./66_nonlocal/trace2.F90

ABINIT/trace2

ABINIT/trace2 [ Functions ]

NAME

 trace2

FUNCTION

 Sum indices to compute trace of rank 2 tensor gxa related to l=2
 $trace=sum_{i,j} {gxa(i,j) gmet(i,j)}$

 Copyright (C) 1998-2018 ABINIT group (DCA, XG, GMR)
 This file is distributed under the terms of the
 GNU General Public License, see ~abinit/COPYING
 or http://www.gnu.org/copyleft/gpl.txt .
 For the initials of contributors, see ~abinit/doc/developers/contributors.txt.

INPUTS

  gxa(2,6) = $sum_{G} {e^(2 \pi i G cdot t} {{f_2(|k+G|)} \over {|k+G|^2}} (k+G) cdot (k+G) C(G_{nk})}$
  gmet(3,3)=(symmetric) metric tensor in reciprocal space (bohr^-2)

OUTPUT

  trace(2)=sum_{i,j} {gxa(i,j) gmet(i,j)}$ (Re and Im).

NOTES

 Here index 6 refers to vector components
 of (k+G) but note tensor is symmetric=>only 6 components.
 The components are given in the order 11 22 33 32 31 21.
 The initial 2 handles the Re and Im parts.

PARENTS

      nonlop_pl

CHILDREN

SOURCE

37 #if defined HAVE_CONFIG_H
38 #include "config.h"
39 #endif
40 
41 #include "abi_common.h"
42 
43 
44 subroutine trace2(gxa,gmet,trace)
45 
46  use defs_basis
47 
48 !This section has been created automatically by the script Abilint (TD).
49 !Do not modify the following lines by hand.
50 #undef ABI_FUNC
51 #define ABI_FUNC 'trace2'
52 !End of the abilint section
53 
54  implicit none
55 
56 !Arguments ------------------------------------
57 !arrays
58  real(dp),intent(in) :: gmet(3,3),gxa(2,6)
59  real(dp),intent(out) :: trace(2)
60 
61 !Local variables-------------------------------
62 !scalars
63  integer :: reim
64 
65 ! *************************************************************************
66 
67 !Write out index summation, Re and Im parts
68  do reim=1,2
69    trace(reim)=gxa(reim,1)*gmet(1,1)+gxa(reim,2)*gmet(2,2)+&
70 &   gxa(reim,3)*gmet(3,3)+&
71 &   2.0d0*(gxa(reim,4)*gmet(3,2)+gxa(reim,5)*gmet(3,1)+&
72 &   gxa(reim,6)*gmet(2,1))
73  end do
74 
75 end subroutine trace2

TABLE OF CONTENTS

ABINIT/trace2 [ Functions ]