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// -*- C++ -*-
// $Id: testInversion.cc,v 1.2 2003/08/13 20:00:12 garren Exp $
//
// This file is a part of CLHEP - a Class Library for High Energy Physics.
//
// This is a collection of parts of programs that are useful
// for testing matrix inversion algorithms
// 9/97, Mario Stanke
#include <time.h>
#include <iostream>
#include "CLHEP/Matrix/defs.h"
#include "CLHEP/Matrix/Matrix.h"
#include "CLHEP/Matrix/SymMatrix.h"
#include "CLHEP/Matrix/DiagMatrix.h"
using std::cout;
using std::endl;
using namespace CLHEP;
int main()
{
//int n , i, j, k, ierr1, ierr2;
int n, j, ierr1, ierr2;
time_t zeit1, zeit2;
// ****compare the speed of inversion algorithms
HepSymMatrix A(5,1);
// for (j=1;j <= 100; j++)
// for (k=1; k<=j; k++)
// A(j,k)=rand()%9-5;
A(1,1)=6;
A(1,2)=.8545;
A(1,3)=-.684651;
A(1,4)=.372547;
A(1,5)=.68151;
//A(1,6)=.068151;
A(2,2)=4;
A(2,3)=.5151;
A(2,4)=.5151;
A(2,5)=.651651;
//A(2,6)=.9651651;
A(3,3)=5;
A(3,4)=.3;
A(3,5)=.363;
//A(3,6)=.7363;
A(4,4)=-3;
A(4,5)=-.23753;
//A(4,6)=-.23753;
A(5,5)=-5;
//A(5,6)=-2;
//A(6,6)=-3;
HepSymMatrix B(A);
HepSymMatrix D(A);
HepSymMatrix C(5,0);
HepMatrix M(A);
cout << "M inverse" << M.inverse(ierr2) << endl;
C = B.inverse(ierr1);
D.invert(ierr2);
cout << "B " << B << endl;
cout << "B inverse" << C << endl;
#ifndef INSTALLATION_CHECK
cout << "B * inverse" << B * C << endl;
#endif
cout << "ierr1: " << ierr1 << endl;
cout << "D * inverse" << D * C << endl;
cout << "ierr2: " << ierr2 << endl;
cout << "M inverse" << M.inverse(ierr2) << endl;
#ifndef INSTALLATION_CHECK
cout << "M * inverse" << M * M.inverse(ierr2)<< endl;
#endif
cout << "ierr2: " << ierr2 << endl;
#ifndef INSTALLATION_CHECK
n = 100000;
#else
n = 10;
#endif
zeit1 = time(NULL);
cout << "Executing " << n << " inversions ..." << endl;
for (j=0; j<n; j++)
{
B.invert(ierr1);
if (ierr1)
cout << "B: error in invert" << endl;
}
zeit2 = time(NULL);
cout << "B: duration of inversion: " << zeit2-zeit1 << " secs" << endl;
zeit1 = time(NULL);
cout << "Executing " << n << " inversions ..." << endl;
for (j=0; j<n; j++)
{
D.invert(ierr2);
if (ierr2)
cout << "D: error in invert" << endl;
}
zeit2 = time(NULL);
cout << D << endl;
cout << "D: duration of inversion: " << zeit2-zeit1 << " secs" << endl;
/***** check correctness and compare results of inversion algorithms
double dist1, dist2;
HepSymMatrix A(5,1), B(5), C(5), I(5,1);
HepSymMatrix M(5);
n = 200000;
for (j=1; j <= n ; j++)
{
A(1,1)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(1,2)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(1,3)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(1,4)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(1,5)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
//A(1,6)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(2,2)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(2,3)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(2,4)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(2,5)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
//A(2,6)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(3,3)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(3,4)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(3,5)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
//A(3,6)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(4,4)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(4,5)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
//A(4,6)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
A(5,5)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
//A(5,6)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
//A(6,6)=(((rand()%7-3)))+ (rand()%3-1)*1e-10;
M=B=C=A;
B.invert(ierr2);
M.old_invert(ierr1);
dist2 = norm_infinity(B*C-I);
dist1 = norm_infinity(M*C-I);
if (ierr1 != ierr2)
{
cout << C << endl;
cout << "B " << B << endl;
cout << "B*C" << B*C << endl;
cout << "M*C" << M*C << endl;
cout << "M " << M << endl;
cout << "determinant " << C.determinant() << endl;
cout << "dist2 " << dist2 << endl;
cout << "dist1 " << dist1 << endl;
cout << "ierr2 " << ierr2 <<endl;
cout << "ierr1 " << ierr1 <<endl;
cout << "j " << j << endl;
}
if (ierr2==0 && dist2 > 1e-4)
{
cout << "bunch failed to invert but did not indicate" << endl;
cout << C << endl;
cout << "B " << B << endl;
cout << "B*C" << B*C << endl;
cout << "M*C" << M*C << endl;
cout << "determinant " << C.determinant() << endl;
cout << "dist2 " << dist2 << endl;
cout << "dist1 " << dist1 << endl;
cout << "ierr2 " << ierr2 <<endl;
cout << "ierr1 " << ierr1 <<endl;
cout << "j " << j << endl;
}
if (ierr2==1)
{
// bunch thinks it is singular
if (norm_infinity(M*C-I) < 1e-6)
{
cout << "bunch said it is singular but old could invert"
<< endl;
cout << C << endl;
cout << "B*C" << B*C << endl;
cout << "M*C" << M*C << endl;
cout << "determinant " << C.determinant() << endl;
cout << "dist2" << dist2 << endl;
cout << "ierr2 " << ierr2 <<endl;
cout << "ierr1 " << ierr1 <<endl;
cout << "j " << j << endl;
}
}
if (ierr1==0 && dist1 > 1e-4 && ierr2==0)
{
cout << "old failed to invert but did not indicate" << endl;
cout << C << endl;
cout << "B*C" << B*C << endl;
cout << "M*C" << M*C << endl;
cout << "determinant " << C.determinant() << endl;
cout << "ierr2 " << ierr2 <<endl;
cout << "ierr1 " << ierr1 <<endl;
cout << "dist1 " << dist1 << endl;
cout << "j " << j << endl;
return 0;
}
if (ierr1==1)
{
// old thinks it is singular
if (norm_infinity(B*C-I) < 1e-6)
{
cout << "old said it is singular but bunch could invert"
<< endl;
cout << C << endl;
cout << "B*C" << B*C << endl;
cout << "M*C" << M*C << endl;
cout << "determinant " << C.determinant() << endl;
cout << "dist1" << dist1 << endl;
cout << "dist2" << dist2 << endl;
cout << "ierr2 " << ierr2 <<endl;
cout << "ierr1 " << ierr1 <<endl;
cout << "j " << j << endl;
return 0;
}
}
}
*/
/*** one tough symmetric matrix from real physical data
sm(1,1)=5347.51;
sm(1,2)=-142756;
sm(1,3)= -1.86624e+06;
sm(1,4)=0.0164743;
sm(1,5)=0.0915348;
sm(1,6)=0.421851;
sm(2,2)=3.81277;
sm(2,3)=4.98668e+07;
sm(2,4)=-0.0697533;
sm(2,5)=12.8555;
sm(2,6)=-2.01124;
sm(3,3)=6.52498e+08;
sm(3,4)=3.87491;
sm(3,5)=365.965;
sm(3,6)=93.3686;
sm(4,4)=7.77672e-05;
sm(4,5)=0.0032134;
sm(4,6)=0.00194407;
sm(5,5)=0.132845;
sm(5,6)=0.0803294;
sm(6,6)=0.0485992;
*/
/**** a group of near singular (nonsingular) matrices
int n=5;
HepSymMatrix sm(n); // nxn Hilbert Matrix
for(i=1;i<=n;i++)
for(k=i;k<=n;k++)
sm(i,k)=1./(i+k-1);
*/
return 0;
} // end of main
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