Package org.ejml.dense.row.decomposition

Class TriangularSolver_FDRM

java.lang.Object

org.ejml.dense.row.decomposition.TriangularSolver_FDRM

public class TriangularSolver_FDRM
extends java.lang.Object

This contains algorithms for solving systems of equations where T is a non-singular triangular matrix:

T*x = b

where x and b are vectors, and T is an n by n matrix. T can either be a lower or upper triangular matrix.

These functions are designed for use inside of other algorithms. To use them directly is dangerous since no sanity checks are performed.

Constructor Summary

Constructors

Constructor	Description
TriangularSolver_FDRM()

Method Summary

Modifier and Type	Method	Description
static void	invertLower(float[] L, float[] L_inv, int m)
static void	invertLower(float[] L, int m)	Inverts a square lower triangular matrix: L = L-1
static void	solveL(float[] L, float[] b, int n)	Solves for non-singular lower triangular matrices using forward substitution.
static void	solveL(float[] L, float[] b, int m, int n)	L is a m by m matrix B is a m by n matrix
static void	solveTranL(float[] L, float[] b, int n)	This is a forward substitution solver for non-singular lower triangular matrices.
static void	solveU(float[] U, float[] b, int n)	This is a forward substitution solver for non-singular upper triangular matrices.
static void	solveU(float[] U, float[] b, int sideLength, int minRow, int maxRow)
static void	solveU(float[] U, int startU, int strideU, int widthU, float[] b, int startB, int strideB, int widthB)	This is a forward substitution solver for non-singular upper triangular matrices which are a sub-matrix inside a larger.

Methods inherited from class java.lang.Object

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

Constructor Detail

TriangularSolver_FDRM

public TriangularSolver_FDRM()

Method Detail

invertLower

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

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

Parameters:

L -

m -

invertLower

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

solveL

public static void solveL(float[] L,
                          float[] b,
                          int n)

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

where b is a vector, L is an n by n matrix.

Parameters:

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

b - A vector of length n. Modified.

n - The size of the matrices.

solveL

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

L is a m by m matrix B is a m by n matrix

Parameters:

L -

b -

m -

n -

solveTranL

public static void solveTranL(float[] L,
                              float[] b,
                              int n)

This is a forward substitution solver for non-singular lower triangular matrices.
b = (L^T)^-1b

where b is a vector, L is an n by n matrix.

L is a lower triangular matrix, but it comes up with a solution as if it was an upper triangular matrix that was computed by transposing L.

Parameters:

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

b - A vector of length n. Modified.

n - The size of the matrices.

solveU

public static void solveU(float[] U,
                          float[] b,
                          int n)

This is a forward substitution solver for non-singular upper triangular matrices.
b = U^-1b

where b is a vector, U is an n by n matrix.

Parameters:

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

b - A vector of length n. Modified.

n - The size of the matrices.

solveU

public static void solveU(float[] U,
                          float[] b,
                          int sideLength,
                          int minRow,
                          int maxRow)

solveU

public static void solveU(float[] U,
                          int startU,
                          int strideU,
                          int widthU,
                          float[] b,
                          int startB,
                          int strideB,
                          int widthB)

This is a forward substitution solver for non-singular upper triangular matrices which are a sub-matrix inside a larger. The columns of 'b' are solved for individually
b = U^-1b

where b is a matrix, U is an n by n matrix.

Parameters:

U - Matrix containing the upper triangle system

startU - Index of the first element in U

strideU - stride between rows

widthU - How wide the square matrix is

b - Matrix containing the solution to the system. Overwritten with the solution.

startB - Index of the first element in B

strideB - stride between rows

widthB - How wide the matrix is. Length is the same as U's width