./32_util/sbf8.F90

ABINIT/sbf8

ABINIT/sbf8 [ Functions ]

NAME

 sbf8

FUNCTION

 Computes set of spherical bessel functions using accurate algorithm
 based on downward recursion in order and normalization sum.
 Power series used at small arguments.

 Copyright (C) 1998-2017 ABINIT group (DRH)
 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

  nm=maximum angular momentum wanted + one 
  xx=argument of sbf

OUTPUT

  sb_out(nm)=values of spherical bessel functions for l=0,nm-1

PARENTS

      posdoppler,psp8nl,qijb_kk,qmc_prep_ctqmc,smatrix_pawinit

CHILDREN

SOURCE

 32 #if defined HAVE_CONFIG_H
 33 #include "config.h"
 34 #endif
 35 
 36 #include "abi_common.h"
 37 
 38 subroutine sbf8(nm,xx,sb_out)
 39 
 40  use defs_basis
 41  use m_profiling_abi
 42 
 43 !This section has been created automatically by the script Abilint (TD).
 44 !Do not modify the following lines by hand.
 45 #undef ABI_FUNC
 46 #define ABI_FUNC 'sbf8'
 47 !End of the abilint section
 48 
 49  implicit none
 50 
 51 !Arguments----------------------------------------------------------
 52 !scalars
 53  integer,intent(in) :: nm
 54  real(dp),intent(in) :: xx
 55 !arrays
 56  real(dp),intent(out) :: sb_out(nm)
 57 
 58 !Local variables-------------------------------
 59 !scalars
 60  integer :: nlim,nn
 61  real(dp) :: fn,sn,xi,xn,xs
 62 !arrays
 63  real(dp),allocatable :: sb(:)
 64 
 65 ! *************************************************************************
 66 
 67  if(xx<= 1.0e-36_dp) then
 68 !  zero argument section
 69    sb_out(:)=zero
 70    sb_out(1)=one
 71  else if(xx<1.e-3_dp) then
 72 !  small argument section
 73    xn=one
 74    xs=half*xx**2
 75    do nn=1,nm
 76      sb_out(nn)=xn*(one - xs*(one - xs/(4*nn+6))/(2*nn+1))
 77      xn=xx*xn/(2*nn+1)
 78    end do
 79  else
 80 !  recursion method
 81    if(xx<one) then
 82      nlim=nm+int(15.0e0_dp*xx)+1
 83    else
 84      nlim=nm+int(1.36e0_dp*xx)+15
 85    end if
 86    ABI_ALLOCATE(sb,(nlim+1))
 87    nn=nlim
 88    xi=one/xx
 89    sb(nn+1)=zero
 90    sb(nn)=1.e-18_dp
 91    sn=dble(2*nn-1)*1.e-36_dp
 92    do nn=nlim-1,1,-1
 93      sb(nn)=dble(2*nn+1)*xi*sb(nn+1) - sb(nn+2)
 94    end do
 95    do nn=1,nlim-1
 96      sn=sn + dble(2*nn-1)*sb(nn)*sb(nn)
 97    end do
 98    fn=1.d0/sqrt(sn)
 99    sb_out(:)=fn*sb(1:nm)
100    ABI_DEALLOCATE(sb)
101  end if
102 
103 end subroutine sbf8

TABLE OF CONTENTS

ABINIT/sbf8 [ Functions ]