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/*=========================================================================
*
* Copyright NumFOCUS
*
* 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
*
* https://www.apache.org/licenses/LICENSE-2.0.txt
*
* 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.
*
*=========================================================================*/
#include "VNLSparseLUSolverTraits.h"
#include "itkMath.h" // itk::Math::abs
#include <iostream>
#include <cstdlib>
template <class TVector>
bool
VectorsEquals(const TVector & v1, const TVector & v2, const typename TVector::element_type & tolerance)
{
if (v1.size() != v2.size())
{
std::cerr << "Error: v1.size() != v2.size()" << std::endl;
return false;
}
for (unsigned int i = 0; i < v1.size(); ++i)
{
if (itk::Math::abs(v1(i) - v2(i)) > tolerance)
{
std::cerr << "Error: itk::Math::abs( v1(" << i << ") - v2(" << i << ") ) > " << tolerance << std::endl;
return false;
}
}
return true;
}
int
VNLSparseLUSolverTraitsTest(int, char *[])
{
/**
* Define an sparse LU solver traits type that operates over sparse matrices and
* vectors of type "double"
*/
using CoordinateType = double;
using SolverTraits = VNLSparseLUSolverTraits<CoordinateType>;
using MatrixType = SolverTraits::MatrixType;
using VectorType = SolverTraits::VectorType;
/**
* Build the linear system to solve
*/
unsigned int N = 3;
VectorType Bx = SolverTraits::InitializeVector(N);
Bx.fill(0.);
Bx[0] = 2.1;
VectorType By = SolverTraits::InitializeVector(N);
By.fill(0.);
By[1] = 1.1;
By[2] = -3.;
VectorType Bz = SolverTraits::InitializeVector(N);
Bz.fill(0.);
Bz[0] = 19.4;
Bz[1] = -4.3;
MatrixType A = SolverTraits::InitializeSparseMatrix(N, N);
SolverTraits::FillMatrix(A, 0, 0, 2);
SolverTraits::FillMatrix(A, 0, 1, -1);
SolverTraits::FillMatrix(A, 1, 0, -1);
SolverTraits::FillMatrix(A, 1, 1, 2);
SolverTraits::FillMatrix(A, 1, 2, -1);
SolverTraits::FillMatrix(A, 2, 1, -1);
SolverTraits::FillMatrix(A, 2, 2, 2);
/**
* Define the tolerance and expected results
*/
CoordinateType tolerance = 1e-9;
VectorType Xexpected(N);
Xexpected(0) = 1.575;
Xexpected(1) = 1.05;
Xexpected(2) = 0.525;
VectorType Yexpected(N);
Yexpected(0) = -0.2;
Yexpected(1) = -0.4;
Yexpected(2) = -1.7;
VectorType Zexpected(N);
Zexpected(0) = 12.4;
Zexpected(1) = 5.4;
Zexpected(2) = 2.7;
/**
* Test 1: Check the result of A * X = Bx
*/
{
VectorType X = SolverTraits::InitializeVector(N);
SolverTraits::Solve(A, Bx, X);
if (!VectorsEquals(X, Xexpected, tolerance))
{
return EXIT_FAILURE;
}
}
/**
* Test 2: Check the result of A * X = Bx, A * Y = By
*/
{
VectorType X = SolverTraits::InitializeVector(N);
VectorType Y = SolverTraits::InitializeVector(N);
SolverTraits::Solve(A, Bx, X);
SolverTraits::Solve(A, By, Y);
if (!VectorsEquals(X, Xexpected, tolerance) || !VectorsEquals(Y, Yexpected, tolerance))
{
return EXIT_FAILURE;
}
}
/**
* Test 3: Check the result of A * X = Bx, A * Y = By, A * Z = Bz
*/
{
VectorType X = SolverTraits::InitializeVector(N);
VectorType Y = SolverTraits::InitializeVector(N);
VectorType Z = SolverTraits::InitializeVector(N);
SolverTraits::Solve(A, Bx, X);
SolverTraits::Solve(A, By, Y);
SolverTraits::Solve(A, Bz, Z);
if (!VectorsEquals(X, Xexpected, tolerance) || !VectorsEquals(Y, Yexpected, tolerance) ||
!VectorsEquals(Z, Zexpected, tolerance))
{
return EXIT_FAILURE;
}
}
/**
* Test 4: Check the result of A * X = Bx (reuse the decomposed matrix for multiple back-substitutions)
*/
{
VectorType X = SolverTraits::InitializeVector(N);
SolverTraits::SolverType solver(A);
// First back-substitution
SolverTraits::Solve(solver, Bx, X);
if (!VectorsEquals(X, Xexpected, tolerance))
{
return EXIT_FAILURE;
}
// Second back-substitution (reusing the already factored matrix)
SolverTraits::Solve(solver, Bx, X);
if (!VectorsEquals(X, Xexpected, tolerance))
{
return EXIT_FAILURE;
}
}
/**
* Test 5: Check the result of A * X = Bx, A * Y = By (reuse the decomposed matrix for multiple back-substitutions)
*/
{
VectorType X = SolverTraits::InitializeVector(N);
VectorType Y = SolverTraits::InitializeVector(N);
SolverTraits::SolverType solver(A);
// First back-substitution
SolverTraits::Solve(solver, Bx, X);
SolverTraits::Solve(solver, By, Y);
if (!VectorsEquals(X, Xexpected, tolerance) || !VectorsEquals(Y, Yexpected, tolerance))
{
return EXIT_FAILURE;
}
// Second back-substitution (reusing the already factored matrix)
SolverTraits::Solve(solver, Bx, X);
SolverTraits::Solve(solver, By, Y);
if (!VectorsEquals(X, Xexpected, tolerance) || !VectorsEquals(Y, Yexpected, tolerance))
{
return EXIT_FAILURE;
}
}
/**
* Test 6: Check the result of A * X = Bx, A * Y = By, A * Z = Bz (reuse the decomposed matrix for multiple
* back-substitutions)
*/
{
VectorType X = SolverTraits::InitializeVector(N);
VectorType Y = SolverTraits::InitializeVector(N);
VectorType Z = SolverTraits::InitializeVector(N);
SolverTraits::SolverType solver(A);
// First back-substitution
SolverTraits::Solve(solver, Bx, X);
SolverTraits::Solve(solver, By, Y);
SolverTraits::Solve(solver, Bz, Z);
if (!VectorsEquals(X, Xexpected, tolerance) || !VectorsEquals(Y, Yexpected, tolerance) ||
!VectorsEquals(Z, Zexpected, tolerance))
{
return EXIT_FAILURE;
}
// Second back-substitution (reusing the already factored matrix)
SolverTraits::Solve(solver, Bx, X);
SolverTraits::Solve(solver, By, Y);
SolverTraits::Solve(solver, Bz, Z);
if (!VectorsEquals(X, Xexpected, tolerance) || !VectorsEquals(Y, Yexpected, tolerance) ||
!VectorsEquals(Z, Zexpected, tolerance))
{
return EXIT_FAILURE;
}
}
return EXIT_SUCCESS;
}
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