block_matrix_sqrt()

template<typename WRootMat >

void stan::math::internal::block_matrix_sqrt ( WRootMat &  W_root, const Eigen::SparseMatrix< double > &  W, const Eigen::Index  block_size  )

inline

Returns the principal square root of a symmetric positive semi-definite block diagonal matrix.

Each block is symmetrised and decomposed with a symmetric eigensolver. Eigenvalues that are negative only at rounding level, as the zero eigenvalues of a rank-deficient block are (for example the negative Hessian of a likelihood with more latent variables than observations), are clamped to zero. An eigenvalue below -block_size * epsilon * max(|eigenvalues|) means the block is not positive semi-definite.

Template Parameters

WRootMat

A type inheriting from Eigen::EigenBase.

Parameters

W_root	The output matrix to store the square root.
W	The input block diagonal matrix.
block_size	The size of each block in the block diagonal matrix.

Exceptions

std::domain_error

if a block has non-finite entries or is not positive semi-definite.

Definition at line 242 of file laplace_marginal_density_estimator.hpp.