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A fast and easy to use dense and sparse matrix linear algebra library written in Java.
/*
* Copyright (c) 2009-2017, Peter Abeles. All Rights Reserved.
*
* This file is part of Efficient Java Matrix Library (EJML).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.ejml.dense.row.decomposition;
/**
*
* 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
*/
public class TriangularSolver_FDRM {
/**
*
* Inverts a square lower triangular matrix: L = L-1
*
*
*
* @param L
* @param m
*/
public static void invertLower( float L[] , int m ) {
for( int i = 0; i < m; i++ ) {
float L_ii = L[ i*m + i ];
for( int j = 0; j < i; j++ ) {
float val = 0;
for( int k = j; k < i; k++ ) {
val += L[ i*m + k] * L[ k*m + j ];
}
L[ i*m + j ] = -val / L_ii;
}
L[ i*m + i ] = 1.0f / L_ii;
}
}
public static void invertLower( float L[] , float L_inv[] , int m ) {
for( int i = 0; i < m; i++ ) {
float L_ii = L[ i*m + i ];
for( int j = 0; j < i; j++ ) {
float val = 0;
for( int k = j; k < i; k++ ) {
val -= L[ i*m + k] * L_inv[ k*m + j ];
}
L_inv[ i*m + j ] = val / L_ii;
}
L_inv[ i*m + i ] = 1.0f / L_ii;
}
}
/**
*
* 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.
*
*
* @param L An n by n non-singular lower triangular matrix. Not modified.
* @param b A vector of length n. Modified.
* @param n The size of the matrices.
*/
public static void solveL( float L[] , float []b , int n )
{
// for( int i = 0; i < n; i++ ) {
// float sum = b[i];
// for( int k=0; k
* This is a forward substitution solver for non-singular lower triangular matrices.
*
* b = (LT)-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.
*
*
* @param L An n by n non-singular lower triangular matrix. Not modified.
* @param b A vector of length n. Modified.
* @param n The size of the matrices.
*/
public static void solveTranL( float L[] , float []b , int n )
{
for( int i =n-1; i>=0; i-- ) {
float sum = b[i];
for( int k = i+1; k
* 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.
*
*
* @param U An n by n non-singular upper triangular matrix. Not modified.
* @param b A vector of length n. Modified.
* @param n The size of the matrices.
*/
public static void solveU( float U[] , float []b , int n )
{
// for( int i =n-1; i>=0; i-- ) {
// float sum = b[i];
// for( int j = i+1; j =0; i-- ) {
float sum = b[i];
int indexU = i*n+i+1;
for( int j = i+1; j =minRow; i-- ) {
// float sum = b[i];
// for( int j = i+1; j =minRow; i-- ) {
float sum = b[i];
int indexU = i*sideLength+i+1;
for( int j = i+1; j
* 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.
*
*
* @param U Matrix containing the upper triangle system
* @param startU Index of the first element in U
* @param strideU stride between rows
* @param widthU How wide the square matrix is
* @param b Matrix containing the solution to the system. Overwritten with the solution.
* @param startB Index of the first element in B
* @param strideB stride between rows
* @param widthB How wide the matrix is. Length is the same as U's width
*/
public static void solveU( float []U , int startU , int strideU , int widthU ,
float []b , int startB , int strideB , int widthB )
{
for( int colB = 0; colB < widthB; colB++ ) {
for( int i =widthU-1; i>=0; i-- ) {
float sum = b[startB + i*strideB + colB];
for( int j = i+1; j