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green.f
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c
c MINEOS version 1.0 by Guy Masters, John Woodhouse, and Freeman Gilbert
c
c This program is free software; you can redistribute it and/or modify
c it under the terms of the GNU General Public License as published by
c the Free Software Foundation; either version 2 of the License, or
c (at your option) any later version.
c
c This program is distributed in the hope that it will be useful,
c but WITHOUT ANY WARRANTY; without even the implied warranty of
c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
c GNU General Public License for more details.
c
c You should have received a copy of the GNU General Public License
c along with this program; if not, write to the Free Software
c Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
c
c**************************************************************************
c
c green program computes for a single event and a given set of stations,
c the Green functions.
c
c**************************************************************************
program green
implicit none
include "green.h"
include "fdb/fdb_io.h"
include "fdb/fdb_site.h"
include "fdb/fdb_sitechan.h"
include "fdb/fdb_wfdisc.h"
c---
real*4 scalrs(8)
real*8 co,si,c1,c2,s1,s2,z,zp,cz,sz,caz,saz,prp
common/dheadX/d0,th,ph,jy,jd,jh,jm,sec,tstart
common/zfXX/z(3,ml),zp(3,ml)
common/grnX/grn(12*mseis)
common/modeX/om(meig),a0(meig),omt(meig),a0t(meig)
common/vecnlX/vecnl(8,meig),vecnlt(4,meig)
common/wts/wt(6,meig)
common/sclrX/n,l,e1,e2,e3,e4,au,av
common/propX/prp(6*mseis)
c--- local variables ---
integer*4 lnblnk,numchan(msitechan),numsta(msite)
real*8 time,endtime,htoepoch
real*4 d0,th,ph,sec,tstart,ss,dt,slat,slon,sdep,
* sss, grn, om, a0, omt, a0t, vecnl, vecnlt,
* wt,e1,e2,e3,e4,au,av,pi,rad,fmin,fmax,
* t0,p0,c0,s0,t1,p1,dp,del,azim
integer*4 i,lmax,nmodes,nmodet,j,lp1,indx,
* jy,jd,jh,jm,nscan,iy,id,ih,im,jys,jds,jhs,jms,
* n,l,len,mchn,icomp,itype1,iscan,ifl,isq,ii
integer*4 nchan,inchn,iseq,jdate,ierr,nc(100),ns(100)
real*4 ang(3)
character*8 ename
character*256 efname
c--- equivalence and data ---
equivalence (n,scalrs)
data pi,rad,tstart/3.14159265359,57.29578,0./
data icomp,itype1/0,1/
c
c read input parameters
c
c....read in dbname with static relations: sta, stachan
write(*,*) '============= Program green ===================='
write(*,*) 'enter path to db with sta & stachan:'
read(*,'(a256)') dbin
write(*,*) dbin(1:lnblnk(dbin))
c....read in name of file containing list of dbnames.
c....each dbname in list refferes ito db with .eigen relation.
write(*,*) 'enter name of file within list of nmodes db:'
read(*,'(a256)') fname3
write(*,*) fname3(1:lnblnk(fname3))
c....read in file within event and moment tensor info
write(*,*) 'enter input CMT file name:'
read(*,'(a256)') fname4
write(*,*) fname4(1:lnblnk(fname4))
c....read in frequency range in mHz
write(*,*) 'min and max frequencies to be considered (mHz) : '
read(*,*) fmin,fmax
write(*,*) fmin,fmax
c....read in number of samples in Green function
write(*,*) 'enter # pts in greens fns .le. ',mseis,' :'
read(*,*) iscan
write(*,*) iscan
c.... read in output path to gsf name to store Green functions
write(*,*) 'enter Green functions output db file name:'
read(*,'(a256)') dbout
write(*,*) dbout(1:lnblnk(dbout))
write(*,*) '===================================================='
c
c.....open event file for which you want to compute green's functions
c.....read first line to get source and moment tensor info
c
open(12,file=fname4,status='old')
read(12,*) ename,jys,jds,jhs,jms,sss,slat,slon,sdep,dt
close (12)
write(*,1001) ename,jys,jds,jhs,jms,sss,slat,slon
write(*,1002) sdep
1001 format(' green: Event: ',a8,2x,i4,1x,i3,1x,i2,':',i2,':',f6.3,1x,
* 'lat = ',f8.3,', lon = ',f9.3)
1002 format(' green: source depth =',f5.1,' km')
write(*,1003) dt,iscan
1003 format(' green: step = ',f8.3,' sec, nsamples =',i7)
c convert human time to epoch time
time = htoepoch (jys,jds,jhs,jms,dble(sss))
endtime = time+dt*(iscan-1)
jdate = jys*1000+jds
c--
d0=sdep
cxx th=90.-slat
c.....convert event geographic latitude to geocentric
th = 90.0-atan(0.99329534*tan(slat/rad))*rad
ph=slon
jy=jys
jd=jds
jh=jhs
jm=jms
sec=sss
c
c.....open output file for green's functions
c
fmin = fmin*pi/500.
fmax = fmax*pi/500.
call source(fmin,fmax,lmax,nmodes,nmodet)
if(lmax.le.ml) goto 5
write(*,*) 'ERR010: green: max l =',lmax,' must be .le.',ml
stop ' '
cxx goto 99
5 iscan = iscan/2
call factor(iscan)
iscan = 2*iscan
if(iscan.gt.mseis) then
write(*,*) 'WARNING: green: # of points in Green ',
* 'functions is stripped to ',mseis
endif
iscan=min0(iscan,mseis)
t0=th/rad
p0=ph/rad
c0=cos(t0)
s0=sin(t0)
c
c====loop over records
c........read event header
c
c.....open file with station & channel info ---
write(*,*) 'green: Input dbname : ',dbin(1:lnblnk(dbin))
call read_site
call read_sitechan
c.....select channel sequence ---
call select_sitechan(jdate,nchan,numchan,numsta)
open(12,file=fname4,status='old')
inchn = 1
ifl = 0
c.....choose new single or triple of station(s)
6 iseq = 1
cxx
do ii = 1,12*iscan
grn(ii) = 0.0
enddo
cxx if(ifl.ge.30) goto 88
66 if(inchn.gt.nchan) goto 88
nc(iseq) = iabs(numchan(inchn))
ns(iseq) = numsta(inchn)
inchn = inchn+1
iseq = iseq+1
if(numchan(inchn-1).le.0) goto 7
goto 66
7 iseq = iseq-1
c.....print station and channel info ---
write(*,1004) sta_site(ns(1)),lat_site(ns(1)),
* lon_site(ns(1)),iseq
1004 format(' green: Station: ',a6,1x,f9.4,f10.4,' , Channels: ',i1)
do i = 1,iseq
write(*,*) 'green: Channel: # ',i,' ',sta_sitechan(nc(i)),
* chan_sitechan(nc(i)),hang_sitechan(nc(i)),
* vang_sitechan(nc(i))
enddo
c....check channels sequence: Z,N,E ---
if(iseq.gt.3) then
write(*,*) 'WARNING: green: # of channels is stripped to 3'
iseq = 3
endif
if(iseq.eq.2) then
write(*,*) 'WARNING: green: # of channels is stripped to 1'
iseq = 1
endif
ang(1) = (vang_sitechan(nc(1))-90.0)/rad
if(abs(vang_sitechan(nc(1))).gt.0.5) then
write(*,*)
* 'WARNING: green: Channel: # ',1,' is not vertical. ',
* 'Sequence ignored'
goto 6
endif
do i = 2,iseq
ang(i) = hang_sitechan(nc(i))/rad
if(abs(vang_sitechan(nc(i))-90.0).gt.0.5) then
write(*,*)
* 'WARNING: green: Channel: # ',i,' is not horizontal. ',
* 'Sequence ignored'
goto 6
endif
enddo
c
c compute green functions for selected channels
c
icomp = 0
do 90 isq=1,iseq
c.....extract channel parameters from relation tables
ifl = ifl+1
mchn = isq
iy = jy
id = jd
ih = jh
im = jm
ss = sec
cxx t1 = (90.0-lat_site(ns(1)))/rad
c.....convert station geographic latitude to geocentric
t1 = (90.0-atan(0.99329534*tan(lat_site(ns(1))/rad))*rad)/rad
p1 = lon_site(ns(1))
if(p1.lt.0.0) p1 = 360.0+p1
p1 = p1/rad
if(icomp.eq.2) goto 500
len=0
if(icomp.eq.1) goto 35
c
c....do some trigonometry
c epicentral distance: co, si
c azimuth of source: caz,saz
c
c1=cos(t1)
s1=sin(t1)
dp=p1-p0
co=c0*c1+s0*s1*cos(dp)
si=dsqrt(1.d0-co*co)
del = datan2(si,co)
del = del/pi*180.
write(*,'(a,f10.3)')' green: Epicentral Distance : ',del
sz=s1*sin(dp)/si
cz=(c0*co-c1)/(s0*si)
saz=-s0*sin(dp)/si
caz=(c0-co*c1)/(si*s1)
azim = datan2(saz,caz)
azim = azim/pi*180.
write(*,'(a,f10.3)')' green: Azimuth of Source : ',azim
c2=2.d0*(cz**2-sz**2)
s2=8.d0*cz*sz
c1=2.d0*cz
s1=2.d0*sz
c
c....generate the spherical harmonics
c
call zfcns(lmax,co,si)
if(mchn.ne.1) goto 35
c*** vertical component ***
icomp=1
do 25 i=1,nmodes
do 30 j=1,8
30 scalrs(j) = vecnl(j,i)
lp1=l+1
c
c....initial amplitudes at time t=0
c
wt(1,i)=e1*z(1,lp1)*au
wt(2,i)=e2*z(1,lp1)*au
wt(3,i)=e3*z(2,lp1)*au
wt(4,i)=e4*z(3,lp1)*au
25 continue
call prop(om,a0,dt,tstart,nmodes,len,iscan,4,prp)
call s4t6(grn,iscan,c1,s1,c2,s2)
goto 500
c*** theta and phi components ***
c*** spheroidal modes ***
35 icomp=2
do 40 i=1,nmodes
do 45 j=1,8
45 scalrs(j)=vecnl(j,i)
lp1=l+1
c
c....initial amplitudes at time t=0
c
wt(1,i)=e1*zp(1,lp1)*av
wt(2,i)=e2*zp(1,lp1)*av
wt(3,i)=e3*zp(2,lp1)*av
wt(4,i)=e4*zp(3,lp1)*av
wt(5,i)=e3*z(2,lp1)*av/si
40 wt(6,i)=e4*z(3,lp1)*av/si
call prop(om,a0,dt,tstart,nmodes,len,iscan,6,prp)
len=6*iscan
c
c*** toroidal modes ***
c
if(nmodet.eq.0) goto 61
do 60 i=1,nmodet
do 65 j=1,4
65 scalrs(j)=vecnlt(j,i)
lp1=l+1
c
c....initial amplitudes at time t=0
c
wt(1,i)=e1*z(2,lp1)/si
wt(2,i)=e2*z(3,lp1)/si
wt(3,i)=e1*zp(2,lp1)
60 wt(4,i)=e2*zp(3,lp1)
call prop(omt,a0t,dt,tstart,nmodet,len,iscan,4,prp)
61 continue
call s10t12(grn,iscan,c1,s1,c2,s2)
call rotate(grn,iscan,caz,saz,ang(2),ang(3))
c
c....greens function longer than data ? : add flags to data !
c
cxx 500 nscan=iscan
500 indx=0
if(mchn.eq.3) indx=6*iscan
len=6*iscan
c
c....write out green's functions
c
nscan = 6 * iscan
write(*,1000) ifl,sta_sitechan(nc(1)),chan_sitechan(nc(isq)),
* jys,jds,jhs,jms,sss,dt,nscan
1000 format(' green: ',i4,1x,a6,1x,a8,i4,1x,i3,1x,i2,':',i2,':',
* f6.3,1x,f8.3,1x,i6)
c write wfdisc relation with green functions
call default_wfdisc(1)
nrowwfdisc = 1
sta_wfdisc(1) = sta_sitechan(nc(1))
chan_wfdisc(1) = chan_sitechan(nc(isq))
chanid_wfdisc(1) = nc(isq)
time_wfdisc(1) = time
wfid_wfdisc(1) = ifl
jdate_wfdisc(1) = jdate
endtime_wfdisc(1) = time+(nscan-1)/dt
nsamp_wfdisc(1) = nscan
calib_wfdisc(1) = 1.0
calper_wfdisc(1) = 20.0
samprate_wfdisc(1) = 1.0/dt
segtype_wfdisc(1) = 'g'
foff_wfdisc(1) = 0
dir_wfdisc(1) = '.'
write(efname,'("g.",i5)') ifl
do i = 1,7
if(efname(i:i).eq.' ') efname(i:i) = '0'
enddo
dfile_wfdisc(1) = efname
do i = 1,nscan
grn(indx+i) = -grn(indx+i)
enddo
call put_wfdisc(1,nscan,grn(indx+1),ierr)
call write_wfdisc
90 continue
goto 6
88 continue
close(12)
99 continue
end
subroutine prop(om,a0,dt,tst,nmodes,len,npts,nfun,prp)
include "green.h"
real*8 ddt,dts,dt0,dt1,prp(nfun,npts),phi,ain
real*8 b0,b1,c0,c1,c2
common/propc/ddt,dts,dt0,dt1,phi,ain,b0,b1,c0,c1,c2
common/grnX/grn(12*mseis)
common/wts/wt(6,meig)
dimension om(*),a0(*)
c
c....stores green's function in multiplexed form
c
ddt = dt
dts = tst
dt0 = dts - 2*ddt
dt1 = dts - ddt
do 10 j=1,npts
do 10 i=1,nfun
10 prp(i,j) = 0.d0
c
c====loop over modes
c
do 50 j=1,nmodes
c
c....initialize propagator
c
b0 = -exp(-2*a0(j)*ddt)
b1 = 2*cos(om(j)*ddt) * exp( -a0(j)*ddt)
c0 = cos(om(j)*dt0) * exp( -a0(j)*dt0)
c1 = cos(om(j)*dt1) * exp( -a0(j)*dt1)
c
c====loop over time points
c
do 40 i=1,npts
c2 = b1*c1 + b0*c0
do 30 n=1,nfun
30 prp(n,i) = prp(n,i) + wt(n,j)*c2
c0 = c1
c1 = c2
40 continue
50 continue
c
c....demultiplex green's function
c
k=len
do 60 i=1,npts
k = k+1
do 60 n=1,nfun
grn((n-1)*npts+k) = prp(n,i)
60 continue
return
end
c***************************************************************
c source sub reads eigen functions from flat databases.
c List of dbnames are defined in dbnames.dat file. source read
c .eigen relations and select eigen functions for S & T modes
c****************************************************************
subroutine source(fmin,fmax,lmax,nmodes,nmodet)
implicit none
include "green.h"
include "fdb/fdb_eigen.h"
integer*4 lmax,nmodes,nmodet
real*4 fmin,fmax
c --- common blocks -------------------------------
real*4 d0,t0,p0,sec,tstart
integer*4 jy,jd,jh,jm
common/dheadX/d0,t0,p0,jy,jd,jh,jm,sec,tstart
real*4 x1,r0,x2,f
common/sclXXX/x1,r0,x2,f(4,3)
real*4 vecnl,vecnlt
common/vecnlX/vecnl(8,meig),vecnlt(4,meig)
real*4 om,a0,omt,a0t
common/modeX/om(meig),a0(meig),omt(meig),a0t(meig)
c --- other variables
real* 4 w,q,p,rn,wn,accn
real*4 pi2,fot,vn,rs,fl,fl1,fl3,u,v
real*4 wsq,e14,au,av,wr,aw
integer*4 npts,nrecl,ieig,idat,ierr,ifl,i,is,j,js
integer*4 ll,lll,m,l,n,ik
character*2 tendia,endian
c ---
character*64 dir
character*256 dbname
real*4 fnl(2),r(mk),buf(6,mk)
c ---
equivalence (fnl(1),n),(fnl(2),l)
data fot/1.33333333333/
pi2 = datan(1.0d0)*8.0d0
nmodes = 0
nmodet = 0
lmax=0
ieig = 9
idat = 10
c===================================================================
c Main loop by dbase names
c===================================================================
open(7,file=fname3,status='old')
c*** read dbnames list
8 read(7,'(a256)',end=9) dbname
nrecl = 2000
call open_eigen(dbname,ieig,idat,nrecl,dir,'r',ierr)
call read_eigen(ieig,ierr)
nrecl = (ncol_eigen*nraw_eigen+npar_eigen)*4
npts = nraw_eigen
call close_eigen(ieig,idat)
c
c....read in spheroidal and toroidal modes
c....in frequency band fmin < f < fmax
c
ifl = 0
call open_eigen(dbname,ieig,idat,nrecl,dir,'r',ierr)
10 ifl = ifl+1
call read_eigen(ieig,ierr)
if(ierr.ne.0) goto 30
if(ifl.ne.eigid_eigen) stop
* 'ERR011:eigen: flat and bin indices are different.'
w = pi2/per_eigen
if (w.lt.fmin) goto 10
if (w.le.fmax) goto 11
goto 10
11 read(idat,rec=eigid_eigen) n,l,w,q,rn,vn,accn,
+ (r(lll),(buf(ll,lll),ll=1,ncol_eigen-1),lll=1,nraw_eigen)
if(ncol_eigen.eq.3) then
do ik = 1,nraw_eigen
buf(3,ik) = 0.0
buf(4,ik) =0.0
enddo
endif
c swap bytes if necessary
tendia = endian()
if(datatype_eigen.ne.tendia) then
call swap1(fnl,4,2)
call swap1(w,4,1)
call swap1(q,4,1)
call swap1(rn,4,1)
call swap1(vn,4,1)
call swap1(accn,4,1)
call swap1(r,4,mk)
call swap1(buf,4,6*mk)
endif
npts = nraw_eigen
wn = vn/rn
c
c find radius interpolation points
c
rs=rn/1000.
r0=1.-(d0/rs)
do 5 i=1,npts
if(r(i).lt.r0)is=i
5 continue
x1=r(is)
js=is+1
x2=r(js)
if (typeo_eigen.eq.'S') then
C
c get source scalars for S mode
c
nmodes=nmodes+1
if(nmodes.ge.meig) then
write(*,*) 'ERR012: green: # sph. modes in band exceed ',
* 'max allowed number ',meig
stop ' '
endif
om(nmodes)=w
a0(nmodes)=q
lmax = max0(l,lmax)
fl=float(l)
fl1=fl+1.
fl3=fl*fl1
m=-1
do i=is,js
m=m+2
do j=1,4
f(j,m)=buf(j,i)
enddo
enddo
call cubic(2)
u=f(1,2)/r0
v=f(3,2)/r0
wsq=(w/wn)**2
e14=f(4,2)+u-v
if(l.eq.0) e14=0.
p = buf(5,npts)
au=-((wsq+2.*fot)*buf(1,npts)+fl1*p)*accn
av=-(wsq*buf(3,npts)-buf(1,npts)*fot-p)*accn
if(l.eq.0) av=0.
vecnl(1,nmodes)=fnl(1)
vecnl(2,nmodes)=fnl(2)
vecnl(3,nmodes)=f(2,2)
vecnl(4,nmodes)=u-.5*fl3*v
vecnl(5,nmodes)=e14
vecnl(6,nmodes)=2*v
vecnl(7,nmodes)=au
vecnl(8,nmodes)=av
c print 800,n,l,(vecnl(i,nmodes),i=3,8)
800 format(2i4,6e15.7)
else if (typeo_eigen.eq.'T') then
c
c get source scalars for T mode
c
nmodet=nmodet+1
if(nmodet.ge.meig) then
write(*,*) 'ERR012: green: # tor. modes in band exceed ',
* 'max allowed number ',meig
stop ' '
endif
omt(nmodet)=w
a0t(nmodet)=q
lmax = max0(l,lmax)
m=-1
do i=is,js
m=m+2
do j=1,2
f(j,m)=buf(j,i)
enddo
enddo
call cubic(1)
wr=f(1,2)/r0
wsq=(w/wn)**2
aw=-buf(1,npts)*wsq*accn
vecnlt(1,nmodet)=fnl(1)
vecnlt(2,nmodet)=fnl(2)
vecnlt(3,nmodet)=aw*(wr-f(2,2))
vecnlt(4,nmodet)=-4.*aw*wr
c print 801,n,l,(vecnlt(i,nmodet),i=3,4)
801 format(2i4,6e15.7)
c 665 continue
endif
goto 10
30 goto 8
9 close(7)
write(*,*) 'green: # sph. modes in band =',nmodes,
* ' must be .le. ',meig
write(*,*) 'green: # tor. modes in band =',nmodet,
* ' must be .le. ',meig
return
end
subroutine s4t6(grn,nscan,c1,s1,c2,s2)
implicit real*8(a-h,o-z)
real*4 grn(nscan,*)
do 1 i=1,nscan
f2=grn(i,2)
f5=grn(i,3)
f6=grn(i,4)
grn(i,2)=f2+f6*c2
grn(i,3)=f2-f6*c2
grn(i,4)=f5*c1
grn(i,5)=f5*s1
1 grn(i,6)=f6*s2
return
end
subroutine s10t12(grn,nscan,c1,s1,c2,s2)
implicit real*8(a-h,o-z)
real*4 grn(nscan,*)
s3=s2/4.d0
do 1 i=1,nscan
f11=grn(i,5)-grn(i,9)
f12=4.d0*grn(i,6)-grn(i,10)
grn(i,9)=f12*s3
grn(i,10)=-f11*s1
grn(i,11)=f11*c1
grn(i,12)=f12*c2
f2=grn(i,2)
f5=grn(i,3)-grn(i,7)
f6=grn(i,4)-grn(i,8)
grn(i,2)=f2+f6*c2
grn(i,3)=f2-f6*c2
grn(i,4)=f5*c1
grn(i,5)=f5*s1
grn(i,6)=f6*s2
grn(i,7)=0.d0
1 grn(i,8)=-f12*s3
return
end
subroutine rotate(grn,nscan,cz,sz,az1,az2)
implicit real*8(a-h,o-z)
real*4 grn(*),az1,az2
data pi/3.14159265358979d0/
pi2=0.5d0*pi
len=6*nscan
if(az1.eq.0.0.and.abs(az2-pi2).lt.1.d-4) then
cxx write(*,*)'Standard position.'
do i=1,len
j=len+i
d1=-grn(i)*cz-grn(j)*sz
d2=-grn(i)*sz+grn(j)*cz
grn(i)=d1
grn(j)=d2
enddo
else
fdel=cos(az2-az1-pi2)
sb=sin(az2-pi2)/fdel
cb=cos(az2-pi2)/fdel
sa=sin(az1)/fdel
ca=cos(az1)/fdel
do i=1,len
j=len+i
d1=-grn(i)*cz-grn(j)*sz
d2=-grn(i)*sz+grn(j)*cz
grn(i)=d1*cb+d2*sb
grn(j)=-d1*sa+d2*ca
enddo
end if
return
end
subroutine cubic(itype)
real*8 a1,a2,c0,c1,c2,c3,x,y,y2,y3
common/sclXXX/x1,r0,x2,f(4,3)
common/cubXXX/y,y2,y3,x,a1,a2
data isw/1/
if(isw.ne.1) goto 10
isw=0
y=x2-x1
y2=y**2
y3=y*y2
x=r0-x1
a1=3./y2
a2=2./y3
10 continue
do 20 i=1,itype
k=2*i
j=k-1
c0=f(j,1)
c1=f(k,1)
c3=f(j,3)-c0
c2=a1*c3-(2.*c1+f(k,3))/y
c3=(c1+f(k,3))/y2-a2*c3
f(j,2)=c0+x*(c1+x*(c2+x*c3))
20 f(k,2)=c1+x*(2.*c2+3.*x*c3)
return
end
subroutine zfcns(lmax,c,s)
c zfcns computes z(m,l,theta) and dz(m,l,theta)/dtheta,
c denoted z and p resp. all functions for 0 le m le
c max(2,l) and 0 le l le lmax are computed. c is cos(theta)
c and s is sin(theta).
c Z(m,l,theta) = b(m,l) * X(m,l,theta) where
c b(m,l) is given in G&D (1975) equation (21)
c and X(m,l,theta) is given in G&D (1975) equation (2)
c G&D = Gilbert & Dziewonski
implicit real*8(a-h,o-z)
include "green.h"
common/zfXX/z(3,ml),p(3,ml)
data pi/3.14159265358979d0/
z(1,1)=1d0/(4.d0*pi)
z(2,1)=0.d0
z(3,1)=0.d0
z(1,2)=3d0*c*z(1,1)
z(2,2)=1.5d0*s*z(1,1)
z(3,2)=0.d0
z(1,3)=2.5d0*(c*z(1,2)-z(1,1))
z(2,3)=5.d0*c*z(2,2)
z(3,3)=1.25d0*s*z(2,2)
p(1,1)=0.d0
p(2,1)=0.d0
p(3,1)=0.d0
p(1,2)=-2.d0*z(2,2)
p(2,2)=0.5d0*z(1,2)
p(3,2)=0.d0
p(1,3)=-2.d0*z(2,3)
p(2,3)=1.5d0*z(1,3)-2.d0*z(3,3)
p(3,3)=0.5d0*z(2,3)
if(lmax.le.2) return
lmaxp1=lmax+1
tlp1=5d0
do 10 lp1=4,lmaxp1
l=lp1-1
lm1=l-1
elmm=l
elpmm1=lm1
tlp1=tlp1+2d0
tlm3=tlp1-4d0
do 10 mp1=1,3
r=tlp1/elmm
q=elpmm1/tlm3
z(mp1,lp1)=r*(c*z(mp1,l)-q*z(mp1,lm1))
p(mp1,lp1)=r*(c*p(mp1,l)-s*z(mp1,l)-q*p(mp1,lm1))
elmm=elmm-1d0
10 elpmm1=elpmm1+1d0
return
end