Package org.ejml.dense.block

Class InnerTriangularSolver_FDRB

java.lang.Object

org.ejml.dense.block.InnerTriangularSolver_FDRB

public class InnerTriangularSolver_FDRB
extends java.lang.Object

Contains triangular solvers for inner blocks of a FMatrixRBlock.

Algorithm for lower triangular inverse:

 for i=1:m
     for j=1:i-1
         val = 0
         for k=j:i-1
             val = val - L(i,k) * X(k,j)
         end
         x(i,j) = val / L(i,i)
     end
     x(i,i) = 1 / L(i,i)
 end
 

Constructor Summary

Constructors

Constructor	Description
InnerTriangularSolver_FDRB()

Method Summary

Modifier and Type	Method	Description
static void	invertLower(float[] L, float[] L_inv, int m, int offsetL, int offsetL_inv)	Inverts a square lower triangular matrix: L = L-1
static void	invertLower(float[] L, int m, int offsetL)	Inverts a square lower triangular matrix: L = L-1
static void	solveL(float[] L, float[] b, int m, int n, int strideL, int offsetL, int offsetB)	Solves for non-singular lower triangular matrices using forward substitution.
static void	solveLTransB(float[] L, float[] b, int m, int n, int strideL, int offsetL, int offsetB)	Solves for non-singular lower triangular matrices using forward substitution.
static void	solveTransL(float[] L, float[] b, int m, int n, int strideL, int offsetL, int offsetB)	Solves for non-singular transposed lower triangular matrices using backwards substitution: B = L-TB where B is a (m by n) matrix, L is a lower triangular (m by m) matrix.
static void	solveTransU(float[] U, float[] b, int m, int n, int strideU, int offsetU, int offsetB)	Solves for non-singular upper triangular matrices using forward substitution.
static void	solveU(float[] U, float[] b, int m, int n, int strideU, int offsetU, int offsetB)	Solves for non-singular upper triangular matrices using backwards substitution.

Methods inherited from class java.lang.Object

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

Constructor Detail

InnerTriangularSolver_FDRB

public InnerTriangularSolver_FDRB()

Method Detail

invertLower

public static void invertLower(float[] L,
                               float[] L_inv,
                               int m,
                               int offsetL,
                               int offsetL_inv)

Inverts a square lower triangular matrix: L = L^-1

Parameters:

L - Lower triangular matrix being inverted. Not modified.

L_inv - Where the inverse is stored. Can be the same as L. Modified.

m - The number of rows and columns.

offsetL - which index does the L matrix start at.

offsetL_inv - which index does the L_inv matrix start at.

invertLower

public static void invertLower(float[] L,
                               int m,
                               int offsetL)

Inverts a square lower triangular matrix: L = L^-1

Parameters:

L - Lower triangular matrix being inverted. Over written with inverted matrix. Modified.

m - The number of rows and columns.

offsetL - which index does the L matrix start at.

solveL

public static void solveL(float[] L,
                          float[] b,
                          int m,
                          int n,
                          int strideL,
                          int offsetL,
                          int offsetB)

Solves for non-singular lower triangular matrices using forward substitution.
B = L^-1B

where B is a (m by n) matrix, L is a lower triangular (m by m) matrix.

Parameters:

L - An m by m non-singular lower triangular matrix. Not modified.

b - An m by n matrix. Modified.

m - size of the L matrix

n - number of columns in the B matrix.

strideL - number of elements that need to be added to go to the next row in L

offsetL - initial index in L where the matrix starts

offsetB - initial index in B where the matrix starts

solveTransL

public static void solveTransL(float[] L,
                               float[] b,
                               int m,
                               int n,
                               int strideL,
                               int offsetL,
                               int offsetB)

Solves for non-singular transposed lower triangular matrices using backwards substitution:
B = L^-TB

where B is a (m by n) matrix, L is a lower triangular (m by m) matrix.

Parameters:

L - An m by m non-singular lower triangular matrix. Not modified.

b - An m by n matrix. Modified.

m - size of the L matrix

n - number of columns in the B matrix.

strideL - number of elements that need to be added to go to the next row in L

offsetL - initial index in L where the matrix starts

offsetB - initial index in B where the matrix starts

solveLTransB

public static void solveLTransB(float[] L,
                                float[] b,
                                int m,
                                int n,
                                int strideL,
                                int offsetL,
                                int offsetB)

Solves for non-singular lower triangular matrices using forward substitution.
B^T = L^-1B^T

where B is a (n by m) matrix, L is a lower triangular (m by m) matrix.

Parameters:

L - An m by m non-singular lower triangular matrix. Not modified.

b - An n by m matrix. Modified.

m - size of the L matrix

n - number of columns in the B matrix.

offsetL - initial index in L where the matrix starts

offsetB - initial index in B where the matrix starts

solveU

public static void solveU(float[] U,
                          float[] b,
                          int m,
                          int n,
                          int strideU,
                          int offsetU,
                          int offsetB)

Solves for non-singular upper triangular matrices using backwards substitution.
B = U^-1B

where B (m by n) is a matrix, U is a (m by m ) upper triangular matrix.

Parameters:

U - An m by m non-singular upper triangular matrix. Not modified.

b - An m by n matrix. Modified.

m - size of the L matrix

n - number of columns in the B matrix.

offsetU - initial index in L where the matrix starts

offsetB - initial index in B where the matrix starts

solveTransU

public static void solveTransU(float[] U,
                               float[] b,
                               int m,
                               int n,
                               int strideU,
                               int offsetU,
                               int offsetB)

Solves for non-singular upper triangular matrices using forward substitution.
B = U^-TB

where B (m by n) is a matrix, U is a (m by m ) upper triangular matrix.

Parameters:

U - An m by m non-singular upper triangular matrix. Not modified.

b - An m by n matrix. Modified.

m - size of the L matrix

n - number of columns in the B matrix.

offsetU - initial index in L where the matrix starts

offsetB - initial index in B where the matrix starts