./32_util/mati3inv.F90

ABINIT/mati3inv

ABINIT/mati3inv [ Functions ]

NAME

 mati3inv

FUNCTION

 Invert and transpose orthogonal 3x3 matrix of INTEGER elements.

 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 .

INPUTS

 mm = integer matrix to be inverted

OUTPUT

 mit = inverse of mm input matrix

NOTES

 Used for symmetry operations.
 This routine applies to ORTHOGONAL matrices only.
 Since these form a group, inverses are also integer
 arrays.  Returned array is TRANSPOSE of inverse, as needed.
 Note use of integer arithmetic.

PARENTS

      cg_rotate,chkgrp,classify_bands,debug_tools,dfpt_nstdy,get_full_kgrid
      get_npert_rbz,getkgrid,ingeo,m_ab7_symmetry,m_crystal,m_ddb,m_dvdb
      m_dynmat,m_fft_mesh,m_fock,m_ptgroups,m_tdep_sym,matpointsym
      memory_eval,optic,read_gkk,setsym,strainsym,thmeig,wfconv

CHILDREN

SOURCE

 38 #if defined HAVE_CONFIG_H
 39 #include "config.h"
 40 #endif
 41 
 42 #include "abi_common.h"
 43 
 44 subroutine mati3inv(mm,mit)
 45 
 46  use defs_basis
 47  use m_profiling_abi
 48  use m_errors
 49 
 50 !This section has been created automatically by the script Abilint (TD).
 51 !Do not modify the following lines by hand.
 52 #undef ABI_FUNC
 53 #define ABI_FUNC 'mati3inv'
 54 !End of the abilint section
 55 
 56  implicit none
 57 
 58 !Arguments ------------------------------------
 59 !arrays
 60  integer,intent(in) :: mm(3,3)
 61  integer,intent(out) :: mit(3,3)
 62 
 63 !Local variables-------------------------------
 64 !scalars
 65  integer :: dd
 66  character(len=500) :: message
 67 !arrays
 68  integer :: tt(3,3)
 69 
 70 ! *************************************************************************
 71 
 72  tt(1,1) = mm(2,2) * mm(3,3) - mm(3,2) * mm(2,3)
 73  tt(2,1) = mm(3,2) * mm(1,3) - mm(1,2) * mm(3,3)
 74  tt(3,1) = mm(1,2) * mm(2,3) - mm(2,2) * mm(1,3)
 75  tt(1,2) = mm(3,1) * mm(2,3) - mm(2,1) * mm(3,3)
 76  tt(2,2) = mm(1,1) * mm(3,3) - mm(3,1) * mm(1,3)
 77  tt(3,2) = mm(2,1) * mm(1,3) - mm(1,1) * mm(2,3)
 78  tt(1,3) = mm(2,1) * mm(3,2) - mm(3,1) * mm(2,2)
 79  tt(2,3) = mm(3,1) * mm(1,2) - mm(1,1) * mm(3,2)
 80  tt(3,3) = mm(1,1) * mm(2,2) - mm(2,1) * mm(1,2)
 81  dd  = mm(1,1) * tt(1,1) + mm(2,1) * tt(2,1) + mm(3,1) * tt(3,1)
 82 
 83 !Make sure matrix is not singular
 84  if (dd/=0) then
 85    mit(:,:)=tt(:,:)/dd
 86  else
 87    write(message, '(2a,2x,9i5,a)' )&
 88 &   ' Attempting to invert integer array',ch10,&
 89 &   mm(:,:),'   ==> determinant is zero.'
 90    MSG_BUG(message)
 91  end if
 92 
 93 !If matrix is orthogonal, determinant must be 1 or -1
 94  if (abs(dd)/=1) then
 95    write(message, '(2a,2x,9i5,a)' )&
 96 &   ' Absolute value of determinant should be one',ch10,&
 97 &   ' but determinant=',dd
 98    MSG_BUG(message)
 99  end if
100 
101 
102 end subroutine mati3inv

TABLE OF CONTENTS

ABINIT/mati3inv [ Functions ]