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/* -------------------------------------------------------------------------- *
* Simbody(tm): SimTKmath *
* -------------------------------------------------------------------------- *
* This is part of the SimTK biosimulation toolkit originating from *
* Simbios, the NIH National Center for Physics-Based Simulation of *
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org/home/simbody. *
* *
* Portions copyright (c) 2006-12 Stanford University and the Authors. *
* Authors: Jack Middleton *
* Contributors: *
* *
* 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. *
* -------------------------------------------------------------------------- */
/**@file
* This is a test program which uses the FactorLU class to do an LU
* factorization on a system of linear equations and then use the
* factored LU matrix to solve for a particular right hand side
*/
/*
The data for this test is from an example FORTRAN program from the
Numerical Algorithms Group (NAG)
URL:http://www.nag.com/lapack-ex/lapack-ex.html
Solves:
Ax = B,
where A is the general matrix
1.80 2.88 2.05 -0.89 9.52
A = 5.25 -2.95 -0.95 -3.80 and B = 24.35
1.58 -2.69 -2.90 -1.04 0.77
-1.11 -0.66 -0.59 0.80 -6.22
Solution
x = 1.0000 -1.0000 3.0000 -5.0000
LU factorization:
1 2 3 4
1 5.2500 -2.9500 -0.9500 -3.8000
2 0.3429 3.8914 2.3757 0.4129
3 0.3010 -0.4631 -1.5139 0.2948
4 -0.2114 -0.3299 0.0047 0.1314
Pivot indices
2 2 3 4
*/
#include "SimTKmath.h"
#include <iostream>
using std::cout; using std::endl;
#define ASSERT(cond) {SimTK_ASSERT_ALWAYS(cond, "Assertion failed");}
using namespace SimTK;
Real A[16] = { 1.80, 2.88, 2.05, -0.89,
5.25, -2.95, -0.95, -3.80,
1.58, -2.69, -2.90, -1.04,
-1.11, -0.66, -0.59, 0.80 };
Real B[4] = { 9.52, 24.35, 0.77, -6.22 };
Real X[4] = { 1., -1., 3., -5. };
int main () {
try {
// Default precision (Real, normally double) test.
Matrix a(4,4, A);
Vector b(4, B);
Vector x_right(4, X);
Vector x; // should get sized automatically to 4 by solve()
FactorLU lu(a); // perform LU factorization
lu.solve( b, x ); // solve for x given a right hand side
cout << " Real SOLUTION: " << x << " errnorm=" << (x-x_right).norm() << endl;
ASSERT((x-x_right).norm() < 10*SignificantReal);
// float test
Matrix_<float> af(4,4); for (int i=0; i<4; ++i) for (int j=0; j<4; ++j) af(i,j)=(float)a(i,j);
Vector_<float> bf(4); for (int i=0; i<4; ++i) bf[i] = (float)b[i];
Vector_<float> xf_right(4); for (int i=0; i<4; ++i) xf_right[i] = (float)x_right[i];
Vector_<float> xf; // should get sized automatically to 4 by solve()
FactorLU luf;
luf.factor(af);
luf.solve(bf, xf);
cout << " float SOLUTION: " << xf << " errnorm=" << (xf-xf_right).norm() << endl;
const float SignificantFloat = NTraits<float>::getSignificant();
ASSERT((xf-xf_right).norm() < 10*SignificantFloat);
luf.factor(a);
lu.solve( b, x ); // solve for x given a right hand side
cout << " Real SOLUTION: " << x << " errnorm=" << (x-x_right).norm() << endl;
ASSERT((x-x_right).norm() < 10*SignificantReal);
Real C[4] = { 1.0, 2.0,
1.0, 3.0 };
Matrix c(2,2, C);
FactorLU clu(c);
Matrix invC;
clu.inverse(invC);
cout << "Inverse c: " << endl;
cout << invC[0] << endl;
cout << invC[1] << endl;
Real Z[4] = { 0.0, 0.0,
0.0, 0.0 };
Matrix z(2,2, Z);
FactorLU zlu(z);
Vector_<double> xz;
Vector_<double> bz(2);
bz(1) = bz(0) = 0.0;
zlu.solve( bz, xz );
cout << " solve with mat all zeros : " << endl;
for(int i=0;i<xz.size();i++) printf("%f ", xz(i) ); printf("\n");
try {
Matrix_<double> z0;
FactorLU z0lu(z0);
Vector_<double> bz0(0);
z0lu.solve( bz0, xz );
cout << " solve with mat(0,0) : " << endl;
for(int i=0;i<xz.size();i++) printf("%f ", xz(i) ); printf("\n");
} catch (const std::exception& e) {
cout << "(EXPECTED EXCEPTION) NULL matrix test: "
<< e.what() << endl;
}
}
catch (const std::exception& e) {
std::printf("FAILED: %s\n", e.what());
return 1;
}
return 0;
}
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