inline bool
check_pos_definite(const char* function,
const char* name,
const Eigen::LLT<Derived>& cholesky) {
if (cholesky.info() != Eigen::Success
|| !(cholesky.matrixLLT().diagonal().array() > 0.0).all())
domain_error(function, "Cholesky decomposition of", " failed", name);
return true;
}
/* ************************************************************************* */
bool choleskyPartial(Matrix& ABC, size_t nFrontal) {
const bool debug = ISDEBUG("choleskyPartial");
assert(ABC.rows() == ABC.cols());
assert(ABC.rows() >= 0 && nFrontal <= size_t(ABC.rows()));
const size_t n = ABC.rows();
// Compute Cholesky factorization of A, overwrites A.
tic(1, "lld");
Eigen::LLT<Matrix, Eigen::Upper> llt = ABC.block(0,0,nFrontal,nFrontal).selfadjointView<Eigen::Upper>().llt();
ABC.block(0,0,nFrontal,nFrontal).triangularView<Eigen::Upper>() = llt.matrixU();
toc(1, "lld");
if(debug) cout << "R:\n" << Eigen::MatrixXd(ABC.topLeftCorner(nFrontal,nFrontal).triangularView<Eigen::Upper>()) << endl;
// Compute S = inv(R') * B
tic(2, "compute S");
if(n - nFrontal > 0) {
ABC.topLeftCorner(nFrontal,nFrontal).triangularView<Eigen::Upper>().transpose().solveInPlace(
ABC.topRightCorner(nFrontal, n-nFrontal));
}
if(debug) cout << "S:\n" << ABC.topRightCorner(nFrontal, n-nFrontal) << endl;
toc(2, "compute S");
// Compute L = C - S' * S
tic(3, "compute L");
if(debug) cout << "C:\n" << Eigen::MatrixXd(ABC.bottomRightCorner(n-nFrontal,n-nFrontal).selfadjointView<Eigen::Upper>()) << endl;
if(n - nFrontal > 0)
ABC.bottomRightCorner(n-nFrontal,n-nFrontal).selfadjointView<Eigen::Upper>().rankUpdate(
ABC.topRightCorner(nFrontal, n-nFrontal).transpose(), -1.0);
if(debug) cout << "L:\n" << Eigen::MatrixXd(ABC.bottomRightCorner(n-nFrontal,n-nFrontal).selfadjointView<Eigen::Upper>()) << endl;
toc(3, "compute L");
// Check last diagonal element - Eigen does not check it
bool ok;
if(llt.info() == Eigen::Success) {
if(nFrontal >= 2) {
int exp2, exp1;
(void)frexp(ABC(nFrontal-2, nFrontal-2), &exp2);
(void)frexp(ABC(nFrontal-1, nFrontal-1), &exp1);
ok = (exp2 - exp1 < underconstrainedExponentDifference);
} else if(nFrontal == 1) {
int exp1;
(void)frexp(ABC(0,0), &exp1);
ok = (exp1 > -underconstrainedExponentDifference);
} else {
ok = true;
}
} else {
ok = false;
}
return ok;
}
void ctms_decompositions()
{
const int maxSize = 16;
const int size = 12;
typedef Eigen::Matrix<Scalar,
Eigen::Dynamic, Eigen::Dynamic,
0,
maxSize, maxSize> Matrix;
typedef Eigen::Matrix<Scalar,
Eigen::Dynamic, 1,
0,
maxSize, 1> Vector;
typedef Eigen::Matrix<std::complex<Scalar>,
Eigen::Dynamic, Eigen::Dynamic,
0,
maxSize, maxSize> ComplexMatrix;
const Matrix A(Matrix::Random(size, size));
const ComplexMatrix complexA(ComplexMatrix::Random(size, size));
const Matrix saA = A.adjoint() * A;
// Cholesky module
Eigen::LLT<Matrix> LLT; LLT.compute(A);
Eigen::LDLT<Matrix> LDLT; LDLT.compute(A);
// Eigenvalues module
Eigen::HessenbergDecomposition<ComplexMatrix> hessDecomp; hessDecomp.compute(complexA);
Eigen::ComplexSchur<ComplexMatrix> cSchur(size); cSchur.compute(complexA);
Eigen::ComplexEigenSolver<ComplexMatrix> cEigSolver; cEigSolver.compute(complexA);
Eigen::EigenSolver<Matrix> eigSolver; eigSolver.compute(A);
Eigen::SelfAdjointEigenSolver<Matrix> saEigSolver(size); saEigSolver.compute(saA);
Eigen::Tridiagonalization<Matrix> tridiag; tridiag.compute(saA);
// LU module
Eigen::PartialPivLU<Matrix> ppLU; ppLU.compute(A);
Eigen::FullPivLU<Matrix> fpLU; fpLU.compute(A);
// QR module
Eigen::HouseholderQR<Matrix> hQR; hQR.compute(A);
Eigen::ColPivHouseholderQR<Matrix> cpQR; cpQR.compute(A);
Eigen::FullPivHouseholderQR<Matrix> fpQR; fpQR.compute(A);
// SVD module
Eigen::JacobiSVD<Matrix> jSVD; jSVD.compute(A, ComputeFullU | ComputeFullV);
}
pca& pca::compute(mat samples, real eps, mat metric) {
mean_ = samples.colwise().mean().transpose();
samples.rowwise() -= mean().transpose();
Eigen::LLT< mat > llt;
if( !metric.empty() ) {
assert( metric.rows() == samples.cols() );
assert( metric.cols() == metric.rows() );
llt.compute( metric );
samples = samples * llt.matrixL();
}
math::svd svd;
svd.compute(samples, eps, Eigen::ComputeThinV );
if( !metric.empty() ) {
basis_ = llt.matrixU().solve( svd.v() );
} else {
basis_ = svd.v();
}
// surprisingly, this one works for both cases (coords = samples *
// U^{-T}) where U is the eigen basis
coords_ = samples * svd.v();
dev_ = svd.singular().cwiseAbs();
rank_ = svd.rank();
// print_vec( cumul() );
return *this;
}
inline void check_pos_definite(const char* function, const char* name,
const Eigen::LLT<Derived>& cholesky) {
if (cholesky.info() != Eigen::Success
|| !(cholesky.matrixLLT().diagonal().array() > 0.0).all())
domain_error(function, "Matrix", " is not positive definite", name);
}