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A fast and easy to use dense matrix linear algebra library written in Java.
/*
* Copyright (c) 2009-2013, 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.alg.block;
/**
*
* Contains triangular solvers for inner blocks of a {@link org.ejml.data.BlockMatrix64F}.
*
*
*
* 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
*
*
*
* @author Peter Abeles
*/
public class BlockInnerTriangularSolver {
/**
*
* Inverts a square lower triangular matrix: L = L-1
*
*
* @param L Lower triangular matrix being inverted. Not modified.
* @oaran K_inv Where the inverse is stored. Can be the same as L. Modified.
* @param m The number of rows and columns.
* @param offsetL which index does the L matrix start at.
* @param offsetL_inv which index does the L_inv matrix start at.
*
*/
public static void invertLower( double L[] ,
double L_inv[] ,
int m ,
int offsetL ,
int offsetL_inv )
{
for( int i = 0; i < m; i++ ) {
double L_ii = L[ offsetL + i*m + i ];
for( int j = 0; j < i; j++ ) {
double val = 0;
for( int k = j; k < i; k++ ) {
val += L[offsetL + i*m + k] * L_inv[ offsetL_inv + k*m + j ];
}
L_inv[ offsetL_inv + i*m + j ] = -val / L_ii;
}
L_inv[ offsetL_inv + i*m + i ] = 1.0 / L_ii;
}
}
/**
*
* Inverts a square lower triangular matrix: L = L-1
*
*
* @param L Lower triangular matrix being inverted. Over written with inverted matrix. Modified.
* @param m The number of rows and columns.
* @param offsetL which index does the L matrix start at.
*
*/
public static void invertLower( double L[] ,
int m ,
int offsetL )
{
for( int i = 0; i < m; i++ ) {
double L_ii = L[ offsetL + i*m + i ];
for( int j = 0; j < i; j++ ) {
double val = 0;
for( int k = j; k < i; k++ ) {
val += L[offsetL + i*m + k] * L[ offsetL + k*m + j ];
}
L[ offsetL + i*m + j ] = -val / L_ii;
}
L[ offsetL + i*m + i ] = 1.0 / L_ii;
}
}
/**
*
* 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.
*
*
* @param L An m by m non-singular lower triangular matrix. Not modified.
* @param b An m by n matrix. Modified.
* @param m size of the L matrix
* @param n number of columns in the B matrix.
* @param strideL number of elements that need to be added to go to the next row in L
* @param offsetL initial index in L where the matrix starts
* @param offsetB initial index in B where the matrix starts
*/
public static void solveL( double L[] , double []b ,
int m , int n ,
int strideL , int offsetL , int offsetB )
{
for( int j = 0; j < n; j++ ) {
for( int i = 0; i < m; i++ ) {
double sum = b[offsetB + i*n+j];
for( int k=0; k
* 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.
*
*
* @param L An m by m non-singular lower triangular matrix. Not modified.
* @param b An m by n matrix. Modified.
* @param m size of the L matrix
* @param n number of columns in the B matrix.
* @param strideL number of elements that need to be added to go to the next row in L
* @param offsetL initial index in L where the matrix starts
* @param offsetB initial index in B where the matrix starts
*/
public static void solveTransL( double L[] , double []b ,
int m , int n ,
int strideL , int offsetL , int offsetB )
{
for( int j = 0; j < n; j++ ) {
for( int i = m-1; i >= 0; i-- ) {
double sum = b[offsetB + i*n+j];
for( int k=i+1; k
* Solves for non-singular lower triangular matrices using forward substitution.
*
* BT = L-1BT
*
* where B is a (n by m) matrix, L is a lower triangular (m by m) matrix.
*
*
* @param L An m by m non-singular lower triangular matrix. Not modified.
* @param b An n by m matrix. Modified.
* @param m size of the L matrix
* @param n number of columns in the B matrix.
* @param offsetL initial index in L where the matrix starts
* @param offsetB initial index in B where the matrix starts
*/
public static void solveLTransB( double L[] , double []b ,
int m , int n ,
int strideL , int offsetL , int offsetB )
{
// for( int j = 0; j < n; j++ ) {
// for( int i = 0; i < m; i++ ) {
// double sum = b[offsetB + j*m+i];
// for( int k=0; k
* 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.
*
*
* @param U An m by m non-singular upper triangular matrix. Not modified.
* @param b An m by n matrix. Modified.
* @param m size of the L matrix
* @paramUn number of columns in the B matrix.
* @param offsetU initial index in L where the matrix starts
* @param offsetB initial index in B where the matrix starts
*/
public static void solveU( double U[] , double []b ,
int m , int n ,
int strideU , int offsetU , int offsetB )
{
for( int j = 0; j < n; j++ ) {
for( int i = m-1; i >= 0; i-- ) {
double sum = b[offsetB + i*n+j];
for( int k=i+1; k
* 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.
*
*
* @param U An m by m non-singular upper triangular matrix. Not modified.
* @param b An m by n matrix. Modified.
* @param m size of the L matrix
* @paramUn number of columns in the B matrix.
* @param offsetU initial index in L where the matrix starts
* @param offsetB initial index in B where the matrix starts
*/
public static void solveTransU( double U[] , double []b ,
int m , int n ,
int strideU , int offsetU , int offsetB )
{
for( int j = 0; j < n; j++ ) {
for( int i = 0; i < m; i++ ) {
double sum = b[offsetB + i*n+j];
for( int k=0; k