IntegerMatrix

java.lang.Object
- cusack.hcg.matrix.IntegerMatrix

All Implemented Interfaces:: java.io.Serializable, java.lang.Cloneable

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

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 int 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||.

 int[][]        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);
                                                                                                                                                                                                                                                                                                                                                                        int     rnorm   = r.normInf();

Version:: 5 August 1998
Author:: The MathWorks, Inc. and the National Institute of Standards and Technology.
See Also:: Serialized Form

Constructor Summary

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

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`IntegerMatrix`	`arrayLeftDivide(IntegerMatrix B)` Element-by-element left division, C = A.\B
`IntegerMatrix`	`arrayLeftDivideEquals(IntegerMatrix B)` Element-by-element left division in place, A = A.\B
`IntegerMatrix`	`arrayRightDivide(IntegerMatrix B)` Element-by-element right division, C = A./B
`IntegerMatrix`	`arrayRightDivideEquals(IntegerMatrix B)` Element-by-element right division in place, A = A./B
`IntegerMatrix`	`arrayTimes(IntegerMatrix B)` Element-by-element multiplication, C = A.*B
`IntegerMatrix`	`arrayTimesEquals(IntegerMatrix B)` Element-by-element multiplication in place, A = A.*B
`java.lang.Object`	`clone()` Clone the Matrix object.
`static IntegerMatrix`	`constructWithCopy(int[][] A)` Construct a matrix from a copy of a 2-D array.
`IntegerMatrix`	`copy()` Make a deep copy of a matrix
`boolean`	`equals(java.lang.Object obj)`
`int`	`get(int i, int j)` Get a single element.
`int[][]`	`getArray()` Access the internal two-dimensional array.
`int[][]`	`getArrayCopy()` Copy the internal two-dimensional array.
`int`	`getColumnDimension()` Get column dimension.
`int[]`	`getColumnPackedCopy()` Make a one-dimensional column packed copy of the internal array.
`IntegerMatrix`	`getMatrix(int[] r, int[] c)` Get a submatrix.
`IntegerMatrix`	`getMatrix(int[] r, int j0, int j1)` Get a submatrix.
`IntegerMatrix`	`getMatrix(int i0, int i1, int[] c)` Get a submatrix.
`IntegerMatrix`	`getMatrix(int i0, int i1, int j0, int j1)` Get a submatrix.
`int`	`getRowDimension()` Get row dimension.
`int[]`	`getRowPackedCopy()` Make a one-dimensional row packed copy of the internal array.
`IntegerMatrix`	`howell(int N)` Return the Howell form of this Matrix, Modulo N
`static IntegerMatrix`	`identity(int m, int n)` Generate identity matrix
`IntegerMatrix`	`minus(IntegerMatrix B)` C = A - B
`IntegerMatrix`	`minusEquals(IntegerMatrix B)` A = A - B
`int`	`norm1()` One norm
`int`	`normF()` Frobenius norm
`int`	`normInf()` Infinity norm
`IntegerMatrix`	`plus(IntegerMatrix B)` C = A + B
`IntegerMatrix`	`plusEquals(IntegerMatrix 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.
`static IntegerMatrix`	`random(int m, int n)` Generate matrix with random elements
`static IntegerMatrix`	`read(java.io.BufferedReader input)` Read a matrix from a stream.
`void`	`set(int i, int j, int s)` Set a single element.
`void`	`setMatrix(int[] r, int[] c, IntegerMatrix X)` Set a submatrix.
`void`	`setMatrix(int[] r, int j0, int j1, IntegerMatrix X)` Set a submatrix.
`void`	`setMatrix(int i0, int i1, int[] c, IntegerMatrix X)` Set a submatrix.
`void`	`setMatrix(int i0, int i1, int j0, int j1, IntegerMatrix X)` Set a submatrix.
`IntegerMatrix`	`times(int s)` Multiply a matrix by a scalar, C = s*A
`IntegerMatrix`	`times(IntegerMatrix B)` Linear algebraic matrix multiplication, A * B
`IntegerMatrix`	`timesEquals(int s)` Multiply a matrix by a scalar in place, A = s*A
`java.lang.String`	`toHTMLString()`
`java.lang.String`	`toString()`
`int`	`trace()` Matrix trace.
`IntegerMatrix`	`transpose()` Matrix transpose.
`IntegerMatrix`	`uminus()` Unary minus

Methods inherited from class java.lang.Object
getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - IntegerMatrix
```
public IntegerMatrix(int m,
                     int n)
```
    Construct an m-by-n matrix of zeros.
    
    Parameters:
    
    m - Number of rows.
    
    n - Number of colums.
  - IntegerMatrix
```
public IntegerMatrix(int m,
                     int n,
                     int 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.
  - IntegerMatrix
```
public IntegerMatrix(int[][] A)
```
    Construct a matrix from a 2-D array.
    
    Parameters:
    
    A - Two-dimensional array of ints.
    
    Throws:
    
    java.lang.IllegalArgumentException - All rows must have the same length
    
    See Also:
    
    constructWithCopy(int[][])
  - IntegerMatrix
```
public IntegerMatrix(int[][] A,
                     int m,
                     int n)
```
    Construct a matrix quickly without checking arguments.
    
    Parameters:
    
    A - Two-dimensional array of ints.
    
    m - Number of rows.
    
    n - Number of colums.
  - IntegerMatrix
```
public IntegerMatrix(int[] vals,
                     int m)
```
    Construct a matrix from a one-dimensional packed array
    
    Parameters:
    
    vals - One-dimensional array of ints, packed by columns (ala Fortran).
    
    m - Number of rows.
    
    Throws:
    
    java.lang.IllegalArgumentException - Array length must be a multiple of m.
- Method Detail
  - constructWithCopy
```
public static IntegerMatrix constructWithCopy(int[][] A)
```
    Construct a matrix from a copy of a 2-D array.
    
    Parameters:
    
    A - Two-dimensional array of ints.
    
    Throws:
    
    java.lang.IllegalArgumentException - All rows must have the same length
  - copy
```
public IntegerMatrix 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 int[][] getArray()
```
    Access the internal two-dimensional array.
    
    Returns:
    
    Pointer to the two-dimensional array of matrix elements.
  - getArrayCopy
```
public int[][] getArrayCopy()
```
    Copy the internal two-dimensional array.
    
    Returns:
    
    Two-dimensional array copy of matrix elements.
  - getColumnPackedCopy
```
public int[] 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 int[] 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 int 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 IntegerMatrix 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 IntegerMatrix 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 IntegerMatrix 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 IntegerMatrix getMatrix(int[] r,
                               int j0,
                               int j1)
```
    Get a submatrix.
    
    Parameters:
    
    r - Array of row indices.
    
    i0 - Initial column index
    
    i1 - Final column index
    
    Returns:
    
    A(r(:),j0:j1)
    
    Throws:
    
    java.lang.ArrayIndexOutOfBoundsException - Submatrix indices
  - set
```
public void set(int i,
                int j,
                int 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,
                      IntegerMatrix 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,
                      IntegerMatrix 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,
                      IntegerMatrix 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,
                      IntegerMatrix 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
  - transpose
```
public IntegerMatrix transpose()
```
    Matrix transpose.
    
    Returns:
    
    A'
  - norm1
```
public int norm1()
```
    One norm
    
    Returns:
    
    maximum column sum.
  - normInf
```
public int normInf()
```
    Infinity norm
    
    Returns:
    
    maximum row sum.
  - normF
```
public int normF()
```
    Frobenius norm
    
    Returns:
    
    sqrt of sum of squares of all elements.
  - uminus
```
public IntegerMatrix uminus()
```
    Unary minus
    
    Returns:
    
    -A
  - plus
```
public IntegerMatrix plus(IntegerMatrix B)
```
    C = A + B
    
    Parameters:
    
    B - another matrix
    
    Returns:
    
    A + B
  - plusEquals
```
public IntegerMatrix plusEquals(IntegerMatrix B)
```
    A = A + B
    
    Parameters:
    
    B - another matrix
    
    Returns:
    
    A + B
  - minus
```
public IntegerMatrix minus(IntegerMatrix B)
```
    C = A - B
    
    Parameters:
    
    B - another matrix
    
    Returns:
    
    A - B
  - minusEquals
```
public IntegerMatrix minusEquals(IntegerMatrix B)
```
    A = A - B
    
    Parameters:
    
    B - another matrix
    
    Returns:
    
    A - B
  - arrayTimes
```
public IntegerMatrix arrayTimes(IntegerMatrix B)
```
    Element-by-element multiplication, C = A.*B
    
    Parameters:
    
    B - another matrix
    
    Returns:
    
    A.*B
  - arrayTimesEquals
```
public IntegerMatrix arrayTimesEquals(IntegerMatrix B)
```
    Element-by-element multiplication in place, A = A.*B
    
    Parameters:
    
    B - another matrix
    
    Returns:
    
    A.*B
  - arrayRightDivide
```
public IntegerMatrix arrayRightDivide(IntegerMatrix B)
```
    Element-by-element right division, C = A./B
    
    Parameters:
    
    B - another matrix
    
    Returns:
    
    A./B
  - arrayRightDivideEquals
```
public IntegerMatrix arrayRightDivideEquals(IntegerMatrix B)
```
    Element-by-element right division in place, A = A./B
    
    Parameters:
    
    B - another matrix
    
    Returns:
    
    A./B
  - arrayLeftDivide
```
public IntegerMatrix arrayLeftDivide(IntegerMatrix B)
```
    Element-by-element left division, C = A.\B
    
    Parameters:
    
    B - another matrix
    
    Returns:
    
    A.\B
  - arrayLeftDivideEquals
```
public IntegerMatrix arrayLeftDivideEquals(IntegerMatrix B)
```
    Element-by-element left division in place, A = A.\B
    
    Parameters:
    
    B - another matrix
    
    Returns:
    
    A.\B
  - times
```
public IntegerMatrix times(int s)
```
    Multiply a matrix by a scalar, C = s*A
    
    Parameters:
    
    s - scalar
    
    Returns:
    
    s*A
  - timesEquals
```
public IntegerMatrix timesEquals(int s)
```
    Multiply a matrix by a scalar in place, A = s*A
    
    Parameters:
    
    s - scalar
    
    Returns:
    
    replace A by s*A
  - times
```
public IntegerMatrix times(IntegerMatrix 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.
  - trace
```
public int trace()
```
    Matrix trace.
    
    Returns:
    
    sum of the diagonal elements.
  - random
```
public static IntegerMatrix 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 IntegerMatrix 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 IntegerMatrix 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.
    
    Parameters:
    
    input - the input stream.
    
    Throws:
    
    java.io.IOException
  - howell
```
public IntegerMatrix howell(int N)
```
    Return the Howell form of this Matrix, Modulo N
    
    Parameters:
    
    N -
    
    Returns:
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Overrides:
    
    equals in class java.lang.Object
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object
  - toHTMLString
```
public java.lang.String toHTMLString()
```

Class IntegerMatrix

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

IntegerMatrix

IntegerMatrix

IntegerMatrix

IntegerMatrix

IntegerMatrix

Method Detail

constructWithCopy

copy

clone

getArray

getArrayCopy

getColumnPackedCopy

getRowPackedCopy

getRowDimension

getColumnDimension

get

getMatrix

getMatrix

getMatrix

getMatrix

set

setMatrix

setMatrix

setMatrix

setMatrix

transpose

norm1

normInf

normF

uminus

plus

plusEquals

minus

minusEquals

arrayTimes

arrayTimesEquals

arrayRightDivide

arrayRightDivideEquals

arrayLeftDivide

arrayLeftDivideEquals

times

timesEquals

times

trace

random

identity

print

print

print

print

read

howell

equals

toString

toHTMLString