org.ejml.ops

Class SpecializedOps

java.lang.Object

org.ejml.ops.SpecializedOps

public class SpecializedOps
extends Object

This contains less common or more specialized matrix operations.

Author:

Peter Abeles

Constructor Summary

Constructors

Constructor and Description
SpecializedOps()

Method Summary

Methods

Modifier and Type	Method and Description
static void	addIdentity(RowD1Matrix64F A, RowD1Matrix64F B, double alpha) Performs the following operation: B = A + αI
static DenseMatrix64F	copyChangeRow(int[] order, DenseMatrix64F src, DenseMatrix64F dst) Creates a copy of a matrix but swaps the rows as specified by the order array.
static DenseMatrix64F	copyTriangle(DenseMatrix64F src, DenseMatrix64F dst, boolean upper) Copies just the upper or lower triangular portion of a matrix.
static DenseMatrix64F	createReflector(DenseMatrix64F u, double gamma) Creates a reflector from the provided vector and gamma. Q = I - γ u uT
static DenseMatrix64F	createReflector(RowD1Matrix64F u) Creates a reflector from the provided vector. Q = I - γ u uT γ = 2/||u||2
static double	diagProd(RowD1Matrix64F T) Computes the product of the diagonal elements.
static double	diffNormF_fast(D1Matrix64F a, D1Matrix64F b)
static double	diffNormF(D1Matrix64F a, D1Matrix64F b) Computes the F norm of the difference between the two Matrices: Sqrt{∑i=1:m ∑j=1:n ( aij - bij)2}
static double	diffNormP1(D1Matrix64F a, D1Matrix64F b) Computes the p=1 p-norm of the difference between the two Matrices: ∑i=1:m ∑j=1:n | aij - bij| where |x| is the absolute value of x.
static double	elementSumSq(D1Matrix64F m) Sums up the square of each element in the matrix.
static DenseMatrix64F	pivotMatrix(DenseMatrix64F ret, int[] pivots, int numPivots, boolean transposed) Creates a pivot matrix that exchanges the rows in a matrix: A' = P*A
static double	qualityTriangular(boolean upper, D1Matrix64F T) Computes the quality of a triangular matrix, where the quality of a matrix is defined in LinearSolver.quality().
static DenseMatrix64F[]	splitIntoVectors(RowD1Matrix64F A, boolean column) Takes a matrix and splits it into a set of row or column vectors.
static void	subvector(RowD1Matrix64F A, int rowA, int colA, int length, boolean row, int offsetV, RowD1Matrix64F v) Extracts a row or column vector from matrix A.

Methods inherited from class java.lang.Object

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

Constructor Detail

SpecializedOps

public SpecializedOps()

Method Detail

createReflector

public static DenseMatrix64F createReflector(RowD1Matrix64F u)

Creates a reflector from the provided vector.

Q = I - γ u u^T
γ = 2/||u||²

In practice VectorVectorMult.householder(double, org.ejml.data.D1Matrix64F, org.ejml.data.D1Matrix64F, org.ejml.data.D1Matrix64F) multHouseholder} should be used for performance reasons since there is no need to calculate Q explicitly.

Parameters:

u - A vector. Not modified.

Returns:

An orthogonal reflector.

createReflector

public static DenseMatrix64F createReflector(DenseMatrix64F u,
                             double gamma)

Creates a reflector from the provided vector and gamma.

Q = I - γ u u^T

In practice VectorVectorMult.householder(double, org.ejml.data.D1Matrix64F, org.ejml.data.D1Matrix64F, org.ejml.data.D1Matrix64F) multHouseholder} should be used for performance reasons since there is no need to calculate Q explicitly.

Parameters:

u - A vector. Not modified.

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

Returns:

An orthogonal reflector.

copyChangeRow

public static DenseMatrix64F copyChangeRow(int[] order,
                           DenseMatrix64F src,
                           DenseMatrix64F dst)

Creates a copy of a matrix but swaps the rows as specified by the order array.

Parameters:

order - Specifies which row in the dest corresponds to a row in the src. Not modified.

src - The original matrix. Not modified.

dst - A Matrix that is a row swapped copy of src. Modified.

copyTriangle

public static DenseMatrix64F copyTriangle(DenseMatrix64F src,
                          DenseMatrix64F dst,
                          boolean upper)

Copies just the upper or lower triangular portion of a matrix.

Parameters:

src - Matrix being copied. Not modified.

dst - Where just a triangle from src is copied. If null a new one will be created. Modified.

upper - If the upper or lower triangle should be copied.

Returns:

The copied matrix.

diffNormF

public static double diffNormF(D1Matrix64F a,
               D1Matrix64F b)

Computes the F norm of the difference between the two Matrices:

Sqrt{∑_i=1:m ∑_j=1:n ( a_ij - b_ij)²}

This is often used as a cost function.

Parameters:

a - m by n matrix. Not modified.

b - m by n matrix. Not modified.

Returns:

The F normal of the difference matrix.

See Also:

NormOps.fastNormF(org.ejml.data.D1Matrix64F)

diffNormF_fast

public static double diffNormF_fast(D1Matrix64F a,
                    D1Matrix64F b)

diffNormP1

public static double diffNormP1(D1Matrix64F a,
                D1Matrix64F b)

Computes the p=1 p-norm of the difference between the two Matrices:

∑_i=1:m ∑_j=1:n | a_ij - b_ij|

where |x| is the absolute value of x.

This is often used as a cost function.

Parameters:

a - m by n matrix. Not modified.

b - m by n matrix. Not modified.

Returns:

The p=1 p-norm of the difference matrix.

addIdentity

public static void addIdentity(RowD1Matrix64F A,
               RowD1Matrix64F B,
               double alpha)

Performs the following operation:

B = A + αI

Parameters:

A - A square matrix. Not modified.

B - A square matrix that the results are saved to. Modified.

alpha - Scaling factor for the identity matrix.

subvector

public static void subvector(RowD1Matrix64F A,
             int rowA,
             int colA,
             int length,
             boolean row,
             int offsetV,
             RowD1Matrix64F v)

Extracts a row or column vector from matrix A. The first element in the matrix is at element (rowA,colA). The next 'length' elements are extracted along a row or column. The results are put into vector 'v' start at its element v0.

Parameters:

A - Matrix that the vector is being extracted from. Not modified.

rowA - Row of the first element that is extracted.

colA - Column of the first element that is extracted.

length - Length of the extracted vector.

row - If true a row vector is extracted, otherwise a column vector is extracted.

offsetV - First element in 'v' where the results are extracted to.

v - Vector where the results are written to. Modified.

splitIntoVectors

public static DenseMatrix64F[] splitIntoVectors(RowD1Matrix64F A,
                                boolean column)

Takes a matrix and splits it into a set of row or column vectors.

Parameters:

A - original matrix.

column - If true then column vectors will be created.

Returns:

Set of vectors.

pivotMatrix

public static DenseMatrix64F pivotMatrix(DenseMatrix64F 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.

diagProd

public static double diagProd(RowD1Matrix64F T)

Computes the product of the diagonal elements. For a diagonal or triangular matrix this is the determinant.

Parameters:

T - A matrix.

Returns:

product of the diagonal elements.

qualityTriangular

public static double qualityTriangular(boolean upper,
                       D1Matrix64F T)

Computes the quality of a triangular matrix, where the quality of a matrix is defined in LinearSolver.quality(). In this situation the quality os the absolute value 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.

Parameters:

upper - if it is upper triangular or not.

T - A matrix. @return product of the diagonal elements.

Returns:

the quality of the system.

elementSumSq

public static double elementSumSq(D1Matrix64F m)

Sums up the square of each element in the matrix. This is equivalent to the Frobenius norm squared.

Parameters:

m - Matrix.

Returns:

Sum of elements squared.