Fix and improvement of the Slater potential

Description

Fix some problems with the Slater potential and improve the numerical stability for the case of singular matrices. This implies a local rotation to the frame for which the spin-density matrix is singular, and to solve the Sylvester equation in the local frame, and to set the last, undefined, component of the exchange potential to zero.

News snippet

Fix some problems with the Slater potential and improve the numerical stability for the case of singular matrices.

Checklist

• I have checked that my code follows the Octopus coding standards
• I have added tests for all the new features added in this request.

testsuite/finite_systems_3d/35-slater_x.test

@@ -8,8 +8,8 @@ Enabled    : Yes
 Input: 35-slater_x.01-gs.inp
 match ; SCF convergence ; GREPCOUNT(static/info, 'SCF converged') ; 1
 Precision: 0.00011
-match ; Total energy     ; GREPFIELD(static/info, 'Total       =', 3) ; -14.99120381
-match ; Exchange energy  ; GREPFIELD(static/info, 'Exchange    =', 3) ; -2.51772271
+match ; Total energy     ; GREPFIELD(static/info, 'Total       =', 3) ; -14.99126765
+match ; Exchange energy  ; GREPFIELD(static/info, 'Exchange    =', 3) ; -2.51774829
 match ; Eigenvalue   [1 up] ; GREPFIELD(static/info, '1   up', 3) ; -0.896475
 match ; Eigenvalue   [1 dn] ; GREPFIELD(static/info, '1   dn', 3) ; -1.063294
 match ; Eigenvalue   [4 up] ; GREPFIELD(static/info, '4   up', 3) ; -0.458220
@@ -18,20 +18,20 @@ match ; Eigenvalue   [4 dn] ; GREPFIELD(static/info, '4   dn', 3) ; -0.614222
 Input: 35-slater_x.02-gs_spinors.inp
 match ; SCF convergence ; GREPCOUNT(static/info, 'SCF converged') ; 1
 Precision: 0.00011
-match ; Total energy     ; GREPFIELD(static/info, 'Total       =', 3) ; -14.59403412
-match ; Exchange energy  ; GREPFIELD(static/info, 'Exchange    =', 3) ; -2.12053211
+match ; Total energy     ; GREPFIELD(static/info, 'Total       =', 3) ; -14.59427926
+match ; Exchange energy  ; GREPFIELD(static/info, 'Exchange    =', 3) ; -2.12078547
 match ; Eigenvalue   [1] ; GREPFIELD(static/info, '1   --', 3) ; -1.063289
-match ; Sx           [1] ; GREPFIELD(static/info, '1   --', 5) ; -0.0001
+match ; Sx           [1] ; GREPFIELD(static/info, '1   --', 5) ;  0.0002
 match ; Sy           [1] ; GREPFIELD(static/info, '1   --', 6) ;  0.0000
 match ; Sz           [1] ; GREPFIELD(static/info, '1   --', 7) ;  0.5000
 
 match ; Eigenvalue   [4] ; GREPFIELD(static/info, '4   --', 3) ; -0.614217
-match ; Sx           [4] ; GREPFIELD(static/info, '4   --', 5) ; -0.0001
+match ; Sx           [4] ; GREPFIELD(static/info, '4   --', 5) ;  0.0002
 match ; Sy           [4] ; GREPFIELD(static/info, '4   --', 6) ;  0.0000
 match ; Sz           [4] ; GREPFIELD(static/info, '4   --', 7) ;  0.5000
 
 match ; Eigenvalue   [6] ; GREPFIELD(static/info, '6   --', 3) ; -0.458229
-match ; Sx           [6] ; GREPFIELD(static/info, '6   --', 5) ;  0.0001
+match ; Sx           [6] ; GREPFIELD(static/info, '6   --', 5) ; -0.0002
 match ; Sy           [6] ; GREPFIELD(static/info, '6   --', 6) ;  0.0000
 match ; Sz           [6] ; GREPFIELD(static/info, '6   --', 7) ; -0.5000