org.ejml.ops

Class CCommonOps

java.lang.Object

org.ejml.ops.CCommonOps

public class CCommonOps
extends java.lang.Object

Common operations on complex numbers

Constructor Summary

Constructors

Constructor and Description
CCommonOps()

Method Summary

Modifier and Type	Method and Description
static void	add(CD1Matrix64F a, CD1Matrix64F b, CD1Matrix64F c) Performs the following operation: c = a + b cij = aij + bij
static CDenseMatrix64F[]	columnsToVector(CDenseMatrix64F A, CDenseMatrix64F[] v) Converts the columns in a matrix into a set of vectors.
static void	conjugate(CD1Matrix64F input, CD1Matrix64F output) Computes the complex conjugate of the input matrix. reali,j = reali,j imaginaryi,j = -1*imaginaryi,j
static void	convert(D1Matrix64F input, CD1Matrix64F output) Converts the real matrix into a complex matrix.
static Complex64F	det(CDenseMatrix64F mat) Returns the determinant of the matrix.
static CDenseMatrix64F	diag(double... data) Creates a new square matrix whose diagonal elements are specified by data and all the other elements are zero. aij = 0 if i ≤ j aij = diag[i] if i = j
static void	elementDivide(CD1Matrix64F input, double real, double imaginary, CD1Matrix64F output) Performs element by element division operation with a complex number on the right outputij = inputij / (real + imaginary*i)
static void	elementDivide(double real, double imaginary, CD1Matrix64F input, CD1Matrix64F output) Performs element by element division operation with a complex number on the right outputij = (real + imaginary*i) / inputij
static double	elementMaxAbs(CDenseMatrix64F a) Returns the absolute value of the element in the matrix that has the largest absolute value. Max{ |aij| } for all i and j
static double	elementMaxImaginary(CD1Matrix64F a) Returns the value of the imaginary element in the matrix that has the minimum value. Min{ aij } for all i and j
static double	elementMaxMagnitude2(CD1Matrix64F a) Returns the magnitude squared of the complex element with the largest magnitude Max{ |aij|^2 } for all i and j
static double	elementMaxReal(CD1Matrix64F a) Returns the value of the real element in the matrix that has the minimum value. Min{ aij } for all i and j
static double	elementMinImaginary(CD1Matrix64F a) Returns the value of the imaginary element in the matrix that has the minimum value. Min{ aij } for all i and j
static double	elementMinReal(CD1Matrix64F a) Returns the value of the real element in the matrix that has the minimum value. Min{ aij } for all i and j
static void	elementMultiply(CD1Matrix64F input, double real, double imaginary, CD1Matrix64F output) Performs element by element multiplication operation with a complex numbert outputij = inputij * (real + imaginary*i)
static CDenseMatrix64F	extract(CDenseMatrix64F src, int srcY0, int srcY1, int srcX0, int srcX1) Creates a new matrix which is the specified submatrix of 'src'
static void	extract(CDenseMatrix64F src, int srcY0, int srcY1, int srcX0, int srcX1, CDenseMatrix64F dst, int dstY0, int dstX0) Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.
static void	fill(CD1Matrix64F a, double real, double imaginary) Sets every element in the matrix to the specified value. aij = value
static CDenseMatrix64F	identity(int width) Creates an identity matrix of the specified size. aij = 0+0i if i ≠ j aij = 1+0i if i = j
static CDenseMatrix64F	identity(int width, int height) Creates a matrix with diagonal elements set to 1 and the rest 0. aij = 0+0i if i ≠ j aij = 1+0i if i = j
static boolean	invert(CDenseMatrix64F A) Performs a matrix inversion operation on the specified matrix and stores the results in the same matrix. a = a-1
static boolean	invert(CDenseMatrix64F input, CDenseMatrix64F output) Performs a matrix inversion operation that does not modify the original and stores the results in another matrix.
static void	magnitude(CD1Matrix64F input, D1Matrix64F output) Computes the magnitude of the complex number in the input matrix and stores the results in the output matrix.
static void	mult(CDenseMatrix64F a, CDenseMatrix64F b, CDenseMatrix64F c) Performs the following operation: c = a * b cij = ∑k=1:n { * aik * bkj}
static void	mult(double realAlpha, double imgAlpha, CDenseMatrix64F a, CDenseMatrix64F b, CDenseMatrix64F c) Performs the following operation: c = α * a * b cij = α ∑k=1:n { * aik * bkj}
static void	multAdd(CDenseMatrix64F a, CDenseMatrix64F b, CDenseMatrix64F c) Performs the following operation: c = c + a * b cij = cij + ∑k=1:n { aik * bkj}
static void	multAdd(double realAlpha, double imgAlpha, CDenseMatrix64F a, CDenseMatrix64F b, CDenseMatrix64F c) Performs the following operation: c = c + α * a * b cij = cij + α * ∑k=1:n { aik * bkj}
static void	setIdentity(CDenseMatrix64F mat) Sets all the diagonal elements equal to one and everything else equal to zero.
static boolean	solve(CDenseMatrix64F a, CDenseMatrix64F b, CDenseMatrix64F x) Solves for x in the following equation: A*x = b
static DenseMatrix64F	stripImaginary(CD1Matrix64F input, DenseMatrix64F output) Places the imaginary component of the input matrix into the output matrix.
static DenseMatrix64F	stripReal(CD1Matrix64F input, DenseMatrix64F output) Places the real component of the input matrix into the output matrix.
static void	subtract(CD1Matrix64F a, CD1Matrix64F b, CD1Matrix64F c) Performs the following operation: c = a - b cij = aij - bij
static void	transpose(CDenseMatrix64F mat) Performs an "in-place" transpose.
static CDenseMatrix64F	transpose(CDenseMatrix64F input, CDenseMatrix64F output) Transposes input matrix 'a' and stores the results in output matrix 'b': bij = aji where 'b' is the transpose of 'a'.
static void	transposeConjugate(CDenseMatrix64F mat) Performs an "in-place" conjugate transpose.
static CDenseMatrix64F	transposeConjugate(CDenseMatrix64F input, CDenseMatrix64F output) Conjugate transposes input matrix 'a' and stores the results in output matrix 'b': b-reali,j = a-realj,i b-imaginaryi,j = -1*a-imaginaryj,i where 'b' is the transpose of 'a'.

Methods inherited from class java.lang.Object

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

Constructor Detail

CCommonOps

public CCommonOps()

Method Detail

identity

public static CDenseMatrix64F identity(int width)

Creates an identity matrix of the specified size.

a_ij = 0+0i if i ≠ j
a_ij = 1+0i if i = j

Parameters:

width - The width and height of the identity matrix.

Returns:

A new instance of an identity matrix.

identity

public static CDenseMatrix64F identity(int width,
                                       int height)

Creates a matrix with diagonal elements set to 1 and the rest 0.

a_ij = 0+0i if i ≠ j
a_ij = 1+0i if i = j

Parameters:

width - The width of the identity matrix.

height - The height of the identity matrix.

Returns:

A new instance of an identity matrix.

diag

public static CDenseMatrix64F diag(double... data)

Creates a new square matrix whose diagonal elements are specified by data and all the other elements are zero.

a_ij = 0 if i ≤ j
a_ij = diag[i] if i = j

Parameters:

data - Contains the values of the diagonal elements of the resulting matrix.

Returns:

A new complex matrix.

convert

public static void convert(D1Matrix64F input,
                           CD1Matrix64F output)

Converts the real matrix into a complex matrix.

Parameters:

input - Real matrix. Not modified.

output - Complex matrix. Modified.

stripReal

public static DenseMatrix64F stripReal(CD1Matrix64F input,
                                       DenseMatrix64F output)

Places the real component of the input matrix into the output matrix.

Parameters:

input - Complex matrix. Not modified.

output - real matrix. Modified.

stripImaginary

public static DenseMatrix64F stripImaginary(CD1Matrix64F input,
                                            DenseMatrix64F output)

Places the imaginary component of the input matrix into the output matrix.

Parameters:

input - Complex matrix. Not modified.

output - real matrix. Modified.

magnitude

public static void magnitude(CD1Matrix64F input,
                             D1Matrix64F output)

Computes the magnitude of the complex number in the input matrix and stores the results in the output matrix.

magnitude = sqrt(real^2 + imaginary^2)

Parameters:

input - Complex matrix. Not modified.

output - real matrix. Modified.

conjugate

public static void conjugate(CD1Matrix64F input,
                             CD1Matrix64F output)

Computes the complex conjugate of the input matrix.

real_i,j = real_i,j
imaginary_i,j = -1*imaginary_i,j

Parameters:

input - Input matrix. Not modified.

output - The complex conjugate of the input matrix. Modified.

fill

public static void fill(CD1Matrix64F a,
                        double real,
                        double imaginary)

Sets every element in the matrix to the specified value.

a_ij = value

Parameters:

a - A matrix whose elements are about to be set. Modified.

real - The real component

imaginary - The imaginary component

add

public static void add(CD1Matrix64F a,
                       CD1Matrix64F b,
                       CD1Matrix64F c)

Performs the following operation:

c = a + b
c_ij = a_ij + b_ij

Matrix C can be the same instance as Matrix A and/or B.

Parameters:

a - A Matrix. Not modified.

b - A Matrix. Not modified.

c - A Matrix where the results are stored. Modified.

subtract

public static void subtract(CD1Matrix64F a,
                            CD1Matrix64F b,
                            CD1Matrix64F c)

Performs the following operation:

c = a - b
c_ij = a_ij - b_ij

Matrix C can be the same instance as Matrix A and/or B.

Parameters:

a - A Matrix. Not modified.

b - A Matrix. Not modified.

c - A Matrix where the results are stored. Modified.

mult

public static void mult(CDenseMatrix64F a,
                        CDenseMatrix64F b,
                        CDenseMatrix64F c)

Performs the following operation:

c = a * b

c_ij = ∑_k=1:n { * a_ik * b_kj}

Parameters:

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

c - Where the results of the operation are stored. Modified.

mult

public static void mult(double realAlpha,
                        double imgAlpha,
                        CDenseMatrix64F a,
                        CDenseMatrix64F b,
                        CDenseMatrix64F c)

Performs the following operation:

c = α * a * b

c_ij = α ∑_k=1:n { * a_ik * b_kj}

Parameters:

realAlpha - real component of scaling factor.

imgAlpha - imaginary component of scaling factor.

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

c - Where the results of the operation are stored. Modified.

multAdd

public static void multAdd(CDenseMatrix64F a,
                           CDenseMatrix64F b,
                           CDenseMatrix64F c)

Performs the following operation:

c = c + a * b
c_ij = c_ij + ∑_k=1:n { a_ik * b_kj}

Parameters:

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

c - Where the results of the operation are stored. Modified.

multAdd

public static void multAdd(double realAlpha,
                           double imgAlpha,
                           CDenseMatrix64F a,
                           CDenseMatrix64F b,
                           CDenseMatrix64F c)

Performs the following operation:

c = c + α * a * b
c_ij = c_ij + α * ∑_k=1:n { a_ik * b_kj}

Parameters:

realAlpha - real component of scaling factor.

imgAlpha - imaginary component of scaling factor.

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

c - Where the results of the operation are stored. Modified.

transpose

public static void transpose(CDenseMatrix64F mat)

Performs an "in-place" transpose.

For square matrices the transpose is truly in-place and does not require additional memory. For non-square matrices, internally a temporary matrix is declared and transpose(org.ejml.data.CDenseMatrix64F, org.ejml.data.CDenseMatrix64F) is invoked.

Parameters:

mat - The matrix that is to be transposed. Modified.

transposeConjugate

public static void transposeConjugate(CDenseMatrix64F mat)

Performs an "in-place" conjugate transpose.

Parameters:

mat - The matrix that is to be transposed. Modified.

See Also:

transpose(org.ejml.data.CDenseMatrix64F)

transpose

public static CDenseMatrix64F transpose(CDenseMatrix64F input,
                                        CDenseMatrix64F output)

Transposes input matrix 'a' and stores the results in output matrix 'b':

b_ij = a_ji
where 'b' is the transpose of 'a'.

Parameters:

input - The original matrix. Not modified.

output - Where the transpose is stored. If null a new matrix is created. Modified.

Returns:

The transposed matrix.

transposeConjugate

public static CDenseMatrix64F transposeConjugate(CDenseMatrix64F input,
                                                 CDenseMatrix64F output)

Conjugate transposes input matrix 'a' and stores the results in output matrix 'b':

b-real_i,j = a-real_j,i
b-imaginary_i,j = -1*a-imaginary_j,i
where 'b' is the transpose of 'a'.

Parameters:

input - The original matrix. Not modified.

output - Where the transpose is stored. If null a new matrix is created. Modified.

Returns:

The transposed matrix.

invert

public static boolean invert(CDenseMatrix64F A)

Performs a matrix inversion operation on the specified matrix and stores the results in the same matrix.

a = a^-1

If the algorithm could not invert the matrix then false is returned. If it returns true that just means the algorithm finished. The results could still be bad because the matrix is singular or nearly singular.

Parameters:

A - The matrix that is to be inverted. Results are stored here. Modified.

Returns:

true if it could invert the matrix false if it could not.

invert

public static boolean invert(CDenseMatrix64F input,
                             CDenseMatrix64F output)

Performs a matrix inversion operation that does not modify the original and stores the results in another matrix. The two matrices must have the same dimension.

b = a^-1

If the algorithm could not invert the matrix then false is returned. If it returns true that just means the algorithm finished. The results could still be bad because the matrix is singular or nearly singular.

For medium to large matrices there might be a slight performance boost to using CLinearSolverFactory instead.

Parameters:

input - The matrix that is to be inverted. Not modified.

output - Where the inverse matrix is stored. Modified.

Returns:

true if it could invert the matrix false if it could not.

solve

public static boolean solve(CDenseMatrix64F a,
                            CDenseMatrix64F b,
                            CDenseMatrix64F x)

Solves for x in the following equation:

A*x = b

If the system could not be solved then false is returned. If it returns true that just means the algorithm finished operating, but the results could still be bad because 'A' is singular or nearly singular.

If repeat calls to solve are being made then one should consider using CLinearSolverFactory instead.

It is ok for 'b' and 'x' to be the same matrix.

Parameters:

a - A matrix that is m by n. Not modified.

b - A matrix that is n by k. Not modified.

x - A matrix that is m by k. Modified.

Returns:

true if it could invert the matrix false if it could not.

det

public static Complex64F det(CDenseMatrix64F mat)

Returns the determinant of the matrix. If the inverse of the matrix is also needed, then using LUDecompositionAlt_CD64 directly (or any similar algorithm) can be more efficient.

Parameters:

mat - The matrix whose determinant is to be computed. Not modified.

Returns:

The determinant.

elementMultiply

public static void elementMultiply(CD1Matrix64F input,
                                   double real,
                                   double imaginary,
                                   CD1Matrix64F output)

Performs element by element multiplication operation with a complex numbert

output_ij = input_ij * (real + imaginary*i)

Parameters:

input - The left matrix in the multiplication operation. Not modified.

real - Real component of the number it is multiplied by

imaginary - Imaginary component of the number it is multiplied by

output - Where the results of the operation are stored. Modified.

elementDivide

public static void elementDivide(CD1Matrix64F input,
                                 double real,
                                 double imaginary,
                                 CD1Matrix64F output)

Performs element by element division operation with a complex number on the right

output_ij = input_ij / (real + imaginary*i)

Parameters:

input - The left matrix in the multiplication operation. Not modified.

real - Real component of the number it is multiplied by

imaginary - Imaginary component of the number it is multiplied by

output - Where the results of the operation are stored. Modified.

elementDivide

public static void elementDivide(double real,
                                 double imaginary,
                                 CD1Matrix64F input,
                                 CD1Matrix64F output)

Performs element by element division operation with a complex number on the right

output_ij = (real + imaginary*i) / input_ij

Parameters:

real - Real component of the number it is multiplied by

imaginary - Imaginary component of the number it is multiplied by

input - The right matrix in the multiplication operation. Not modified.

output - Where the results of the operation are stored. Modified.

elementMinReal

public static double elementMinReal(CD1Matrix64F a)

Returns the value of the real element in the matrix that has the minimum value.

Min{ a_ij } for all i and j

Parameters:

a - A matrix. Not modified.

Returns:

The the minimum value out of all the real values.

elementMinImaginary

public static double elementMinImaginary(CD1Matrix64F a)

Returns the value of the imaginary element in the matrix that has the minimum value.

Min{ a_ij } for all i and j

Parameters:

a - A matrix. Not modified.

Returns:

The the minimum value out of all the real values.

elementMaxReal

public static double elementMaxReal(CD1Matrix64F a)

Returns the value of the real element in the matrix that has the minimum value.

Min{ a_ij } for all i and j

Parameters:

a - A matrix. Not modified.

Returns:

The the minimum value out of all the real values.

elementMaxImaginary

public static double elementMaxImaginary(CD1Matrix64F a)

Returns the value of the imaginary element in the matrix that has the minimum value.

Min{ a_ij } for all i and j

Parameters:

a - A matrix. Not modified.

Returns:

The the minimum value out of all the real values.

elementMaxMagnitude2

public static double elementMaxMagnitude2(CD1Matrix64F a)

Returns the magnitude squared of the complex element with the largest magnitude

Max{ |a_ij|^2 } for all i and j

Parameters:

a - A matrix. Not modified.

Returns:

The max magnitude squared

setIdentity

public static void setIdentity(CDenseMatrix64F mat)

Sets all the diagonal elements equal to one and everything else equal to zero. If this is a square matrix then it will be an identity matrix.

Parameters:

mat - A square matrix.

extract

public static CDenseMatrix64F extract(CDenseMatrix64F src,
                                      int srcY0,
                                      int srcY1,
                                      int srcX0,
                                      int srcX1)

Creates a new matrix which is the specified submatrix of 'src'

s_{i-y0 , j-x0} = o_ij for all y0 ≤ i < y1 and x0 ≤ j < x1

where 's_ij' is an element in the submatrix and 'o_ij' is an element in the original matrix.

Parameters:

src - The original matrix which is to be copied. Not modified.

srcX0 - Start column.

srcX1 - Stop column+1.

srcY0 - Start row.

srcY1 - Stop row+1.

Returns:

Extracted submatrix.

extract

public static void extract(CDenseMatrix64F src,
                           int srcY0,
                           int srcY1,
                           int srcX0,
                           int srcX1,
                           CDenseMatrix64F dst,
                           int dstY0,
                           int dstX0)

Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.

s_{i-y0 , j-x0} = o_ij for all y0 ≤ i < y1 and x0 ≤ j < x1

where 's_ij' is an element in the submatrix and 'o_ij' is an element in the original matrix.

Parameters:

src - The original matrix which is to be copied. Not modified.

srcX0 - Start column.

srcX1 - Stop column+1.

srcY0 - Start row.

srcY1 - Stop row+1.

dst - Where the submatrix are stored. Modified.

dstY0 - Start row in dst.

dstX0 - start column in dst.

columnsToVector

public static CDenseMatrix64F[] columnsToVector(CDenseMatrix64F A,
                                                CDenseMatrix64F[] v)

Converts the columns in a matrix into a set of vectors.

Parameters:

A - Matrix. Not modified.

v - Optional storage for columns.

Returns:

An array of vectors.

elementMaxAbs

public static double elementMaxAbs(CDenseMatrix64F a)

Returns the absolute value of the element in the matrix that has the largest absolute value.

Max{ |a_ij| } for all i and j

Parameters:

a - A matrix. Not modified.

Returns:

The max abs element value of the matrix.