//
// LAPACK++ 1.1 Linear Algebra Package 1.1
// University of Tennessee, Knoxvilee, TN.
// Oak Ridge National Laboratory, Oak Ridge, TN.
// Authors: J. J. Dongarra, E. Greaser, R. Pozo, D. Walker
// (C) 1992-1996 All Rights Reserved
//
// NOTICE
//
// Permission to use, copy, modify, and distribute this software and
// its documentation for any purpose and without fee is hereby granted
// provided that the above copyright notice appear in all copies and
// that both the copyright notice and this permission notice appear in
// supporting documentation.
//
// Neither the Institutions (University of Tennessee, and Oak Ridge National
// Laboratory) nor the Authors make any representations about the suitability
// of this software for any purpose. This software is provided ``as is''
// without express or implied warranty.
//
// LAPACK++ was funded in part by the U.S. Department of Energy, the
// National Science Foundation and the State of Tennessee.
#if 1
#include "lapackpp.h"
#endif
#if 0
#include "lafnames.h" /* macros for LAPACK++ filenames */
#include LA_GEN_MAT_DOUBLE_H
#include LA_VECTOR_DOUBLE_H
#include "blaspp.h"
#include LA_SOLVE_DOUBLE_H
#include LA_GENERATE_MAT_DOUBLE_H
#include LA_EXCEPTION_H
#include LA_UTIL_H
#include "lasvd.h"
#endif
double residual(const LaGenMatDouble &A, const LaVectorDouble &x,
const LaVectorDouble& b)
{
int M = A.size(0);
int N = A.size(1);
std::cout << "\tNorm_Inf(A*x-b)" << Norm_Inf(A*x-b) << std::endl;
std::cout << "\tNorm_Inf(A) " << Norm_Inf(A) << std::endl;
std::cout << "\tNorm_Inf(x) " << Norm_Inf(x) << std::endl;
std::cout << "\tMacheps :" << Mach_eps_double() << std::endl;
if (M>N)
{
LaVectorDouble Axb = A*x-b;
LaVectorDouble R(N);
Blas_Mat_Trans_Vec_Mult(A, Axb, R);
return Norm_Inf(R) /
(Norm_Inf(A)* Norm_Inf(x) * N * Mach_eps_double());
}
else
{
return Norm_Inf(A*x-b ) /
( Norm_Inf(A)* Norm_Inf(x) * N * Mach_eps_double());
}
}
bool testQRsolve(int M, int N)
{
#ifndef HPPA
const char fname[] = "TestGenLinearSolve(LaGenMat, x, b) ";
#else
char *fname = NULL;
#endif
bool error = false;
double aa[] = { 1, 2, 3, 4, 5, 6 };
double bb[] = { 7, 8, 9 };
{
LaGenMatDouble A2tmp(aa, 3, 2, false), A2(A2tmp);
LaGenMatDouble B2(bb, 3, 1, true);
LaGenMatDouble X2(2, 1);
std::cout << fname << ": LaQRLinearSolve: Matrix A=" << A2
<< " Right hand side B=" << B2;
LaQRLinearSolveIP(A2, X2, B2);
std::cout << " Solution X=" << X2;
//std::cout << "Residual " << residual(A2tmp, X2, B2) << std::endl;
double cc2[] = { -1, 2 };
double diff = Norm_Inf(X2 - LaGenMatDouble(cc2, 2, 1));
std::cout << "Diff to known solution: " << diff << std::endl
<< std::endl;
if (diff > 1e-10)
error = true;
}
{
LaGenMatDouble A1(aa, 2, 3, true);
LaGenMatDouble B1(bb, 2, 1, true);
LaGenMatDouble X1(3, 1);
std::cout << fname << ": LaQRLinearSolve: Matrix A=" << A1
<< " Right hand side B=" << B1;
LaQRLinearSolveIP(A1, X1, B1);
std::cout << " Solution X=" << X1;
double cc1[] = { -3.0556, 0.1111, 3.2778 };
double diff = Norm_Inf(X1 - LaGenMatDouble(cc1, 3, 1));
std::cout << "Diff to known solution: " << diff << std::endl
<< std::endl;
if (diff > 1e-4)
error = true;
}
{
LaGenMatDouble A3(aa, 2, 2, true);
LaGenMatDouble B3(bb, 2, 1, true);
LaGenMatDouble X3(2, 1);
std::cout << fname << ": LaQRLinearSolve: Matrix A=" << A3
<< " Right hand side B=" << B3;
LaQRLinearSolveIP(A3, X3, B3);
std::cout << " Solution X=" << X3;
double cc3[] = { -6, 6.5 };
double diff = Norm_Inf(X3 - LaGenMatDouble(cc3, 2, 1));
std::cout << "Diff to known solution: " << diff << std::endl
<< std::endl;
if (diff > 1e-10)
error = true;
}
return error;
}
int TestGenLinearSolve(int M,int N)
{
LaGenMatDouble A(M,N);
LaVectorDouble x(N), b(M);
bool error = false;
#ifndef HPPA
const char fname[] = "TestGenLinearSolve(LaGenMat, x, b) ";
#else
char *fname = NULL;
#endif
//char e = 'e';
double norm;
double res;
#ifdef __x86_64
la::rand(A); // LaGenerateMatDouble doesn't work on amd64
#else
LaGenerateMatDouble(A);
#endif
std::cout << "Generated matrix A=" << std::endl
<< A << std::endl;
// save a snapshot of what A looked like before the solution
LaGenMatDouble old_A = A;
b = 1.1;
std::cerr << fname << ": testing LaLinearSolve(Gen,...) M= "<< M
<< " N = " << N << std::endl;
LaLinearSolve(A, x, b);
if ( (norm = Norm_Inf( old_A - A)) > 0.0) // this is an exact test, not
// necessary to worry about
// round-off issues. We
// are testing to see A was
// overwritten.
{
std::cerr << fname << ": overwrote 1st arg.\n";
std::cerr << " error norm: " << norm << std::endl;
error = true; // exit(1);
}
res = residual(A,x,b);
if (res > 1)
{
std::cerr << fname << "resdiual " << res << " is to too high.\n";
error = true; // exit(1);
}
else
std::cerr << fname << ": LaLinearSolve() success.\n\n";
// now try the in-place solver
std::cerr << fname << ": testing LaLinearSolveIP(Gen,...) \n";
LaLinearSolveIP(A, x, b);
res = residual(old_A, x, b);
if (res > 1)
{
std::cerr << fname << "resdiual " << res << " is to too high.\n";
error = true; // exit(1);
}
else
std::cerr << fname << ": LaLinearSolveIP() success.\n\n";
std::cout << fname << ": Matrix A=" << A
<< std::endl;
LaVectorDouble S(std::min(M,N));
LaGenMatDouble U(M,M), VT(N,N);
// S = 0;
// U = 0;
// VT = 0;
LaSVD_IP(A, S, U, VT);
std::cout << fname << ": Matrix A=" << A
<< " Singular values sigma = " << S
<< " Left S.vect. U = " << U
<< " Right S.vect. VT = " << VT
<< std::endl;
error = error || testQRsolve(M, N);
if (error)
exit(1);
return 0;
}
int main(int argc, char **argv)
{
std::cout.precision(4);
std::cout.setf(std::ios::scientific, std::ios::floatfield);
LaException::enablePrint(true);
if (argc < 2)
{
std::cerr << "Usage " << argv[0] << " M [ N ] " << std::endl;
exit(1);
}
int M = atoi(argv[1]);
int N;
if (argc < 3)
N = M;
else
N = atoi(argv[2]);
std::cout << "Testing " << M << " x " << N << " system." << std::endl;
TestGenLinearSolve(M,N);
return 0;
}
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