bool CalculateNativeAxis(const float* points, int count, unsigned vertex_size, vec3& r, vec3& s, vec3& t)
{
// find covariance matrix
mat3 c = CreateCovarianceMatrix(points, count, vertex_size);
// find eigen values of the covariance matrix
Math::vec3 eigen_values;
if (!EigenValues(c, eigen_values))
return (out_error() << "Can't find eigen values for matrix " << c.ToString() << std::endl, false);
// find eigen vectors of the covariance matrix
Math::vec3 eigen_vectors[3];
if (!EigenVectors(c, eigen_values, eigen_vectors))
return (out_error() << "Can't find eigen values for matrix " << c.ToString() << " with eigen values " << eigen_values.ToString() << std::endl, false);
r = eigen_vectors[0];
s = eigen_vectors[1];
t = eigen_vectors[2];
mat3 a;
a.SetColumn(0, r);
a.SetColumn(1, s);
a.SetColumn(2, t);
out_message() << "Matrix a: " << a.ToString() << std::endl;
mat3 tt = a.Transposed() * c * a;
out_message() << "Matrix tt: " << tt.ToString() << std::endl;
return true;
}
// ======================================================================
// FIXME: Add List
void Eigs(const Operator& A, int NumEigenvalues,
MultiVector& ER, MultiVector& EI)
{
if (A.GetDomainSpace() != A.GetRangeSpace())
ML_THROW("Input Operator is not square", -1);
double time;
time = GetClock();
int length = NumEigenvalues;
double tol = 1e-3;
int restarts = 1;
int output = 10;
bool PrintStatus = true;
// 1.- set parameters for Anasazi
Teuchos::ParameterList AnasaziList;
// MatVec should be either "A" or "ML^{-1}A"
AnasaziList.set("eigen-analysis: matrix operation", "A");
AnasaziList.set("eigen-analysis: use diagonal scaling", false);
AnasaziList.set("eigen-analysis: symmetric problem", false);
AnasaziList.set("eigen-analysis: length", length);
AnasaziList.set("eigen-analysis: block-size",1);
AnasaziList.set("eigen-analysis: tolerance", tol);
AnasaziList.set("eigen-analysis: restart", restarts);
AnasaziList.set("eigen-analysis: output", output);
AnasaziList.get("eigen-analysis: print current status",PrintStatus);
// data to hold real and imag for eigenvalues and eigenvectors
Space ESpace(-1, NumEigenvalues);
ER.Reshape(ESpace);
EI.Reshape(ESpace);
// this is the starting value -- random
Epetra_MultiVector EigenVectors(A.GetRowMatrix()->OperatorDomainMap(),
NumEigenvalues);
EigenVectors.Random();
#ifdef HAVE_ML_ANASAxI
//int NumRealEigenvectors, NumImagEigenvectors;
#endif
AnasaziList.set("eigen-analysis: action", "LM");
#ifdef HAVE_ML_ANASAxI
ML_THROW("fixme...", -1);
/* FIXME
ML_Anasazi::Interface(A.GetRowMatrix(),EigenVectors,ER.GetValues(),
EI.GetValues(), AnasaziList, 0, 0,
&NumRealEigenvectors, &NumImagEigenvectors, 0);
*/
#else
ML_THROW("Anasazi is no longer supported", -1);
#endif
return;
}
void EigenProblemsTest::testSyev()
{
std::cout << "--> Test: syev." <<std::endl;
// turn A to a symmetric matrix
A->randomize_sym();
*Aref = *A;
// Initialize EigenVectors with A
SP::SiconosVector EigenValues(new SiconosVector(size));
SP::SimpleMatrix EigenVectors(new SimpleMatrix(*A));
// *EigenVectors = *A;
Siconos::eigenproblems::syev(*EigenValues, *EigenVectors);
DenseVect error(size);
error *= 0.0;
for( unsigned int i = 0; i < size; ++i )
{
error.plus_assign(ublas::prod( *A->dense(), column(*EigenVectors->dense(), i) ));
error.minus_assign((*EigenValues->dense())(i)*column(*EigenVectors->dense(),i));
}
// Check ...
CPPUNIT_ASSERT_EQUAL_MESSAGE("testSyev 1: ", norm_2(error) < 10 * std::numeric_limits< double >::epsilon() , true);
// Check if A has not been modified
CPPUNIT_ASSERT_EQUAL_MESSAGE("testSyev 2: ", (*A) == (*Aref) , true);
// Now compute only eigenvalues
SP::SiconosVector RefEigenValues(new SiconosVector(*EigenValues));
*EigenVectors = *A;
*EigenValues *= 0.0;
Siconos::eigenproblems::syev(*EigenValues, *EigenVectors, false);
CPPUNIT_ASSERT_EQUAL_MESSAGE("testSyev 3: ", ((*EigenValues) - (*RefEigenValues)).norm2() < 10 * std::numeric_limits< double >::epsilon(), true);
CPPUNIT_ASSERT_EQUAL_MESSAGE("testSyev 4: ", (*A) == (*Aref) , true);
std::cout << "--> Syev test ended with success." <<std::endl;
}
