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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 FactorQTZ class to do an QTZ
* factorization on a system of linear equations and then use the
* factored QTZ matrix to solve a find a least squares solution
* 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 the least squares problem:
Ax = B,
where A is the general matrix
-0.09 0.14 -0.46 0.68 1.29 7.4
-1.56 0.20 0.29 1.09 0.51 4.2
A = -1.48 -0.43 0.89 -0.71 -0.96 B= -8.3
-1.09 0.84 0.77 2.11 -1.27 1.8
0.08 0.55 -1.13 0.14 1.74 8.6
-1.59 -0.72 1.06 1.24 0.34 2.1
The default tolerance of 0.01 is used to determine the effective rank of A
SOLUTION =
0.6344 0.9699 -1.4402 3.3678 3.3992
estimated rank = 4
*/
#include "SimTKmath.h"
#include <cstdio>
#include <cassert>
#include <iostream>
#define ASSERT(cond) {SimTK_ASSERT_ALWAYS(cond, "Assertion failed");}
using namespace SimTK;
using std::printf;
using std::cout;
using std::endl;
Real A[30] = { -0.09, 0.14, -0.46, 0.68, 1.29,
-1.56, 0.20, 0.29, 1.09, 0.51,
-1.48, -0.43, 0.89, -0.71, -0.96,
-1.09, 0.84, 0.77, 2.11, -1.27,
0.08, 0.55, -1.13, 0.14, 1.74,
-1.59, -0.72, 1.06, 1.24, 0.34 };
Real B[6] = { 7.4, 4.2, -8.3, 1.8, 8.6, 2.1 };
Real X[5] = { 0.6344, 0.9699, -1.4402, 3.3678, 3.3992 };
int main () {
try {
// Default precision (Real, normally double) test.
Matrix a(6,5, A);
Vector b(6, B);
Vector x_right(5, X);
Vector x; // should get sized automatically to 5 by solve()
FactorQTZ qtz; // perform QTZ factorization
qtz.factor(a);
printf("\n Estimated rank with default rcond %d \n\n",qtz.getRank() );
ASSERT( qtz.getRank() == 5 );
qtz.factor(a, 0.01);
qtz.solve( b, x ); // solve for x given a right hand side
printf("\n Estimated rank with rcond = 0.01 : %d \n\n",qtz.getRank() );
cout << " Overdetermined Double SOLUTION: " << x << " errnorm=" << (x-x_right).norm() << endl;
ASSERT((x-x_right).norm() < 0.001);
FactorQTZ qtzCopy( qtz );
Vector xc; // should get sized automatically to 5 by solve()
qtzCopy.solve(b, xc );
cout << " copy constructor SOLUTION: " << xc << " errnorm=" << (xc-x_right).norm() << endl;
FactorQTZ qtzAssign = qtz;
Vector xa; // should get sized automatically to 5 by solve()
qtzCopy.solve(b, xa );
cout << " copy assign SOLUTION: " << xa << " errnorm=" << (xa-x_right).norm() << endl;
Matrix_<float> af(6,5); for (int i=0; i<6; ++i) for (int j=0; j<5; ++j) af(i,j)=(float)a(i,j);
Vector_<float> bf(6); for (int i=0; i<6; ++i) bf[i] = (float)b[i];
Vector_<float> xf_right(5); for (int i=0; i<5; ++i) xf_right[i] = (float)x_right[i];
Vector_<float> xf; // should get sized automatically to 5 by solve()
qtz.factor(af, (float)0.01);
qtz.solve(bf,xf);
cout << " Overdetermined Float SOLUTION: " << xf << " errnorm=" << (xf-xf_right).norm() << endl;
const float SignificantFloat = NTraits<float>::getSignificant();
ASSERT((xf-xf_right).norm() < 0.001);
// Underdetermined case adapted from
// http://idlastro.gsfc.nasa.gov/idl_html_help/LA_LEAST_SQUARES.html
Real Au[12] = { 2, 5, 3, 4,
7, 1, 3, 5,
4, 3, 6, 2 };
Real Bu[3] = { 3, 1, 6 };
Real Xu[4] = { -0.0376844, 0.350628, 0.986164, -0.409066 };
Matrix au(3, 4, Au);
Vector bu(3, Bu);
Vector xu_right(4, Xu);
Vector xu; // should get sized automatically to 4 by solve()
Matrix bu2(3,2);
bu2(0) = bu;
bu2(1) = 2*bu;
Matrix xu2; // should get sized 4x2 by solve
FactorQTZ qtzu(au); // perform QTZ factorization
qtzu.solve( bu, xu ); // solve for x given a right hand side
cout << " Underdetermined Double SOLUTION: " << xu << " errnorm=" << (xu-xu_right).norm() << endl;
qtzu.solve( bu2, xu2 );
cout << " multiple rhs solution, double " << xu2 << endl;
Matrix_<float> afu(3,4); for (int i=0; i<3; ++i) for (int j=0; j<4; ++j) afu(i,j)=(float)au(i,j);
Vector_<float> bfu(3); for (int i=0; i<3; ++i) bfu[i] = (float)bu[i];
Vector_<float> xfu_right(4); for (int i=0; i<4; ++i) xfu_right[i] = (float)xu_right[i];
Vector_<float> xfu; // should get sized automatically to 4 by solve()
Matrix_<float> bfu2(3,2);
bfu2(0) = bfu;
bfu2(1) = 2*bfu;
Matrix_<float> xfu2; // should get sized 4x2 by solve
FactorQTZ qtzfu(afu); // perform QTZ factorization
qtzfu.solve( bfu, xfu ); // solve for x given a right hand side
cout << " Underdetermined Float SOLUTION: " << xfu << " errnorm=" << (xfu-xfu_right).norm() << endl;
qtzfu.solve( bfu2, xfu2 );
cout << " multiple rhs solution, float " << xfu2 << endl;
Real C[4] = { 1.0, 2.0,
1.0, 3.0 };
Matrix c(2,2, C);
FactorQTZ cqtz(c);
Matrix invQTZ;
cqtz.inverse(invQTZ);
cout << " FactorQTZ.inverse : " << endl;
cout << invQTZ[0] << endl;
cout << invQTZ[1] << endl;
Real Z[4] = { 0.0, 0.0,
0.0, 0.0 };
Matrix z(2,2, Z);
FactorQTZ zqtz(z);
Vector_<double> xz;
Vector_<double> bz(2);
bz(1) = bz(0) = 0.0;
zqtz.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;
FactorQTZ z0qtz(z0);
Vector_<double> bz0(0);
z0qtz.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;
}
catch (...) {
std::printf("FAILED: Unknown exception\n");
return 1;
}
return 0;
}
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