A./B
      Parameters:
        `B` - another matrix
      Returns:
        A./B

    - #### arrayRightDivideEquals

          public Matrix arrayRightDivideEquals(Matrix B)

      Element-by-element right division in place, A = A./B
      Parameters:
        `B` - another matrix
      Returns:
        A./B

    - #### arrayLeftDivide

          public Matrix arrayLeftDivide(Matrix B)

      Element-by-element left division, C = A.\B
      Parameters:
        `B` - another matrix
      Returns:
        A.\B

    - #### arrayLeftDivideEquals

          public Matrix arrayLeftDivideEquals(Matrix B)

      Element-by-element left division in place, A = A.\B
      Parameters:
        `B` - another matrix
      Returns:
        A.\B

    - #### times

          public Matrix times(double s)

      Multiply a matrix by a scalar, C = s*A
      Parameters:
        `s` - scalar
      Returns:
        s*A

    - #### timesEquals

          public Matrix timesEquals(double s)

      Multiply a matrix by a scalar in place, A = s*A
      Parameters:
        `s` - scalar
      Returns:
        replace A by s*A

    - #### times

          public Matrix times(Matrix B)

      Linear algebraic matrix multiplication, A * B
      Parameters:
        `B` - another matrix
      Returns:
        Matrix product, A * B
      Throws:
        `java.lang.IllegalArgumentException` - Matrix inner dimensions must agree.

    - #### lu

          public LUDecomposition lu()

      LU Decomposition
      Returns:
        LUDecomposition
      See Also:
        `LUDecomposition`

    - #### qr

          public QRDecomposition qr()

      QR Decomposition
      Returns:
        QRDecomposition
      See Also:
        `QRDecomposition`

    - #### chol

          public CholeskyDecomposition chol()

      Cholesky Decomposition
      Returns:
        CholeskyDecomposition
      See Also:
        `CholeskyDecomposition`

    - #### svd

          public SingularValueDecomposition svd()

      Singular Value Decomposition
      Returns:
        SingularValueDecomposition
      See Also:
        `SingularValueDecomposition`

    - #### eig

          public EigenvalueDecomposition eig()

      Eigenvalue Decomposition
      Returns:
        EigenvalueDecomposition
      See Also:
        `EigenvalueDecomposition`

    - #### solve

          public Matrix solve(Matrix B)

      Solve A*X = B
      Parameters:
        `B` - right hand side
      Returns:
        solution if A is square, least squares solution otherwise

    - #### solveTranspose

          public Matrix solveTranspose(Matrix B)

      Solve X*A = B, which is also A'*X' = B'
      Parameters:
        `B` - right hand side
      Returns:
        solution if A is square, least squares solution otherwise.

    - #### inverse

          public Matrix inverse()

      Matrix inverse or pseudoinverse
      Returns:
        inverse(A) if A is square, pseudoinverse otherwise.

    - #### sqrt

          public Matrix sqrt()

      returns the square root of the matrix, i.e., X from the equation X*X = A.
      Steps in the Calculation (see `sqrtm` in Matlab):
      1. perform eigenvalue decomposition
         [V,D]=eig(A)
      2. take the square root of all elements in D (only the ones with positive sign are considered for further computation)
         S=sqrt(D)
      3. calculate the root
         X=V*S/V, which can be also written as X=(V'\(V*S)')'

      Note: since this method uses other high-level methods, it generates several instances of matrices. This can be problematic with large matrices.

      Examples:

      1.       X =
                5   -4    1    0    0
               -4    6   -4    1    0
                1   -4    6   -4    1
                0    1   -4    6   -4
                0    0    1   -4    5

               sqrt(X) =
                2   -1   -0   -0   -0
               -1    2   -1    0   -0
                0   -1    2   -1    0
               -0    0   -1    2   -1
               -0   -0   -0   -1    2

               Matrix m = new Matrix(new double[][]{{5,-4,1,0,0},{-4,6,-4,1,0},{1,-4,6,-4,1},{0,1,-4,6,-4},{0,0,1,-4,5}});

      2.       X =
                7   10
               15   22

               sqrt(X) =
               1.5667    1.7408
               2.6112    4.1779

               Matrix m = new Matrix(new double[][]{{7, 10},{15, 22}});

      Returns:
        sqrt(A)

    - #### regression

          public LinearRegression regression(Matrix y,
                                    double ridge)

      Performs a (ridged) linear regression. (FracPete: taken from old weka.core.Matrix class)
      Parameters:
        `y` - the dependent variable vector
        `ridge` - the ridge parameter
      Returns:
        the coefficients
      Throws:
        `java.lang.IllegalArgumentException` - if not successful

    - #### regression

          public final LinearRegression regression(Matrix y,
                                    double[] w,
                                    double ridge)

      Performs a weighted (ridged) linear regression. (FracPete: taken from old weka.core.Matrix class)
      Parameters:
        `y` - the dependent variable vector
        `w` - the array of data point weights
        `ridge` - the ridge parameter
      Returns:
        the coefficients
      Throws:
        `java.lang.IllegalArgumentException` - if the wrong number of weights were provided.

    - #### det

          public double det()

      Matrix determinant
      Returns:
        determinant

    - #### rank

          public int rank()

      Matrix rank
      Returns:
        effective numerical rank, obtained from SVD.

    - #### cond

          public double cond()

      Matrix condition (2 norm)
      Returns:
        ratio of largest to smallest singular value.

    - #### trace

          public double trace()

      Matrix trace.
      Returns:
        sum of the diagonal elements.

    - #### random

          public static Matrix random(int m,
                      int n)

      Generate matrix with random elements
      Parameters:
        `m` - Number of rows.
        `n` - Number of colums.
      Returns:
        An m-by-n matrix with uniformly distributed random elements.

    - #### identity

          public static Matrix identity(int m,
                        int n)

      Generate identity matrix
      Parameters:
        `m` - Number of rows.
        `n` - Number of colums.
      Returns:
        An m-by-n matrix with ones on the diagonal and zeros elsewhere.

    - #### print

          public void print(int w,
                   int d)

      Print the matrix to stdout. Line the elements up in columns with a Fortran-like 'Fw.d' style format.
      Parameters:
        `w` - Column width.
        `d` - Number of digits after the decimal.

    - #### print

          public void print(java.io.PrintWriter output,
                   int w,
                   int d)

      Print the matrix to the output stream. Line the elements up in columns with a Fortran-like 'Fw.d' style format.
      Parameters:
        `output` - Output stream.
        `w` - Column width.
        `d` - Number of digits after the decimal.

    - #### print

          public void print(java.text.NumberFormat format,
                   int width)

      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.
      Parameters:
        `format` - A Formatting object for individual elements.
        `width` - Field width for each column.
      See Also:
        `DecimalFormat.setDecimalFormatSymbols(java.text.DecimalFormatSymbols)`

    - #### print

          public void print(java.io.PrintWriter output,
                   java.text.NumberFormat format,
                   int width)

      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.
      Parameters:
        `output` - the output stream.
        `format` - A formatting object to format the matrix elements
        `width` - Column width.
      See Also:
        `DecimalFormat.setDecimalFormatSymbols(java.text.DecimalFormatSymbols)`

    - #### read

          public static Matrix read(java.io.BufferedReader input)
                             throws java.io.IOException

      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.

      Note: This format differs from the one that can be read via the Matrix(Reader) constructor! For that format, the write(Writer) method is used (from the original weka.core.Matrix class).
      Parameters:
        `input` - the input stream.
      Throws:
        `java.io.IOException`
      See Also:
        `Matrix(Reader)`, `write(Writer)`

    - #### write

          public void write(java.io.Writer w)
                     throws java.lang.Exception

      Writes out a matrix. The format can be read via the Matrix(Reader) constructor. (FracPete: taken from old weka.core.Matrix class)
      Parameters:
        `w` - the output Writer
      Throws:
        `java.lang.Exception` - if an error occurs
      See Also:
        `Matrix(Reader)`

    - #### toString

          public java.lang.String toString()

      Converts a matrix to a string. (FracPete: taken from old weka.core.Matrix class)
      Overrides:
        `toString` in class `java.lang.Object`
      Returns:
        the converted string

    - #### toMatlab

          public java.lang.String toMatlab()

      converts the Matrix into a single line Matlab string: matrix is enclosed by parentheses, rows are separated by semicolon and single cells by blanks, e.g., [1 2; 3 4].
      Returns:
        the matrix in Matlab single line format

    - #### parseMatlab

          public static Matrix parseMatlab(java.lang.String matlab)
                                    throws java.lang.Exception

      creates a matrix from the given Matlab string.
      Parameters:
        `matlab` - the matrix in matlab format
      Returns:
        the matrix represented by the given string
      Throws:
        `java.lang.Exception`
      See Also:
        `toMatlab()`

    - #### getRevision

          public java.lang.String getRevision()

      Returns the revision string.
      Specified by:
        `getRevision` in interface `RevisionHandler`
      Returns:
        the revision

    - #### main

          public static void main(java.lang.String[] args)

      Main method for testing this class.