void test_boostmultiprec()
{
typedef Matrix<Real,Dynamic,Dynamic> Mat;
typedef Matrix<std::complex<Real>,Dynamic,Dynamic> MatC;
std::cout << "NumTraits<Real>::epsilon() = " << NumTraits<Real>::epsilon() << std::endl;
std::cout << "NumTraits<Real>::dummy_precision() = " << NumTraits<Real>::dummy_precision() << std::endl;
std::cout << "NumTraits<Real>::lowest() = " << NumTraits<Real>::lowest() << std::endl;
std::cout << "NumTraits<Real>::highest() = " << NumTraits<Real>::highest() << std::endl;
std::cout << "NumTraits<Real>::digits10() = " << NumTraits<Real>::digits10() << std::endl;
// chekc stream output
{
Mat A(10,10);
A.setRandom();
std::stringstream ss;
ss << A;
}
{
MatC A(10,10);
A.setRandom();
std::stringstream ss;
ss << A;
}
for(int i = 0; i < g_repeat; i++) {
int s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
CALL_SUBTEST_1( cholesky(Mat(s,s)) );
CALL_SUBTEST_2( lu_non_invertible<Mat>() );
CALL_SUBTEST_2( lu_invertible<Mat>() );
CALL_SUBTEST_2( lu_non_invertible<MatC>() );
CALL_SUBTEST_2( lu_invertible<MatC>() );
CALL_SUBTEST_3( qr(Mat(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_3( qr_invertible<Mat>() );
CALL_SUBTEST_4( qr<Mat>() );
CALL_SUBTEST_4( cod<Mat>() );
CALL_SUBTEST_4( qr_invertible<Mat>() );
CALL_SUBTEST_5( qr<Mat>() );
CALL_SUBTEST_5( qr_invertible<Mat>() );
CALL_SUBTEST_6( selfadjointeigensolver(Mat(s,s)) );
CALL_SUBTEST_7( eigensolver(Mat(s,s)) );
CALL_SUBTEST_8( generalized_eigensolver_real(Mat(s,s)) );
TEST_SET_BUT_UNUSED_VARIABLE(s)
}
CALL_SUBTEST_9(( jacobisvd(Mat(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));
CALL_SUBTEST_10(( bdcsvd(Mat(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));
}
typename GaussianProcess<TScalarType>::MatrixType GaussianProcess<TScalarType>::InvertKernelMatrix(const typename GaussianProcess<TScalarType>::MatrixType &K,
typename GaussianProcess<TScalarType>::InversionMethod inv_method = GaussianProcess<TScalarType>::FullPivotLU,
bool stable) const{
// compute core matrix
if(debug){
std::cout << "GaussianProcess::InvertKernelMatrix: inverting kernel matrix... ";
std::cout.flush();
}
typename GaussianProcess<TScalarType>::MatrixType core;
switch(inv_method){
// standard method: fast but not that accurate
// Uses the LU decomposition with full pivoting for the inversion
case FullPivotLU:{
if(debug) std::cout << " (inversion method: FullPivotLU) " << std::flush;
try{
if(stable){
core = K.inverse();
}
else{
if(debug) std::cout << " (using lapack) " << std::flush;
core = lapack::lu_invert<TScalarType>(K);
}
}
catch(lapack::LAPACKException& e){
core = K.inverse();
}
}
break;
// very accurate and very slow method, use it for small problems
// Uses the two-sided Jacobi SVD decomposition
case JacobiSVD:{
if(debug) std::cout << " (inversion method: JacobiSVD) " << std::flush;
Eigen::JacobiSVD<MatrixType> jacobisvd(K, Eigen::ComputeThinU | Eigen::ComputeThinV);
if((jacobisvd.singularValues().real().array() < 0).any() && debug){
std::cout << "GaussianProcess::InvertKernelMatrix: warning: there are negative eigenvalues.";
std::cout.flush();
}
core = jacobisvd.matrixV() * VectorType(1/jacobisvd.singularValues().array()).asDiagonal() * jacobisvd.matrixU().transpose();
}
break;
// accurate method and faster than Jacobi SVD.
// Uses the bidiagonal divide and conquer SVD
case BDCSVD:{
if(debug) std::cout << " (inversion method: BDCSVD) " << std::flush;
#ifdef EIGEN_BDCSVD_H
Eigen::BDCSVD<MatrixType> bdcsvd(K, Eigen::ComputeThinU | Eigen::ComputeThinV);
if((bdcsvd.singularValues().real().array() < 0).any() && debug){
std::cout << "GaussianProcess::InvertKernelMatrix: warning: there are negative eigenvalues.";
std::cout.flush();
}
core = bdcsvd.matrixV() * VectorType(1/bdcsvd.singularValues().array()).asDiagonal() * bdcsvd.matrixU().transpose();
#else
// this is checked, since BDCSVD is currently not in the newest release
throw std::string("GaussianProcess::InvertKernelMatrix: BDCSVD is not supported by the provided Eigen library.");
#endif
}
break;
// faster than the SVD method but less stable
// computes the eigenvalues/eigenvectors of selfadjoint matrices
case SelfAdjointEigenSolver:{
if(debug) std::cout << " (inversion method: SelfAdjointEigenSolver) " << std::flush;
try{
core = lapack::chol_invert<TScalarType>(K);
}
catch(lapack::LAPACKException& e){
Eigen::SelfAdjointEigenSolver<MatrixType> es;
es.compute(K);
VectorType eigenValues = es.eigenvalues().reverse();
MatrixType eigenVectors = es.eigenvectors().rowwise().reverse();
if((eigenValues.real().array() < 0).any() && debug){
std::cout << "GaussianProcess::InvertKernelMatrix: warning: there are negative eigenvalues.";
std::cout.flush();
}
core = eigenVectors * VectorType(1/eigenValues.array()).asDiagonal() * eigenVectors.transpose();
}
}
break;
}
if(debug) std::cout << "[done]" << std::endl;
return core;
}