mod_sparse_matrices¶

Lines: 28 | Visibility: private

Procedures performing math on sparse matrices. author: Moritz R. Schaefer

Dependencies¶

Uses

Used By

Procedures Summary¶

Name	Type	Description
`derived_matrix_and_eigenvectors_to_derived_eigenval`	Subroutine	Compute the derivative of the eigenvalues of an matrix A, given dA and the corresponding...

Procedure Details¶

subroutine derived_matrix_and_eigenvectors_to_derived_eigenval¶

subroutine derived_matrix_and_eigenvectors_to_derived_eigenval( &
    num_at_orb, &
    norb, &
    non_zero_slice, &
    tmp, &
    num_eigenvec, &
    relevant_eigenvectors, &
    lower, &
    upper, &
    derivative_value &
)

Compute the derivative of the eigenvalues of an matrix A, given dA and the corresponding eigenvectors.

The derivatives of the eigenvalues of a matrix A are given by the the diagonal of I ° (UT dA U). This routine computes I ° (UT dA U) if dA is sparse matrix which allows the following definition: tmp = dA U = non-zero-columns(num_at_orb, :)T U + non-zero-columns(:, num_at_orb)U(rele:vant, :) Where U stores the eigenvectors of A (note the lacking d). Only the non-zero-columns have to be provided. Afterwards we compute I ° (UT tmp) as U_i * tmp for all i. Which gives us the derivatives of the eigenvalues.

Arguments

num_at_orb : integer [in]
norb : integer [in]
non_zero_slice : real(DP) (dim: (norb,num_at_orb)) [in]
tmp : real(DP) (dim: (norb,num_eigenvec)) [inout]
num_eigenvec : integer [in]
relevant_eigenvectors : real(DP) (dim: (norb,num_eigenvec)) [in]
lower : integer [in]– the lower idx of eigenvetors on which non-zero-rows have an effect
upper : integer [in]– the upper idx of eigenvetors on which non-zero-rows have an effect
derivative_value : real(DP) (dim: (num_eigenvec)) [out]

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