Thanks for your input.
In the meantime, I replaced the matrix multiplication
res = A^_{-1}*B
by solving 'p' linear systems
A*res[p] = B[p],
where p is the number of columns of the matrix B.
" That's one way to go. FullMatrix::gauss_jordan() also computes the
inverse of a matrix."
As stated, what I tried is to use the operator= according to
LAPACKFullMatrix<double> new_matrix = my_system_matrix .
However, there is an error message
"error: conversion from ‘dealii::SparseMatrix<double>’ to non-scalar type
‘dealii::LAPACKFullMatrix<double>’ requested
LAPACKFullMatrix<double> new_matrix = tangent_matrix"
How can I fix this?
Best
Simon
Am Mo., 22. Aug. 2022 um 08:45 Uhr schrieb Wolfgang Bangerth <
bange...@colostate.edu>:
> On 8/19/22 13:14, Simon Wiesheier wrote:
> >
> > I also need the system matrix A for a second purpose, namely
> > to compute a matrix multiplication:
> > res = A^{-1} * B ,
> > where B is another matrix.
> > -To be more precise, I need the inverse of the 19x19 submatrix
> > corresponding to the unconstrained DoFs only -- not the inverse of the
> > full system matrix..
>
> Right. But the inverse of the 19x19 matrix is the 19x19 subblock of the
> 20x20 big matrix. That's because after zeroing out the row and column,
> you have a block diagonal matrix where the inverse of the matrix
> consists of the inverses of the individual blocks.
>
> > I could not find a function which computes the inverse of a sparse
> > matrix directly (without solving a linear system).
> > What I tried is,
> > LAPACKFullMatrix<double> new_matrix = my_system_matrix ,
> > thence calling the invert function.
> > But I am not sure if this is the right way to go.
>
> That's one way to go. FullMatrix::gauss_jordan() also computes the
> inverse of a matrix.
>
>
> > -Also, after calling constraints.distribute_local_to_global(),
> > does it make sense at all to compute an inverse matrix, given that some
> > rows and columns were set to zero?
>
> Yes -- as mentioned above, you should consider the resulting matrix as
> block diagonal.
>
> Best
> W.
>
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: bange...@colostate.edu
> www: http://www.math.colostate.edu/~bangerth/
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