invhess: Compute the Covariance Matrix / Inverse Hessian Matrix

Description

Computes the inverse Hessian matrix. The covariance matrix is computed as a pseudo-inverse derived from the eigenvalues and eigenvectors by a singular value decomposition (get.svd()) of the Hessian matrix. Otherwise, if neither the Hessian matrix nor the eigenvalues need to be stored, the inverse Hessian can directly be computed from the contact, interaction and distance matrices.

Usage

build.invhess(svd_obj, singularity = 6)
get.cov(cm, im, deltas)

Arguments

svd_obj

svd object computed by get.svd() containing the eigenvector matrices, the eigenvalues and the index vector

singularity

number of eigenvalues equal/close to zero due to symmetries

contact map for a protein

matrix of interaction strengths between the amino acids of the protein

deltas

difference matrices (x, y, z, squared) for all pairs of $C_{\alpha}$ atoms as derived from build.contacts()

Value

Return value is the covariance matrix (also called inverse Hessian matrix).

Details

The calculation of the matrix omits by default the first six eigenvalues, because of translational and rotational symmetry in the model. The computation depends on the eigenvalues and -vectors. The number of eigenvalues to omit in the calculation can be specified by singularity. If the number of eigenvalues equalling zero is unknown and should be determined, the parameter singularity can be set to NULL. The threshold for zero is set to $10^{-8}$.

References