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m2caux3-Coul.F
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m2caux3-Coul.F
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c Modificada en julio de 2002 para calcular las matrices de rotacion
c al menos hasta l = mxmlt (el orden del multipolo mas alto)
c
c difiere del m2caux2.f en la subrutina stoel1. he cambiado la forma
c de almacenamiento de las matrices stoa y stob. ahora funciona para
c cualquier valor de mxn y mxl
c
c modificada en septiembre de 2006 para los nuevos algoritmos de las
c integrales tricentricas
c
c---------------------------------------------------------------------
c
subroutine subrot (rl,rl2,rlvec)
implicit real * 8 (a-h,o-z)
include 'comun.inc'
include 'm2cdat.inc'
dimension rlvec(mxrotdm)
& , rl(-mxl:mxl,-mxl:mxl,0:mxl)
& , rl2(-mxl:mxl,-mxl:mxl,0:mxl)
do i = 1, mxrotdm
rlvec(i) = 0.d0
enddo
c
c calcula las matrices de rotacion y las almacena en el vector
c rlvec (por columnas)
c calcula tambien las distancias entre pares de centros
c
ienlac = 0
irl = 0
do 50 k = 2, ncen
lb = lmaxc(k)
do 60 i = 1, k-1
lmax = max(1,lmaxc(i),lb,mxmlt)
c
c el "1" en el max(...) es debido a que es necesario en algunas
c ocasiones (3c1e) rotar coordenadas.
c
ienlac = ienlac + 1
xab = r(k,1) - r(i,1)
yab = r(k,2) - r(i,2)
zab = r(k,3) - r(i,3)
xy = dsqrt(xab*xab + yab*yab)
a = distab(ienlac)
if (xy .gt. tol) then
sinal = yab / xy
cosal = xab / xy
else
sinal = 0.d0
cosal = 1.d0
endif
sinbet = xy / a
cosbet = zab / a
singa = 0.d0
cosga = 1.d0
call rotar (lmax, mxl, cosal, sinal, cosbet, sinbet, cosga,
, singa, rl2, rl)
irlind(ienlac) = irl + 1
do 62 l = 0, lmax
do 64 mp = -l,l
do 64 m = -l,l
irl = irl+1
rlvec(irl) = rl(m,mp,l)
64 continue
62 continue
60 continue
50 continue
return
end
c
c---------------------------------------------------------------------
c
subroutine leerl (j, i, rlvec, rl)
implicit real * 8 (a-h,o-z)
c
c importante: j: indice del centro "a"
c i: indice del centro "b"
c
include 'comun.inc'
include 'm2cdat.inc'
dimension rlvec(mxrotdm), rl(-mxl:mxl,-mxl:mxl,0:mxl)
c
c recupera en rl las matrices de rotacion del centro i al j
c
if (i .eq. j) stop 'error en leerl: i = j '
lmax = max( 1 , lmaxc(i), lmaxc(j), mxmlt )
c
c ver comentario en subrot acerca del "1" en el max(...)
c
if (i .gt. j) then
k = irlind(ind(i-2)+j)
do 10 l = 0, lmax
do 10 mp = -l,l
do 10 m = -l,l
rl(m,mp,l) = rlvec(k)
k = k + 1
10 continue
else
k = irlind(ind(j-2)+i)
sl = 1.d0
do 20 l = 0, lmax
sm = -1.d0
do 30 mp = -l,-1
do 40 m = -l,l
rl(m,mp,l) = sm * rlvec(k)
k = k + 1
40 continue
sm = -sm
30 continue
sm = sl
do 50 mp = 0,l
do 60 m = -l,l
rl(m,mp,l) = sm * rlvec(k)
k = k + 1
60 continue
sm = -sm
50 continue
sl = -sl
20 continue
endif
902 format(2x,'the rotation matrices for lmax up to ',i2,' are:')
return
end
c
c---------------------------------------------------------------------
c
subroutine leerl2 (i, j, rlvec, rl, rl2)
implicit real * 8 (a-h,o-z)
include 'comun.inc'
include 'm2cdat.inc'
dimension rlvec(mxrotdm), rl(-mxl:mxl,-mxl:mxl,0:mxl)
& , rl2(-mxl:mxl,-mxl:mxl,0:mxl)
c
c recupera en rl las matrices de rotacion del centro i al j
c y en rl2 las matrices de rotacion del centro j al i
c
if (i .eq. j) stop 'error en leerl: i = j '
lmax = max( 1, lmaxc(i), lmaxc(j), mxmlt )
c
c ver comentario en subrot acerca del "1" en el max(...)
c
k = irlind( ind( max(i,j)-2 )+min(i,j) )
sl = 1.d0
do 20 l = 0, lmax
sm = -1.d0
do 30 mp = -l,-1
do 40 m = -l,l
rl(m,mp,l) = rlvec(k)
rl2(m,mp,l) = sm * rlvec(k)
k = k + 1
40 continue
sm = -sm
30 continue
sm = sl
do 50 mp = 0,l
do 60 m = -l,l
rl(m,mp,l) = rlvec(k)
rl2(m,mp,l) = sm * rlvec(k)
k = k + 1
60 continue
sm = -sm
50 continue
sl = -sl
20 continue
902 format(2x,'the rotation matrices for lmax up to ',i2,' are:')
return
end
c
c---------------------------------------------------------------------
c
subroutine consta
implicit real * 8 (a-h,o-z)
include 'comun.inc'
PARAMETER (PI = 3.14159265358979312D0)
PARAMETER (dospi = 2.d0 * PI)
parameter ( raiz2 = 1.414213562373095d0 )
Common / extrapolacion / extrapol(6,2)
Common / cuadratura5 / ugausspat0(5), wgausspat0(5)
Common / cuadratura11 / ugausspat1(11), wgausspat1(11)
Common / cuadratura23 / ugausspat2(23), wgausspat2(23)
Common / cuadratura47 / ugausspat3(47), wgausspat3(47)
Common / cuadratura95 / ugausspat4(95), wgausspat4(95)
Common / cuadratura191 / ugausspat5(191), wgausspat5(191)
Common / cuadratura383 / ugausspat6(383), wgausspat6(383)
common /emecom/ msv(-lmxmnach:lmxmnach,-lmxmnach:lmxmnach),
& mdv(-lmxmnach:lmxmnach,-lmxmnach:lmxmnach),
& ssv(-lmxmnach:lmxmnach,-lmxmnach:lmxmnach),
& sdv(-lmxmnach:lmxmnach,-lmxmnach:lmxmnach)
ind(0) = 0
1 continue
do 10 i = 1, mxind
ind(i) = ind(i-1) + i
10 continue
root(0 ) = 0.d0
do 15 i = 1, mxroot
root(i) = dsqrt(dfloat(i))
rooti(i) = 1.d0 / root(i)
15 continue
fact(0) = 1.d0
facti(0) = 1.d0
facts(-1) = 0.177245385090552d1
factsi(-1) = 1.D0/facts(-1)
facts(0) = facts(-1) * .5d0
factsi(0) = 1.D0/facts(0)
do 20 i = 1, mxfact
fact(i) = fact(i-1) * dfloat(i)
facts(i) = facts(i-1) * (2*i+1) * .5d0
facti(i) = 1.d0 / fact(i)
factsi(i) = 1.d0 / facts(i)
20 continue
real(0) = 0.d0
dosl1(0) = 1.d0
dosl1p(0) = 1.d0
rll1(0) = 0.d0
ri(0) = 1.d250
do 30 l = 1, mxreal
real(l) = dfloat(l)
real(-l) = -real(l)
dosl1(l) = dfloat(2*l+1)
dosl1(-l) = dfloat(-2*l+1)
dosl1p(l) = 1 / dosl1(l)
dosl1p(-l) = 1 / dosl1(-l)
ri(l) = 1.d0 / real(l)
ri(-l) = -ri(l)
rll1(l) = dfloat(l*(l+1))
30 continue
c1r(0) = real(2) * ri(3)
c2r(0) = c1r(0)
c3r(0) = 0.d0
do 40 l = 1, mxc123
c1r(l) = rll1(l+1) * dosl1p(l) * dosl1p(l+1)
c2r(l) = 1.d0 - real(l+1)**2 * dosl1p(l) * dosl1p(l+1)
& - real(l) ** 2 * dosl1p(l-1) * dosl1p(l)
c3r(l) = rll1(l-1) * dosl1p(l-1) * dosl1p(l)
40 continue
ang(0,0) = 0.282094791773878d0
do 50 l = 1, mxangl
ang(l,0) = ang(0,0) * dsqrt(dfloat(2*l+1))
aux = ang(l,0) * root(2)
do 50 m = 1, min(l,mxangm)
aux = aux / dsqrt(dfloat((l-m+1)*(l+m)))
ang(l,m) = aux
50 continue
do 60 i = 0, linter
faux(i,0) = dosl1(i)
do 60 m = 1, min(i,2*mxl)
faux(i,m) = dosl1(i) * (fact(i-m) / fact(i+m))**2
60 continue
rl2l1p(0) = 0.d0
rl12l1(0) = 1.d0
do 61 i = 1, linter
rl2l1p(i) = real(i) * dosl1p(i)
rl12l1(i) = real(i+1) * dosl1p(i)
61 continue
lmax = mxlcf
call acof(lmax)
call bcof(lmax)
call stoel1
call zzzhv
call cpcomg
call cgen
c para las integrales tricentricas con armonicos irregulares
c cuadratura xknum 0-1
call abcpes5(ugausspat0,wgausspat0,0.D0)
call abcpes11(ugausspat1,wgausspat1,0.D0)
call abcpes23(ugausspat2,wgausspat2,0.D0)
call abcpes47(ugausspat3,wgausspat3,0.D0)
call abcpes95(ugausspat4,wgausspat4,0.D0)
call abcpes191(ugausspat5,wgausspat5,0.D0)
call abcpes383(ugausspat6,wgausspat6,0.D0)
c extrapolacion
extrapol(1,1)=6.30957D-2
extrapol(1,2)=1.D-2
extrapol(2,1)=1.58489D-2
extrapol(2,2)=1.D-3
extrapol(3,1)=3.98107D-3
extrapol(3,2)=1.D-4
extrapol(4,1)=1.D-3
extrapol(4,2)=1.D-5
extrapol(5,1)=2.51189D-4
extrapol(5,2)=1.D-6
extrapol(6,1)=6.30957D-5
extrapol(6,2)=1.D-7
do m2 = -lmxmnach, lmxmnach
do m1 = -lmxmnach, lmxmnach
call emes ( m1, m2, ms, md, ss, sd )
msv(m1,m2) = ms
mdv(m1,m2) = md
ssv(m1,m2) = ss
sdv(m1,m2) = sd
enddo
enddo
do l2 = 0,lmxmnach
do l1 = 0,lmxmnach
do m2 = -l2, l2
do m1 = -l1, l1
l1l1 = ind(l1)
l2l2 = ind(l2)
m1a = iabs(m1)
m2a = iabs(m2)
if ( l1.eq.l2 ) then
k1 = l1l1 + max(m1a,m2a)
k12 = ind(k1) + l1l1 + min(m1a,m2a)
elseif (l1.gt.l2) then
k1 = l1l1 + m1a
k12 = ind(k1) + l2l2 + m2a
else
k1 = l2l2 + m2a
k12 = ind(k1) + l1l1 + m1a
endif
indk12(l1*(l1+1)+m1+1,l2*(l2+1)+m2+1)=k12
il=-1
do l = l1+l2,Iabs(l1-l2),-2
il=il+1
av((lmxmnach+1)*k12+il+1)=app(k12,l)
bv((lmxmnach+1)*k12+il+1)=bpp(k12,l)
end do
end do
end do
end do
end do
dm(0) = 1.d0
unom(0) = 1.d0
dpf(0) = 1.d0
p5(0) = 1.d0
do i = 1,40
dm(i) = dm(i-1)*(-2.D0)
p5(i) = p5(i-1)*0.5D0
dpf(i) = 2.D0*dpf(i-1)/dfloat(i)
unom(i) = unom(i-1)*(-1.D0)
enddo
Do l=0,10
f=Dfloat(2*l+1)*1.591549430918953D-1
xarm(l*(l+1)+1)=Dsqrt(0.5D0*f)
Do m=1,l
xarm(l*(l+1)+m+1)=Dsqrt(f*fact(l-m)*facti(l+m))
xarm(l*(l+1)-m+1)=xarm(l*(l+1)+m+1)
enddo
enddo
cip
kalg1 = 0
kalg2 = 0
do m2 = -2*mxl, 2*mxl
do m1 = -2*mxl, 2*mxl
call emes ( m1, m2, ms, md, ss, sd )
msvec(m1,m2) = ms
mdvec(m1,m2) = md
ssvec(m1,m2) = ss
sdvec(m1,m2) = sd
enddo
enddo
lma = 0
do la = 0, mxl
do ma = -la, la
mma = iabs(ma)
lma = lma + 1
if (ma .eq. 0) then
aux = raiz2 * dospi
else
aux = dospi
endif
lmb = 0
do lb = 0, mxl
do mb = -lb, lb
mmb = iabs(mb)
lmb = lmb + 1
if (mb .eq. 0) then
bux = raiz2 * aux
else
bux = aux
endif
auxlnor(lma,lmb) = bux * dsqrt(fact(la+mma) * fact(lb+mmb)
& / (fact(la-mma) * fact(lb-mmb)) )
enddo
enddo
enddo
enddo
* Los coeficientes cfbk0 y cfbk1 se usan en la relacion de
* recurrencia de las funciones K de Bessel redefinidas como:
* bk(n) = Exp[z] * BesselK[n+1/2,z] / (n+1/2)!
* cfbk0(i) = 1 / ((2i+1) * (2i+3))
* cfbk1(i) = (2i+1) / (2i+3)
do i = 0, mxk
cfbk0(i) = ri(i+i+3) * ri(i+i+1)
cfbk1(i) = real(i+i+1) * ri(i+i+3)
enddo
* tabula los coeficientes ckplm para los factores radiales
* en la traslacion de distribuciones bicentricas
call subckplma(mxk,mxk,ckplm)
call subckplmb(mxk,mxk,ckplm)
call subckplmc(mxk,mxk,ckplm)
* tabula los coeficientes cffk para los factores radiales
* de las funciones 2s (para acelerar el calculo)
do k = 1, mxk
cffk21(k) = -2.d0*real(k)
cffk22(k) = real(2*k+1)
cffk23(k) = -2.d0*real(k+1)
enddo
cffk21(0) = 0.d0
cffk22(0) = 1.d0
cffk23(0) = -2.d0
return
end
c***********************************************************************
c *
c subroutine rotar *
c *
c this subroutine yields the rotation matrices r(m',m;l) that are *
c necessary to perform a coordinate transformation used to align *
c two sets of real spherical harmonics centered at different points *
c (a and b). *
c this transformation converts each original real spherical harmonic *
c in a linear combination of the real spherical harmonics with the *
c same l and different m. *
c the maximum value for the orbital quantum number l is 12, to extend*
c this program to greater values of l it is necessary to extend the *
c common sqroot (needed in the subroutine dlmn) with the values of *
c the square roots of the first 2*ltot+1 integers and their *
c reciprocals. *
c *
c***********************************************************************
subroutine rotar(lmax,ltot,cosal,sinal,cosbet,sinbet,cosga,singa,
& dl,rl)
implicit real*8(a-h,o-z)
dimension rl(-ltot:ltot,-ltot:ltot,0:ltot)
dimension dl(-ltot:ltot,-ltot:ltot,0:ltot)
data root2/1.4142135623730950488016887242096970d0/,
- zero/0.0d0/,one/1.0d0/,two/2.0d0/
c
c computation of the initial matrices d0, r0, d1 and r1
c
dl(0,0,0) = one
rl(0,0,0) = one
if(lmax.eq.0) go to 201
dl(1,1,1) = (one+cosbet)/two
dl(1,0,1) =-sinbet/root2
dl(1,-1,1) = (one-cosbet)/two
dl(0,1,1) =-dl(1,0,1)
dl(0,0,1) = dl(1,1,1)-dl(1,-1,1)
dl(0,-1,1) = dl(1,0,1)
dl(-1,1,1) = dl(1,-1,1)
dl(-1,0,1) = dl(0,1,1)
dl(-1,-1,1)= dl(1,1,1)
cosag = cosal * cosga - sinal * singa
cosamg = cosal * cosga + sinal * singa
sinag = sinal * cosga + cosal * singa
sinamg = sinal * cosga - cosal * singa
rl(0,0,1) = dl(0,0,1)
rl(1,0,1) = root2 * dl(0,1,1) * cosal
rl(-1,0,1) = root2 * dl(0,1,1) * sinal
rl(0,1,1) = root2 * dl(1,0,1) * cosga
rl(0,-1,1) =-root2 * dl(1,0,1) * singa
rl(1,1,1) = dl(1,1,1) * cosag - dl(1,-1,1) * cosamg
rl(1,-1,1) =-dl(1,1,1) * sinag - dl(1,-1,1) * sinamg
rl(-1,1,1) = dl(1,1,1) * sinag - dl(1,-1,1) * sinamg
rl(-1,-1,1)= dl(1,1,1) * cosag + dl(1,-1,1) * cosamg
c
c the remaining matrices are calculated using symmetry and
c recurrence relations by means of the subroutine dlmn.
c
if ( dabs(sinbet) .lt. 1.d-14 ) then
tgbet2 = zero
sinbet = zero
cosbet = dsign(one,cosbet)
elseif ( dabs(sinbet) .lt. 1.d-10 ) then
tgbet2 = zero
print*, 'WARNING in ROTAR: sinbet = ', sinbet, ' takes 0'
sinbet = zero
cosbet = dsign(one,cosbet)
else
tgbet2 = ( one - cosbet ) / sinbet
endif
do 10 l = 2, lmax
l1 = l
call dlmn(l1,ltot,sinal,cosal,cosbet,tgbet2,singa,cosga,dl,rl)
10 continue
201 continue
return
end
c***********************************************************************
c *
c subroutine dlmn *
c *
c this subroutine generates the matrices dl(m',m;l) for a fixed value*
c of the orbital quantum number l, and it needs the dl(l-2;m',m) and *
c dl(l-1;m',m) matrices. this subroutine uses symmetry and recurrence*
c relations. the matrices dl(m',m;l) are the rotation matrices for *
c complex spherical harmonics. *
c *
c***********************************************************************
subroutine dlmn(l,ltot,sinal,cosal,cosbet,tgbet2,singa,cosga,
& dl,rl)
implicit real*8 (a-h,o-z)
dimension rl(-ltot:ltot,-ltot:ltot,0:ltot)
dimension dl(-ltot:ltot,-ltot:ltot,0:ltot)
include 'comun.inc'
data root2/1.4142135623730950488016887242096970d0/,
- one/1.0d0/,two/2.0d0/
iinf=1-l
isup=-iinf
c
c computation of the dl(m',m;l) matrix, mp is m' and m is m.
c
c
c first row by recurrence: see equations 19 and 20 of reference (6)
c
dl(l,l,l)=dl(isup,isup,l-1)*(one+cosbet)/two
dl(l,-l,l)=dl(isup,-isup,l-1)*(one-cosbet)/two
do 10 m=isup,iinf,-1
dl(l,m,l)=-tgbet2 * root(l+m+1) * rooti(l-m) * dl(l,m+1,l)
10 continue
c
c the rows of the upper quarter triangle of the dl(m',m;l) matrix
c see equation 21 of reference (6)
c
al=l
al1= al-one
tal1= al+al1
ali=one / al1
cosaux = cosbet*al*al1
do 11 mp=l-1,0,-1
amp=mp
laux=l+mp
lbux=l-mp
aux= rooti(laux) * rooti(lbux) * ali
cux= root(laux-1) * root(lbux-1) * al
do 12 m=isup,iinf,-1
am=m
lauz=l+m
lbuz=l-m
auz= rooti(lauz) * rooti(lbuz)
factor= aux * auz
term=tal1*(cosaux-am*amp)*dl(mp,m,l-1)
if(lbuz.ne.1.and.lbux.ne.1) then
cuz= root(lauz-1) * root(lbuz-1)
term=term-dl(mp,m,l-2)*cux*cuz
endif
dl(mp,m,l)=factor*term
12 continue
iinf=iinf+1
isup=isup-1
11 continue
c
c the remaining elements of the dl(m',m;l) matrix are calculated
c using the corresponding symmetry relations:
c reflexion ---> ((-1)**(m-m')) dl(m,m';l) = dl(m',m;l), m'<=m
c inversion ---> ((-1)**(m-m')) dl(-m',-m;l) = dl(m',m;l)
c
c
c reflexion
c
sign=one
iinf=-l
isup=l-1
do 13 m=l,1,-1
do 14 mp=iinf,isup
dl(mp,m,l)=sign*dl(m,mp,l)
sign=-sign
14 continue
iinf=iinf+1
isup=isup-1
13 continue
c
c inversion
c
iinf=-l
isup=iinf
do 15 m=l-1,-l,-1
sign=-one
do 16 mp=isup,iinf,-1
dl(mp,m,l)=sign*dl(-mp,-m,l)
sign=-sign
16 continue
isup=isup+1
15 continue
c
c computation of the rotation matrices rl(m',m;l) for real spherical
c harmonics using the matrices dl(m',m;l) for complex spherical
c harmonics: see equations 10 to 18 of reference (6)
c
rl(0,0,l)=dl(0,0,l)
cosmal = cosal
sinmal = sinal
sign = - one
do 17 mp = 1, l
cosmga = cosga
sinmga = singa
aux = root2 * dl(0,mp,l)
rl(mp,0,l) = aux * cosmal
rl(-mp,0,l)= aux * sinmal
do 18 m = 1, l
aux = root2 * dl(m,0,l)
rl(0,m,l) = aux * cosmga
rl(0,-m,l)=-aux * sinmga
d1 = dl(-mp,-m,l)
d2 = sign * dl(mp,-m,l)
cosag = cosmal * cosmga - sinmal * sinmga
cosagm= cosmal * cosmga + sinmal * sinmga
sinag = sinmal * cosmga + cosmal * sinmga
sinagm= sinmal * cosmga - cosmal * sinmga
rl(mp,m,l) = d1 * cosag + d2 * cosagm
rl(mp,-m,l) =-d1 * sinag + d2 * sinagm
rl(-mp,m,l) = d1 * sinag + d2 * sinagm
rl(-mp,-m,l)= d1 * cosag - d2 * cosagm
aux = cosmga * cosga - sinmga * singa
sinmga = sinmga * cosga + cosmga * singa
cosmga = aux
18 continue
sign = - sign
aux = cosmal * cosal - sinmal * sinal
sinmal = sinmal * cosal + cosmal * sinal
cosmal = aux
17 continue
return
end
************************************************************************
* *
* subroutine matprt *
* *
* this subroutine is used to print out the matrices rl(l;m',m) with
* an appropriate format. *
* *
************************************************************************
* subroutine matprt(lmax,ltot,rl)
subroutine m2cmatprt(lmax,ltot,rl)
implicit real*8 (a-h,o-z)
dimension rl(-ltot:ltot,-ltot:ltot,0:ltot)
c
1000 format(12x,3(i3,15x),i3)
1002 format(1x,i3,2x,4d18.10)
1003 format(/,2x,'rotation matrix for l = ',i2)
c
c do 2000 l=1,lmax
do 2000 l=0,lmax
write(6,1003) l
ind=1
ilow=-l
1 iupp=ilow+3
if(iupp-l)3,2,2
2 iupp=l
ind=0
3 write(6,1000)(j,j=ilow,iupp)
do 4 i=-l,l
write(6,1002)i,(rl(i,j,l),j=ilow,iupp)
4 continue
if(ind.eq.0) go to 5
ilow=ilow+4
go to 1
5 continue
2000 continue
return
end
c
c *******************************************************************
c
subroutine acof( lmax )
implicit real * 8 ( a-h,o-z )
include 'comun.inc'
do j = 0, 2*mxlcf+1
do i = 0, mxkcof
app(i,j) = 0.d0
enddo
enddo
if ( lmax .gt. mxlcf ) stop ' lmax mayor que mxlcf en acof'
c
c elementos de partida app(lm,00)(n) = delta(l,n)
c
k1 = 0
do 10 l = 0 , lmax
do 10 m = 0 , l
kk = k1*(k1+1) / 2
app(kk,l) = 1.d0
k1 = k1 + 1
10 continue
c
c elementos del tipo app(lm,m'm')(n)
c
do 20 mp = 1 , lmax
k2 = mp*(mp+1)/2 + mp
k20 = (mp-1)*mp/2 + mp-1
do 20 l = mp , lmax
if ( l.eq.mp ) then
m1 = mp
else
m1 = 0
endif
do 20 m = m1 , l
k1 = l*(l+1)/2 + m
kk = k1*(k1+1)/2 + k2
kk0 = k1*(k1+1)/2 + k20
do 20 n = l-mp , l+mp , 2
if ( n.ge.m+mp) then
app(kk,n) = (2*mp-1) * ( app(kk0,n-1)/dfloat(n+n-1)
& - app(kk0,n+1)/dfloat(n+n+3) )
endif
20 continue
c
c elementos del tipo app(lm,l'm')(n)
c
do 30 mp = 0 , lmax
do 30 lp = mp+1 , lmax
k2 = lp*(lp+1)/2 + mp
k20 = (lp-1)*lp/2 + mp
k200 = (lp-2)*(lp-1)/2 + mp
do 30 l = lp , lmax
if ( l.eq.lp ) then
m1 = mp
else
m1 = 0
endif
do 30 m = m1 , l
k1 = l*(l+1)/2 + m
kk = k1*(k1+1)/2 + k2
kk0 = k1*(k1+1)/2 + k20
kk00 = k1*(k1+1)/2 + k200
do 30 n = l-lp , l+lp , 2
if ( n.ge.m+mp) then
aux = app(kk0,n+1) * (n+m+mp+1) / dfloat(n+n+3)
if ( n.gt.m+mp )
& aux = aux + app(kk0,n-1) * (n-m-mp) / dfloat(n+n-1)
aux = aux * ( lp+lp-1 )
if ( lp.gt.mp+1 ) aux = aux - (lp+mp-1) * app(kk00,n)
app(kk,n) = aux / dfloat(lp-mp)
endif
30 continue
return
end
c
c *******************************************************************
c
subroutine bcof( lmax )
implicit real * 8 ( a-h,o-z )
include 'comun.inc'
if ( lmax .gt. mxlcf ) stop ' lmax mayor que mxlcf en bcof'
do j = 0, 2*mxlcf+1
do i = 0, mxkcof
bpp(i,j) = 0.d0
enddo
enddo
c
c elementos de partida bpp(lm,00)(n) = delta(l,n)
c
k1 = 0
do 10 l = 0 , lmax
do 10 m = 0 , l
kk = k1*(k1+1) / 2
bpp(kk,l) = 1.d0
k1 = k1 + 1
10 continue
c
c elementos del tipo bpp(lm,m'm')(n)
c
do 20 mp = 1 , lmax
k2 = mp*(mp+1)/2 + mp
k20 = (mp-1)*mp/2 + mp-1
do 20 l = mp , lmax
if ( l.eq.mp ) then
m1 = mp
else
m1 = 0
endif
do 20 m = m1 , l
k1 = l*(l+1)/2 + m
kk = k1*(k1+1)/2 + k2
kk0 = k1*(k1+1)/2 + k20
do 20 n = l-mp , l+mp , 2
if ( mp.gt.m ) then
t1 = 1.d0
t2 = 1.d0
else
t1 = -(n-(m-mp+1))*(n-(m-mp+1)+1)
t2 = -(n+(m-mp+1))*(n+(m-mp+1)+1)
endif
if ( n.ge.abs(m-mp)) then
if (n.eq.0) then
bux=0.d0
else
bux=t1*bpp(kk0,n-1)/dfloat(n+n-1)
endif
bpp(kk,n) = (2*mp-1) * ( bux
& - t2*bpp(kk0,n+1)/dfloat(n+n+3) )
endif
20 continue
c
c elementos del tipo bpp(lm,l'm')(n)
c
do 30 mp = 0 , lmax
do 30 lp = mp+1 , lmax
k2 = lp*(lp+1)/2 + mp
k20 = (lp-1)*lp/2 + mp
k200 = (lp-2)*(lp-1)/2 + mp
do 30 l = lp , lmax
if ( l.eq.lp ) then
m1 = mp
else
m1 = 0
endif
do 30 m = m1 , l
k1 = l*(l+1)/2 + m
kk = k1*(k1+1)/2 + k2
kk0 = k1*(k1+1)/2 + k20
kk00 = k1*(k1+1)/2 + k200
do 30 n = l-lp , l+lp , 2
mmp = abs(m-mp)
if ( n.ge.mmp) then
aux = bpp(kk0,n+1) * (n+mmp+1) / dfloat(n+n+3)
if ( n.gt.mmp )
& aux = aux + bpp(kk0,n-1) * (n-mmp) / dfloat(n+n-1)
aux = aux * ( lp+lp-1 )
if ( lp.gt.mp+1 ) aux = aux - (lp+mp-1) * bpp(kk00,n)
bpp(kk,n) = aux / dfloat(lp-mp)
endif
30 continue
return
end
c
c---------------------------------------------------------------------
c
subroutine indab ( l1 , m1 , l2 , m2 , l1l1 , l2l2 , k12 )
c
c devuelve la fila, k, en las matrices a y b, correspondiente a la
c descomposicion de dos polinomios de legendre
c
implicit real*8 (a-h,o-z)
include 'comun.inc'
m1a = iabs(m1)
m2a = iabs(m2)
if ( l1.eq.l2 ) then
k1 = l1l1 + max(m1a,m2a)
k12 = ind(k1) + l1l1 + min(m1a,m2a)
elseif (l1.gt.l2) then
k1 = l1l1 + m1a
k12 = ind(k1) + l2l2 + m2a
else
k1 = l2l2 + m2a
k12 = ind(k1) + l1l1 + m1a
endif
return
end
c
c ******************************************************************
c
subroutine emes ( m1, m2, ms, md, ss, sd )
implicit real * 8 (a-h,o-z)
parameter ( pt5 = 0.5d0 )
s1 = sign(1,m1)
s2 = sign(1,m2)
s12 = s1 * s2
m1a = iabs(m1)
m2a = iabs(m2)
ms = s12 * ( m1a + m2a )
md = s12 * iabs( m1a - m2a )
if ( ms.eq.md ) then
ss = 1.d0
sd = 0.d0
return
endif
if ( m1.lt.0 .and. m2.lt.0 ) then
ss = -pt5
else
ss = pt5
endif
if ( s12.gt.0.d0 ) then
sd = pt5
elseif ( md.eq.0 ) then
sd = 0.d0
elseif ( sign(1,m1a-m2a) .eq. s1 ) then
sd = - pt5
else
sd = pt5
endif
return
end
c***********************************************************************
c *
c subroutine matpr *
c *
c this subroutine is used to print out *
c matrices with an appropriate format. *
c *
c *
c***********************************************************************
subroutine matpr(idim, jdim, imax, jmax, sm)
implicit real*8 (a-h,o-z)
dimension sm(idim,jdim)
c
1000 format(12x,3(i3,15x),i3)
1002 format(1x,i3,2x,4d18.10)
c
indi=1
jlow=1
1 jupp=jlow+3
if(jupp-jmax)3,2,2
2 jupp=jmax
indi=0
3 write(6,1000)(j,j=jlow,jupp)
do 4 i= 1, imax
write(6,1002)i,(sm(i,j),j=jlow,jupp)
4 continue
if(indi.eq.0) go to 5
jlow=jlow+4
go to 1
5 continue
return
end
c
c *******************************************************************
c
subroutine ro1 ( la, lb, lc, ld, v, r )
implicit real * 8 (a-h,o-z)
include 'comun.inc'
dimension r(-mxl:mxl,-mxl:mxl,0:mxl)
dimension v(-mxl:mxl,-mxl:mxl,-mxl:mxl,-mxl:mxl),aux(-mxl:mxl)
if ( la.eq.0 ) return
do 3 md =-ld,ld
do 3 mc =-lc,lc
do 3 mb =-lb,lb
do 2 ma =-la,la
bux = 0.d0
do 1 m = -la,la
bux = bux + r(ma,m,la) * v(m,mb,mc,md)
1 continue
aux(ma) = bux
2 continue
do 4 ma = -la,la
v(ma,mb,mc,md) = aux(ma)
4 continue
3 continue
return
end
c
c *******************************************************************
c
subroutine ro2 ( la, lb, lc, ld, v, r )
implicit real * 8 (a-h,o-z)
include 'comun.inc'
dimension r(-mxl:mxl,-mxl:mxl,0:mxl)
dimension v(-mxl:mxl,-mxl:mxl,-mxl:mxl,-mxl:mxl),aux(-mxl:mxl)
if ( lb.eq.0 ) return
do 3 md =-ld,ld
do 3 mc =-lc,lc
do 3 ma =-la,la
do 2 mb =-lb,lb
bux = 0.d0
do 1 m = -lb,lb
bux = bux + r(mb,m,lb) * v(ma,m,mc,md)
1 continue
aux(mb) = bux
2 continue
do 4 mb = -lb,lb
v(ma,mb,mc,md) = aux(mb)
4 continue
3 continue
return
end
c
c *******************************************************************
c
subroutine ro3 ( la, lb, lc, ld, v, r )
implicit real * 8 (a-h,o-z)
include 'comun.inc'
dimension r(-mxl:mxl,-mxl:mxl,0:mxl)
dimension v(-mxl:mxl,-mxl:mxl,-mxl:mxl,-mxl:mxl),aux(-mxl:mxl)
if ( lc.eq.0 ) return
do 3 md =-ld,ld
do 3 mb =-lb,lb
do 3 ma =-la,la
do 2 mc =-lc,lc
bux = 0.d0
do 1 m = -lc,lc