void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2)
{
typedef typename NumTraits<typename VectorType::Scalar>::Real RealScalar;
VERIFY(vec1.cols() == 1);
VERIFY(vec2.cols() == 1);
VERIFY(vec1.rows() == vec2.rows());
for (int k = 1; k <= vec1.rows(); ++k)
{
VERIFY_IS_APPROX(vec1.array().pow(RealScalar(k)).sum(), vec2.array().pow(RealScalar(k)).sum());
}
}
template<typename VectorType> void lpNorm(const VectorType& v)
{
VectorType u = VectorType::Random(v.size());
VERIFY_IS_APPROX(u.template lpNorm<Infinity>(), u.cwiseAbs().maxCoeff());
VERIFY_IS_APPROX(u.template lpNorm<1>(), u.cwiseAbs().sum());
VERIFY_IS_APPROX(u.template lpNorm<2>(), internal::sqrt(u.array().abs().square().sum()));
VERIFY_IS_APPROX(internal::pow(u.template lpNorm<5>(), typename VectorType::RealScalar(5)), u.array().abs().pow(5).sum());
}
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;
}
static ScalarType asum(std::size_t /*N*/, VectorType const & x)
{ return x.array().abs().sum(); }
void ContinuousAction::Unnormalize( const VectorType& scales,
const VectorType& offsets )
{
output = ( output.array() * scales.array() ).matrix() + offsets;
}
void ContinuousAction::Normalize( const VectorType& scales,
const VectorType& offsets )
{
output = ( ( output - offsets ).array() / scales.array() ).matrix();
}
