Hello everyone,
Is there a reliable way to get the natural logarithm of a symmetric
positive definite tensor in deal.ii? I'm trying
`LAPACKFullMatrix.compute_eigenvalues_symmetric`, taking the `std::log` of
the eigenvalues and then multiplying by the eigenvectors appropriately:
const SymmetricTensor<2, dim, Number> symmetric_positive_definite_t;
LAPACKFullMatrix<Number> lapack_full_matrix(dim, dim);
for(unsigned int i=0; i<dim; ++i)
for(unsigned int j=0; j<dim; ++j)
lapack_full_matrix.set(i, j, symmetric_positive_definite_t[i][j]);
Vector<Number> eigenvalues(dim);
FullMatrix<Number> eigenvectors(dim, dim);
lapack_full_matrix.compute_eigenvalues_symmetric(
-symmetric_positive_definite_t.norm(), symmetric_positive_definite_t.norm
(), 0, eigenvalues, eigenvectors);
FullMatrix<Number> diag_log_eigenvalues(dim, dim);
for(unsigned int i=0; i<dim; ++i) {
diag_log_eigenvalues(i, i) = std::log(eigenvalues(i));
}
FullMatrix<Number> Q_log_lambda(dim, dim);
eigenvectors.mmult(Q_log_lambda, diag_log_eigenvalues);
FullMatrix<Number> Q_log_lambda_Qt(dim, dim);
Q_log_lambda.mTmult(Q_log_lambda_Qt, eigenvectors);
SymmetricTensor<2, dim, Number> log_symmetric_positive_definite_t;
for(unsigned int i=0; i<dim; ++i)
for(unsigned int j=0; j<dim; ++j) {
log_symmetric_positive_definite_t[i][j] = Q_log_lambda_Qt(i, j);
}
But this is not reliable, as I've run into situations where the returned
eigenvalues are fewer than `dim` (I'm not sure how
`compute_eigenvalues_symmetric` treats repeated eigenvalues). I've looked
at using `compute_svd`, but it seems to me that I could only access the
`singular_value`s that way, but not the `svd_u` and `svd_vt` matrices.
Thanks,
Maien
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