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adj_sub.f
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c
c This module contains subroutines from adj
c
c----------------------------------------------------------
function current (du, ua, c, nmax, dth0, th0a, imax, imax1,
1 fm, chi, cur)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
real(kind=dp) current
integer nmax, imax, imax1
real(kind=dp) du, c, dth0
real(kind=dp), dimension(0:nmax - 1) :: ua
real(kind=dp), dimension(0:imax - 1) :: th0a
real(kind=dp), dimension(0:nmax - 1) :: fm
real(kind=dp), dimension(0:imax1 - 1,0:nmax - 1) :: chi
real(kind=dp), dimension(0:imax - 1) :: cur
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: n, i
real(kind=dp) :: pi
ctest
integer :: j
real(kind=dp) :: chi_norm
C-----------------------------------------------
pi = 4*datan(1.0d0)
cur(:imax-1) = 0
do n = 0, nmax - 1
cur(:imax-1) = cur(:imax-1) + chi(:imax-1,n)*fm(n)*ua(n)**3/
1 dsqrt(1 + (ua(n)/c)**2)
end do
current=dot_product(dsin(th0a(:imax-1))*dcos(th0a(:imax-1)),cur(:
1 imax-1))
current = 4*pi*du*dth0*current
return
end function current
subroutine decomp(chi, nmax, nmax1, imax, imax1, lmaxa, lmaxa1,
1 th0a, dth0, legp, chil)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
integer nmax, nmax1, imax, imax1, lmaxa, lmaxa1
real(kind=dp) dth0
real(kind=dp), dimension(0:imax1 - 1,0:nmax - 1) :: chi
real(kind=dp), dimension(0:imax - 1) :: th0a
real(kind=dp), dimension(0:imax1 - 1,lmaxa1) :: legp
real(kind=dp), dimension(0:nmax1 - 1,lmaxa1) :: chil
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: la, l, n, i
real(kind=dp) :: sn
C-----------------------------------------------
do la = 1, lmaxa
l = max(2*la - 1,0)
chil(:nmax-1,la) = 0
do i = 0, imax - 1
sn = dsin(th0a(i))*legp(i,la)
chil(:nmax-1,la) = chil(:nmax-1,la) + chi(i,:nmax-1)*sn
end do
chil(:nmax-1,la) = (2*l + 1)*dth0*chil(:nmax-1,la)
end do
return
end subroutine decomp
function deltab (phi, eps)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
real(kind=dp) phi, eps
real(kind=dp) deltab
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
C-----------------------------------------------
deltab = 2*eps*dsin(phi/2)**2/(1 + eps*dcos(phi))
return
end function deltab
subroutine error(du, ua, umax, nmax, dth0, th0a, th0max, imax,
1 imax1, resid, chi, abserr, relerr, aerr, rerr)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
integer nmax, imax, imax1
real(kind=dp) du, umax, dth0, th0max, abserr, relerr
real(kind=dp), dimension(0:nmax - 1) :: ua
real(kind=dp), dimension(0:imax - 1) :: th0a
real(kind=dp), dimension(0:imax1 - 1,0:nmax - 1) :: resid, chi
real(kind=dp), dimension(0:imax - 1) :: aerr, rerr
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: i, n
C-----------------------------------------------
aerr(:imax-1) = 0
rerr(:imax-1) = 0
do n = 0, nmax - 1
aerr(:imax-1) = aerr(:imax-1) + resid(:imax-1,n)**2*(ua(n)**2)
rerr(:imax-1) =rerr(:imax-1)+(resid(:imax-1,n)/max(1.0E-16_dp,
1 abs(chi(:imax-1,n))))**2*(ua(n)**2)
end do
abserr = dot_product(dsin(th0a(:imax-1)),aerr(:imax-1))
relerr = dot_product(dsin(th0a(:imax-1)),rerr(:imax-1))
abserr = dsqrt(abserr*du*dth0/(umax**3/3*(1 -dcos(th0max))))
relerr = dsqrt(relerr*du*dth0/(umax**3/3*(1 -dcos(th0max))))
return
end subroutine error
subroutine hinit(eps, kmax, lmaxa1, harr, garr, dthp, dl, bb)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
integer kmax, lmaxa1
real(kind=dp) eps, dthp
real(kind=dp), dimension(((lmaxa1 - 1)
1 *lmaxa1*(2*lmaxa1-1))/6+(lmaxa1- 1)*lmaxa1+lmaxa1):: harr
real(kind=dp),dimension((((lmaxa1+3)-1)*
1 (lmaxa1+3))/2+(lmaxa1+1))::garr
real(kind=dp), dimension(0:kmax - 1) :: dl, bb
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: k, la, la1, la2, l, l1
real(kind=dp) :: b, pi
C-----------------------------------------------
C E x t e r n a l F u n c t i o n s
C-----------------------------------------------
real(kind=dp) , EXTERNAL :: deltab
C-----------------------------------------------
pi = 4*datan(1.0d0)
C
C Initialize |harr| and set the edge values of |garr| to zero.
C
do la = 1, lmaxa1
do la1 = 1, la
harr((la-1)*la*(2*la-1)/6+(la1-1)*la+1:la*(la*(2*(la-1)-1)+1
1 )/6+la1*la) = 0
end do
end do
do la = -2, lmaxa1 - 1
garr((((la+3)-1)*(la+3))/2+(0+1)) = 0
end do
do la = -1, lmaxa1 - 1
garr((((la+3)-1)*(la+3))/2+(la+1+1)) = 0
garr((((la+3)-1)*(la+3))/2+(la+2+1)) = 0
end do
garr((((1+3)-1)*(1+3))/2+(1+1)) = 1
c write(*,*)'hinit 0 garr',garr
do k = 0, kmax - 1
c phi=2*pi*(k+0.25e0)/kmax
b = bb(k)
C Use the recursion relation for 'g' to fill garr
C
do la = 2, lmaxa1
l = max(2*la - 1,0)
do la1 = 1, la
l1 = max(2*la1 - 1,0)
garr((((la+3)-1)*(la+3))/2+(la1+1)) = (2*(2*l - 3)*(l**2
1 - 3*l + 1)*garr((((la-1+3)-1)*(la-1+3))/2+(la1+1))-(l
2 -3)*(l-2)*(2*l-1)*garr((((la-2+3)-1)*(la-2+3))/2+(la1+
3 1)))/(l*(l - 1)*(2*l - 5)) + (2*l - 3)*(2*l - 1)*b*((
4 l1 + 1)*(l1 + 2)*garr((((la-1+3)-1)*(la-1+3))/2+(la1+1
5 +1))/((2*l1+3)*(2*l1+5))-2*(l1**2+l1-1)*garr((((la-1+3
6 )-1)*(la-1+3))/2+(la1+1))/((2*l1-1)*(2*l1+3))+l1*(l1-1
7 )*garr((((la-1+3)-1)*(la-1+3))/2+(la1-1+1))/((2*l1-3)*
8 (2*l1-1)))/(l*(l - 1))
end do
end do
c write(*,*)'hinit 1 garr',garr
do la = 1, lmaxa1
do la1 = 1, la
harr((la-1)*la*(2*la-1)/6+(la1-1)*la+1:la*(la*(2*(la-1)-1
1 )+1)/6+la1*la) = harr((la-1)*la*(2*la-1)/6+(la1-1)*la+
2 1:la*(la*(2*(la-1)-1)+1)/6+la1*la) + b*garr(((la+3)*(
3 la+3)-3-la)/2+la1+1)*garr((la*(la+5)+6)/2+2:la+1+(la*(
4 la+5)+6)/2)*dl(k)
end do
end do
end do
do la = 1, lmaxa1
do la1 = 1, la
do la2 = 1, la
harr(((la-1)*la*(2*la-1))/6+(la1-1)*la+la2) = (2*max(2*la
1 - 1,0) + 1)/real(2*max(2*la2 - 1,0) + 1)*harr(((la-1)
2 *la*(2*la-1))/6+(la1-1)*la+la2)
end do
end do
end do
c write(*,*)'hinit 3 harr',harr
return
end subroutine hinit
subroutine initjy(ua, c, nmax, nmax1, lmaxa, lmaxa1, legjy, jarray
1 , djarray, lmax1)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
integer nmax, nmax1, lmaxa, lmaxa1, lmax1
real(kind=dp) c
real(kind=dp), dimension(0:nmax - 1) :: ua
real(kind=dp), dimension(0:nmax1 - 1,0:6,0:3,0:lmaxa1) :: legjy
real(kind=dp), dimension((-lmax1) - 1:lmax1,
1 0:6) :: jarray, djarray
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: n, mult, la, l, a
C-----------------------------------------------
C E x t e r n a l F u n c t i o n s
C-----------------------------------------------
EXTERNAL legjn
C-----------------------------------------------
do n = 0, nmax - 1
call legjn(ua(n),c,max(2*lmaxa-1,0),jarray,djarray,lmax1)
do la = 0, lmaxa
l = max(2*la - 1,0,0)
mult = (-1)**(l + 1)
legjy(n,:6,0,la) = jarray(l,:6)
legjy(n,:6,1,la) = mult*jarray((-l)-1,:6)
legjy(n,:6,2,la) = djarray(l,:6)
legjy(n,:6,3,la) = mult*djarray((-l)-1,:6)
end do
end do
return
end subroutine initjy
subroutine initp(x, imax, imax1, lmaxa, lmaxa1, legp, leg0)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
integer imax, imax1, lmaxa, lmaxa1
real(kind=dp), dimension(0:imax - 1) :: x
real(kind=dp), dimension(0:imax1 - 1,lmaxa1) :: legp
real(kind=dp), dimension(0:imax - 1) :: leg0
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: i, l, la
C-----------------------------------------------
if (lmaxa < 1) return
la = 1
leg0(:imax-1) = 1
legp(:imax-1,la) = x(:imax-1)
do la = 2, lmaxa
l = max(2*la - 1,0)
leg0(:imax-1) = (((2*l) - 3)*x(:imax-1)*legp(:imax-1,la-1)-(l-2
1 )*leg0(:imax-1))/(l - 1)
legp(:imax-1,la) = (((2*l) - 1)*x(:imax-1)*leg0(:imax-1)-(l-1)*
1 legp(:imax-1,la-1))/l
end do
return
end subroutine initp
subroutine isotrop(ua, du, c, fm, chil, nmax, nmax1, legjy, psid,
1 ze, zi, duug, fu, dtt, work)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
integer nmax, nmax1
real(kind=dp) du, c, ze, zi
real(kind=dp), dimension(0:nmax - 1) :: ua, fm, chil
real(kind=dp), dimension(0:nmax1 - 1,0:6,0:3) :: legjy
real(kind=dp), dimension(0:nmax1 - 1,0:4,0:1) :: psid
real(kind=dp), dimension(0:nmax) :: duug
real(kind=dp), dimension(0:nmax - 1) :: fu, dtt
real(kind=dp), dimension(0:nmax + (nmax1 + 1)*7*2 - 1) :: work
C-----------------------------------------------
C L o c a l P a r a m e t e r s
C-----------------------------------------------
integer, parameter :: p0 = 0
integer, parameter :: p02 = 1
integer, parameter :: p022 = 2
integer, parameter :: p1 = 3
integer, parameter :: p11 = 4
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: n
real(kind=dp) :: pi, g, u
C-----------------------------------------------
C E x t e r n a l F u n c t i o n s
C-----------------------------------------------
EXTERNAL pot
C-----------------------------------------------
call pot (ua, du, c, fm, chil, nmax, nmax1, legjy, psid, work(0),
1 work(nmax))
pi = 4*datan(1.0d0)
do n = 0, nmax - 1
u = ua(n)
g = dsqrt(1 + (u/c)**2)
duug(n) = ze*4*pi*g/u*(2*g**2*psid(n,p02,1)-u*psid(n,p0,0)-8*g
1 **2/c**2*psid(n,p022,1)+8*u/c**4*psid(n,p022,0))
dtt(n) = ze*4*pi/(g*u)*((-g**2*psid(n,p02,1))-u/c**2*psid(n,p02
1 ,0)+4*g**2/c**2*psid(n,p022,1)-4*u/c**4*psid(n,p022,0)) + zi
2 *g/(2*u)
fu(n) = ze*4*pi*g*((-psid(n,p1,1))+2/c**2*psid(n,p11,1))
end do
duug(nmax) = (3*duug(nmax-1)-duug(nmax-2))/2
duug(nmax-1:1:(-1)) = (duug(nmax-1:1:(-1))+duug(nmax-2:0:(-1)))/2
duug(0) = duug(0)
return
end subroutine isotrop
function lam1 (eps, th0, kmax, dthp, dl, b)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
real(kind=dp) lam1
integer kmax
real(kind=dp) eps, th0, dthp
real(kind=dp), dimension(0:kmax - 1) :: dl, b
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: k
real(kind=dp) :: deltabv, sum, costh
C-----------------------------------------------
C E x t e r n a l F u n c t i o n s
C-----------------------------------------------
real(kind=dp) , EXTERNAL :: deltab
C-----------------------------------------------
c pi=4*datan(1.0d0)
sum = 0
do k = 0, kmax - 1
c phi=2*pi*(k+0.25e0)/kmax
deltabv = b(k) - 1.d0
c----------------------------------------------------------------
c costh=cos(theta)/cos(theta_0)
c---------------------------------------------------------------
if (dabs(deltabv).lt.1.d-12) then
costh=1.d0
else
costh = dsqrt(1 - min(1.0d0,deltabv*dtan(th0)**2))
endif
c costh = dsqrt(1 - min(1.0_dp,deltabv*dtan(th0)**2))
sum = sum + 1/costh*dl(k)
end do
lam1 = sum
return
end function lam1
function lam2 (eps, th0, kmax, dthp, dl, b)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
real(kind=dp) lam2
integer kmax
real(kind=dp) eps, th0, dthp
real(kind=dp), dimension(0:kmax - 1) :: dl, b
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: k
real(kind=dp) :: deltabv, sum, costh
C-----------------------------------------------
C E x t e r n a l F u n c t i o n s
C-----------------------------------------------
real(kind=dp) , EXTERNAL :: deltab
C-----------------------------------------------
c write(*,*)'in lam2 eps,th0,kmax,dthp',eps,th0,kmax,dthp
c pi=4*datan(1.0d0)
sum = 0
do k = 0, kmax - 1
c phi=2*pi*(k+0.25e0)/kmax
deltabv = b(k) - 1.
c----------------------------------------------------------------
c costh=cos(theta)/cos(theta_0)
c---------------------------------------------------------------
if (dabs(deltabv).lt.1.d-12) then
costh=1.d0
else
costh = dsqrt(1 - min(1.0d0,deltabv*dtan(th0)**2))
endif
c costh = dsqrt(1 - min(1.0E0_dp,deltabv*tan(th0)**2))
c write(*,*)'b(k),deltabv,th0,dtan(th0),tan(th0)',
c & b(k),deltabv,th0,dtan(th0),tan(th0)
c write(*,*)'deltabv*dtan(th0)**2',deltabv*tan(th0)**2
c write(*,*)'min(1.0E0_dp,deltabv*dtan(th0)**2)',
c & min(1.0E0_dp,deltabv*dtan(th0)**2)
cSAP070812
c sum = sum + costh/(1 + deltabv)*dl(k)/b(k)
sum = sum + costh/(1 + deltabv)*dl(k)
c write(*,*)'lam2 k,costh,deltabv,dl(k),b(k),dl(k)/b(k)',
c & k,costh,deltabv,dl(k),b(k),dl(k)/b(k)
c write(*,*)'lam2 sum',sum
end do
lam2 = sum
return
end function lam2
subroutine legjn(u, c, lmax, jarray, djarray, lmax1)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
integer lmax, lmax1
real(kind=dp) u, c
real(kind=dp), dimension((-lmax1) - 1:lmax1,
1 0:6) :: jarray, djarray
C-----------------------------------------------
C L o c a l P a r a m e t e r s
C-----------------------------------------------
integer, parameter :: j0 = 0
integer, parameter :: j1 = 1
integer, parameter :: j2 = 2
integer, parameter :: j02 = 3
integer, parameter :: j11 = 4
integer, parameter :: j22 = 5
integer, parameter :: j022 = 6
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: l, a, amax
real(kind=dp) :: scale, g
C-----------------------------------------------
C E x t e r n a l F u n c t i o n s
C-----------------------------------------------
EXTERNAL legjs
C-----------------------------------------------
amax = 2
call legjs (u/c, lmax + 2, amax, jarray, lmax1)
scale = 1
do l = 1, lmax + 2
scale = scale*u/(2*l + 1)
jarray(l,:amax) = scale*jarray(l,:amax)
end do
scale = 1
do l = -1, (-lmax) - 2, -1
scale = scale/u*(2*l + 3)
jarray(l,:amax) = scale*jarray(l,:amax)
end do
do l = (-lmax) - 2, lmax
jarray(l,j02) = u/2*jarray(l+1,1)
jarray(l,j11) = u/2*jarray(l+1,0)
jarray(l,j22) = u/2*jarray(l+1,1) + (u/c)**2/2*jarray(l+2,0)
jarray(l,j022) = u**2/8*jarray(l+2,0)
end do
g = dsqrt(1 + (u/c)**2)
do a = 0, 6
do l = (-lmax) - 1, lmax
djarray(l,a) = jarray(l-1,a)/g - (l + 1)/u*jarray(l,a)
end do
end do
return
end subroutine legjn
subroutine legjs(z, lmax, amax, jarray, lmax1)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
integer lmax, amax, lmax1
real(kind=dp) z
real(kind=dp), dimension((-lmax1) - 1:lmax1,0:amax) :: jarray
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: l, a, lstart
real(kind=dp) :: z2, g, ja0, ja1, ja2, ratio, sigma
C-----------------------------------------------
if (amax<0 .or. lmax<0) return
if (lmax > lmax1) return
z2 = z**2
g = dsqrt(1 + z2)
do a = 1, amax
C**************a=0 is excluded
ja2 = 1
C********ja(a-1,a)
ja1 = g
C**********ja(a-2,a)
do l = a - 3, lmax - 1, -1
C
C Get things started by iterating down to $|lmax|-1$ if need be.
C This is from equation (A29)
C
ja0=g*ja1-z2*(l-a+2)*(l+a+2)*ja2/((2*l+3)*(2*l+5))
ja2 = ja1
ja1 = ja0
end do
l = min(lmax,a - 1)
jarray(l,a) = ja2
l = l - 1
jarray(l,a) = ja1
do l = min(lmax,a - 1) - 2, max((-a),(-lmax) - 1), -1
jarray(l,a) = g*jarray(l+1,a) - z2*(l - a + 2)*(l + a + 2)*
1 jarray(l+2,a)/((2*l + 3)*(2*l + 5))
end do
end do
C
C Calculate the scaled Legendre functions for the other easy case, namely
C $l<-a$.
C
do a = 0, min(amax,lmax)
l = (-a) - 1
jarray(l,a) = 1
l = l - 1
if (l >= (-lmax) - 1) jarray(l,a) = g
do l = (-a) - 3, (-lmax) - 1, -1
jarray(l,a) = g*jarray(l+1,a) - z2*(l - a + 2)*(l + a + 2)*
1 jarray(l+2,a)/((2*l + 3)*(2*l + 5))
end do
end do
C
C Calculate scaled Legendre functions for -a.<= l <=a
C
C
C Calculate $\ja{l\ge0,0}$. Depending on the magnitude of the argument we
C either use backwards recursion (for $z \le |lmax|+1$) or forwards
C recursion using $\ja{-1,0}=1$ and $\ja{0,0} = (\sinh^{-1} z)/z$.
C
a = 0
if (abs(z) <= lmax + 1) then
C
C Estimate where to start the recursion. The 10 is a extra guard.
C
lstart=lmax+log(1.0E-16)/(2*log((1.0E-16+abs(z))/(g+1)))+10
ratio = 2/(g + 1)
do l = lstart, lmax - 1, -1
ratio=1/(g-z2*(l-a+2)*(l+a+2)*ratio/((2*l+3)*(2*l+5)))
C***At this point, |ratio| is approximation for $\ja{l+1,a}/\ja{l,a}$. **
end do
jarray(lmax,a) = ratio
ja0 = 1
do l = lmax - 2, -1, -1
jarray(l+1,a) = ja0
ja0 = g*jarray(l+1,a) - z2*(l - a + 2)*(l + a + 2)*jarray(l+
1 2,a)/((2*l + 3)*(2*l + 5))
end do
ja0 = 1/ja0
jarray(0:lmax,a) = ja0*jarray(0:lmax,a)
else
C********** Use forward recurrence for $z>|lmax|+1$. **
sigma = log(g + abs(z))
C******$\sinh^{-1}(\abs z)$ **
l = 0
jarray(l,a) = sigma/abs(z)
C********* Starting value. We assume
C that $\ja{-1,0}$ has already been set to $1$. */
do l = 1, lmax
C***********Equation (A29)***************
jarray(l,a) = (g*jarray(l-1,a)-jarray(l-2,a))*(2*l - 1)*(2*l
1 + 1)/(z2*(l - a)*(l + a))
end do
endif
C
C Do the other cases, i.e., $a>0$, $l\ge a$.
C
C < Do the other cases, i.e., $a>0$, $l\ge a$ @>=
C
do a = 1, min(lmax,amax)
l = lmax
jarray(l,a) = ((2*l + 1)*jarray(l-1,a-1)-(l+1-a)*g*jarray(l,a-1
1 ))/(l + a)
l = lmax - 1
if (l == 0) then
C
C implies that a=1. Use ja(-1,0)=1
C
ja0 = ((2*l + 1) - (l + 1 - a)*g*jarray(l,a-1))/(l + a)
else
ja0=((2*l+1)*jarray(l-1,a-1)-(l+1-a)*g*jarray(l,a-1))/(l+a)
endif
do l = lmax - 2, a - 1, -1
jarray(l+1,a) = ja0
ja0 = g*jarray(l+1,a) - z2*(l - a + 2)*(l + a + 2)*jarray(l+
1 2,a)/((2*l + 3)*(2*l + 5))
end do
ja0 = 1/ja0
jarray(a:lmax,a) = ja0*jarray(a:lmax,a)
end do
return
end subroutine legjs
subroutine matinit(du, ua, ug, nmax, nmax1, dth0, th0a, th0g, imax
1 , imax1, duug, fu, dtt, lam1a, lam2g, uinv, th0inv, rho)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
integer nmax, nmax1, imax, imax1
real(kind=dp) du, dth0, rho
real(kind=dp), dimension(0:nmax - 1) :: ua
real(kind=dp), dimension(0:nmax) :: ug
real(kind=dp), dimension(0:imax - 1) :: th0a
real(kind=dp), dimension(0:imax) :: th0g
real(kind=dp), dimension(0:nmax) :: duug
real(kind=dp), dimension(0:nmax - 1) :: fu, dtt
real(kind=dp), dimension(0:imax - 1) :: lam1a
real(kind=dp), dimension(0:imax) :: lam2g
real(kind=dp), dimension(0:nmax1 - 1,-1:1) :: uinv
real(kind=dp), dimension(0:imax1 - 1,-1:1) :: th0inv
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: n, i
C-----------------------------------------------
C
C Define matrices for inversion of diffusion and friction operator. These
C are one-dimensional because the operator is independent of $\theta_0$.
C
uinv(:nmax-1,-1) = ug(:nmax-1)**2*duug(:nmax-1)/((ua(:nmax-1)**2)*
1 (du**2))
uinv(:nmax-1,1) = ug(1:nmax)**2*duug(1:nmax)/((ua(:nmax-1)**2)*(du
1 **2))
uinv(:nmax-1,0) = (-uinv(:nmax-1,-1)) - uinv(:nmax-1,1)
uinv(:nmax-1,-1) = uinv(:nmax-1,-1) - fu(:nmax-1)/(2*du)
uinv(:nmax-1,1) = uinv(:nmax-1,1) + fu(:nmax-1)/(2*du)
n = 0
uinv(n,0) = uinv(n,0) - uinv(n,-1)
uinv(n,-1) = 0
n = nmax - 1
uinv(n,-1) = uinv(n,-1) - rho*uinv(n,1)
uinv(n,0) = uinv(n,0) + (1 + rho)*uinv(n,1)
uinv(n,1) = 0
uinv(:nmax-1,-1) = uinv(:nmax-1,-1)*(ua(:nmax-1)**2)/dtt(:nmax-1)
uinv(:nmax-1,0) = uinv(:nmax-1,0)*(ua(:nmax-1)**2)/dtt(:nmax-1)
uinv(:nmax-1,1) = uinv(:nmax-1,1)*(ua(:nmax-1)**2)/dtt(:nmax-1)
C
C Define matrices for inversion of pitch-angle scattering operator. These
C are one-dimensional because, after divided out $D_{\theta\theta,0}/u^2$,
C the operator is independent of $u$.
C
th0inv(:imax-1,-1) =dsin(th0g(:imax-1))*lam2g(:imax-1)/((lam1a(:
1 imax-1)*(dsin(th0a(:imax-1))))*(dth0**2))
cSAP080320 in lam1a it was bellow: lam1a(:imax-
c - was at 73 position
th0inv(:imax-1,1) = dsin(th0g(1:imax))*lam2g(1:imax)/((lam1a(:imax
1 -1)*(dsin(th0a(:imax-1))))*(dth0**2))
th0inv(:imax-1,0) = (-th0inv(:imax-1,-1)) - th0inv(:imax-1,1)
i = 0
i = imax - 1
c write(*,*)'th0inv(imax-1,-1),th0inv(imax-1,1),th0inv(imax-1,0)',
c &th0inv(imax-1,-1),th0inv(imax-1,1),th0inv(imax-1,0)
c write(*,*)'th0inv(imax-1,-1),th0inv(imax-1,1),th0inv(imax-1,0)',
c &th0inv(imax-1,-1),th0inv(imax-1,1),th0inv(imax-1,0)
c write(*,*)'dsin(th0g(imax)),lam2g(imax)',
c &dsin(th0g(imax)),lam2g(imax)
c write(*,*)'dsin(th0a(imax-1)),lam1a(imax-1)',
c &dsin(th0a(imax-1)),lam1a(imax-1)
th0inv(i,0) = th0inv(i,0) - th0inv(i,1)
c write(*,*)'th0inv(imax-1,0)',th0inv(imax-1,0)
th0inv(i,1) = 0
c write(*,*)'in matinit th0inv'
c do i=1,imax-1
c write(*,*)'i,th0g(i),th0a(i),lam2g(i),lam1a(i)',
c & i,th0g(i),th0a(i),lam2g(i),lam1a(i)
c write(*,*)'th0inv(i,-1),th0inv(i,0),th0inv(i,1)',
c & th0inv(i,-1),th0inv(i,0),th0inv(i,1)
c enddo
C* :86 *
*line 1805 "adj.web"
return
end subroutine matinit
subroutine maxwel(ua, du, c, nmax, fm, t)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
integer nmax
real(kind=dp) du, c, t
real(kind=dp), dimension(0:nmax - 1) :: ua, fm
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: n
real(kind=dp) :: sum, pi
C-----------------------------------------------
fm(:nmax-1)=dexp((-ua(:nmax-1)**2/(dsqrt(1+(ua(:nmax-1)/c)**2)+1)/
1 t))
sum = dot_product(ua(:nmax-1)**2,fm(:nmax-1))
pi = 4*datan(1.0d0)
sum = 4*pi*du*sum
fm(:nmax-1) = fm(:nmax-1)/sum
return
end subroutine maxwel
c subroutine operinit ! not used
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
c use kind_spec
c implicit none
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
C-----------------------------------------------
c open(unit=20, file='adjout', form='unformatted', status='unknown')
c open(unit=29, file='adjinp', form='unformatted', status='old')
c return
c end subroutine operinit ! not used
subroutine pot(ua,du,c,fm,chil,nmax,nmax1,legjy,psid,fla,ijy)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
integer nmax, nmax1
real(kind=dp) du, c
real(kind=dp), dimension(0:nmax - 1) :: ua, fm, chil
real(kind=dp), dimension(0:nmax1 - 1,0:6,0:3) :: legjy
real(kind=dp), dimension(0:nmax1 - 1,0:4,0:1) :: psid
real(kind=dp), dimension(0:nmax - 1) :: fla
real(kind=dp), dimension(0:nmax1,0:6,0:1) :: ijy
C-----------------------------------------------
C L o c a l P a r a m e t e r s
C-----------------------------------------------
integer, parameter :: p0 = 0
integer, parameter :: p02 = 1
integer, parameter :: p022 = 2
integer, parameter :: p1 = 3
integer, parameter :: p11 = 4
integer, parameter :: j0 = 0
integer, parameter :: j1 = 1
integer, parameter :: j2 = 2
integer, parameter :: j02 = 3
integer, parameter :: j11 = 4
integer, parameter :: j22 = 5
integer, parameter :: j022 = 6
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: n, a
C-----------------------------------------------
C Define various indefinite integrals needed in the definition of the
C potentials. First do the integration to cell edges and then interpolate
C to the cell centers.
fla(:nmax-1) = fm(:nmax-1)*chil(:nmax-1)*ua(:nmax-1)**2/dsqrt(1 +(
1 ua(:nmax-1)/c)**2)*du/2
do a = 0, 6
ijy(1:nmax,a,0) = fla(:nmax-1)*legjy(:nmax-1,a,0)
ijy(:nmax-1,a,1) = fla(:nmax-1)*legjy(:nmax-1,a,1)
ijy(0,a,0) = 0
ijy(nmax,a,1) = 0
end do
do n = 1, nmax
ijy(n,:6,0) = ijy(n-1,:6,0) + ijy(n,:6,0)
end do
do n = nmax - 1, 0, -1
ijy(n,:6,1) = ijy(n+1,:6,1) + ijy(n,:6,1)
end do
ijy(:nmax-1,:6,0) = ijy(:nmax-1,:6,0) + ijy(1:nmax,:6,0)
ijy(:nmax-1,:6,1) = ijy(:nmax-1,:6,1) + ijy(1:nmax,:6,1)
C
C Define various indefinite integrals needed in the definition of
C the potentials. First do the integration to cell edges and then
C interpolate to the cell centers.
C
psid(:nmax-1,p0,0) = legjy(:nmax-1,j0,1)*ijy(:nmax-1,j0,0) + ijy(:
1 nmax-1,j0,1)*legjy(:nmax-1,j0,0)
psid(:nmax-1,p02,0) = legjy(:nmax-1,j0,1)*ijy(:nmax-1,j02,0) +
1 legjy(:nmax-1,j02,1)*ijy(:nmax-1,j2,0) + ijy(:nmax-1,j0,1)*
2 legjy(:nmax-1,j02,0) + ijy(:nmax-1,j02,1)*legjy(:nmax-1,j2,0)
psid(:nmax-1,p022,0) = legjy(:nmax-1,j0,1)*ijy(:nmax-1,j022,0) +
1 legjy(:nmax-1,j02,1)*ijy(:nmax-1,j22,0) + legjy(:nmax-1,j022,1)
2 *ijy(:nmax-1,j2,0) + ijy(:nmax-1,j0,1)*legjy(:nmax-1,j022,0) +
3 ijy(:nmax-1,j02,1)*legjy(:nmax-1,j22,0) + ijy(:nmax-1,j022,1)*
4 legjy(:nmax-1,j2,0)
psid(:nmax-1,p1,0) = legjy(:nmax-1,j1,1)*ijy(:nmax-1,j1,0) + ijy(:
1 nmax-1,j1,1)*legjy(:nmax-1,j1,0)
psid(:nmax-1,p11,0) = legjy(:nmax-1,j1,1)*ijy(:nmax-1,j11,0) +
1 legjy(:nmax-1,j11,1)*ijy(:nmax-1,j1,0) + ijy(:nmax-1,j1,1)*
2 legjy(:nmax-1,j11,0) + ijy(:nmax-1,j11,1)*legjy(:nmax-1,j1,0)
psid(:nmax-1,p0,1) = legjy(:nmax-1,j0,3)*ijy(:nmax-1,j0,0) + ijy(:
1 nmax-1,j0,1)*legjy(:nmax-1,j0,2)
psid(:nmax-1,p02,1) = legjy(:nmax-1,j0,3)*ijy(:nmax-1,j02,0) +
1 legjy(:nmax-1,j02,3)*ijy(:nmax-1,j2,0) + ijy(:nmax-1,j0,1)*
2 legjy(:nmax-1,j02,2) + ijy(:nmax-1,j02,1)*legjy(:nmax-1,j2,2)
psid(:nmax-1,p022,1) = legjy(:nmax-1,j0,3)*ijy(:nmax-1,j022,0) +
1 legjy(:nmax-1,j02,3)*ijy(:nmax-1,j22,0) + legjy(:nmax-1,j022,3)
2 *ijy(:nmax-1,j2,0) + ijy(:nmax-1,j0,1)*legjy(:nmax-1,j022,2) +
3 ijy(:nmax-1,j02,1)*legjy(:nmax-1,j22,2) + ijy(:nmax-1,j022,1)*
4 legjy(:nmax-1,j2,2)
psid(:nmax-1,p1,1) = legjy(:nmax-1,j1,3)*ijy(:nmax-1,j1,0) + ijy(:
1 nmax-1,j1,1)*legjy(:nmax-1,j1,2)
psid(:nmax-1,p11,1) = legjy(:nmax-1,j1,3)*ijy(:nmax-1,j11,0) +
1 legjy(:nmax-1,j11,3)*ijy(:nmax-1,j1,0) + ijy(:nmax-1,j1,1)*
2 legjy(:nmax-1,j11,2) + ijy(:nmax-1,j11,1)*legjy(:nmax-1,j1,2)
return
end subroutine pot
subroutine reactall(ua, du, c, fm, t, chil, nmax, nmax1, imax,
1 imax1, lam1a, legjy, psid, legp, harr, ze, lmaxa, lmaxa1, react
2 , reactl, chila, work)
C...Translated by Pacific-Sierra Research VAST-90 2.06G2 09:55:56 6/14/01
C...Switches: -p4 -yb
use kind_spec
implicit none
C-----------------------------------------------
C D u m m y A r g u m e n t s
C-----------------------------------------------
integer nmax, nmax1, imax, imax1, lmaxa, lmaxa1
real(kind=dp) du, c, t, ze
real(kind=dp), dimension(0:nmax - 1) :: ua, fm
real(kind=dp), dimension(0:nmax1 - 1,lmaxa1) :: chil
real(kind=dp), dimension(0:imax - 1) :: lam1a
real(kind=dp), dimension(0:nmax1 - 1,0:6,0:3,lmaxa1) :: legjy
real(kind=dp), dimension(0:nmax1 - 1,0:4,0:1) :: psid
real(kind=dp), dimension(0:imax1 - 1,lmaxa1) :: legp
real(kind=dp), dimension(((lmaxa1 - 1)*
1 lmaxa1*(2*lmaxa1-1))/6+(lmaxa1-1)*lmaxa1+lmaxa1):: harr
real(kind=dp), dimension(0:imax1 - 1,0:nmax - 1) :: react
real(kind=dp), dimension(0:nmax - 1) :: reactl, chila
real(kind=dp), dimension(0:nmax + (nmax1 + 1)*7*2 - 1) :: work
C-----------------------------------------------
C L o c a l V a r i a b l e s
C-----------------------------------------------
integer :: la, la1, la2, n, i
C-----------------------------------------------
C E x t e r n a l F u n c t i o n s
C-----------------------------------------------
EXTERNAL reaction
C-----------------------------------------------
react(:imax-1,:nmax-1) = 0
do la1 = 1, lmaxa
reactl(:nmax-1) = 0
do la = la1, lmaxa
chila(:nmax-1) = 0
do la2 = 1, la
chila(:nmax-1) = chila(:nmax-1) + harr(((la-1)*la*(2*la-1
1 ))/6+(la1-1)*la+la2)*chil(:nmax-1,la2)
end do
call reaction (ua, du, c, fm, t, chila, nmax, nmax1, legjy(0