./64_psp/der

ABINIT/der_int

ABINIT/der_int [ Functions ]

NAME

 der_int

FUNCTION

 Given input function f(i) on Teter radial grid, and grid spacing
 dr(i), compute function derivative df/dr on points from 0 to n.
 Integrate function f(i) on grid r(i) from r(0) to r(nlast).
 Note that array dimensions start at 0.

 Copyright (C) 1998-2017 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

  f(0 to nlast)=function values on grid
  r(0 to nlast)=radial grid points
  dr(0 to nlast)=INVERSE of spacing on grid
  nlast=radial grid point for upper limit

OUTPUT

  df(0 to n)=derivative $ \frac{df}{dr}$ on grid
  smf= $ \int_{r(0)}^{r(nlast)} f(r) dr $.

PARENTS

      psp1lo,psp1nl

CHILDREN

SOURCE

 36 #if defined HAVE_CONFIG_H
 37 #include "config.h"
 38 #endif
 39 
 40 #include "abi_common.h"
 41 
 42 
 43 subroutine der_int(ff,df,rr,dr,nlast,smf)
 44 
 45  use defs_basis
 46  use m_errors
 47  use m_profiling_abi
 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 'der_int'
 53 !End of the abilint section
 54 
 55  implicit none
 56 
 57 !Arguments ------------------------------------
 58 !nmax sets standard number of grid points ! SHOULD BE REMOVED
 59 !scalars
 60  integer,parameter :: nmax=2000
 61  integer,intent(in) :: nlast
 62  real(dp),intent(out) :: smf
 63 !no_abirules
 64 !Note that dimension here starts at 0
 65  real(dp), intent(in) :: dr(0:nmax),ff(0:nmax),rr(0:nmax)
 66  real(dp), intent(out) :: df(0:nmax)
 67 
 68 !Local variables-------------------------------
 69 !scalars
 70  integer :: jj
 71  real(dp),parameter :: div12=1.d0/12.d0
 72  real(dp) :: hh
 73  character(len=500) :: message
 74 
 75 ! *************************************************************************
 76 
 77 !Check that nlast lie within 0 to nmax
 78  if (nlast<0.or.nlast>nmax) then
 79    write(message, '(a,i12,a,i12)' )&
 80 &   ' nlast=',nlast,' lies outside range [0,nmax] with dimension nmax=',nmax
 81    MSG_BUG(message)
 82  end if
 83 
 84 !Compute derivatives at lower end, near r=0
 85  df(0)=-25.d0/12.d0*ff(0)+4.d0*ff(1)-3.d0*ff(2)+4.d0/3.d0*ff(3)&
 86 & -1.d0/4.d0*ff(4)
 87  df(1)=-1.d0/4.d0*ff(0)-5.d0/6.d0*ff(1)+3.d0/2.d0*ff(2)&
 88 & -1.d0/2.d0*ff(3)+1.d0/12.d0*ff(4)
 89 
 90 !Run over range from just past r=0 to near r(n), using central differences
 91  do jj=2,nlast-2
 92    df(jj)=(ff(jj-2)-8.d0*(ff(jj-1)-ff(jj+1))-ff(jj+2))*div12
 93  end do
 94 
 95 !Compute derivative at upper end of range
 96  if (nlast < 4) then 
 97    message = ' der_int: ff does not have enough elements. nlast is too low'
 98    MSG_ERROR(message)
 99  end if
100 
101  df(nlast-1)=-1.d0/12.d0*ff(nlast-4)&
102 & +1.d0/2.d0*ff(nlast-3)&
103 & -3.d0/2.d0*ff(nlast-2)&
104 & +5.d0/6.d0*ff(nlast-1)&
105 & +1.d0/4.d0*ff(nlast)
106  df(nlast)=1.d0/4.d0*ff(nlast-4)&
107 & -4.d0/3.d0*ff(nlast-3)&
108 & +3.d0*ff(nlast-2)&
109 & -4.d0*ff(nlast-1)&
110 & +25.d0/12.d0*ff(nlast)
111 
112 !Apply correct normalization over full range
113  do jj=0,nlast
114    df(jj)=df(jj)*dr(jj)
115  end do
116 
117  smf=0.d0
118  do jj=0,nlast-1
119    hh=rr(jj+1)-rr(jj)
120    smf=smf+hh*(6.d0*(ff(jj)+ff(jj+1))+hh*(df(jj)-df(jj+1)))
121  end do
122  smf=smf/12.d0
123 
124 end subroutine der_int

TABLE OF CONTENTS

ABINIT/der_int [ Functions ]