org.ejml.dense.row.decompose.TriangularSolver_ZDRM Maven / Gradle / Ivy
/*
* Copyright (c) 2020, 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.decompose;
/**
*
* This contains algorithms for solving systems of equations where T is a
* non-singular triangular complex 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_ZDRM {
/**
*
* 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( double[] U, double[] b, int n ) {
// for( int i =n-1; i>=0; i-- ) {
// double sum = b[i];
// for( int j = i+1; j = 0; i--) {
double sumReal = b[i*2];
double sumImg = b[i*2 + 1];
int indexU = i*stride + i*2 + 2;
for (int j = i + 1; j < n; j++) {
double realB = b[j*2];
double imgB = b[j*2 + 1];
double realU = U[indexU++];
double imgU = U[indexU++];
sumReal -= realB*realU - imgB*imgU;
sumImg -= realB*imgU + imgB*realU;
}
// b = sum/U
double realU = U[i*stride + i*2];
double imgU = U[i*stride + i*2 + 1];
double normU = realU*realU + imgU*imgU;
b[i*2] = (sumReal*realU + sumImg*imgU)/normU;
b[i*2 + 1] = (sumImg*realU - sumReal*imgU)/normU;
}
}
/**
*
* Solves for non-singular lower triangular matrices with real valued diagonal elements
* 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_diagReal( double[] L, double[] b, int n ) {
// for( int i = 0; i < n; i++ ) {
// double sum = b[i];
// for( int k=0; k
* This is a forward substitution solver for non-singular lower triangular matrices with
* real valued diagonal elements.
*
* b = (LCT)-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 conjugate 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 solveConjTranL_diagReal( double[] L, double[] b, int n ) {
// for( int i =n-1; i>=0; i-- ) {
// double sum = b[i];
// for( int k = i+1; k = 0; i--) {
double realSum = b[i*2];
double imagSum = b[i*2 + 1];
int indexB = (i + 1)*2;
for (int k = i + 1; k < n; k++) {
int indexL = (k*n + i)*2;
double realL = L[indexL];
double imagL = L[indexL + 1];
double realB = b[indexB++];
double imagB = b[indexB++];
realSum -= realL*realB + imagL*imagB;
imagSum -= realL*imagB - imagL*realB;
}
double realL = L[(i*n + i)*2];
b[i*2] = realSum/realL;
b[i*2 + 1] = imagSum/realL;
}
}
}