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ddcosmo.f90
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ddcosmo.f90
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module ddcosmo
implicit none
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!
! 888 888 .d8888b. .d88888b. .d8888b. 888b d888 .d88888b.
! 888 888 d88P Y88b d88P" "Y88b d88P Y88b 8888b d8888 d88P" "Y88b
! 888 888 888 888 888 888 Y88b. 88888b.d88888 888 888
! .d88888 .d88888 888 888 888 "Y888b. 888Y88888P888 888 888
! d88" 888 d88" 888 888 888 888 "Y88b. 888 Y888P 888 888 888
! 888 888 888 888 888 888 888 888 "888 888 Y8P 888 888 888
! Y88b 888 Y88b 888 Y88b d88P Y88b. .d88P Y88b d88P 888 " 888 Y88b. .d88P
! "Y88888 "Y88888 "Y8888P" "Y88888P" "Y8888P" 888 888 "Y88888P"
!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! COPYRIGHT (C) 2015 by Filippo Lipparini, Benjamin Stamm, Paolo Gatto !
! Eric Cancès, Yvon Maday, Jean-Philip Piquemal, Louis Lagardère and !
! Benedetta Mennucci. !
! ALL RIGHT RESERVED. !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!
! A modular implementation of COSMO using a domain decomposition linear scaling
! strategy.
!
! This code is governed by the LGPL license and abiding by the rules of
! distribution of free software.
! This program is distributed in the hope that it will be useful, but
! WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
! or FITNESS FOR A PARTICULAR PURPOSE.
! See the GNU Lesser General Public License for more details.
!
! Users of this code are asked to include the following references in their
! publications:
!
! [1] E. Cancès, Y. Maday, B. Stamm
! "Domain decomposition for implicit solvation models"
! J. Chem. Phys. 139, 054111 (2013)
!
! [2] F. Lipparini, B. Stamm, E. Cancès, Y. Maday, B. Mennucci
! "Fast Domain Decomposition Algorithm for Continuum Solvation Models:
! Energy and First Derivatives"
! J. Chem. Theory Comput. 9, 3637–3648 (2013)
!
! Also, include one of the three following reference depending on whether you
! use this code in conjunction with a QM [3], Semiempirical [4] or Classical [5]
! description of the solute:
!
! [3] F. Lipparini, G. Scalmani, L. Lagardère, B. Stamm, E. Cancès, Y. Maday,
! J.-P. Piquemal, M. J. Frisch, B. Mennucci
! "Quantum, classical, and hybrid QM/MM calculations in solution: General
! implementation of the ddCOSMO linear scaling strategy"
! J. Chem. Phys. 141, 184108 (2014)
! (for quantum mechanical models)
!
! [4] F. Lipparini, L. Lagardère, G. Scalmani, B. Stamm, E. Cancès, Y. Maday,
! J.-P. Piquemal, M. J. Frisch, B. Mennucci
! "Quantum Calculations in Solution for Large to Very Large Molecules:
! A New Linear Scaling QM/Continuum Approach"
! J. Phys. Chem. Lett. 5, 953-958 (2014)
! (for semiempirical models)
!
! [5] F. Lipparini, L. Lagardère, C. Raynaud, B. Stamm, E. Cancès, B. Mennucci
! M. Schnieders, P. Ren, Y. Maday, J.-P. Piquemal
! "Polarizable Molecular Dynamics in a Polarizable Continuum Solvent"
! J. Chem. Theory Comput. 11, 623-634 (2015)
! (for classical models, including polarizable force fields
!
! The users of this code should also include the appropriate reference to the
! COSMO model. This distribution includes the routines to generate lebedev
! grids by D. Laikov and C. van Wuellen, as publicly available on CCL. If the
! routines are used, the following reference should also be included:
!
! [6] V.I. Lebedev, and D.N. Laikov
! "A quadrature formula for the sphere of the 131st
! algebraic order of accuracy"
! Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
!
! Written by Filippo Lipparini, October 2015.
!
!-------------------------------------------------------------------------------
!
!
! - numerical constants
!
integer, parameter :: ndiis=25, iout=6, nngmax=100
real*8, parameter :: zero=0.d0, pt5=0.5d0, one=1.d0, two=2.d0, four=4.d0
real*8, parameter :: se = -1.0d0
!
! - numerical constants explicitly computed
!
real*8 :: pi, sq2
!
! - quantities contained in control file
!
! iprint - printing flag
! nproc - number of openMP threads ; 0) no parallelization
! lmax - max angular momentum of spherical harmonics basis
! ngrid - desired number of Lebedev integration points
! iconv - threshold for iterative solver ( 10^-iconv )
! igrad - 1) compute forces ; 0) do not compute forces
! eps - dielectric constant of the solvent
! eta - regularization parameters
!
integer :: iprint, nproc, lmax, ngrid, iconv, igrad
real*8 :: eps, eta
!
! - other quantities
!
! nsph - number of spheres/atoms
! ncav - number of integration points on cavity's boundary
! nylm - number of basis functions, i.e., spherical harmonics
!
integer :: nsph, ncav, nylm
!
! - workspaces
!
integer, allocatable :: inl(:), nl(:)
real*8, allocatable :: rsph(:), csph(:,:), ccav(:,:)
real*8, allocatable :: w(:), grid(:,:), basis(:,:)
real*8, allocatable :: fact(:), facl(:), facs(:)
real*8, allocatable :: fi(:,:), ui(:,:), zi(:,:,:)
!
! - miscellanea
!
logical :: grad
!
! - subroutines & functions
! =========================
!
! ddinit - initialize data structure
! memfree - free data structure
! sprod - scalar product
! fsw - switch function
! dfsw - derivative of switch function
! ptcart - print routine
! prtsph - print routine
! intrhs - integrate spherical harmonics expansion
! ylmbas - compute spherical harmonics Y_l^m
! dbasis - compute derivatives of spherical harmonics
! polleg - compute Legendre polynomials
! trgev - service routine for computation of spherical harmonics
! intmlp - compute quantity needed for COSMO action
! wghpot - weigh potential at cavity points
! hsnorm - compute H-norm on unit sphere
! adjrhs - auxiliary routine for COSMO adjoint action
! header - print header
! fdoka - compute the first part of <S,L^(x)X>
! fdokb - compute the the second part of <S,L^(x)X>
! fdoga - compute the U^(x)\Phi contribution to <S,g^(x)>
! calcv - auxiliary routine for COSMO action
! ddmkxi - compute the xi intermediate
!
contains
!
!
!--------------------------------------------------------------------------------------------------
subroutine ddinit(n,x,y,z,rvdw)
implicit none
!
! allocate the various arrays needed for ddcosmo,
! assemble the cavity and the various associated geometrical quantities.
!
integer, intent(in) :: n
real*8, dimension(n), intent(in) :: x, y, z, rvdw
!
integer :: isph, jsph, i, ii, lnl, l, ind, m, igrid, inear, jnear
integer :: istatus
real*8 :: fac, fl, ffl, fnorm, d2, r2, v(3), vv, t, xt, swthr
!
real*8, allocatable :: vcos(:), vsin(:), vplm(:)
integer, parameter :: nllg=32
!
integer, dimension(nllg) :: ng0
data ng0/6,14,26,38,50,74,86,110,146,170,194,230,266,302,350,434,590,770,974, &
1202,1454,1730,2030,2354,2702,3074,3470,3890,4334,4802,5294,5810/
!
! openMP parallelization:
!
if (nproc.eq.0) nproc = 1
!$ call omp_set_num_threads(nproc)
pi = four*atan(one)
sq2 = sqrt(two)
nsph = n
!
! choose the lebedev grid with number of points closest to ngrid:
!
igrid = 0
inear = 100000
do i = 1, nllg
jnear = iabs(ng0(i)-ngrid)
if (jnear.lt.inear) then
inear = jnear
igrid = i
end if
end do
ngrid = ng0(igrid)
!
! print a nice header:
!
call header
!
! allocate:
!
grad = igrad.ne.0
nylm = (lmax+1)*(lmax+1)
allocate( rsph(nsph), csph(3,nsph), w(ngrid), grid(3,ngrid), basis(nylm,ngrid), &
inl(nsph+1), nl(nsph*nngmax), fi(ngrid,nsph), ui(ngrid,nsph), &
fact(max(2*lmax+1,2)), facl(nylm), facs(nylm) , stat=istatus )
if ( istatus.ne.0 ) then
write(*,*)'ddinit : [1] allocation failed !'
stop
endif
if (grad) allocate( zi(3,ngrid,nsph), stat=istatus)
if ( istatus.ne.0 ) then
write(*,*)'ddinit : [1] allocation failed !'
stop
endif
!
! precompute various quantities (diagonal blocks of ddcosmo matrix,
! normalization factors for spherical harmonics, factorials)
!
fact(1) = one
fact(2) = one
do i = 3, 2*lmax + 1
fact(i) = dble(i-1)*fact(i-1)
end do
!
do l = 0, lmax
ind = l*l + l + 1
fl = (two*dble(l) + one)/(four*pi)
ffl = sqrt(fl)
facl(ind-l:ind+l) = fl
facs(ind) = ffl
do m = 1, l
fnorm = sq2*ffl*sqrt(fact(l-m+1)/fact(l+m+1))
if (mod(m,2).eq.1) fnorm = -fnorm
facs(ind+m) = fnorm
facs(ind-m) = fnorm
end do
end do
!
! set the centers and radii of the spheres:
!
csph(1,:) = x
csph(2,:) = y
csph(3,:) = z
rsph = rvdw
!
! load a lebedev grid:
!
call llgrid(ngrid,w,grid)
!
! build a basis of spherical harmonics at the gridpoints:
!
allocate (vplm(nylm),vcos(lmax+1),vsin(lmax+1), stat=istatus)
if ( istatus.ne.0 ) then
write(*,*)'ddinit : [2] allocation failed !'
stop
endif
!$omp parallel do default(shared) private(i,vplm,vcos,vsin)
do i = 1, ngrid
call ylmbas(grid(:,i),basis(:,i),vplm,vcos,vsin)
end do
!$omp end parallel do
deallocate (vplm,vcos,vsin, stat=istatus)
if ( istatus.ne.0 ) then
write(*,*)'ddinit : [1] deallocation failed!'
stop
endif
!
if (iprint.ge.4) then
call prtsph('facs',1,0,facs)
call prtsph('facl',1,0,facs)
call prtsph('basis',ngrid,0,basis)
call ptcart('grid',3,0,grid)
call ptcart('weights',1,0,w)
end if
!
! build neighbors list (CSR format)
! =================================
!
! \\ jsph |
! isph \\ | 1 2 3 4 5 6
! -----------------------------------
! 1 | x x x
! 2 | x x x x
! 3 | x x x
! 4 | x x x x
! 5 | x x x
! 6 | x x x
!
!
! inl = 1, 4, 8, 11, 15, 18,21 pointer to 1st neighbor
!
! | | | | | |
! v V V V V V
!
! 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|17|18|19|20
!
! nl = 2, 4, 5, 1, 3, 5, 6, 2, 4, 6, 1, 3, 5, 6, 1, 2, 4, 2, 3, 4 neighbors list
!
!
! index of nl
!
ii = 1
lnl = 0
do isph = 1, nsph
inl(isph) = lnl + 1
do jsph = 1, nsph
if (isph.ne.jsph) then
d2 = (csph(1,isph) - csph(1,jsph))**2 + (csph(2,isph) - csph(2,jsph))**2 + (csph(3,isph) - csph(3,jsph))**2
r2 = (rsph(isph) + rsph(jsph))**2
if (d2.le.r2) then
nl(ii) = jsph
ii = ii + 1
lnl = lnl + 1
end if
end if
end do
end do
inl(nsph+1) = lnl+1
!
1000 format(t3,'neighbours of sphere ',i6)
1010 format(t5,12i6)
!
if (iprint.ge.4) then
write(iout,*) ' inl:'
write(iout,'(10i6)') inl(1:nsph+1)
write(iout,*)
do isph = 1, nsph
write(iout,1000) isph
write(iout,1010) nl(inl(isph):inl(isph+1)-1)
end do
write(iout,*)
end if
!
!-----------------------------------------------------------------------
! Define :
!
! N_i = list of neighbors of i-sphere [ excluding i-sphere ]
!
! | r_i + rho_i s_n - r_j |
! t_n^ij = -------------------------
! rho_j
!
! fi(n,i) = sum \chi( t_n^ij )
! j \in N_i
!
! Notice that the derivative of fi(n,i) wrt to r_k is (possibly) nonzero
! when either k = i, or k \in N_j .
!
!-----------------------------------------------------------------------
!
! build arrays fi, ui, zi
! =======================
fi = zero
ui = zero
if (grad) zi = zero
!
!$omp parallel do default(shared) private(isph,i,ii,jsph,v,vv,t,xt,swthr,fac)
!
! loop over spheres
do isph = 1,nsph
!
! loop over integration points
do i = 1,ngrid
!
! loop over neighbors of i-sphere
do ii = inl(isph),inl(isph+1)-1
!
! neighbor's number
jsph = nl(ii)
!
! compute t_n^ij
v(:) = csph(:,isph) + rsph(isph)*grid(:,i) - csph(:,jsph)
vv = sqrt(dot_product(v,v))
t = vv/rsph(jsph)
!
! compute \chi( t_n^ij )
xt = fsw( t, se, eta )
!
! upper bound of switch region
swthr = one + (se + 1.d0)*eta / 2.d0
!
! t_n^ij belongs to switch region
if ( grad .and. ( t.lt.swthr .and. t.gt.swthr-eta ) ) then
!
fac = dfsw( t, se, eta ) / rsph(jsph)
!
! accumulate for zi
! -----------------
zi(:,i,isph) = zi(:,i,isph) + fac*v(:)/vv
!
endif
!
! accumulate for fi
! -----------------
fi(i,isph) = fi(i,isph) + xt
!
enddo
!
! compute ui
! ----------
if ( fi(i,isph).le.one ) ui(i,isph) = one - fi(i,isph)
!
enddo
enddo
!$omp end parallel do
!
if (iprint.ge.4) then
call ptcart('fi',nsph,0,fi)
call ptcart('ui',nsph,0,ui)
end if
!
! build cavity array
! ==================
!
! initialize number of cavity points
ncav=0
!
! loop over spheres
do isph = 1,nsph
!
! loop over integration points
do i = 1,ngrid
!
! positive contribution from integration point
if ( ui(i,isph).gt.zero ) then
!
! accumulate
ncav = ncav + 1
!
endif
enddo
enddo
!
! allocate cavity array
allocate( ccav(3,ncav) , stat=istatus )
if ( istatus .ne. 0 ) then
write(*,*)'ddinit : [3] allocation failed!'
stop
endif
!
!
! initialize cavity array index
ii = 0
!
! loop over spheres
do isph = 1,nsph
!
! loop over integration points
do i = 1,ngrid
!
! positive contribution from integration point
if ( ui(i,isph).gt.zero ) then
!
! advance cavity array index
ii = ii + 1
!
! store point
ccav(:,ii) = csph(:,isph) + rsph(isph)*grid(:,i)
!
endif
enddo
enddo
!
1100 format(t3,i8,3f14.6)
!
if (iprint.ge.4) then
write(iout,*) ' external cavity points:'
do ii = 1, ncav
write(iout,1100) ii, ccav(:,ii)
end do
write(iout,*)
end if
!
return
!
!
end subroutine ddinit
!---------------------------------------------------------------------------------
!
!
!
!
!
!---------------------------------------------------------------------------------
subroutine memfree
!
implicit none
integer :: istatus, istatus0
!
!---------------------------------------------------------------------------------
!
! initialize deallocation flags
istatus0 = 0
istatus = 0
!
! deallocate the arrays
if( allocated(rsph) ) deallocate( rsph , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(csph) ) deallocate( csph , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(ccav) ) deallocate( ccav , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(w) ) deallocate( w , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(grid) ) deallocate( grid , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(basis) ) deallocate( basis , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(inl) ) deallocate( inl , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(nl) ) deallocate( nl , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(fact) ) deallocate( fact , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(facl) ) deallocate( facl , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(facs) ) deallocate( facs , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(ui) ) deallocate( ui , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(fi) ) deallocate( fi , stat=istatus ) ; istatus0 = istatus0 + istatus
if( allocated(zi) ) deallocate( zi , stat=istatus ) ; istatus0 = istatus0 + istatus
!
if ( istatus0.ne.0 ) then
write(*,*)'memfree : dallocation failed!'
stop
endif
!
end subroutine memfree
!---------------------------------------------------------------------------------
!
!
!
!
!
!---------------------------------------------------------------------------------
real*8 function sprod(n,u,v)
!
implicit none
integer, intent(in) :: n
real*8, dimension(n), intent(in) :: u, v
!
integer :: i
real*8 :: ss
!---------------------------------------------------------------------------------
!
! initialize
ss = zero
!
do i = 1, n
!
! accumulate
ss = ss + u(i)*v(i)
!
enddo
!
! redirect
sprod = ss
!
return
!
!
end function sprod
!------------------------------------------------------------------------------------------------
!
!
!
!
!------------------------------------------------------------------------------------------------
! Purpose : switch function (5th degree polynomial)
!------------------------------------------------------------------------------------------------
real*8 function fsw( t, s, eta )
!
implicit none
real*8, intent(in) :: t
real*8, intent(in) :: s
real*8, intent(in) :: eta
!
real*8 :: a, b, flow, x
real*8, parameter :: f6=6.0d0, f10=10.d0, f12=12.d0, f15=15.d0
!
!------------------------------------------------------------------------------------------------
!
! shift :
! s = 0 => t - eta/2 [ CENTERED ]
! s = 1 => t - eta [ EXTERIOR ]
! s = -1 => t [ INTERIOR ]
!
! apply shift
x = t - (s + 1.d0)*eta / 2.d0
!
! lower bound of switch region
flow = one - eta
!
! define switch function \chi
if ( x.ge.one ) then
!
fsw = zero
!
elseif ( x.le.flow ) then
!
fsw = one
!
else
!
a = f15*eta - f12
b = f10*eta*eta - f15*eta + f6
fsw = ( (x-one)*(x-one)*(one-x)*(f6*x*x + a*x + b) ) / (eta**5)
!
endif
!
!
end function fsw
!------------------------------------------------------------------------------------------------
!
!
!
!
!------------------------------------------------------------------------------------------------
! Purpose : first derivative of switch function
!------------------------------------------------------------------------------------------------
real*8 function dfsw( t, s, eta )
!
implicit none
real*8, intent(in) :: t
real*8, intent(in) :: s
real*8, intent(in) :: eta
!
real*8 flow, x
real*8, parameter :: f30=30.0d0
!
!------------------------------------------------------------------------------------------------
!
! shift :
! s = 0 => t - eta/2 [ CENTERED ]
! s = 1 => t - eta [ EXTERIOR ]
! s = -1 => t [ INTERIOR ]
!
! apply shift
x = t - (s + 1.d0)*eta / 2.d0
!
! lower bound of switch region
flow = one - eta
!
! define derivative of switch function \chi
if ( x.ge.one ) then
!
dfsw = zero
!
elseif ( x.le.flow ) then
!
dfsw = zero
!
else
!
dfsw = f30*(one-x)*(x-one)*(x-one+eta)*(x-one+eta)/(eta**5)
!
endif
!
!
end function dfsw
!------------------------------------------------------------------------------------------------
!
!
!
!
!
!
!
!------------------------------------------------------------------------------------------------
! Purpose : dump an array (ngrid,ncol) or just a column.
!------------------------------------------------------------------------------------------------
subroutine ptcart( label, ncol, icol, x )
!
implicit none
!
character (len=*), intent(in) :: label
integer, intent(in) :: ncol, icol
real*8, dimension(ngrid,ncol), intent(in) :: x
!
integer :: ig, noff, nprt, ic, j
!
!------------------------------------------------------------------------------------------------
!
! print header :
if (ncol.eq.1) then
write (iout,'(3x,a,1x,"(column ",i4")")') label, icol
else
write (iout,'(3x,a)') label
endif
!
! print entries :
if (ncol.eq.1) then
do ig = 1, ngrid
write(iout,1000) ig, x(ig,1)
enddo
!
else
noff = mod (ncol,5)
nprt = max(ncol - noff,0)
do ic = 1, nprt, 5
write(iout,1010) (j, j = ic, ic+4)
do ig = 1, ngrid
write(iout,1020) ig, x(ig,ic:ic+4)
end do
end do
write (iout,1010) (j, j = nprt+1, nprt+noff)
do ig = 1, ngrid
write(iout,1020) ig, x(ig,nprt+1:nprt+noff)
end do
end if
!
1000 format(1x,i5,f14.8)
1010 format(6x,5i14)
1020 format(1x,i5,5f14.8)
!
return
!
!
end subroutine ptcart
!------------------------------------------------------------------------------------------------
!
!
!
!
!
!------------------------------------------------------------------------------------------------
! Purpose : dump an array (nylm,ncol) or just a column.
!------------------------------------------------------------------------------------------------
subroutine prtsph(label,ncol,icol,x)
!
implicit none
!
character (len=*), intent(in) :: label
integer, intent(in) :: ncol, icol
real*8, dimension(nylm,ncol), intent(in) :: x
!
integer :: l, m, ind, noff, nprt, ic, j
!
!------------------------------------------------------------------------------------------------
!
! print header :
if (ncol.eq.1) then
write (iout,'(3x,a,1x,"(column ",i4")")') label, icol
else
write (iout,'(3x,a)') label
endif
!
! print entries :
if (ncol.eq.1) then
do l = 0, lmax
ind = l*l + l + 1
do m = -l, l
write(iout,1000) l, m, x(ind+m,1)
end do
end do
!
else
noff = mod (ncol,5)
nprt = max(ncol - noff,0)
do ic = 1, nprt, 5
write(iout,1010) (j, j = ic, ic+4)
do l = 0, lmax
ind = l*l + l + 1
do m = -l, l
write(iout,1020) l, m, x(ind+m,ic:ic+4)
end do
end do
end do
write (iout,1010) (j, j = nprt+1, nprt+noff)
do l = 0, lmax
ind = l*l + l + 1
do m = -l, l
write(iout,1020) l, m, x(ind+m,nprt+1:nprt+noff)
end do
end do
end if
!
1000 format(1x,i3,i4,f14.8)
1010 format(8x,5i14)
1020 format(1x,i3,i4,5f14.8)
!
return
!
!
end subroutine prtsph
!------------------------------------------------------------------------------------------------
!
!
!
!
!------------------------------------------------------------------------------------------------
! Purpose : integrate against spherical harmonics
!------------------------------------------------------------------------------------------------
subroutine intrhs( isph, x, xlm )
!
implicit none
integer, intent(in) :: isph
real*8, dimension(ngrid), intent(in) :: x
real*8, dimension(nylm), intent(inout) :: xlm
!
integer :: ig
!
!------------------------------------------------------------------------------------------------
!
! initialize
xlm = zero
!
! accumulate over integration points
do ig = 1, ngrid
!
xlm = xlm + basis(:,ig)*w(ig)*x(ig)
!
enddo
!
! printing
if ( iprint.ge.5 ) then
!
call ptcart('pot',1,isph,x)
call prtsph('vlm',1,isph,xlm)
!
endif
!
return
!
!
end subroutine intrhs
!------------------------------------------------------------------------------------------------
!
!
!
!
!------------------------------------------------------------------------------------------------
! Purpose : compute spherical harmonics
!------------------------------------------------------------------------------------------------
subroutine ylmbas( x, basloc, vplm, vcos, vsin )
!
implicit none
real*8, dimension(3), intent(in) :: x
real*8, dimension(nylm), intent(out) :: basloc, vplm
real*8, dimension(lmax+1), intent(out) :: vcos, vsin
!
integer :: l, m, ind
real*8 :: cthe, sthe, cphi, sphi, plm
!
!------------------------------------------------------------------------------------------------
!
! get cos(\theta), sin(\theta), cos(\phi) and sin(\phi) from the cartesian
! coordinates of x.
!
! evaluate cos( theta ) ; sin( theta )
cthe = x(3)
sthe = sqrt(one - cthe*cthe)
!
! evalutate cos( phi ) ; sin( phi )
if (sthe.ne.zero) then
cphi = x(1)/sthe
sphi = x(2)/sthe
else
cphi = zero
sphi = zero
endif
!
! evaluate cos(m*phi) and sin(m*phi) arrays. notice that this is
! pointless if z = 1, as the only non vanishing terms will be the
! ones with m=0.
if(sthe.ne.zero) then
call trgev(cphi,sphi,vcos,vsin)
else
vcos = one
vsin = zero
endif
!
! evaluate the generalized legendre polynomials
call polleg(cthe,sthe,vplm)
!
! now build the spherical harmonics. we will distinguish m=0,
! m>0 and m<0:
do l = 0, lmax
ind = l**2 + l + 1
!
! m = 0
basloc(ind) = facs(ind)*vplm(ind)
!
do m = 1, l
!
plm = vplm(ind+m)
!
! m > 0
basloc(ind+m) = facs(ind+m)*plm*vcos(m+1)
!
! m < 0
basloc(ind-m) = facs(ind-m)*plm*vsin(m+1)
!
enddo
enddo
!
return
!
!
end subroutine ylmbas
!------------------------------------------------------------------------------------------------
!
!
!
!
!------------------------------------------------------------------------------------------------
! Purpose : compute first derivatives of spherical harmonics
!------------------------------------------------------------------------------------------------
subroutine dbasis( x, basloc, dbsloc, vplm, vcos, vsin )
!
implicit none
real*8, dimension(3), intent(in) :: x
real*8, dimension(nylm), intent(inout) :: basloc, vplm
real*8, dimension(3,nylm), intent(inout) :: dbsloc
real*8, dimension(lmax+1), intent(inout) :: vcos, vsin
!
integer :: l, m, ind, VC, VS
real*8 :: cthe, sthe, cphi, sphi, plm, fln, pp1, pm1, pp
real*8 :: et(3), ep(3)
!
!------------------------------------------------------------------------------------------------
!
! get cos(\theta), sin(\theta), cos(\phi) and sin(\phi) from the cartesian
! coordinates of x.
cthe = x(3)
sthe = sqrt(one - cthe*cthe)
!
! not ( NORTH or SOUTH pole )
if ( sthe.ne.zero ) then
cphi = x(1)/sthe
sphi = x(2)/sthe
!
! NORTH or SOUTH pole
else
cphi = one
sphi = zero
end if
!
! evaluate the derivatives of theta and phi:
!
et(1) = cthe*cphi
et(2) = cthe*sphi
et(3) = -sthe
! not ( NORTH or SOUTH pole )
if( sthe.ne.zero ) then
ep(1) = -sphi/sthe
ep(2) = cphi/sthe
ep(3) = zero
!
! NORTH or SOUTH pole
else
ep(1) = zero
ep(2) = one
ep(3) = zero
!
end if
!
! evaluate cos(m*phi) and sin(m*phi) arrays. notice that this is
! pointless if z = 1, as the only non vanishing terms will be the
! ones with m=0.
!
! not ( NORTH or SOUTH pole )
if ( sthe.ne.zero ) then
!
call trgev( cphi, sphi, vcos, vsin )
!
! NORTH or SOUTH pole
else
!
vcos = one
vsin = zero
!
end if
VC=zero
VS=cthe
!
! evaluate the generalized legendre polynomials.
!
call polleg( cthe, sthe, vplm )
!
! now build the spherical harmonics. we will distinguish m=0,
! m>0 and m<0:
!
basloc = zero
dbsloc = zero
do l = 0, lmax
ind = l*l + l + 1
! m = 0
fln = facs(ind)
basloc(ind) = fln*vplm(ind)
if (l.gt.0) then
dbsloc(:,ind) = fln*vplm(ind+1)*et(:)
else
dbsloc(:,ind) = zero
end if
!dir$ simd
do m = 1, l
fln = facs(ind+m)
plm = fln*vplm(ind+m)
pp1 = zero
if (m.lt.l) pp1 = -pt5*vplm(ind+m+1)
pm1 = pt5*(dble(l+m)*dble(l-m+1)*vplm(ind+m-1))
pp = pp1 + pm1
!