com.imsl.math
Class Matrix

java.lang.Object
  com.imsl.math.Matrix

public class Matrix
extends Object

Matrix manipulation functions.

See Also:

Example

Method Summary

static double[][]	add(double[][] a, double[][] b) Add two rectangular arrays, a + b.
static void	checkMatrix(double[][] a) Check that all of the rows in the matrix have the same length.
static void	checkSquareMatrix(double[][] a) Check that the matrix is square.
static double	frobeniusNorm(double[][] a) Return the Frobenius norm of a matrix.
static double	infinityNorm(double[][] a) Return the infinity norm of a matrix.
static double[][]	inverseLowerTriangular(double[][] a) Returns the inverse of the lower triangular matrix a.
static double[][]	inverseUpperTriangular(double[][] a) Returns the inverse of the upper triangular matrix a.
static double[]	multiply(double[][] a, double[] x) Multiply the rectangular array a and the column array x.
static double[][]	multiply(double[][] a, double[][] b) Multiply two rectangular arrays, a * b.
static double[][]	multiply(double[][] a, double[][] b, int processors) Multiply two rectangular arrays, a * b, using multiple processors.
static double[]	multiply(double[] x, double[][] a) Return the product of the row array x and the rectangular array a.
static double	oneNorm(double[][] a) Return the matrix one norm.
static double[][]	subtract(double[][] a, double[][] b) Subtract two rectangular arrays, a - b.
static double[][]	transpose(double[][] a) Return the transpose of a matrix.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

add

public static double[][] add(double[][] a,
                             double[][] b)

Add two rectangular arrays, a + b.

Parameters:

a - a double rectangular array

b - a double rectangular array

Returns:

a double rectangular array representing the matrix sum of the two arguments

checkMatrix

public static void checkMatrix(double[][] a)

Check that all of the rows in the matrix have the same length.

Parameters:

a - a double matrix

checkSquareMatrix

public static void checkSquareMatrix(double[][] a)

Check that the matrix is square.

Parameters:

a - a double matrix

frobeniusNorm

public static double frobeniusNorm(double[][] a)

Return the Frobenius norm of a matrix.

Parameters:

a - a double rectangular array

Returns:

a double scalar value equal to the Frobenius norm of the matrix.

infinityNorm

public static double infinityNorm(double[][] a)

Return the infinity norm of a matrix.

Parameters:

a - a double rectangular array

Returns:

a double scalar value equal to the maximum of the row sums of the absolute values of the array elements

inverseLowerTriangular

public static double[][] inverseLowerTriangular(double[][] a)

Returns the inverse of the lower triangular matrix a.

Parameters:

a - a double square lower triangular matrix

Returns:

a double matrix containing the inverse of a

inverseUpperTriangular

public static double[][] inverseUpperTriangular(double[][] a)

Returns the inverse of the upper triangular matrix a.

Parameters:

a - a double square upper triangular matrix

Returns:

a double matrix containing the inverse of a

multiply

public static double[] multiply(double[][] a,
                                double[] x)

Multiply the rectangular array a and the column array x.

Parameters:

a - a double rectangular matrix

x - a double column array

Returns:

a double vector representing the product of the arguments, a*x

multiply

public static double[][] multiply(double[][] a,
                                  double[][] b)

Multiply two rectangular arrays, a * b.

Parameters:

a - a double rectangular array

b - a double rectangular array

Returns:

the double matrix product of a times b

multiply

public static double[][] multiply(double[][] a,
                                  double[][] b,
                                  int processors)

Multiply two rectangular arrays, a * b, using multiple processors.

Parameters:

a - a double rectangular array

b - a double rectangular array

processors - An int which specifies the number of processors to use. If processors is less than 1, then processors = 1 is used.

Returns:

the double matrix product of a times b

multiply

public static double[] multiply(double[] x,
                                double[][] a)

Return the product of the row array x and the rectangular array a.

Parameters:

x - a double row array

a - a double rectangular matrix

Returns:

a double vector representing the product of the arguments, x*a.

oneNorm

public static double oneNorm(double[][] a)

Return the matrix one norm.

Parameters:

a - a double rectangular array

Returns:

a double value equal to the maximum of the column sums of the absolute values of the array elements

subtract

public static double[][] subtract(double[][] a,
                                  double[][] b)

Subtract two rectangular arrays, a - b.

Parameters:

a - a double rectangular array

b - a double rectangular array

Returns:

a double rectangular array representing the matrix difference of the two arguments

transpose

public static double[][] transpose(double[][] a)

Return the transpose of a matrix.

Parameters:

a - a double matrix

Returns:

a double matrix which is the transpose of the argument