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Cleanup of spherical bessel functions. 

Added a routine to compute the derivativs of spherical bessel functions (used by calc_btq).
C.S.


git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@1450 c92efa57-630b-4861-b058-cf58834340f0
This commit is contained in:
sbraccia 2004-11-17 12:05:53 +00:00
parent 5f208f2c3b
commit 36c6f48b0f
3 changed files with 327 additions and 181 deletions
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1
flib/Makefile
View File

@ -22,6 +22,7 @@ scnds.o \
simpsn.o \
sort.o \
sph_bes.o \
sph_dbes.o \
transto.o \
date_and_tim.o \
sort_gvec.o \

398
flib/sph_bes.f90
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@ -1,247 +1,283 @@
!
! Copyright (C) 2001 PWSCF group
! Copyright (C) 2001-2004 PWSCF-FPMD-CP90 group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
!
!--------------------------------------------------------------------
subroutine sph_bes (msh, r, q, l, jl)
!--------------------------------------------------------------------
!----------------------------------------------------------------------------
SUBROUTINE sph_bes( msh, r, q, l, jl )
!----------------------------------------------------------------------------
!
! input:
! msh = number of grid points points
! r(1:msh)= radial grid
! q = q
! l = angular momentum (-1 <= l <= 6)
! output:
! jl(1:msh) = j_l(q*r(i)) (j_l = spherical bessel function)
! ... input:
! ... msh = number of grid points points
! ... r(1:msh)= radial grid
! ... q = q
! ... l = angular momentum (-1 <= l <= 6)
! ... output:
! ... jl(1:msh) = j_l(q*r(i)) (j_l = spherical bessel function)
!
use kinds, only: DP
implicit none
USE kinds, ONLY : DP
USE constants, ONLY : eps8
!
integer :: msh, l
real(kind=DP) :: r (msh), q, jl (msh)
IMPLICIT NONE
!
real(kind=DP), parameter :: eps = 1.d-8
integer :: ir, ir0
INTEGER :: msh, l
REAL(kind=DP) :: r(msh), q, jl(msh)
!
#if defined __MASS
real(kind=DP) :: qr(msh), sin_qr(msh), cos_qr(msh)
INTEGER :: ir, ir0
!
#if defined (__MASS)
REAL(kind=DP) :: qr(msh), sin_qr(msh), cos_qr(msh)
#endif
!
if (abs (q) < eps) then
if (l == -1) then
call errore ('sph_bes', 'j_{-1}(0) ?!?', 1)
elseif (l == 0) then
jl(:) = 1.d0
else
jl(:) = 0.d0
endif
else
if (abs (q * r (1) ) > eps) then
IF ( ABS( q ) < eps8 ) THEN
!
IF ( l == -1 ) THEN
!
CALL errore( 'sph_bes', 'j_{-1}(0) ?!?', 1 )
!
ELSE IF ( l == 0 ) THEN
!
jl(:) = 1.D0
!
ELSE
!
jl(:) = 0.D0
!
END IF
!
ELSE
!
IF ( ABS( q*r(1) ) > eps8 ) THEN
!
ir0 = 1
else
if (l == -1) then
call errore ('sph_bes', 'j_{-1}(0) ?!?', 2)
elseif (l == 0) then
jl (1) = 1.d0
else
jl (1) = 0.d0
endif
!
ELSE
!
IF (l == -1) THEN
!
CALL errore( 'sph_bes', 'j_{-1}(0) ?!?', 2 )
!
ELSE IF ( l == 0 ) THEN
!
jl(1) = 1.D0
!
ELSE
!
jl(1) = 0.D0
!
ENDIF
!
ir0 = 2
endif
if (l == - 1) then
#if defined __MASS
!
END IF
!
IF ( l == - 1 ) THEN
!
#if defined (__MASS)
!
qr = q * r
call vcos( cos_qr, qr, msh)
do ir = ir0, msh
!
CALL vcos( cos_qr, qr, msh)
!
DO ir = ir0, msh
jl (ir) = cos_qr(ir) / (q * r (ir) )
enddo
END DO
!
#else
do ir = ir0, msh
jl (ir) = cos (q * r (ir) ) / (q * r (ir) )
enddo
!
DO ir = ir0, msh
jl (ir) = COS (q * r (ir) ) / (q * r (ir) )
END DO
!
#endif
elseif (l == 0) then
#if defined __MASS
!
ELSE IF ( l == 0 ) THEN
!
#if defined (__MASS)
!
qr = q * r
call vsin( sin_qr, qr, msh)
do ir = ir0, msh
!
CALL vsin( sin_qr, qr, msh)
!
DO ir = ir0, msh
jl (ir) = sin_qr(ir) / (q * r (ir) )
enddo
END DO
!
#else
do ir = ir0, msh
jl (ir) = sin (q * r (ir) ) / (q * r (ir) )
enddo
!
DO ir = ir0, msh
jl (ir) = SIN (q * r (ir) ) / (q * r (ir) )
END DO
!
#endif
elseif (l == 1) then
#if defined __MASS
!
ELSE IF ( l == 1 ) THEN
!
#if defined (__MASS)
!
qr = q * r
call vcos( cos_qr, qr, msh)
call vsin( sin_qr, qr, msh)
do ir = ir0, msh
!
CALL vcos( cos_qr, qr, msh)
CALL vsin( sin_qr, qr, msh)
!
DO ir = ir0, msh
jl (ir) = ( sin_qr(ir) / (q * r (ir) ) - cos_qr(ir) ) / (q * r (ir) )
enddo
END DO
!
#else
do ir = ir0, msh
jl (ir) = (sin (q * r (ir) ) / (q * r (ir) ) - cos (q * r ( &
!
DO ir = ir0, msh
jl (ir) = (SIN (q * r (ir) ) / (q * r (ir) ) - COS (q * r ( &
ir) ) ) / (q * r (ir) )
enddo
END DO
!
#endif
elseif (l == 2) then
#if defined __MASS
!
ELSE IF ( l == 2 ) THEN
!
#if defined (__MASS)
!
qr = q * r
call vcos( cos_qr, qr, msh)
call vsin( sin_qr, qr, msh)
do ir = ir0, msh
!
CALL vcos( cos_qr, qr, msh)
CALL vsin( sin_qr, qr, msh)
!
DO ir = ir0, msh
jl (ir) = ( (3.d0 / (q * r (ir) ) - (q * r (ir) ) ) * sin_qr( &
ir ) - 3.d0 * cos_qr(ir) ) / (q * r (ir) ) ** 2
enddo
END DO
!
#else
do ir = ir0, msh
jl (ir) = ( (3.d0 / (q * r (ir) ) - (q * r (ir) ) ) * sin ( &
q * r (ir) ) - 3.d0 * cos (q * r (ir) ) ) / (q * r (ir) ) ** &
2
enddo
!
DO ir = ir0, msh
jl (ir) = ( (3.d0 / (q * r (ir) ) - (q * r (ir) ) ) * SIN ( &
q * r (ir) ) - 3.d0 * COS (q * r (ir) ) ) / (q * r (ir) ) ** 2
END DO
!
#endif
elseif (l == 3) then
#if defined __MASS
!
ELSE IF ( l == 3 ) THEN
!
#if defined (__MASS)
!
qr = q * r
call vcos( cos_qr, qr, msh)
call vsin( sin_qr, qr, msh)
do ir = ir0, msh
!
CALL vcos( cos_qr, qr, msh)
CALL vsin( sin_qr, qr, msh)
!
DO ir = ir0, msh
jl (ir) = (sin_qr (ir) * (15.d0 / (q * r (ir) ) &
- 6.d0 * (q * r (ir) ) ) + cos_qr (ir) * ( (q * r (ir) &
) **2 - 15.d0) ) / (q * r (ir) ) **3
enddo
ENDDO
!
#else
do ir = ir0, msh
jl (ir) = (sin (q * r (ir) ) * (15.d0 / (q * r (ir) ) &
- 6.d0 * (q * r (ir) ) ) + cos (q * r (ir) ) * ( (q * r (ir) &
) **2 - 15.d0) ) / (q * r (ir) ) **3
enddo
!
DO ir = ir0, msh
jl (ir) = (SIN (q * r (ir) ) * (15.d0 / (q * r (ir) ) &
- 6.d0 * (q * r (ir) ) ) + COS (q * r (ir) ) * ( (q * r (ir) &
) **2 - 15.d0) ) / (q * r (ir) ) ** 3
END DO
!
#endif
elseif (l == 4) then
#if defined __MASS
!
ELSE IF ( l == 4 ) THEN
!
#if defined (__MASS)
!
qr = q * r
call vcos( cos_qr, qr, msh)
call vsin( sin_qr, qr, msh)
do ir = ir0, msh
!
CALL vcos( cos_qr, qr, msh)
CALL vsin( sin_qr, qr, msh)
!
DO ir = ir0, msh
jl (ir) = (sin_qr (ir) * (105.d0 - 45.d0 * (q * r (ir) &
) **2 + (q * r (ir) ) **4) + cos_qr (ir) * (10.d0 * &
(q * r (ir) ) **3 - 105.d0 * (q * r (ir) ) ) ) / (q * r (ir) &
) **5
enddo
END DO
!
#else
do ir = ir0, msh
jl (ir) = (sin (q * r (ir) ) * (105.d0 - 45.d0 * (q * r (ir) &
) **2 + (q * r (ir) ) **4) + cos (q * r (ir) ) * (10.d0 * &
!
DO ir = ir0, msh
jl (ir) = (SIN (q * r (ir) ) * (105.d0 - 45.d0 * (q * r (ir) &
) **2 + (q * r (ir) ) **4) + COS (q * r (ir) ) * (10.d0 * &
(q * r (ir) ) **3 - 105.d0 * (q * r (ir) ) ) ) / (q * r (ir) &
) **5
enddo
END DO
!
#endif
elseif (l == 5) then
#if defined __MASS
!
ELSE IF ( l == 5 ) THEN
!
#if defined (__MASS)
!
qr = q * r
call vcos( cos_qr, qr, msh)
call vsin( sin_qr, qr, msh)
do ir = ir0, msh
!
CALL vcos( cos_qr, qr, msh )
CALL vsin( sin_qr, qr, msh )
!
DO ir = ir0, msh
jl (ir) = (-cos_qr(ir) - (945.d0*cos_qr(ir))/(q*r(ir)) ** 4 + &
(105.d0*cos_qr(ir))/ (q*r(ir)) ** 2 + &
(945.d0*sin_qr(ir))/ (q*r(ir)) ** 5 - &
(420.d0*sin_qr(ir))/(q*r(ir)) ** 3 + &
(15.d0*sin_qr(ir))/ (q*r(ir)))/(q*r(ir))
end do
END DO
!
#else
do ir = ir0, msh
jl (ir) = (-cos(q*r(ir)) - (945.d0*cos(q*r(ir)))/(q*r(ir)) ** 4 + &
(105.d0*cos(q*r(ir)))/ (q*r(ir)) ** 2 + &
(945.d0*sin(q*r(ir)))/ (q*r(ir)) ** 5 - &
(420.d0*sin(q*r(ir)))/(q*r(ir)) ** 3 + &
(15.d0*sin(q*r(ir)))/ (q*r(ir)))/(q*r(ir))
end do
!
DO ir = ir0, msh
jl (ir) = (-COS(q*r(ir)) - (945.d0*COS(q*r(ir)))/(q*r(ir)) ** 4 + &
(105.d0*COS(q*r(ir)))/ (q*r(ir)) ** 2 + &
(945.d0*SIN(q*r(ir)))/ (q*r(ir)) ** 5 - &
(420.d0*SIN(q*r(ir)))/(q*r(ir)) ** 3 + &
(15.d0*SIN(q*r(ir)))/ (q*r(ir)))/(q*r(ir))
END DO
!
#endif
elseif (l == 6) then
#if defined __MASS
!
ELSE IF ( l == 6 ) THEN
!
#if defined (__MASS)
!
qr = q * r
call vcos( cos_qr, qr, msh)
call vsin( sin_qr, qr, msh)
do ir = ir0, msh
!
CALL vcos( cos_qr, qr, msh )
CALL vsin( sin_qr, qr, msh )
!
DO ir = ir0, msh
jl (ir) = ((-10395.d0*cos_qr(ir))/(q*r(ir)) ** 5 + &
(1260.d0*cos_qr(ir))/(q*r(ir)) ** 3 - &
(21.d0*cos_qr(ir))/ (q*r(ir)) - sin_qr(ir) + &
(10395.d0*sin_qr(ir))/(q*r(ir)) ** 6 - &
(4725.d0*sin_qr(ir))/ (q*r(ir)) ** 4 + &
(210.d0*sin_qr(ir))/(q*r(ir)) ** 2)/(q*r(ir))
end do
END DO
!
#else
do ir = ir0, msh
jl (ir) = ((-10395.d0*cos(q*r(ir)))/(q*r(ir)) ** 5 + &
(1260.d0*cos(q*r(ir)))/(q*r(ir)) ** 3 - &
(21.d0*cos(q*r(ir)))/ (q*r(ir)) - sin(q*r(ir)) + &
(10395.d0*sin(q*r(ir)))/(q*r(ir)) ** 6 - &
(4725.d0*sin(q*r(ir)))/ (q*r(ir)) ** 4 + &
(210.d0*sin(q*r(ir)))/(q*r(ir)) ** 2)/(q*r(ir))
end do
!
DO ir = ir0, msh
jl (ir) = ((-10395.d0*COS(q*r(ir)))/(q*r(ir)) ** 5 + &
(1260.d0*COS(q*r(ir)))/(q*r(ir)) ** 3 - &
(21.d0*COS(q*r(ir)))/ (q*r(ir)) - SIN(q*r(ir)) + &
(10395.d0*SIN(q*r(ir)))/(q*r(ir)) ** 6 - &
(4725.d0*SIN(q*r(ir)))/ (q*r(ir)) ** 4 + &
(210.d0*SIN(q*r(ir)))/(q*r(ir)) ** 2)/(q*r(ir))
END DO
!
#endif
else
call errore ('sph_bes', 'not implemented', l)
endif
endif
!
ELSE
!
CALL errore ('sph_bes', 'not implemented', l)
!
END IF
!
END IF
!
return
end subroutine sph_bes
RETURN
!
END SUBROUTINE sph_bes

109
flib/sph_dbes.f90 Normal file
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@ -0,0 +1,109 @@
!
! Copyright (C) 2001-2004 PWSCF-FPMD-CP90 group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
!----------------------------------------------------------------------------
SUBROUTINE sph_dbes( MMAX, R, XG, L, DJL )
!----------------------------------------------------------------------------
!
! ... calculates derivatives of spherical bessel functions j_l(Gr)
! ... with respect to h_alpha,beta (without the factor GAGK(KK,IG)*HTM1)
! ... i.e. -x * D(jl(x))/dx
!
USE kinds, ONLY : DP
USE constants, ONLY : eps8
!
IMPLICIT NONE
!
INTEGER :: MMAX, L
REAL(KIND=DP) :: XG
REAL(KIND=DP) :: DJL(MMAX), R(MMAX)
!
INTEGER :: IR
REAL(KIND=DP) :: XRG, XRG2
!
!
IF ( L == 1 ) THEN ! S PART
IF( XG < eps8 ) THEN
DO IR=1,MMAX
DJL(IR) = 0.D0
END DO
ELSE
DJL(1) = 0.D0
DO IR=2,MMAX
XRG=R(IR)*XG
DJL(IR) = SIN(XRG)/XRG-COS(XRG)
END DO
ENDIF
ENDIF
!
IF ( L == 2 ) THEN ! P PART
IF( XG < eps8 ) THEN
DO IR=1,MMAX
DJL(IR) = 0.D0
END DO
ELSE
DJL(1) = 0.D0
DO IR=2,MMAX
XRG=R(IR)*XG
DJL(IR) = 2.D0*(SIN(XRG)/XRG-COS(XRG))/XRG - SIN(XRG)
END DO
ENDIF
ENDIF
!
IF ( L == 3 ) THEN ! D PART
IF ( XG < eps8 ) THEN
DO IR=1,MMAX
DJL(IR) = 0.D0
END DO
ELSE
DJL(1) = 0.D0
DO IR=2,MMAX
XRG=R(IR)*XG
DJL(IR) = ( SIN(XRG)*(9.D0/(XRG*XRG)-4.D0) - &
9.D0*COS(XRG)/XRG ) /XRG + COS(XRG)
END DO
END IF
END IF
!
IF ( L == 4 ) THEN ! F PART
IF ( XG < eps8 ) THEN
DO IR=1,MMAX
DJL(IR) = 0.D0
END DO
ELSE
DJL(1) = 0.D0
DO IR=2,MMAX
XRG=R(IR)*XG
XRG2=XRG*XRG
DJL(IR) = SIN(XRG)*(60.D0/(XRG2*XRG2)-27.D0/XRG2+1.d0) - &
COS(XRG)*(60.D0/XRG2-7.D0)/XRG
END DO
END IF
END IF
!
IF ( L == 5 ) THEN ! G PART
IF ( XG < eps8 ) THEN
DO IR=1,MMAX
DJL(IR) = 0.D0
END DO
ELSE
DJL(1) = 0.D0
DO IR=2,MMAX
XRG=R(IR)*XG
XRG2=XRG*XRG
DJL(IR) = SIN(XRG)*(525.D0/(XRG2*XRG2)-240.D0/XRG2+11.D0)/XRG - &
COS(XRG)*(525.D0/(XRG2*XRG2)-65.D0/XRG2+1.D0)
END DO
END IF
END IF
!
IF ( L <= 0 .OR. L >= 6 ) &
CALL errore( 'sph_dbes', ' L NOT PROGRAMMED, L= ',L )
!
RETURN
!
END SUBROUTINE sph_dbes