./66_nonlocal/cont22.F90

ABINIT/cont22

ABINIT/cont22 [ Functions ]

NAME

 cont22

FUNCTION

 Contract symmetric rank 2 tensor gxa with itself using gmet to
 produce symmetric rank 2 tensor.

 Copyright (C) 1998-2018 ABINIT group (DXA, XG)
 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)=rank 2 complex tensor
  gmet(3,3)=real symmetric metric tensor (full storage)

OUTPUT

  rank2(6)=rank 2 real tensor (symmetric storage)

NOTES

 Symmetric gxa is stored as 11 22 33 32 31 21;
 gmet(3,3) is symmetric but stored fully (9 elements);
 output rank2 is stored as 11 22 33 32 31 21.
 Want $2 Re[contraction]$.
 $rank2(a,b)=2 Re[gxa(i,a)^"*" gmet(i,j) gxa(j,b)]$.

PARENTS

      nonlop_pl

CHILDREN

SOURCE

 38 #if defined HAVE_CONFIG_H
 39 #include "config.h"
 40 #endif
 41 
 42 #include "abi_common.h"
 43 
 44 
 45 subroutine cont22(gxa,gmet,rank2)
 46 
 47  use defs_basis
 48 
 49 !This section has been created automatically by the script Abilint (TD).
 50 !Do not modify the following lines by hand.
 51 #undef ABI_FUNC
 52 #define ABI_FUNC 'cont22'
 53 !End of the abilint section
 54 
 55  implicit none
 56 
 57 !Arguments ------------------------------------
 58 !arrays
 59  real(dp),intent(in) :: gmet(3,3),gxa(2,6)
 60  real(dp),intent(out) :: rank2(6)
 61 
 62 !Local variables-------------------------------
 63 !scalars
 64  integer,parameter :: im=2,re=1
 65 
 66 ! *************************************************************************
 67 
 68 !Simply write out index summations
 69 !a=1, b=1 in rank2(a,b) --> maps to index 1
 70  rank2(1)=2.0d0*(&
 71 & gmet(1,1)*(gxa(re,1)*gxa(re,1)+gxa(im,1)*gxa(im,1))+&
 72 & gmet(2,2)*(gxa(re,6)*gxa(re,6)+gxa(im,6)*gxa(im,6))+&
 73 & gmet(3,3)*(gxa(re,5)*gxa(re,5)+gxa(im,5)*gxa(im,5))+&
 74 & 2.0d0*(&
 75 & gmet(3,2)*(gxa(re,5)*gxa(re,6)+gxa(im,5)*gxa(im,6))+&
 76 & gmet(3,1)*(gxa(re,5)*gxa(re,1)+gxa(im,5)*gxa(im,1))+&
 77 & gmet(2,1)*(gxa(re,6)*gxa(re,1)+gxa(im,6)*gxa(im,1))))
 78 
 79 !a=2, b=2 in rank2(a,b) --> maps to index 2
 80  rank2(2)=2.0d0*(&
 81 & gmet(1,1)*(gxa(re,6)*gxa(re,6)+gxa(im,6)*gxa(im,6))+&
 82 & gmet(2,2)*(gxa(re,2)*gxa(re,2)+gxa(im,2)*gxa(im,2))+&
 83 & gmet(3,3)*(gxa(re,4)*gxa(re,4)+gxa(im,4)*gxa(im,4))+&
 84 & 2.0d0*(&
 85 & gmet(3,2)*(gxa(re,4)*gxa(re,2)+gxa(im,4)*gxa(im,2))+&
 86 & gmet(3,1)*(gxa(re,4)*gxa(re,6)+gxa(im,4)*gxa(im,6))+&
 87 & gmet(2,1)*(gxa(re,2)*gxa(re,6)+gxa(im,2)*gxa(im,6))))
 88 
 89 !a=3, b=3 in rank2(a,b) --> maps to index 3
 90  rank2(3)=2.0d0*(&
 91 & gmet(1,1)*(gxa(re,5)*gxa(re,5)+gxa(im,5)*gxa(im,5))+&
 92 & gmet(2,2)*(gxa(re,4)*gxa(re,4)+gxa(im,4)*gxa(im,4))+&
 93 & gmet(3,3)*(gxa(re,3)*gxa(re,3)+gxa(im,3)*gxa(im,3))+&
 94 & 2.0d0*(&
 95 & gmet(3,2)*(gxa(re,4)*gxa(re,3)+gxa(im,4)*gxa(im,3))+&
 96 & gmet(3,1)*(gxa(re,5)*gxa(re,3)+gxa(im,5)*gxa(im,3))+&
 97 & gmet(2,1)*(gxa(re,5)*gxa(re,4)+gxa(im,5)*gxa(im,4))))
 98 
 99 !a=3, b=2 in rank2(a,b) --> maps to index 4
100  rank2(4)=2.0d0*(&
101 & gmet(1,1)*(gxa(re,5)*gxa(re,6)+gxa(im,5)*gxa(im,6))+&
102 & gmet(2,2)*(gxa(re,4)*gxa(re,2)+gxa(im,4)*gxa(im,2))+&
103 & gmet(3,3)*(gxa(re,3)*gxa(re,4)+gxa(im,3)*gxa(im,4))+&
104 & gmet(3,2)*(gxa(re,3)*gxa(re,2)+gxa(im,3)*gxa(im,2))+&
105 & gmet(3,1)*(gxa(re,3)*gxa(re,6)+gxa(im,3)*gxa(im,6))+&
106 & gmet(2,1)*(gxa(re,4)*gxa(re,6)+gxa(im,4)*gxa(im,6))+&
107 & gmet(2,3)*(gxa(re,4)*gxa(re,4)+gxa(im,4)*gxa(im,4))+&
108 & gmet(1,3)*(gxa(re,5)*gxa(re,4)+gxa(im,5)*gxa(im,4))+&
109 & gmet(1,2)*(gxa(re,5)*gxa(re,2)+gxa(im,5)*gxa(im,2)))
110 
111 !a=3, b=1 in rank2(a,b) --> maps to index 5
112  rank2(5)=2.0d0*(&
113 & gmet(1,1)*(gxa(re,5)*gxa(re,1)+gxa(im,5)*gxa(im,1))+&
114 & gmet(2,2)*(gxa(re,4)*gxa(re,6)+gxa(im,4)*gxa(im,6))+&
115 & gmet(3,3)*(gxa(re,3)*gxa(re,5)+gxa(im,3)*gxa(im,5))+&
116 & gmet(3,2)*(gxa(re,3)*gxa(re,6)+gxa(im,3)*gxa(im,6))+&
117 & gmet(3,1)*(gxa(re,3)*gxa(re,1)+gxa(im,3)*gxa(im,1))+&
118 & gmet(2,1)*(gxa(re,4)*gxa(re,1)+gxa(im,4)*gxa(im,1))+&
119 & gmet(2,3)*(gxa(re,4)*gxa(re,5)+gxa(im,4)*gxa(im,5))+&
120 & gmet(1,3)*(gxa(re,5)*gxa(re,5)+gxa(im,5)*gxa(im,5))+&
121 & gmet(1,2)*(gxa(re,5)*gxa(re,6)+gxa(im,5)*gxa(im,6)))
122 
123 !a=2, b=1 in rank2(a,b) --> maps to index 6
124  rank2(6)=2.0d0*(&
125 & gmet(1,1)*(gxa(re,6)*gxa(re,1)+gxa(im,6)*gxa(im,1))+&
126 & gmet(2,2)*(gxa(re,2)*gxa(re,6)+gxa(im,2)*gxa(im,6))+&
127 & gmet(3,3)*(gxa(re,4)*gxa(re,5)+gxa(im,4)*gxa(im,5))+&
128 & gmet(3,2)*(gxa(re,4)*gxa(re,6)+gxa(im,4)*gxa(im,6))+&
129 & gmet(3,1)*(gxa(re,4)*gxa(re,1)+gxa(im,4)*gxa(im,1))+&
130 & gmet(2,1)*(gxa(re,2)*gxa(re,1)+gxa(im,2)*gxa(im,1))+&
131 & gmet(2,3)*(gxa(re,2)*gxa(re,5)+gxa(im,2)*gxa(im,5))+&
132 & gmet(1,3)*(gxa(re,6)*gxa(re,5)+gxa(im,6)*gxa(im,5))+&
133 & gmet(1,2)*(gxa(re,6)*gxa(re,6)+gxa(im,6)*gxa(im,6)))
134 
135 end subroutine cont22

TABLE OF CONTENTS

ABINIT/cont22 [ Functions ]