testSMatrix.cxx

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#include <cmath>
#include "Math/SVector.h"
#include "Math/SMatrix.h"

#include <iomanip>
#include <iostream>
#include <limits>
#include <string>
#include <vector>

using namespace ROOT::Math;

using std::cout;
using std::endl;

//#define TEST_STATIC_CHECK  // for testing compiler failures (static check)

#define XXX

template <typename T>
void compare_fail(T a, T b, int ulps, T tolerance, const std::string &what)
{
   cout << std::boolalpha << std::endl << "FAILED COMPARISON: " << what << std::endl << a << " != " << b << std::endl;

   if (std::is_floating_point<T>::value) {
      cout << std::scientific << std::setprecision(16) << "difference: " << std::abs(a - b) << " ( "
           << std::abs(a - b) / tolerance << " ulps)" << std::endl
           << " tolerance: " << tolerance << " (" << ulps << " ulps)" << std::endl;
   }
}

template <typename T>
typename std::enable_if<!std::is_floating_point<T>::value, int>::type compare(T a, T b, const std::string &s = "",
                                                                              int ulps = 10)
{
   if (a != b) compare_fail(a, b, T(0), T(0), s);
   return a == b ? 0 : 1;
}

template <typename T>
typename std::enable_if<std::is_floating_point<T>::value, int>::type compare(T a, T b, const std::string &s = "",
                                                                             int ulps = 10)
{
   using std::abs;

   if (a == b) return 0;

   T tol = ulps * std::numeric_limits<T>::epsilon();

   if (abs(a * b) > tol * tol) tol *= T(0.5) * (abs(a) + abs(b));

   if (abs(a - b) > tol) {
      compare_fail(a, b, ulps, tol, s);
      return 1;
   }
   return 0;
}

int test1()
{

   SVector<float, 3> x(4, 5, 6);
   SVector<float, 2> y(2.0, 3.0);
   std::cout << "x: " << x << std::endl;
   std::cout << "y: " << y << std::endl;

   //   float yy1=2.; float yy2 = 3;
   //   SVector<float,2> y2(yy1,yy2);

   SMatrix<float, 4, 3> A;
   SMatrix<float, 2, 2> B;

   A.Place_in_row(y, 1, 1);
   A.Place_in_col(x, 1, 0);
   A.Place_in_col(x + 2, 1, 0);
   A.Place_in_row(y + 3, 1, 1);

#ifndef _WIN32
   A.Place_at(B, 2, 1);
#else
   // Windows need template parameters
   A.Place_at<2, 2>(B, 2, 1);
#endif
   std::cout << "A: " << std::endl << A << std::endl;

   SVector<float, 3> z(x + 2);
   z.Place_at(y, 1);
   z.Place_at(y + 3, 1);
   std::cout << "z: " << std::endl << z << std::endl;

#ifdef TEST_STATIC_CHECK
   // create a vector of size 2 from 3 arguments
   SVector<float, 2> vbad(1, 2, 3);
#endif

   // test STL interface

   // float p[2] = {1,2};
   float m[4] = {1, 2, 3, 4};

   // SVector<float, 2> sp(p,2);
   SMatrix<float, 2, 2> sm(m, 4);

   // std::cout << "sp: " << std::endl << sp << std::endl;
   std::cout << "sm: " << std::endl << sm << std::endl;

   // std::vector<float> vp(sp.begin(), sp.end() );
   std::vector<float> vm(sm.begin(), sm.end());

   SVector<float, 4> sp1(m, 4);
   SVector<float, 4> sp2(sm.begin(), sm.end());
   SMatrix<float, 2, 2> sm2(vm.begin(), vm.end());

   if (sp1 != sp2) {
      std::cout << "Test STL interface for SVector failed" << std::endl;
      return -1;
   }
   if (sm2 != sm) {
      std::cout << "Test STL interface for SMatrix failed" << std::endl;
      return -1;
   }

   // test construction from identity
   SMatrix<float, 3, 3> i3 = SMatrixIdentity();

   std::cout << "3x3 Identity\n" << i3 << std::endl;

   SMatrix<float, 2, 3> i23 = SMatrixIdentity();
   std::cout << "2x3 Identity\n" << i23 << std::endl;

   SMatrix<float, 3, 3, MatRepSym<float, 3>> is3 = SMatrixIdentity();
   std::cout << "Sym matrix Identity\n" << is3 << std::endl;

   // test operator = from identity
   A = SMatrixIdentity();
   std::cout << "4x3 Identity\n" << A << std::endl;

   std::vector<float> v(6);
   for (int i = 0; i < 6; ++i) v[i] = double(i + 1);
   SMatrix<float, 3, 3, MatRepSym<float, 3>> s3(v.begin(), v.end());
   std::cout << s3 << std::endl;

   return 0;
}

int test2()
{
#ifdef XXX
   SMatrix<double, 3> A;
   A(0, 0) = A(1, 0) = 1;
   A(0, 1) = 3;
   A(1, 1) = A(2, 2) = 2;
   std::cout << "A: " << std::endl << A << std::endl;

   SVector<double, 3> x = A.Row(0);
   std::cout << "x: " << x << std::endl;

   SVector<double, 3> y = A.Col(1);
   std::cout << "y: " << y << std::endl;

   return 0;
#endif
}

int test3()
{
#ifdef XXX
   SMatrix<double, 3> A;
   A(0, 0) = A(0, 1) = A(1, 0) = 1;
   A(1, 1) = A(2, 2) = 2;

   SMatrix<double, 3> B = A; // save A in B
   std::cout << "A: " << std::endl << A << std::endl;

   double det = 0.;
   A.Det(det);
   std::cout << "Determinant: " << det << std::endl;
   // WARNING: A has changed!!
   std::cout << "A again: " << std::endl << A << std::endl;
   A = B;

   A.Invert();
   std::cout << "A^-1: " << std::endl << A << std::endl;

   // check if this is really the inverse:
   std::cout << "A^-1 * B: " << std::endl << A * B << std::endl;

   return 0;
#endif
}

int test4()
{
#ifdef XXX
   SMatrix<double, 3> A;
   A(0, 0) = A(0, 1) = A(1, 0) = 1;
   A(1, 1) = A(2, 2) = 2;
   std::cout << " A: " << std::endl << A << std::endl;

   SVector<double, 3> x(1, 2, 3);
   std::cout << "x: " << x << std::endl;

   // we add 1 to each component of x and A
   std::cout << " (x+1)^T * (A+1) * (x+1): " << Similarity(x + 1, A + 1) << std::endl;

   return 0;
#endif
}

int test5()
{
#ifdef XXX
   SMatrix<float, 4, 3> A;
   A(0, 0) = A(0, 1) = A(1, 1) = A(2, 2) = 4.;
   A(2, 3) = 1.;
   std::cout << "A: " << std::endl << A << std::endl;
   SVector<float, 4> x(1, 2, 3, 4);
   std::cout << " x: " << x << std::endl;
   SVector<float, 3> a(1, 2, 3);
   std::cout << " a: " << a << std::endl;
   SVector<float, 4> y = x + A * a;
   //    SVector<float,4> y = A * a;
   std::cout << " y: " << y << std::endl;

   SVector<float, 3> b = (x + 1) * (A + 1);
   std::cout << " b: " << b << std::endl;

   return 0;
#endif
}

int test6()
{
#ifdef XXX
   SMatrix<float, 4, 2> A;
   A(0, 0) = A(0, 1) = A(1, 1) = A(2, 0) = A(3, 1) = 4.;
   std::cout << "A: " << std::endl << A << std::endl;

   SMatrix<float, 2, 3> S;
   S(0, 0) = S(0, 1) = S(1, 1) = S(0, 2) = 1.;
   std::cout << " S: " << std::endl << S << std::endl;

   SMatrix<float, 4, 3> C = A * S;
   std::cout << " C: " << std::endl << C << std::endl;

   return 0;
#endif
}

int test7()
{
#ifdef XXX
   SVector<float, 3> xv(4, 4, 4);
   SVector<float, 3> yv(5, 5, 5);
   SVector<float, 2> zv(64, 64);
   SMatrix<float, 2, 3> x;
   x.Place_in_row(xv, 0, 0);
   x.Place_in_row(xv, 1, 0);
   SMatrix<float, 2, 3> y;
   y.Place_in_row(yv, 0, 0);
   y.Place_in_row(yv, 1, 0);
   SMatrix<float, 2, 3> z;
   z.Place_in_col(zv, 0, 0);
   z.Place_in_col(zv, 0, 1);
   z.Place_in_col(zv, 0, 2);

   std::cout << "x\n" << x << "y\n" << y << "z\n" << z << std::endl;

   // element wise multiplication
   std::cout << "x * (- y) : " << std::endl << Times(x, -y) << std::endl;

   x += z - y;
   std::cout << "x += z - y: " << std::endl << x << std::endl;

   // element wise square root
   std::cout << "sqrt(z): " << std::endl << sqrt(z) << std::endl;

   // element wise multiplication with constant
   std::cout << "2 * y: " << std::endl << 2 * y << std::endl;

// a more complex expression (failure on Win32)
#ifndef _WIN32
   // std::cout << "fabs(-z + 3*x): " << std::endl << fabs(-z + 3*x) << std::endl;
   std::cout << "fabs(3*x -z): " << std::endl << fabs(3 * x - z) << std::endl;
#else
   // doing directly gives internal compiler error on windows
   SMatrix<float, 2, 3> ztmp = 3 * x - z;
   std::cout << " fabs(-z+3*x) " << std::endl << fabs(ztmp) << std::endl;
#endif

   return 0;
#endif
}

int test8()
{
#ifdef XXX
   SMatrix<float, 2, 3> A;
   SVector<float, 3> av1(5., 15., 5.);
   SVector<float, 3> av2(15., 5., 15.);
   A.Place_in_row(av1, 0, 0);
   A.Place_in_row(av2, 1, 0);

   std::cout << "A: " << std::endl << A << std::endl;

   SVector<float, 3> x(1, 2, 3);
   SVector<float, 3> y(4, 5, 6);

   std::cout << "dot(x,y): " << Dot(x, y) << std::endl;

   std::cout << "mag(x): " << Mag(x) << std::endl;

   std::cout << "cross(x,y): " << Cross(x, y) << std::endl;

   std::cout << "unit(x): " << Unit(x) << std::endl;

   SVector<float, 3> z(4, 16, 64);
   std::cout << "x + y: " << x + y << std::endl;

   std::cout << "x + y(0) " << (x + y)(0) << std::endl;

   std::cout << "x * -y: " << x * -y << std::endl;
   x += z - y;
   std::cout << "x += z - y: " << x << std::endl;

   // element wise square root
   std::cout << "sqrt(z): " << sqrt(z) << std::endl;

   // element wise multiplication with constant
   std::cout << "2 * y: " << 2 * y << std::endl;

   // a more complex expression
   std::cout << "fabs(-z + 3*x): " << fabs(-z + 3 * x) << std::endl;

   SVector<float, 4> a;
   SVector<float, 2> b(1, 2);
   a.Place_at(b, 2);
   std::cout << "a: " << a << std::endl;
#endif

   SVector<float, 3> x2 = Square(x);
   std::cout << x2 << std::endl;

   return 0;
}

int test9()
{
   // test non mutating inversions
   SMatrix<double, 3> A;
   A(0, 0) = A(0, 1) = A(1, 0) = 1;
   A(1, 1) = A(2, 2) = 2;

   double det = 0.;
   A.Det2(det);
   std::cout << "Determinant: " << det << std::endl;

   int ifail;
   SMatrix<double, 3> Ainv = A.Inverse(ifail);
   if (ifail) {
      std::cout << "inversion failed\n";
      return -1;
   }
   std::cout << "A^-1: " << std::endl << Ainv << std::endl;

   // check if this is really the inverse:
   std::cout << "A^-1 * A: " << std::endl << Ainv * A << std::endl;

   return 0;
}

int test10()
{
   // test slices
   int iret = 0;
   double d[9] = {1, 2, 3, 4, 5, 6, 7, 8, 9};
   SMatrix<double, 3> A(d, d + 9);

   std::cout << "A: " << A << std::endl;

   SVector<double, 2> v23 = A.SubRow<SVector<double, 2>>(0, 1);
   SVector<double, 2> v69 = A.SubCol<SVector<double, 2>>(2, 1);

   std::cout << " v23 =  " << v23 << " \tv69 = " << v69 << std::endl;
   iret |= compare(Dot(v23, v69), double(2 * 6 + 3 * 9));

   //    SMatrix<double,2,2> subA1 = A.Sub<2,2>( 1,0);
   //    SMatrix<double,2,3> subA2 = A.Sub<2,3>( 0,0);
   SMatrix<double, 2, 2> subA1 = A.Sub<SMatrix<double, 2, 2>>(1, 0);
   SMatrix<double, 2, 3> subA2 = A.Sub<SMatrix<double, 2, 3>>(0, 0);
   std::cout << " subA1 =  " << subA1 << " \nsubA2 = " << subA2 << std::endl;
   iret |= compare(subA1(0, 0), subA2(1, 0));
   iret |= compare(subA1(0, 1), subA2(1, 1));

   SVector<double, 3> diag = A.Diagonal();
   std::cout << " diagonal =  " << diag << std::endl;
   iret |= compare(Mag2(diag), double(1 + 5 * 5 + 9 * 9));
   iret |= compare(A.Trace(), double(1 + 5 + 9));

   SMatrix<double, 3> B = Transpose(A);
   std::cout << " B = " << B << std::endl;

#ifdef UNSUPPORTED_TEMPLATE_EXPRESSION
   // in this case  function is templated. Need to pass the 6
   SVector<double, 6> vU = A.UpperBlock<SVector<double, 6>>();
   SVector<double, 6> vL = B.LowerBlock<SVector<double, 6>>();
#else
   // standards
   SVector<double, 6> vU = A.UpperBlock();
   SVector<double, 6> vL = B.LowerBlock();
#endif
   std::cout << " vU =  " << vU << " \tvL = " << vL << std::endl;
   // need to test mag since order can change
   iret |= compare(Mag(vU), Mag(vL));

   // test subvector
   SVector<double, 3> subV = vU.Sub<SVector<double, 3>>(1);
   std::cout << " sub vU =  " << subV << std::endl;

   iret |= compare(vU[2], subV[1]);

   // test constructor from subVectors
   SMatrix<double, 3> C(vU, false);
   SMatrix<double, 3> D(vL, true);

   //   std::cout << " C =  " << C << std::endl;
   //   std::cout << " D =  " << D << std::endl;

   iret |= compare(static_cast<int>(C == D), 1);

   SMatrix<double, 3, 3, MatRepSym<double, 3>> C2(vU, false);
   SMatrix<double, 3, 3, MatRepSym<double, 3>> D2(vL, true);

   iret |= compare(static_cast<int>(C == C2), 1);
   iret |= compare(static_cast<int>(D == D2), 1);

   return iret;
}

int test11()
{

   int iret = 0;
   double dSym[15] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
   double d3[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
   double d2[10] = {10, 1, 4, 5, 8, 2, 3, 6, 7, 9};

   SVector<double, 15> vsym(dSym, 15);

   SMatrix<double, 5, 5> m1(vsym);
   SMatrix<double, 2, 5> m2(d2, d2 + 10);
   SMatrix<double, 5, 2> m3(d3, d3 + 10);
   // SMatrix<double,5,5> I;

   SMatrix<double, 5, 5> m32 = m3 * m2;

   SMatrix<double, 5, 5> m4 = m1 - m32 * m1;
   SMatrix<double, 5, 5> m5 = m3 * m2;

   // now thanks to the IsInUse() function this should work
   m5 = m1 - m5 * m1;

   // this works probably becuse here multiplication is done first

   SMatrix<double, 5, 5> m6 = m3 * m2;
   // m6 =  - m6 * m1 + m1;
   // this does not work if use reference in binary and unary operators , better this
   m6 = -m32 * m1 + m1;

   std::cout << m4 << std::endl;
   std::cout << m5 << std::endl;
   std::cout << m6 << std::endl;

   // this is test will now work
   iret |= compare(m4 == m5, true);
   iret |= compare(m4 == m6, true);

   return iret;
}

int test12()
{
   // test of symmetric matrices

   int iret = 0;
   SMatrix<double, 2, 2, MatRepSym<double, 2>> S;
   S(0, 0) = 1.233;
   S(0, 1) = 2.33;
   S(1, 1) = 3.45;
   std::cout << "S\n" << S << std::endl;

   double a = 3;
   std::cout << "S\n" << a * S << std::endl;

   // test inversion
   int ifail1 = 0;
   // int ifail2 = 0;
   SMatrix<double, 2, 2, MatRepSym<double, 2>> Sinv1 = S.Inverse(ifail1);
   // SMatrix<double,2,2,MatRepSym<double,2> > Sinv2 = S.Sinverse(ifail2);
   // std::cout << "Inverse:  S-1 " <<  Sinv1 << "\nifail=" << ifail1 << std::endl;
   // std::cout << "Sinverse: S-1"  << Sinv2 << "\nifail=" << ifail2 << std::endl;

   SMatrix<double, 2> IS1 = S * Sinv1;
   // SMatrix<double,2> IS2 = S*Sinv2;
   double d1 = std::sqrt(IS1(1, 0) * IS1(1, 0) + IS1(0, 1) * IS1(0, 1));
   // double d2 = std::sqrt( IS2(1,0)*IS2(1,0) + IS2(0,1)*IS2(0,1) );

   iret |= compare(d1 < 1E-6, true, "inversion1");
   // iret |= compare( d2 < 1E-6,true,"inversion2" );

   SMatrix<double, 2, 3> M1 = SMatrixIdentity();
   M1(0, 1) = 1;
   M1(1, 0) = 1;
   M1(0, 2) = 1;
   M1(1, 2) = 1;
   SMatrix<double, 2, 3> M2 = SMatrixIdentity();
   SMatrix<double, 2, 2, MatRepSym<double, 2>> S2 = S;
   // S2 -= M1*Transpose(M2);  // this should fails to compile
   SMatrix<double, 2> mS2(S2);
   mS2 -= M1 * Transpose(M2);
   // std::cout << "S2=S-M1*M2T\n" << mS2 << std::endl;
   iret |= compare(mS2(0, 1), S(0, 1) - 1);
   mS2 += M1 * Transpose(M2);
   iret |= compare(mS2(0, 1), S(0, 1));

   // std::cout << "S2+=M1*M2T\n" << mS2 << std::endl;

   SMatrix<float, 100, 100, MatRepSym<float, 100>> mSym;
   SMatrix<float, 100> m;
   // std::cout << " Symmetric matrix size: " << sizeof(mSym) << std::endl;
   // std::cout << " Normal    matrix size: " << sizeof( m  ) << std::endl;

   SMatrix<float, 100, 100, MatRepSym<float, 100>> mSym2;
   // std::cout << " Symmetric matrix size: " << sizeof(mSym2) << std::endl;

   return iret;
}

int test13()
{
   // test of operation with a constant;

   int iret = 0;

   int a = 2;
   float b = 3;

   SVector<double, 2> v(1, 2);
   SVector<double, 2> v2 = v + a;
   iret |= compare(v2[1], v[1] + a);
   SVector<double, 2> v3 = a + v;
   iret |= compare(v3[1], v[1] + a);
   iret |= compare(v3[0], v2[0]);

   v2 = v - a;
   iret |= compare(v2[1], v[1] - a);
   v3 = a - v;
   iret |= compare(v3[1], a - v[1]);

   // test now with expression
   v2 = b * v + a;
   iret |= compare(v2[1], b * v[1] + a);
   v3 = a + v * b;
   iret |= compare(v3[1], b * v[1] + a);
   v2 = v * b - a;
   iret |= compare(v2[1], b * v[1] - a);
   v3 = a - b * v;
   iret |= compare(v3[1], a - b * v[1]);

   v2 = a * v / b;
   iret |= compare(v2[1], a * v[1] / b);

   SVector<double, 2> p(1, 2);
   SVector<double, 2> q(3, 4);
   v = p + q;
   v2 = a * (p + q);
   iret |= compare(v2[1], a * v[1]);
   v3 = (p + q) * b;
   iret |= compare(v3[1], b * v[1]);
   v2 = (p + q) / b;
   iret |= compare(v2[1], v[1] / b);

   // std::cout << "tested vector -constant operations : v2 = " << v2 << " v3 = " << v3 << std::endl;

   // now test the matrix (normal)

   SMatrix<double, 2, 2> m;
   m.Place_in_row(p, 0, 0);
   m.Place_in_row(q, 1, 0);

   SMatrix<double, 2, 2> m2, m3;

   m2 = m + a;
   iret |= compare(m2(1, 0), m(1, 0) + a);
   m3 = a + m;
   iret |= compare(m3(1, 0), m(1, 0) + a);
   iret |= compare(m3(0, 0), m2(0, 0));

   m2 = m - a;
   iret |= compare(m2(1, 0), m(1, 0) - a);
   m3 = a - m;
   iret |= compare(m3(1, 0), a - m(1, 0));

   // test now with expression
   m2 = b * m + a;
   iret |= compare(m2(1, 0), b * m(1, 0) + a);
   m3 = a + m * b;
   iret |= compare(m3(1, 0), b * m(1, 0) + a);
   m2 = m * b - a;
   iret |= compare(m2(1, 0), b * m(1, 0) - a);
   m3 = a - b * m;
   iret |= compare(m3(1, 0), a - b * m(1, 0));

   m2 = a * m / b;
   iret |= compare(m2(1, 0), a * m(1, 0) / b);

   SMatrix<double, 2> u = m;
   SMatrix<double, 2> w;
   w(0, 0) = 5;
   w(0, 1) = 6;
   w(1, 0) = 7;
   w(1, 1) = 8;

   m = u + w;
   m2 = a * (u + w);
   iret |= compare(m2(1, 0), a * m(1, 0));
   m3 = (u + w) * b;
   iret |= compare(m3(1, 0), b * m(1, 0));
   m2 = (u + w) / b;
   iret |= compare(m2(1, 0), m(1, 0) / b);

   // std::cout << "tested general matrix -constant operations :\nm2 =\n" << m2 << "\nm3 =\n" << m3 << std::endl;

   // now test the symmetric matrix

   SMatrix<double, 2, 2, MatRepSym<double, 2>> s;
   s(0, 0) = 1;
   s(1, 0) = 2;
   s(1, 1) = 3;

   SMatrix<double, 2, 2, MatRepSym<double, 2>> s2, s3;

   s2 = s + a;
   iret |= compare(s2(1, 0), s(1, 0) + a);
   s3 = a + s;
   iret |= compare(s3(1, 0), s(1, 0) + a);
   iret |= compare(s3(0, 0), s2(0, 0));

   s2 = s - a;
   iret |= compare(s2(1, 0), s(1, 0) - a);
   s3 = a - s;
   iret |= compare(s3(1, 0), a - s(1, 0));

   // test now with expression
   s2 = b * s + a;
   iret |= compare(s2(1, 0), b * s(1, 0) + a);
   s3 = a + s * b;
   iret |= compare(s3(1, 0), b * s(1, 0) + a);
   s2 = s * b - a;
   iret |= compare(s2(1, 0), b * s(1, 0) - a);
   s3 = a - b * s;
   iret |= compare(s3(1, 0), a - b * s(1, 0));

   s2 = a * s / b;
   iret |= compare(s2(1, 0), a * s(1, 0) / b);

   SMatrix<double, 2, 2, MatRepSym<double, 2>> r = s;
   SMatrix<double, 2, 2, MatRepSym<double, 2>> t;
   t(0, 0) = 4;
   t(0, 1) = 5;
   t(1, 1) = 6;

   s = r + t;
   s2 = a * (r + t);
   iret |= compare(s2(1, 0), a * s(1, 0), "a*(r+t)");
   s3 = (t + r) * b;
   iret |= compare(s3(1, 0), b * s(1, 0), "(t+r)*b");
   s2 = (r + t) / b;
   iret |= compare(s2(1, 0), s(1, 0) / b, "(r+t)/b");

   // std::cout << "tested sym matrix -constant operations :\ns2 =\n" << s2 << "\ns3 =\n" << s3 << std::endl;

   return iret;
}

int test14()
{
   // test place_at (insertion) of all type of matrices

   int iret = 0;

   // test place at with sym matrices

   SMatrix<double, 2, 2, MatRepSym<double, 2>> S;
   S(0, 0) = 1;
   S(0, 1) = 2;
   S(1, 1) = 3;

   double u[6] = {1, 2, 3, 4, 5, 6};
   SMatrix<double, 2, 3, MatRepStd<double, 2, 3>> U(u, u + 6);

   // place general matrix in general matrix
   SMatrix<double, 4, 4> A;
   A.Place_at(U, 1, 0);
   // std::cout << "Test general matrix placed in general at 1,0 :\nA=\n" << A << std::endl;
   iret |= compare(A(1, 0), U(0, 0));
   iret |= compare(A(1, 1), U(0, 1));
   iret |= compare(A(2, 1), U(1, 1));
   iret |= compare(A(2, 2), U(1, 2));

   A.Place_at(-2 * U, 1, 0);
   iret |= compare(A(1, 0), -2 * U(0, 0));
   iret |= compare(A(1, 1), -2 * U(0, 1));
   iret |= compare(A(2, 1), -2 * U(1, 1));
   iret |= compare(A(2, 2), -2 * U(1, 2));

   // place symmetric in general (should work always)
   A.Place_at(S, 0, 0);
   // std::cout << "Test symmetric matrix placed in general at 0,0:\nA=\n" << A << std::endl;
   iret |= compare(A(0, 0), S(0, 0));
   iret |= compare(A(1, 0), S(0, 1));
   iret |= compare(A(1, 1), S(1, 1));

   A.Place_at(2 * S, 0, 0);
   iret |= compare(A(0, 0), 2 * S(0, 0));
   iret |= compare(A(1, 0), 2 * S(0, 1));
   iret |= compare(A(1, 1), 2 * S(1, 1));

   A.Place_at(S, 2, 0);
   // std::cout << "A=\n" << A << std::endl;
   iret |= compare(A(2, 0), S(0, 0));
   iret |= compare(A(3, 0), S(0, 1));
   iret |= compare(A(3, 1), S(1, 1));

   SMatrix<double, 3, 3, MatRepSym<double, 3>> B;

   // place symmetric in symmetric (OK for col=row)
   B.Place_at(S, 1, 1);
   // std::cout << "Test symmetric matrix placed in symmetric at 1,1:\nB=\n" << B << std::endl;
   iret |= compare(B(1, 1), S(0, 0));
   iret |= compare(B(2, 1), S(0, 1));
   iret |= compare(B(2, 2), S(1, 1));

   B.Place_at(-S, 0, 0);
   // std::cout << "B=\n" << B << std::endl;
   iret |= compare(B(0, 0), -S(0, 0));
   iret |= compare(B(1, 0), -S(0, 1));
   iret |= compare(B(1, 1), -S(1, 1));

// this should assert at run time
// B.Place_at(S,1,0);
// B.Place_at(2*S,1,0);

// place general in symmetric should fail to compiler
#ifdef TEST_STATIC_CHECK
   B.Place_at(U, 0, 0);
   B.Place_at(-U, 0, 0);
#endif

   // test place vector in matrices
   SVector<double, 2> v(1, 2);

   A.Place_in_row(v, 1, 1);
   iret |= compare(A(1, 1), v[0]);
   iret |= compare(A(1, 2), v[1]);
   A.Place_in_row(2 * v, 1, 1);
   iret |= compare(A(1, 1), 2 * v[0]);
   iret |= compare(A(1, 2), 2 * v[1]);

   A.Place_in_col(v, 1, 1);
   iret |= compare(A(1, 1), v[0]);
   iret |= compare(A(2, 1), v[1]);
   A.Place_in_col(2 * v, 1, 1);
   iret |= compare(A(1, 1), 2 * v[0]);
   iret |= compare(A(2, 1), 2 * v[1]);

   // place vector in sym matrices
   B.Place_in_row(v, 0, 1);
   // std::cout << "B=\n" << B << std::endl;
   iret |= compare(B(0, 1), v[0]);
   iret |= compare(B(1, 0), v[0]);
   iret |= compare(B(2, 0), v[1]);
   B.Place_in_row(2 * v, 1, 1);
   iret |= compare(B(1, 1), 2 * v[0]);
   iret |= compare(B(2, 1), 2 * v[1]);

   B.Place_in_col(v, 1, 0);
   // std::cout << "B=\n" << B << std::endl;
   iret |= compare(B(0, 1), v[0]);
   iret |= compare(B(1, 0), v[0]);
   iret |= compare(B(0, 2), v[1]);
   B.Place_in_col(2 * v, 1, 1);
   iret |= compare(B(1, 1), 2 * v[0]);
   iret |= compare(B(1, 2), 2 * v[1]);

   // test Sub
   SMatrix<double, 2, 2, MatRepSym<double, 2>> sB = B.Sub<SMatrix<double, 2, 2, MatRepSym<double, 2>>>(1, 1);
   iret |= compare(sB(0, 0), B(1, 1));
   iret |= compare(sB(1, 0), B(1, 2));
   iret |= compare(sB(1, 1), B(2, 2));

   SMatrix<double, 2, 3, MatRepStd<double, 2, 3>> sA = A.Sub<SMatrix<double, 2, 3, MatRepStd<double, 2, 3>>>(1, 0);
   iret |= compare(sA(0, 0), A(1, 0));
   iret |= compare(sA(1, 0), A(2, 0));
   iret |= compare(sA(1, 1), A(2, 1));
   iret |= compare(sA(1, 2), A(2, 2));

   sA = B.Sub<SMatrix<double, 2, 3, MatRepStd<double, 2, 3>>>(0, 0);
   iret |= compare(sA(0, 0), B(0, 0));
   iret |= compare(sA(1, 0), B(1, 0));
   iret |= compare(sA(0, 1), B(0, 1));
   iret |= compare(sA(1, 1), B(1, 1));
   iret |= compare(sA(1, 2), B(1, 2));

// this should run assert
//  sA = A.Sub<SMatrix<double,2,3,MatRepStd<double,2,3> > > (0,2);
//  sB = B.Sub<SMatrix<double,2,2,MatRepSym<double,2> > > (0,1);

#ifdef TEST_STATIC_CHECK
   sB = A.Sub<SMatrix<double, 2, 2, MatRepSym<double, 2>>>(0, 0);
   SMatrix<double, 5, 2> tmp1 = A.Sub<SMatrix<double, 5, 2>>(0, 0);
   SMatrix<double, 2, 5> tmp2 = A.Sub<SMatrix<double, 2, 5>>(0, 0);
#endif

// test setDiagonal

#ifdef TEST_STATIC_CHECK
   SVector<double, 3> w(-1, -2, 3);
   sA.SetDiagonal(w);
   sB.SetDiagonal(w);
#endif

   sA.SetDiagonal(v);
   iret |= compare(sA(1, 1), v[1]);
   sB.SetDiagonal(v);
   iret |= compare(sB(0, 0), v[0]);

   // test Trace
   iret |= compare(sA.Trace(), v[0] + v[1]);
   iret |= compare(sB.Trace(), v[0] + v[1]);
   SMatrix<double, 3, 2> sAt = Transpose(sA);
   iret |= compare(sAt.Trace(), v[0] + v[1]);

   return iret;
}

int test15()
{
   // test using iterators
   int iret = 0;

   double u[12] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12};
   double w[6] = {1, 2, 3, 4, 5, 6};

   SMatrix<double, 3, 4> A1(u, 12);
   iret |= compare(A1(0, 0), u[0]);
   iret |= compare(A1(1, 2), u[6]);
   iret |= compare(A1(2, 3), u[11]);
   // std::cout << A1 << std::endl;

   SMatrix<double, 3, 4> A2(w, 6, true, true);
   iret |= compare(A2(0, 0), w[0]);
   iret |= compare(A2(1, 0), w[1]);
   iret |= compare(A2(2, 0), w[3]);
   iret |= compare(A2(2, 2), w[5]);
   // std::cout << A2 << std::endl;

   // upper diagonal (needs 9 elements)
   SMatrix<double, 3, 4> A3(u, 9, true, false);
   iret |= compare(A3(0, 0), u[0]);
   iret |= compare(A3(0, 1), u[1]);
   iret |= compare(A3(0, 2), u[2]);
   iret |= compare(A3(1, 2), u[5]);
   iret |= compare(A3(2, 3), u[8]);
   // std::cout << A3 << std::endl;

   // std::cout << "test sym matrix " << std::endl;
   SMatrix<double, 3, 3, MatRepSym<double, 3>> S1(w, 6, true);
   iret |= compare(S1(0, 0), w[0]);
   iret |= compare(S1(1, 0), w[1]);
   iret |= compare(S1(1, 1), w[2]);
   iret |= compare(S1(2, 0), w[3]);
   iret |= compare(S1(2, 1), w[4]);
   iret |= compare(S1(2, 2), w[5]);

   SMatrix<double, 3, 3, MatRepSym<double, 3>> S2(w, 6, true, false);
   iret |= compare(S2(0, 0), w[0]);
   iret |= compare(S2(1, 0), w[1]);
   iret |= compare(S2(2, 0), w[2]);
   iret |= compare(S2(1, 1), w[3]);
   iret |= compare(S2(2, 1), w[4]);
   iret |= compare(S2(2, 2), w[5]);

   // check retrieve
   double *pA1 = A1.begin();
   for (int i = 0; i < 12; ++i) iret |= compare(pA1[i], u[i]);

   double *pS1 = S1.begin();
   for (int i = 0; i < 6; ++i) iret |= compare(pS1[i], w[i]);

   // check with SetElements
   std::vector<double> vu(u, u + 12);
   std::vector<double> vw(w, w + 6);
   SMatrix<double, 3, 4> B1;
   B1.SetElements(vu.begin(), 10);
   iret |= compare(B1(0, 0), u[0]);
   iret |= compare(B1(1, 2), u[6]);
   iret |= compare(B1(2, 3), 0.0);

   B1.SetElements(vu.begin(), vu.end());
   iret |= compare(B1(0, 0), vu[0]);
   iret |= compare(B1(1, 2), vu[6]);
   iret |= compare(B1(2, 3), vu[11]);

   B1.SetElements(vw.begin(), vw.end(), true, true);
   iret |= compare(B1(0, 0), w[0]);
   iret |= compare(B1(1, 0), w[1]);
   iret |= compare(B1(2, 0), w[3]);
   iret |= compare(B1(2, 2), w[5]);

   SVector<double, 12> v1;
   v1.SetElements(vu.begin(), vu.end());
   for (unsigned int i = 0; i < v1.kSize; ++i) iret |= compare(v1[i], vu[i]);

   // v1.SetElements(vw.begin(),vw.end() ); // this assert at run-time
   v1.SetElements(vw.begin(), vw.size());
   for (unsigned int i = 0; i < vw.size(); ++i) iret |= compare(v1[i], vw[i]);

   return iret;
}

int test16()
{
   // test IsInUse() function  to create automatically temporaries
   int iret = 0;

   double a[6] = {1, 2, 3, 4, 5, 6};
   double w[9] = {10, 2, 3, 4, 50, 6, 7, 8, 90};

   SMatrix<double, 3, 3, MatRepSym<double, 3>> A(a, a + 6);
   SMatrix<double, 3, 3, MatRepSym<double, 3>> B;
   //   SMatrix<double,3,3,MatRepSym<double,3> > C;

   B = Transpose(A);
   A = Transpose(A);
   iret |= compare(A == B, true, "transp");

   SMatrix<double, 3> W(w, w + 9);
   SMatrix<double, 3> Y = W.Inverse(iret);
   SMatrix<double, 3> Z;
   Z = W * Y;
   Y = W * Y;
#ifndef _WIN32
   // this fails on Windows (bad calculations)
   iret |= compare(Z == Y, true, "mult");
#else
   for (int i = 0; i < 9; ++i) {
      // avoid small value of a
      double a = Z.apply(i);
      double eps = std::numeric_limits<double>::epsilon();
      if (a < eps) a = 0;
      iret |= compare(a, Y.apply(i), "index");
   }
#endif

   Z = (A + W) * (B + Y);
   Y = (A + W) * (B + Y);

   iret |= compare(Z == Y, true, "complex mult");

   // test of assign sym
   //   AssignSym::Evaluate(A,  W * A * Transpose(W)  );
   //   AssignSym::Evaluate(B,  W * A * Transpose(W)  );
   //   iret |= compare( A==B,true,"assignsym");

   return iret;
}

int test17()
{
   int iret = 0;
   // tets tensor product
   SVector<double, 2> v1(1, 2);
   SVector<double, 3> v2(1, 2, 3);

   SMatrix<double, 2, 3> m = TensorProd(v1, v2);
   for (int i = 0; i < m.kRows; ++i)
      for (int j = 0; j < m.kCols; ++j) iret |= compare(m(i, j), v1(i) * v2(j));
   // std::cout << "Tensor Product \n" << m << std::endl;

   SVector<double, 4> a1(2, -1, 3, 4);
   SVector<double, 4> a2(5, 6, 1, -2);

   SMatrix<double, 4> A = TensorProd(a1, a2);
   double r1 = Dot(a1, A * a2);
   double r2 = Dot(a1, a1) * Dot(a2, a2);
   iret |= compare(r1, r2, "tensor prod");

   A = TensorProd(2. * a1, a2);
   r1 = Dot(a1, A * a2) / 2;
   r2 = Dot(a1, a1) * Dot(a2, a2);
   iret |= compare(r1, r2, "tensor prod");

   A = TensorProd(a1, 2 * a2);
   r1 = Dot(a1, A * a2) / 2;
   r2 = Dot(a1, a1) * Dot(a2, a2);
   iret |= compare(r1, r2, "tensor prod");

   A = TensorProd(0.5 * a1, 2 * a2);
   r1 = Dot(a1, A * a2);
   r2 = Dot(a1, a1) * Dot(a2, a2);
   iret |= compare(r1, r2, "tensor prod");

   return iret;
}

// test inverison of large matrix (double)
int test18()
{
   int iret = 0;
   // data for a 7x7 sym matrix to invert
   SMatrix<double, 7, 7, MatRepSym<double, 7>> S;
   for (int i = 0; i < 7; ++i) {
      for (int j = 0; j <= i; ++j) {
         if (i == j)
            S(i, j) = 10 * double(std::rand()) / (RAND_MAX); // generate between 0,10
         else
            S(i, j) = 2 * double(std::rand()) / (RAND_MAX)-1; // generate between -1,1
      }
   }
   int ifail = 0;
   SMatrix<double, 7, 7, MatRepSym<double, 7>> Sinv = S.Inverse(ifail);
   iret |= compare(ifail, 0, "sym7x7 inversion");
   SMatrix<double, 7> Id = S * Sinv;

   for (int i = 0; i < 7; ++i)
      for (int j = 0; j < 7; ++j)
         // The tolerance below is high because matrix inversion leads to large errors.
         // The comparisons below eventually fail with any value less than ~10000 ulps.
         iret |= compare(Id(i, j), i == j ? 1.0 : 0.0, "sym7x7 inversion result", 50000);

   // now test inversion of general
   SMatrix<double, 7> M;
   for (int i = 0; i < 7; ++i) {
      for (int j = 0; j < 7; ++j) {
         if (i == j)
            M(i, j) = 10 * double(std::rand()) / (RAND_MAX); // generate between 0,10
         else
            M(i, j) = 2 * double(std::rand()) / (RAND_MAX)-1; // generate between -1,1
      }
   }
   ifail = 0;
   SMatrix<double, 7> Minv = M.Inverse(ifail);
   iret |= compare(ifail, 0, "7x7 inversion");
   Id = M * Minv;

   for (int i = 0; i < 7; ++i)
      for (int j = 0; j < 7; ++j)
         // The tolerance below is high because matrix inversion leads to large errors.
         // The comparisons below eventually fail with any value less than ~10000 ulps.
         iret |= compare(Id(i, j), i == j ? 1.0 : 0.0, "sym7x7 inversion result", 50000);

   return iret;
}

// test inversion of large matrices (float)
int test19()
{
   int iret = 0;
   // data for a 7x7 sym matrix to invert
   SMatrix<float, 7, 7, MatRepSym<float, 7>> S;
   for (int i = 0; i < 7; ++i) {
      for (int j = 0; j <= i; ++j) {
         if (i == j)
            S(i, j) = 10 * float(std::rand()) / (RAND_MAX); // generate between 0,10
         else
            S(i, j) = 2 * float(std::rand()) / (RAND_MAX)-1; // generate between -1,1
      }
   }
   int ifail = 0;
   SMatrix<float, 7, 7, MatRepSym<float, 7>> Sinv = S.Inverse(ifail);
   iret |= compare(ifail, 0, "sym7x7 inversion");
   SMatrix<float, 7> Id = S * Sinv;

   // std::cout << S << "\n" << Sinv << "\n" << Id << "\n";

   for (int i = 0; i < 7; ++i)
      for (int j = 0; j < 7; ++j)
         // The tolerance below is high because matrix inversion leads to large errors.
         // The comparisons below eventually fail with any value less than ~10000 ulps.
         iret |= compare(Id(i, j), i == j ? 1.0f : 0.0f, "sym7x7 inversion result", 50000);

   // now test inversion of general
   SMatrix<float, 7> M;
   for (int i = 0; i < 7; ++i) {
      for (int j = 0; j < 7; ++j) {
         if (i == j)
            M(i, j) = 10 * float(std::rand()) / (RAND_MAX); // generate between 0,10
         else
            M(i, j) = 2 * float(std::rand()) / (RAND_MAX)-1; // generate between -1,1
      }
   }
   ifail = 0;
   SMatrix<float, 7> Minv = M.Inverse(ifail);
   iret |= compare(ifail, 0, "7x7 inversion");
   Id = M * Minv;

   // std::cout << M << "\n" << Minv << "\n" << Id << "\n";

   for (int i = 0; i < 7; ++i)
      for (int j = 0; j < 7; ++j)
         // The tolerance below is high because matrix inversion leads to large errors.
         // The comparisons below eventually fail with any value less than ~10000 ulps.
         iret |= compare(Id(i, j), i == j ? 1.0f : 0.0f, "sym7x7 inversion result", 50000);

   return iret;
}

int test20()
{
   // test operator += , -=
   int iret = 0;
   // std::cout.precision(18);

   double d1[6] = {1, 2, 3, 4, 5, 6};
   double d2[6] = {1, 2, 5, 3, 4, 6};

   SMatrix<double, 2> m1_0(d1, 4);
   SMatrix<double, 2> m2_0(d2, 4);
   SMatrix<double, 2> m1 = m1_0;
   SMatrix<double, 2> m2 = m2_0;
   SMatrix<double, 2> m3;

   m3 = m1 + m2;
   m1 += m2;

   if (iret) std::cout << "m1+= m2" << m1 << std::endl;

   iret |= compare(m1 == m3, true);

   m3 = m1 + 3;
   m1 += 3;
   iret |= compare(m1 == m3, true);
   if (iret) std::cout << "m1 + 3\n" << m1 << " \n  " << m3 << std::endl;

   m3 = m1 - m2;
   m1 -= m2;
   iret |= compare(m1 == m3, true);
   if (iret) std::cout << "m1-= m2\n" << m1 << " \n  " << m3 << std::endl;

   m3 = m1 - 3;
   m1 -= 3;
   iret |= compare(m1 == m3, true);
   if (iret) std::cout << "m1-= 3\n" << m1 << " \n " << m3 << std::endl;

   m3 = m1 * 2;
   m1 *= 2;
   iret |= compare(m1 == m3, true);
   if (iret) std::cout << "m1*= 2\n" << m1 << "\n" << m3 << std::endl;

   // matrix multiplication (*= works only for squared matrix mult.)
   m3 = m1 * m2;
   m1 *= m2;
   iret |= compare(m1 == m3, true);
   if (iret) std::cout << "m1*= m2\n" << m1 << " \n " << m3 << std::endl;

   m3 = m1 / 2;
   m1 /= 2;
   iret |= compare(m1 == m3, true);
   if (iret) std::cout << "m1/=2\n" << m1 << " \n " << m3 << std::endl;

   // test mixed with a scalar
   double a = 2;
   m3 = m2 + a * m1;
   m2 += a * m1;
   iret |= compare(m2 == m3, true);
   if (iret) std::cout << "m2 += a*m1\n" << m2 << "\n  " << m3 << std::endl;

   // more complex op (passing expressions)

   m1 = m1_0;
   m2 = m2_0;

   m3 = m1 + (m1 * m2);
   m1 += m1 * m2;
   iret |= compare(m1 == m3, true);
   if (iret) std::cout << "m1 += m1*m2\n" << m1 << "\n  " << m3 << std::endl;

   m3 = m1 - (m1 * m2);
   m1 -= m1 * m2;
   iret |= compare(m1 == m3, true);
   if (iret) std::cout << "m1 -= m1*m2\n" << m1 << " \n " << m3 << std::endl;

   m3 = m1 * (m1 * m2);
   m1 *= m1 * m2;
   iret |= compare(m1 == m3, true);
   if (iret) std::cout << "m1 *= m1*m2\n" << m1 << "\n  " << m3 << std::endl;

   // test operation involving 2 expressions
   // (check bug 35076)

   // reset initial matrices to avoid numerical problems
   m1 = m1_0;
   m2 = m2_0;

   m3 = m1 + m2;
   SMatrix<double, 2> m4;
   SMatrix<double, 2> m5;
   m4 = (m1 * m2) + (m1 * m3);
   m5 = m1 * m2;
   m5 += m1 * m3;
   iret |= compare(m4 == m5, true);
   if (iret) std::cout << "m5 = m1*m3\n" << m4 << "\n  " << m5 << std::endl;

   m4 = (m1 * m2) - (m1 * m3);
   m5 = m1 * m2;
   m5 -= m1 * m3;
   iret |= compare(m4 == m5, true);
   if (iret) std::cout << "m5 -= m1*m3\n" << m4 << "\n  " << m5 << std::endl;

   m4 = (m1 + m2) * (m1 - m3);
   m5 = m1 + m2;
   m5 = m5 * (m1 - m3);
   iret |= compare(m4 == m5, true);

   if (iret) std::cout << "m5= m5*(m1-m3) \n" << m4 << " \n " << m5 << std::endl;

   // test with vectors
   SVector<double, 4> v1(d1, 4);
   SVector<double, 4> v2(d2, 4);
   SVector<double, 4> v3;

   v3 = v1 + v2;
   v1 += v2;
   iret |= compare(v1 == v3, true);

   v3 = v1 + 2;
   v1 += 2;
   iret |= compare(v1 == v3, true);

   v3 = v1 + (v1 + v2);
   v1 += v1 + v2;
   iret |= compare(v1 == v3, true);

   v3 = v1 - v2;
   v1 -= v2;
   iret |= compare(v1 == v3, true);

   v3 = v1 - 2;
   v1 -= 2;
   iret |= compare(v1 == v3, true);

   v3 = v1 - (v1 + v2);
   v1 -= v1 + v2;
   iret |= compare(v1 == v3, true);

   v3 = v1 * 2;
   v1 *= 2;
   iret |= compare(v1 == v3, true);

   v3 = v1 / 2;
   v1 /= 2;
   iret |= compare(v1 == v3, true);

   // test with symmetric matrices

   // double d1[6]={1,2,3,4,5,6};
   SMatrix<double, 3, 3, MatRepSym<double, 3>> ms1(d1, d1 + 6);
   SMatrix<double, 3, 3, MatRepSym<double, 3>> ms2(d1, d1 + 6, true, false);
   SMatrix<double, 3, 3, MatRepSym<double, 3>> ms3;
   SMatrix<double, 3, 3, MatRepSym<double, 3>> ms4;

   // using complex expressions
   ms3 = ms1 + (ms1 + ms2);
   ms1 += ms1 + ms2;
   iret |= compare(ms1 == ms3, true);

   ms3 = ms1 - (ms1 + ms2);
   ms1 -= ms1 + ms2;
   iret |= compare(ms1 == ms3, true);

   a = 2;
   ms3 = ms1 + a * ms2;

   ms4 = ms1;
   ms4 += a * ms2;

   iret |= compare(ms3 == ms4, true);

   ms3 = ms1 - a * ms2;
   ms4 = ms1;
   ms4 -= a * ms2;
   iret |= compare(ms3 == ms4, true);

   return iret;
}

int test21()
{

   // test global matrix function (element-wise operations)

   int iret = 0;

   double d1[4] = {4, 6, 3, 4};
   double d2[4] = {2, 3, 1, 4};

   SMatrix<double, 2> m1(d1, 4);
   SMatrix<double, 2> m2(d2, 4);
   SMatrix<double, 2> m3;

   // test element-wise multiplication
   m3 = Times(m1, m2);
   for (int i = 0; i < 4; ++i) iret |= compare(m3.apply(i), m1.apply(i) * m2.apply(i));

   // matrix division is element-wise division
   m3 = Div(m1, m2);
   for (int i = 0; i < 4; ++i) iret |= compare(m3.apply(i), m1.apply(i) / m2.apply(i));

   return iret;
}

int test22()
{

   // test conversion to scalar for size 1 matrix and vectors

   int iret = 0;
   SMatrix<double, 1> m1(2);
   iret |= compare(m1(0, 0), 2.);

   SVector<double, 1> v1;
   v1 = 2;
   iret |= compare(m1(0, 0), 2.);

   return iret;
}

int test23()
{
   // test cholesky inversion and solving
   int iret = 0;

   double m[] = {100, .15, 2.3, 0.01, .01, 1.};
   SMatrix<double, 3, 3, MatRepSym<double, 3>> smat(m, m + 6);

   // std::cout << "Perform inversion  of matrix \n" << smat << std::endl;

   int ifail = 0;
   SMatrix<double, 3, 3, MatRepSym<double, 3>> imat = smat.InverseChol(ifail);
   iret |= compare(ifail == 0, true, "inversion");

   // test max deviations from identity for m = imat * smat

   SMatrix<double, 3> mid = imat * smat;
   int n = 3;
   double prod = 1;
   double vmax = 0;
   for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
         if (i == j)
            prod *= mid(i, i);
         else {
            if (std::abs(mid(i, j)) > vmax) vmax = std::abs(mid(i, j));
         }
      }
   }
   iret |= compare(prod, 1., "max dev diagonal");
   iret |= compare(vmax, 0., "max dev offdiag ", 10);

   // test now solving of linear system
   SVector<double, 3> vec(1, 2, 3);

   SVector<double, 3> x = SolveChol(smat, vec, ifail);

   // std::cout << "linear system solution " << x << std::endl;

   iret |= compare((ifail == 0), true, "solve chol");

   SVector<double, 3> v2 = smat * x;

   for (int i = 0; i < 3; ++i) iret |= compare(v2[i], vec[i], "v2 ==vec");

   return iret;
}

int test24()
{
   // add transpose test
   // see bug #65531
   double a[9] = {1, -2, 3, 4, -5, 6, -7, 8, 9};
   double b[9] = {1, -1, 0, 0, 2, 0, -1, 0, 3};

   SMatrix<double, 3> A(a, a + 9);
   SMatrix<double, 3> B(b, b + 9);

   SMatrix<double, 3> R = A * B * Transpose(A);

   SMatrix<double, 3> temp1 = A * B;
   SMatrix<double, 3> R1 = temp1 * Transpose(A);

   SMatrix<double, 3> temp2 = B * Transpose(A);
   SMatrix<double, 3> R2 = A * temp2;

   int iret = 0;
   iret |= compare(R1 == R2, true);
   iret |= compare(R == R1, true);
   return iret;
}

int test25()
{
   // add test of vector * matrix multiplication with aliasing
   // bug #6157
   ROOT::Math::SMatrix<double, 3, 3, ROOT::Math::MatRepSym<double, 3>> m;
   m(0, 0) = 10;
   m(0, 1) = 7;
   m(0, 2) = 5;
   m(1, 1) = 9;
   m(1, 2) = 6;
   m(2, 2) = 8;

   ROOT::Math::SVector<double, 3> v1(1, 2, 3), v2;

   v2 = m * v1;
   v1 = m * v1;

   int iret = 0;
   iret |= compare(v1 == v2, true);

   return iret;
}

#define TEST(N)                                                   \
   itest = N;                                                     \
   if (test##N() == 0)                                            \
      std::cerr << " Test " << itest << "  OK " << std::endl;     \
   else {                                                         \
      std::cerr << " Test " << itest << "  FAILED " << std::endl; \
      iret += 1;                                                  \
   };

int testSMatrix()
{

   int iret = 0;
   int itest;
   TEST(1);
   TEST(2);
   TEST(3);
   TEST(4);
   TEST(5);
   TEST(6);
   TEST(7);
   TEST(8);
   TEST(9);
   TEST(10);
   TEST(11);
   TEST(12);
   TEST(13);
   TEST(14);
   TEST(15);
   TEST(16);
   TEST(17);
   TEST(18);
   TEST(19);
   TEST(20);
   TEST(21);
   TEST(22);
   TEST(23);
   TEST(24);
   TEST(25);

   return iret;
}

int main()
{
   int ret = testSMatrix();
   if (ret)
      std::cerr << "test SMatrix:\t  FAILED !!! " << std::endl;
   else
      std::cerr << "test SMatrix: \t OK " << std::endl;
   return ret;
}