About Solving Inverse Matrix

General Discussion
1

Dear FF users,

I understand that FF primarily solves linear systems of the form Ax = b . However, my current work requires explicitly computing matrix inverses — for example, A = C^{-1} D , where both C and D are matrices. Can FF support this functionality?

Wishing you all a wonderful day.

2

This can be done in two ways:

  1. With the interface with lapack if it has been installed correctly on your computer.
    You have to invoke load "lapack", then the inverse is called with ^-1. It works on an array with two indices (not on a sparse matrix), thus if you start from a sparse matrix you have to convert it to an array.
    Example (from Getting Problem to get Superconvergence results in Hybrid Higher Order (HHO) Method in Poisson Equation - #6 by fb77 HHO-reduced.edp line 91). If A is a square sparse matrix of size ns
  real[int,int] Arr(ns,ns);
  real[int,int] Arrinv(ns,ns);
  //Arr=A;//not possible in this form
  for (int i=0;i<ns;i++){
   for (int j=0;j<ns;j++){
    Arr(i,j)=A(i,j);
   }
  }
  Arrinv=Arr^-1;//inverse with lapack
  matrix Ainv=Arrinv;//recover a sparse matrix
  1. You can solve successively the system Ax=b for b base element. If A is a square sparse matrix of size ns
  matrix Ainv(ns,ns);
  for (int j=0;j<ns;j++){
   real[int] vec(ns);
   vec=0.;
   vec(j)=1.;
   real[int] solvec=A^-1*vec;
   for (int i=0;i<ns;i++){
    Ainv(i,j)=solvec(i);
   }
  }

In any case, this will be possible only if the matrix is small.