com.imsl.math

Class Matrix

java.lang.Object

com.imsl.math.Matrix

public class Matrix
extends Object

Manipulation methods for real-valued rectangular matrices.

See Also:

Example

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	Matrix.MatrixType Indicates which matrix type is used.

Method Summary

Modifier and Type	Method and Description
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	CheckMatrix(double[][] a) Deprecated. Use Matrix.checkMatrix(double[][]) instead.
static void	checkSquareMatrix(double[][] a) Check that the matrix is square.
static void	CheckSquareMatrix(double[][] a) Deprecated. Use Matrix.checkSquareMatrix(double[][]) instead.
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 boolean	isSymmetric(double[][] a) Check if the matrix is symmetric.
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 numberOfThreads) Multiply two rectangular arrays, a * b, using multiple java.lang.Threads.
static double[]	multiply(double[][] a, Matrix.MatrixType aType, double[] x) Multiply the rectangular array a and the column array x.
static double[][]	multiply(double[][] a, Matrix.MatrixType aType, double[][] b, Matrix.MatrixType bType, int numberOfThreads) Multiply two rectangular arrays, a * b.
static double[]	multiply(double[] x, double[][] a) Return the product of the row array x and the rectangular array a.
static double[]	multiply(double[] x, double[][] a, Matrix.MatrixType aType) Return the product of the row array x and the rectangular array a.
static double	multiply(double[] x, double[][] a, Matrix.MatrixType aType, double[] y, boolean equalVectors) Compute vector-matrix-vector product trans(x) * a * y.
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

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

CheckMatrix

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

Deprecated. Use Matrix.checkMatrix(double[][]) instead.

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

CheckSquareMatrix

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

Deprecated. Use Matrix.checkSquareMatrix(double[][]) instead.

Check that the matrix is square.

Parameters:

a - a double matrix

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

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

multiply

public static double[] multiply(double[] x,
                                double[][] a,
                                Matrix.MatrixType aType)

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

Parameters:

x - a double row array

a - a double rectangular matrix

aType - a MatrixType indicating if matrix a is general or symmetric

Returns:

a double vector representing the product of the arguments, x*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,
                                Matrix.MatrixType aType,
                                double[] x)

Multiply the rectangular array a and the column array x.

Parameters:

a - a double rectangular matrix

aType - a MatrixType indicating if matrix a is general or symmetric

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 numberOfThreads)

Multiply two rectangular arrays, a * b, using multiple java.lang.Threads.

Parameters:

a - a double rectangular array

b - a double rectangular array

numberOfThreads - An int which specifies the number of java.lang.Thread instances to use. If numberOfThreads is less than 1, then numberOfThreads = 1 is used.

Returns:

the double matrix product of a times b

multiply

public static double[][] multiply(double[][] a,
                                  Matrix.MatrixType aType,
                                  double[][] b,
                                  Matrix.MatrixType bType,
                                  int numberOfThreads)

Multiply two rectangular arrays, a * b.

Parameters:

a - a double rectangular array

aType - a MatrixType indicating if matrix a is general or symmetric

b - a double rectangular array

bType - a matrixType indicating if matrix b is general or symmetric

numberOfThreads - An int which specifies the number of java.lang.Thread instances to use. If numberOfThreads is less than 1, then numberOfThreads = 1 is used.

Returns:

the double matrix product of a times b

multiply

public static double multiply(double[] x,
                              double[][] a,
                              Matrix.MatrixType aType,
                              double[] y,
                              boolean equalVectors)

Compute vector-matrix-vector product trans(x) * a * y.

Parameters:

x - a double array

a - a double rectangular matrix

aType - a MatrixType indicating if matrix a is general or symmetric

y - a double array

equalVectors - a boolean indicating if the two vectors x and y are numerically equal

Returns:

a double scalar representing the product of the arguments, trans(x)*a*y

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

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

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

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

isSymmetric

public static boolean isSymmetric(double[][] a)

Check if the matrix is symmetric.

Parameters:

a - a double rectangular array

Returns:

a boolean which is true if the matrix is symmetric and false otherwise

Throws:

IllegalArgumentException - This exception is thrown if the lengths of the rows of the input matrix are not uniform.

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