Class VisualNumerics.math.ComplexMatrix 
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Class VisualNumerics.math.ComplexMatrix 

java.lang.Object
   |
   +----VisualNumerics.math.ComplexMatrix
public class ComplexMatrix
extends Object
Double precision matrix manipulation functions. This class cannot be instantiated because all of its methods are static.

Method Index

o add(Complex[][], Complex[][])
Add two rectangular arrays, a + b.
o adjoint(Complex[][])
Return the adjoint of the matrix.
o determinant(Complex[][])
Return the determinant of the matrix from its LU factorization.
o frobeniusNorm(Complex[][])
Return the frobenius norm of a matrix.
o infinityNorm(Complex[][])
Return the infinity norm of a matrix.
o inverse(Complex[][])
Return the inverse of the matrix a using its LU factorization.
o multiply(Complex[], Complex[][])
Return the product of the row vector x and the rectangular array a.
o multiply(Complex[][], Complex[])
Multiply the rectangular array a and the column vector x.
o multiply(Complex[][], Complex[][])
Multiply two rectangular arrays, a * b.
o oneNorm(Complex[][])
Return the matrix one norm.
o QRsolve(Complex[][], Complex[])
Solve ax=b for x, using the QR decomposition of a.
o solve(Complex[][], Complex[])
Solve ax=b for x using the LU factorization of a.
o subtract(Complex[][], Complex[][])
Take the difference between two arrays, a - b.
o trace(Complex[][])
Return the sum of the diagonal elements.
o transpose(Complex[][])
Return the transpose of a matrix.

Constructors

o ComplexMatrix 
  public ComplexMatrix()

Methods

o transpose 
  public static Complex[][] transpose(Complex a[][]) throws IllegalArgumentException
Return the transpose of a matrix.
Parameters:
a - A Complex matrix.
Returns:
The matrix transpose of the argument.
Throws: IllegalArgumentException
This exception is thrown when the lengths of the rows of the input matrix are not uniform.
o adjoint 
  public static Complex[][] adjoint(Complex a[][]) throws IllegalArgumentException
Return the adjoint of the matrix.
Parameters:
a - A Complex matrix.
Returns:
The adjoint (complex conjugate transpose) of the argument.
Throws: IllegalArgumentException
This exception is thrown when the lengths of the rows of the input matrix are not uniform.
o multiply 
  public static Complex[] multiply(Complex x[],
                                   Complex a[][]) throws IllegalArgumentException
Return the product of the row vector x and the rectangular array a.
Parameters:
x - A row vector with Complex elements.
a - A Complex matrix.
Returns:
The product of the arguments.
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 elements in the input vector is not equal to the number of rows of the matrix.
o multiply 
  public static Complex[] multiply(Complex a[][],
                                   Complex x[]) throws IllegalArgumentException
Multiply the rectangular array a and the column vector x.
Parameters:
a - A Complex matrix.
x - A column vector with Complex elements.
Returns:
The product of the arguments.
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.
o multiply 
  public static Complex[][] multiply(Complex a[][],
                                     Complex b[][]) throws IllegalArgumentException
Multiply two rectangular arrays, a * b.
Parameters:
a - An (m x n) rectangular array with Complex elements.
b - An (n x p) rectangular array with Complex elements.
Returns:
The matrix product of the two arguments with dimensions (m x p).
Throws: IllegalArgumentException
This exception is thrown when (1) the lengths of the rows of either of the input matrices are not uniform, and (2) the number of columns in a is not equal to the number of rows in b.
o add 
  public static Complex[][] add(Complex a[][],
                                Complex b[][]) throws IllegalArgumentException
Add two rectangular arrays, a + b.
Parameters:
a - A rectangular array with Complex elements.
b - A rectangular array with Complex elements.
Returns:
The sum of the two arrays.
Throws: IllegalArgumentException
This exception is thrown when (1) the lengths of the rows of either of the input matrices are not uniform, and (2) corresponding dimensions of the two matrices are not equal to each other.
o subtract 
  public static Complex[][] subtract(Complex a[][],
                                     Complex b[][]) throws IllegalArgumentException
Take the difference between two arrays, a - b.
Parameters:
a - A rectangular array with Complex elements.
b - A rectangular array with Complex elements.
Returns:
The difference between the two arrays.
Throws: IllegalArgumentException
This exception is thrown when (1) the lengths of the rows of either of the input matrices are not uniform, and (2) corresponding dimensions of the two matrices are not equal to each other.
o solve 
  public static Complex[] solve(Complex a[][],
                                Complex b[]) throws IllegalArgumentException, MathException
Solve ax=b for x using the LU factorization of a.
Parameters:
a - A square matrix with Complex elements.
b - A column vector with Complex elements.
Returns:
A column vector containing the solution to the linear system of equations.
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 rows in the input matrix is not equal to the number of elements in x.
Throws: MathException
This exception is thrown when the matrix is singular.
o inverse 
  public static Complex[][] inverse(Complex a[][]) throws IllegalArgumentException, MathException
Return the inverse of the matrix a using its LU factorization.
Parameters:
a - A square matrix with Complex elements.
Returns:
The matrix inverse of a.
Throws: IllegalArgumentException
This exception is thrown when (1) the lengths of the rows of the input matrix are not uniform, and (2) the input matrix is not square.
Throws: MathException
This exception is thrown when the matrix is singular.
o determinant 
  public static Complex determinant(Complex a[][]) throws IllegalArgumentException, MathException
Return the determinant of the matrix from its LU factorization.
Parameters:
a - A square matrix with Complex elements.
Returns:
A Complex value equal to the determinant of the matrix.
Throws: IllegalArgumentException
This exception is thrown when (1) the lengths of the rows of the input matrix are not uniform, and (2) the input matrix is not square.
Throws: MathException
This exception is thrown when the matrix is singular.
o QRsolve 
  public static Complex[] QRsolve(Complex a[][],
                                  Complex b[]) throws IllegalArgumentException, MathException
Solve ax=b for x, using the QR decomposition of a. When a is not square, it returns the least squares solution.
Parameters:
a - A rectangular array with Complex elements.
b - A column vector with Complex elements.
Returns:
A column vector with Complex elements containing the least squares solution to the linear system.
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 rows in the input matrix is not equal to the number of elements in the input vector.
Throws: MathException
This exception is thrown when the upper triangular matrix R from the QR factorization has a zero diagonal element.
o trace 
  public static Complex trace(Complex array[][]) throws MathException
Return the sum of the diagonal elements.
Parameters:
a - A square matrix with Complex elements.
Returns:
A Complex value equal to the sum of the diagonal elements.
Throws: MathException
This exception is thrown when the matrix is not square.
o oneNorm 
  public static double oneNorm(Complex array[][])
Return the matrix one norm.
Parameters:
array - A rectangular array with Complex elements.
Returns:
A double value equal to the maximum of the column sums of the absolute values of the array elements.
o frobeniusNorm 
  public static double frobeniusNorm(Complex array[][])
Return the frobenius norm of a matrix.
Parameters:
array - A rectangular matrix with Complex elements.
Returns:
A double value equal to the frobenius norm of the matrix.
o infinityNorm 
  public static double infinityNorm(Complex array[][])
Return the infinity norm of a matrix.
Parameters:
array - A rectangular matrix with Complex elements.
Returns:
A double value equal to the maximum of the row sums of the absolute values of the array elements. 
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