com.imsl.math

Class ComplexMatrix

java.lang.Object

com.imsl.math.ComplexMatrix

public class ComplexMatrix
extends Object

Complex matrix manipulation functions.

See Also:

Example

Nested Class Summary

Nested Classes

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

Method Summary

Modifier and Type	Method and Description
static Complex[][]	add(Complex[][] a, Complex[][] b) Add two rectangular Complex arrays, a + b.
static void	checkMatrix(Complex[][] a) Check that all of the rows in the Complex matrix have the same length.
static void	CheckMatrix(Complex[][] a) Deprecated. Use ComplexMatrix.checkMatrix(Complex[][]) instead.
static void	checkSquareMatrix(Complex[][] a) Check that the Complex matrix is square.
static void	CheckSquareMatrix(Complex[][] a) Deprecated. Use ComplexMatrix.checkSquareMatrix(Complex[][]) instead.
static double	frobeniusNorm(Complex[][] a) Return the Frobenius norm of a Complex matrix.
static double	infinityNorm(Complex[][] a) Return the infinity norm of a Complex matrix.
static boolean	isHermitian(Complex[][] a) Check if the Complex matrix is Hermitian.
static boolean	isSymmetric(Complex[][] a) Check if the Complex matrix is symmetric.
static Complex[]	multiply(Complex[][] a, Complex[] x) Multiply the rectangular array a and the column vector x, both Complex.
static Complex[][]	multiply(Complex[][] a, Complex[][] b) Multiply two Complex rectangular arrays, a * b.
static Complex[][]	multiply(Complex[][] a, Complex[][] b, int numberOfThreads) Multiply two Complex rectangular arrays, a * b, using multiple java.lang.Threads.
static Complex[]	multiply(Complex[][] a, ComplexMatrix.MatrixType aType, Complex[] x) Multiply the rectangular array a and the column vector x, both Complex.
static Complex[][]	multiply(Complex[][] a, ComplexMatrix.MatrixType aType, Complex[][] b, ComplexMatrix.MatrixType bType, int numberOfThreads) Multiply two Complex rectangular arrays of type MatrixType, a * b, using multiple java.lang.Threads.
static Complex[]	multiply(Complex[] x, Complex[][] a) Return the product of the row vector x and the rectangular array a, both Complex.
static Complex[]	multiply(Complex[] x, Complex[][] a, ComplexMatrix.MatrixType aType) Return the product of the row vector x and the rectangular array a, both Complex.
static Complex	multiply(Complex[] x, Complex[][] a, ComplexMatrix.MatrixType aType, Complex[] y, boolean equalVectors) Compute vector-matrix-vector product trans(conj(x)) * a * y.
static double	oneNorm(Complex[][] a) Return the Complex matrix one norm.
static Complex[][]	subtract(Complex[][] a, Complex[][] b) Subtract two Complex rectangular arrays, a - b.
static Complex[][]	transpose(Complex[][] a) Return the transpose of a Complex 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(Complex[][] a)

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

Parameters:

a - a Complex matrix

Throws:

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

CheckMatrix

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

Deprecated. Use ComplexMatrix.checkMatrix(Complex[][]) instead.

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

Parameters:

a - a Complex matrix

Throws:

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

checkSquareMatrix

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

Check that the Complex matrix is square.

Parameters:

a - a Complex matrix

Throws:

IllegalArgumentException - This exception is thrown if the matrix is not square.

CheckSquareMatrix

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

Deprecated. Use ComplexMatrix.checkSquareMatrix(Complex[][]) instead.

Check that the Complex matrix is square.

Parameters:

a - a Complex matrix

Throws:

IllegalArgumentException - This exception is thrown if the matrix is not square.

transpose

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

Return the transpose of a Complex matrix.

Parameters:

a - a Complex matrix

Returns:

the Complex matrix transpose of the argument

Throws:

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

multiply

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

Return the product of the row vector x and the rectangular array a, both Complex.

Parameters:

x - a Complex row vector

a - a Complex rectangular matrix

Returns:

a Complex vector containing the product of the arguments, x*a.

Throws:

IllegalArgumentException - This exception is thrown if (1) the lengths of the rows of the input matrix are not uniform, or (2) the number of elements in the input vector is not equal to the number of rows of the matrix.

multiply

public static Complex[] multiply(Complex[] x,
                                 Complex[][] a,
                                 ComplexMatrix.MatrixType aType)

Return the product of the row vector x and the rectangular array a, both Complex.

Parameters:

x - a Complex row vector

a - a Complex rectangular matrix

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

Returns:

a Complex vector containing the product of the arguments, x*a.

Throws:

IllegalArgumentException - This exception is thrown when (1) the lengths of the rows of the input matrix are not uniform, or (2) the number of elements in the input vector is not equal to the number of rows of the matrix, or (3) the input matrix is not square in the symmetric or Hermitian case.

multiply

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

Multiply the rectangular array a and the column vector x, both Complex.

Parameters:

a - a Complex rectangular matrix

x - a Complex vector

Returns:

a Complex vector containing the product of the arguments, a*x

Throws:

IllegalArgumentException - This exception is thrown when (1) the lengths of the rows of the input matrix are not uniform, and (2) the number of columns in the input matrix is not equal to the number of elements in the input vector.

multiply

public static Complex[] multiply(Complex[][] a,
                                 ComplexMatrix.MatrixType aType,
                                 Complex[] x)

Multiply the rectangular array a and the column vector x, both Complex.

Parameters:

a - a Complex rectangular matrix

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

x - a Complex vector

Returns:

a Complex vector containing the product of the arguments, a*x

Throws:

IllegalArgumentException - This exception is thrown if (1) the lengths of the rows of the input matrix are not uniform, or (2) the number of columns in the input matrix is not equal to the number of elements in the input vector, or (3) the input matrix is not square in the symmetric or Hermitian case.

multiply

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

Multiply two Complex rectangular arrays, a * b.

Parameters:

a - a Complex rectangular array

b - a Complex rectangular array

Returns:

the Complex matrix product of a times b

Throws:

IllegalArgumentException - This exception is thrown if (1) the lengths of the rows of either of the input matrices are not uniform, or (2) the number of columns in a is not equal to the number of rows in b.

multiply

public static Complex[][] multiply(Complex[][] a,
                                   Complex[][] b,
                                   int numberOfThreads)

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

Parameters:

a - a Complex rectangular array

b - a Complex 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 Complex matrix product of a times b

Throws:

IllegalArgumentException - This exception is thrown if (1) the lengths of the rows of either of the input matrices are not uniform, or (2) the number of columns in a is not equal to the number of rows in b.

multiply

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

Multiply two Complex rectangular arrays of type MatrixType, a * b, using multiple java.lang.Threads.

Parameters:

a - a Complex rectangular array

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

b - a Complex rectangular array

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

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 Complex matrix product of a times b

Throws:

IllegalArgumentException - This exception is thrown if (1) the lengths of the rows of either of the input matrices are not uniform, or (2) the number of columns in a is not equal to the number of rows in b, or (3) a symmetric or Hermitian input matrix a or b is not square.

multiply

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

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

Parameters:

x - a Complex vector

a - a Complex rectangular matrix

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

y - a Complex vector

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

Returns:

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

add

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

Add two rectangular Complex arrays, a + b.

Parameters:

a - a Complex rectangular array

b - a Complex rectangular array

Returns:

the Complex matrix sum of the two arguments

Throws:

IllegalArgumentException - This exception is thrown if (1) the lengths of the rows of either of the input matrices are not uniform, or (2) the matrices are not the same size.

subtract

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

Subtract two Complex rectangular arrays, a - b.

Parameters:

a - a Complex rectangular array

b - a Complex rectangular array

Returns:

the Complex matrix difference of the two arguments.

Throws:

IllegalArgumentException - This exception is thrown if (1) the lengths of the rows of either of the input matrices are not uniform, or (2) the matrices are not the same size.

oneNorm

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

Return the Complex matrix one norm.

Parameters:

a - a Complex rectangular array

Returns:

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

Throws:

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

frobeniusNorm

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

Return the Frobenius norm of a Complex matrix.

Parameters:

a - a Complex rectangular matrix

Returns:

a double value equal to the Frobenius norm of the matrix

Throws:

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

infinityNorm

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

Return the infinity norm of a Complex matrix.

Parameters:

a - a Complex rectangular matrix

Returns:

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

Throws:

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

isSymmetric

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

Check if the Complex matrix is symmetric.

Parameters:

a - a Complex 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.

isHermitian

public static boolean isHermitian(Complex[][] a)

Check if the Complex matrix is Hermitian.

Parameters:

a - a Complex rectangular array

Returns:

a boolean which is true if the matrix is Hermitian and false otherwise.

Throws:

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