Package org.ejml.dense.row

Class SpecializedOps_ZDRM

java.lang.Object

org.ejml.dense.row.SpecializedOps_ZDRM

public class SpecializedOps_ZDRM
extends Object

Various highly specialized operations that are probably not of interest to most people.

Method Summary

Modifier and Type	Method	Description
static ZMatrixRMaj	createReflector(ZMatrixRMaj u)	Creates a reflector from the provided vector. Q = I - γ u uT γ = 2/||u||2
static ZMatrixRMaj	createReflector(ZMatrixRMaj u, double gamma)	Creates a reflector from the provided vector and gamma. Q = I - γ u uH
static double	elementDiagMaxMagnitude2(ZMatrixRMaj a)	Returns the magnitude squared of the complex element along the diagonal with the largest magnitude Max{ |aij|^2 } for all i and j
static ZMatrixRMaj	householder(ZMatrixRMaj u, double gamma)	Q = I - gamma*u*uH
static ZMatrixRMaj	householderVector(ZMatrixRMaj x)	Computes the householder vector used in QR decomposition.
static ZMatrixRMaj	pivotMatrix(@Nullable ZMatrixRMaj ret, int[] pivots, int numPivots, boolean transposed)	Creates a pivot matrix that exchanges the rows in a matrix: A' = P*A
static double	qualityTriangular(ZMatrixRMaj T)	Computes the quality of a triangular matrix, where the quality of a matrix is defined in LinearSolver.quality().

Methods inherited from class java.lang.Object

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

Method Details

createReflector

public static ZMatrixRMaj createReflector(ZMatrixRMaj u)

Creates a reflector from the provided vector.

Q = I - γ u u^T
γ = 2/||u||²

Parameters:

u - A vector. Not modified.

Returns:

An orthogonal reflector.

createReflector

public static ZMatrixRMaj createReflector(ZMatrixRMaj u,
 double gamma)

Creates a reflector from the provided vector and gamma.

Q = I - γ u u^H

Parameters:

u - A vector. Not modified.

gamma - To produce a reflector gamma needs to be equal to 2/||u||.

Returns:

An orthogonal reflector.

pivotMatrix

public static ZMatrixRMaj pivotMatrix(@Nullable
 @Nullable ZMatrixRMaj ret,
 int[] pivots,
 int numPivots,
 boolean transposed)

Creates a pivot matrix that exchanges the rows in a matrix:
A' = P*A

For example, if element 0 in 'pivots' is 2 then the first row in A' will be the 3rd row in A.

Parameters:

ret - If null then a new matrix is declared otherwise the results are written to it. Is modified.

pivots - Specifies the new order of rows in a matrix.

numPivots - How many elements in pivots are being used.

transposed - If the transpose of the matrix is returned.

Returns:

A pivot matrix.

elementDiagMaxMagnitude2

public static double elementDiagMaxMagnitude2(ZMatrixRMaj a)

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

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

Parameters:

a - A matrix. Not modified.

Returns:

The max magnitude squared

qualityTriangular

public static double qualityTriangular(ZMatrixRMaj T)

Computes the quality of a triangular matrix, where the quality of a matrix is defined in LinearSolver.quality(). In this situation the quality is the magnitude of the product of each diagonal element divided by the magnitude of the largest diagonal element. If all diagonal elements are zero then zero is returned.

Returns:

the quality of the system.

householder

public static ZMatrixRMaj householder(ZMatrixRMaj u,
 double gamma)

Q = I - gamma*u*u^H

householderVector

public static ZMatrixRMaj householderVector(ZMatrixRMaj x)

Computes the householder vector used in QR decomposition. u = x / max(x) u(0) = u(0) + |u| u = u / u(0)

Parameters:

x - Input vector. Unmodified.

Returns:

The found householder reflector vector