org.ejml.alg.dense.decomposition
Class TriangularSolver

java.lang.Object
  org.ejml.alg.dense.decomposition.TriangularSolver

public class TriangularSolver
extends 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.

Author:

Peter Abeles

Constructor Summary

TriangularSolver()

Method Summary

static void	invertLower(double[] L, double[] L_inv, int m)
static void	invertLower(double[] L, int m) Inverts a square lower triangular matrix: L = L-1
static void	solveL(double[] L, double[] b, int n) Solves for non-singular lower triangular matrices using forward substitution.
static void	solveL(double[] L, double[] b, int m, int n) L is a m by m matrix B is a m by n matrix
static void	solveTranL(double[] L, double[] b, int n) This is a forward substitution solver for non-singular lower triangular matrices.
static void	solveU(double[] U, double[] b, int n) This is a forward substitution solver for non-singular upper triangular matrices.
static void	solveU(double[] U, double[] b, int sideLength, int minRow, int maxRow)
static void	solveU(double[] U, int startU, int strideU, int widthU, double[] 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

public TriangularSolver()

Method Detail

invertLower

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

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

Parameters:

L -

m -

invertLower

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

solveL

public static void solveL(double[] L,
                          double[] 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(double[] L,
                          double[] 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(double[] L,
                              double[] 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(double[] U,
                          double[] 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(double[] U,
                          double[] b,
                          int sideLength,
                          int minRow,
                          int maxRow)

solveU

public static void solveU(double[] U,
                          int startU,
                          int strideU,
                          int widthU,
                          double[] 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