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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 FactorSVD class to compute
* eigen values and eigen vectors
*/
/*
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 for the singular valus and vectors for the
following matrix
A = 2.27 0.28 -0.48 1.07 -2.35 0.62
-1.54 -1.67 -3.09 1.22 2.93 -7.39
1.15 0.94 0.99 0.79 -1.45 1.03
-1.94 -0.78 -0.21 0.63 2.30 -2.57
SOLUTION =
Singular values
9.9966 3.6831 1.3569 0.5000
Left singular vectors
1 2 3 4
1 -0.1921 0.8030 0.0041 -0.5642
2 0.8794 0.3926 -0.0752 0.2587
3 -0.2140 0.2980 0.7827 0.5027
4 0.3795 -0.3351 0.6178 -0.6017
Right singular vectors by row (first m rows of V**T)
1 2 3 4 5 6
1 -0.2774 -0.2020 -0.2918 0.0938 0.4213 -0.7816
2 0.6003 0.0301 -0.3348 0.3699 -0.5266 -0.3353
3 -0.1277 0.2805 0.6453 0.6781 0.0413 -0.1645
4 0.1323 0.7034 0.1906 -0.5399 -0.0575 -0.3957
Error estimate for the singular values
1.1E-15
Error estimates for the left singular vectors
1.8E-16 4.8E-16 1.3E-15 1.3E-15
Error estimates for the right singular vectors
1.8E-16 4.8E-16 1.3E-15 2.2E-15
*/
#include "SimTKmath.h"
#include <cstdio>
#include <cassert>
#include <iostream>
#define ASSERT(cond) {SimTK_ASSERT_ALWAYS(cond, "Assertion failed");}
static const double EPS = 0.00001;
using namespace SimTK;
using std::printf;
using std::cout;
using std::endl;
Real A[24] = { 2.27, 0.28, -0.48, 1.07, -2.35, 0.62,
-1.54, -1.67, -3.09, 1.22, 2.93, -7.39,
1.15, 0.94, 0.99, 0.79, -1.45, 1.03,
-1.94, -0.78, -0.21, 0.63, 2.30, -2.57 };
Real X[4] = { 9.9966, 3.6831, 1.3569, 0.5000 };
int main () {
try {
// Default precision (Real, normally double) test.
Matrix a(4,6, A);
Vector singularValues( 4 );
Vector expectedValues( 4, X );
Matrix rightVectors;
Matrix leftVectors;
FactorSVD svd(a, 0.01); // setup the eigen system
svd.getSingularValues( singularValues ); // solve for the singular values
cout << " SingularValues rcond = 0.01 : " << singularValues << endl;
svd.factor(a ); // setup the eigen system
cout << " SingularValues rcond = default : " << singularValues << " errnorm=" << (singularValues-expectedValues).norm() << endl;
svd.getSingularValuesAndVectors( singularValues, leftVectors, rightVectors ); // solve for the singular values
ASSERT((singularValues-expectedValues).norm() < 0.001);
printf("Left Vectors = \n");
for(int i=0;i<leftVectors.ncol();i++) {
for(int j=0;j<leftVectors.nrow();j++) printf("%f ",leftVectors(i,j) );
printf("\n");
}
printf("Right Vectors = \n");
for(int i=0;i<rightVectors.ncol();i++) {
for(int j=0;j<rightVectors.nrow();j++) printf("%f ",rightVectors(i,j) );
printf("\n");
}
Real C[4] = { 1.0, 2.0,
1.0, 3.0 };
Matrix c(2,2, C);
FactorSVD csvd(c);
Matrix invSVD;
csvd.inverse(invSVD);
cout << " FactorSVD.inverse : " << endl;
cout << invSVD[0] << endl;
cout << invSVD[1] << endl;
Real Z[4] = { 0.0, 0.0,
0.0, 0.0 };
Matrix z(2,2, Z);
FactorSVD zsvd(z);
Vector_<double> xz;
Vector_<double> bz(2);
bz(1) = bz(0) = 0.0;
zsvd.solve( bz, xz );
cout << " solve with mat all zeros : " << endl;
for(int i=0;i<xz.size();i++) printf("%f ", xz(i) ); printf("\n");
Matrix_<double> z0;
FactorSVD z0svd(z0);
Vector_<double> bz0(0);
z0svd.solve( bz0, xz );
cout << " solve with mat(0,0) : " << endl;
for(int i=0;i<xz.size();i++) printf("%f ", xz(i) ); printf("\n");
cout << " SVD factorization with mat(0,0) : " << endl;
FactorSVD z0fsvd(z0);
z0fsvd.getSingularValuesAndVectors( singularValues, leftVectors, rightVectors ); // solve for the singular values
cout << " Real SOLUTION: " << singularValues << endl;
printf("Left Vectors = \n");
for(int i=0;i<leftVectors.ncol();i++) {
for(int j=0;j<leftVectors.nrow();j++) printf("%f ",leftVectors(i,j) );
printf("\n");
}
printf("Right Vectors = \n");
for(int i=0;i<rightVectors.ncol();i++) {
for(int j=0;j<rightVectors.nrow();j++) printf("%f ",rightVectors(i,j) );
printf("\n");
}
return 0;
}
catch (std::exception& e) {
std::printf("FAILED: %s\n", e.what());
return 1;
}
}
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