java.lang.Object

org.ejml.dense.row.SpecializedOps_DDRM

public class SpecializedOps_DDRM extends Object

This contains less common or more specialized matrix operations.

Method Summary

Modifier and Type

Method

Description

static void

addIdentity(DMatrix1Row A, DMatrix1Row B, double alpha)

Performs the following operation:

B = A + αI

static DMatrixRMaj

copyChangeRow(int[] order, DMatrixRMaj src, @Nullable DMatrixRMaj dst)

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

static DMatrixRMaj

copyTriangle(DMatrixRMaj src, @Nullable DMatrixRMaj dst, boolean upper)

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

static DMatrixRMaj

createReflector(DMatrix1Row u)

Creates a reflector from the provided vector.

Q = I - γ u u^T
γ = 2/||u||²

static DMatrixRMaj

createReflector(DMatrixRMaj u, double gamma)

Creates a reflector from the provided vector and gamma.

Q = I - γ u u^T

static double

diagProd(DMatrix1Row T)

Computes the product of the diagonal elements.

static double

diffNormF(DMatrixD1 a, DMatrixD1 b)

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

Sqrt{∑_i=1:m ∑_j=1:n ( a_ij - b_ij)²}

static double

diffNormF_fast(DMatrixD1 a, DMatrixD1 b)

static double

diffNormP1(DMatrixD1 a, DMatrixD1 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.

static double

elementDiagonalMaxAbs(DMatrixD1 a)

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

Max{ |a_ij| } for all i and j

static double

elementSumSq(DMatrixD1 m)

Sums up the square of each element in the matrix.

static void

multLowerTranA(DMatrixRMaj mat)

Performs L = L^T*L

static void

multLowerTranB(DMatrixRMaj mat)

Performs L = L*L^T

static DMatrixRMaj

pivotMatrix(@Nullable DMatrixRMaj ret, int[] pivots, int numPivots, boolean transposed)

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

static double

qualityTriangular(DMatrixD1 T)

Computes the quality of a triangular matrix, where the quality of a matrix is defined in LinearSolver.quality().

static DMatrixRMaj[]

splitIntoVectors(DMatrix1Row A, boolean column)

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

static void

subvector(DMatrix1Row A, int rowA, int colA, int length, boolean row, int offsetV, DMatrix1Row 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

Method Details
- createReflector
  
  public static DMatrixRMaj createReflector(DMatrix1Row u)
  
  Creates a reflector from the provided vector.
  
  Q = I - γ u u^T
  γ = 2/||u||²
  
  In practice VectorVectorMult_DDRM.householder(double, DMatrixD1, DMatrixD1, DMatrixD1) 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 DMatrixRMaj createReflector(DMatrixRMaj u, double gamma)
  
  Creates a reflector from the provided vector and gamma.
  
  Q = I - γ u u^T
  
  In practice VectorVectorMult_DDRM.householder(double, DMatrixD1, DMatrixD1, DMatrixD1) 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 DMatrixRMaj copyChangeRow(int[] order, DMatrixRMaj src, @Nullable @Nullable DMatrixRMaj 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 DMatrixRMaj copyTriangle(DMatrixRMaj src, @Nullable @Nullable DMatrixRMaj 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.
- multLowerTranB
  
  public static void multLowerTranB(DMatrixRMaj mat)
  
  Performs L = L*L^T
- multLowerTranA
  
  public static void multLowerTranA(DMatrixRMaj mat)
  
  Performs L = L^T*L
- diffNormF
  
  public static double diffNormF(DMatrixD1 a, DMatrixD1 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_DDRM.fastNormF(org.ejml.data.DMatrixD1)
- diffNormF_fast
  
  public static double diffNormF_fast(DMatrixD1 a, DMatrixD1 b)
- diffNormP1
  
  public static double diffNormP1(DMatrixD1 a, DMatrixD1 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(DMatrix1Row A, DMatrix1Row 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(DMatrix1Row A, int rowA, int colA, int length, boolean row, int offsetV, DMatrix1Row 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 DMatrixRMaj[] splitIntoVectors(DMatrix1Row 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 DMatrixRMaj pivotMatrix(@Nullable @Nullable DMatrixRMaj 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(DMatrix1Row 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.
- elementDiagonalMaxAbs
  
  public static double elementDiagonalMaxAbs(DMatrixD1 a)
  
  Returns the absolute value of the digonal 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.
- qualityTriangular
  
  public static double qualityTriangular(DMatrixD1 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:
  
  T - A matrix.
  
  Returns:
  
  the quality of the system.
- elementSumSq
  
  public static double elementSumSq(DMatrixD1 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.

Class SpecializedOps_DDRM

Method Summary

Methods inherited from class java.lang.Object

Method Details

createReflector

createReflector

copyChangeRow

copyTriangle

multLowerTranB

multLowerTranA

diffNormF

diffNormF_fast

diffNormP1

addIdentity

subvector

splitIntoVectors

pivotMatrix

diagProd

elementDiagonalMaxAbs

qualityTriangular

elementSumSq