From 3b2826fe0d979bf7b549d021539e82a46d3f6cf1 2023-06-02 16:33:00 From: Roberto Flores Date: 2023-06-02 16:33:00 Subject: [PATCH] add Ffiles --- diff --git a/schainf/Ffiles/acf2.pyf b/schainf/Ffiles/acf2.pyf new file mode 100644 index 0000000..ed0d093 --- /dev/null +++ b/schainf/Ffiles/acf2.pyf @@ -0,0 +1,520 @@ +! -*- f90 -*- +! Note: the context of this file is case sensitive. + +python module fdjac2__user__routines + interface fdjac2_user_interface + subroutine fcn(m,n,x,wa,iflag) ! in :full_profile_profile:lmdif1.f:fdjac2:unknown_interface + integer, optional,check(len(wa)>=m),depend(wa) :: m=len(wa) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: wa + integer :: iflag + end subroutine fcn + end interface fdjac2_user_interface +end python module fdjac2__user__routines +python module lmdif__user__routines + interface lmdif_user_interface + subroutine fcn(m,n,x,fvec,iflag) ! in :full_profile_profile:lmdif1.f:lmdif:unknown_interface + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + integer :: iflag + end subroutine fcn + end interface lmdif_user_interface +end python module lmdif__user__routines +python module full_profile_profile ! in + interface ! in :full_profile_profile + subroutine profile(acf_sum,acf_err,power,en,alag,thb2,bfm2,ote,ete,oti,eti,oph,eph,ophe,ephe,range2,ut,nhts,nacf,ibits,acf_avg_real,status) ! in :full_profile_profile:full_profile_profile.f + complex dimension(4,nhts,ibits) :: acf_sum + real dimension(nhts,ibits),depend(nhts,ibits) :: acf_err + real dimension(nhts),depend(nhts) :: power + real dimension(nhts),depend(nhts) :: en + real dimension(ibits),depend(ibits) :: alag + real dimension(nhts),depend(nhts) :: thb2 + real dimension(nhts),depend(nhts) :: bfm2 + real dimension(nacf),depend(nacf) :: ote + real dimension(nacf),depend(nacf) :: ete + real dimension(nacf),depend(nacf) :: oti + real dimension(nacf),depend(nacf) :: eti + real dimension(nacf),depend(nacf) :: oph + real dimension(nacf),depend(nacf) :: eph + real dimension(nacf),depend(nacf) :: ophe + real dimension(nacf),depend(nacf) :: ephe + real dimension(nhts),depend(nhts) :: range2 + real :: ut + integer, optional,check(shape(acf_sum,1)==nhts),depend(acf_sum) :: nhts=shape(acf_sum,1) + integer :: nacf + integer, optional,check(shape(acf_sum,2)==ibits),depend(acf_sum) :: ibits=shape(acf_sum,2) + real dimension(nhts,ibits),depend(nhts,ibits), :: acf_avg_real + real dimension(1) :: status + real :: chi2 + real dimension(91) :: densp + real dimension(91) :: tep + real dimension(91) :: trp + real dimension(91) :: tip + real dimension(91) :: hfp + real dimension(91) :: hefp + real dimension(91) :: altp + real :: r0 + real :: dr + real :: wl + real dimension(16,91) :: plag + real dimension(16,91) :: plag_errors + real :: sconst + real dimension(91) :: edensp + real dimension(91) :: etep + real dimension(91) :: etip + real dimension(91) :: ehfp + real dimension(91) :: ehefp + real dimension(85) :: bfld_prof + real dimension(85) :: alpha_prof + integer :: imode + real :: uttime + real dimension(34) :: ta + real dimension(30,5) :: bcoef + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + common /chisq/ chi2 + common /fpa/ densp,tep,trp,tip,hfp,hefp,altp,r0,dr,wl + common /data/ plag,plag_errors + common /sys/ sconst + common /errs/ edensp,etep,etip,ehfp,ehefp + common /mag/ bfld_prof,alpha_prof + common /mode/ imode + common /utime/ uttime + common /spline/ ta,bcoef + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + end subroutine profile + subroutine grid ! in :full_profile_profile:full_profile_profile.f + real dimension(34) :: ta + real dimension(30,5) :: bcoef + real dimension(91) :: densp + real dimension(91) :: tep + real dimension(91) :: trp + real dimension(91) :: tip + real dimension(91) :: hfp + real dimension(91) :: hefp + real dimension(91) :: altp + real :: r0 + real :: dr + real :: wl + real dimension(16,91) :: plag + real dimension(16,91) :: plag_errors + real :: sconst + real dimension(91) :: edensp + real dimension(91) :: etep + real dimension(91) :: etip + real dimension(91) :: ehfp + real dimension(91) :: ehefp + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + real :: chi2 + real :: uttime + common /spline/ ta,bcoef + common /fpa/ densp,tep,trp,tip,hfp,hefp,altp,r0,dr,wl + common /data/ plag,plag_errors + common /sys/ sconst + common /errs/ edensp,etep,etip,ehfp,ehefp + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /chisq/ chi2 + common /utime/ uttime + end subroutine grid + subroutine propagate(xe) ! in :full_profile_profile:full_profile_profile.f + real dimension(150) :: xe + real dimension(91) :: densp + real dimension(91) :: tep + real dimension(91) :: trp + real dimension(91) :: tip + real dimension(91) :: hfp + real dimension(91) :: hefp + real dimension(91) :: altp + real :: r0 + real :: dr + real :: wl + real dimension(16,91) :: plag + real dimension(16,91) :: plag_errors + real :: sconst + real dimension(91) :: edensp + real dimension(91) :: etep + real dimension(91) :: etip + real dimension(91) :: ehfp + real dimension(91) :: ehefp + real dimension(34) :: ta + real dimension(30,5) :: bcoef + common /fpa/ densp,tep,trp,tip,hfp,hefp,altp,r0,dr,wl + common /data/ plag,plag_errors + common /sys/ sconst + common /errs/ edensp,etep,etip,ehfp,ehefp + common /spline/ ta,bcoef + end subroutine propagate + subroutine fcn_lpreg(m,n,x,fvec,iflag) ! in :full_profile_profile:full_profile_profile.f + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + integer :: iflag + real dimension(34) :: ta + real dimension(30,5) :: bcoef + real dimension(91) :: densp + real dimension(91) :: tep + real dimension(91) :: trp + real dimension(91) :: tip + real dimension(91) :: hfp + real dimension(91) :: hefp + real dimension(91) :: altp + real :: r0 + real :: dr + real :: wl + real dimension(16,91) :: plag + real dimension(16,91) :: plag_errors + real :: sconst + real dimension(91) :: edensp + real dimension(91) :: etep + real dimension(91) :: etip + real dimension(91) :: ehfp + real dimension(91) :: ehefp + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + real :: chi2 + real :: uttime + common /spline/ ta,bcoef + common /fpa/ densp,tep,trp,tip,hfp,hefp,altp,r0,dr,wl + common /data/ plag,plag_errors + common /sys/ sconst + common /errs/ edensp,etep,etip,ehfp,ehefp + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /chisq/ chi2 + common /utime/ uttime + end subroutine fcn_lpreg + subroutine get_scale(plag2) ! in :full_profile_profile:full_profile_profile.f + real dimension(16,75) :: plag2 + real dimension(91) :: densp + real dimension(91) :: tep + real dimension(91) :: trp + real dimension(91) :: tip + real dimension(91) :: hfp + real dimension(91) :: hefp + real dimension(91) :: altp + real :: r0 + real :: dr + real :: wl + real dimension(16,91) :: plag + real dimension(16,91) :: plag_errors + real :: sconst + real dimension(91) :: edensp + real dimension(91) :: etep + real dimension(91) :: etip + real dimension(91) :: ehfp + real dimension(91) :: ehefp + common /fpa/ densp,tep,trp,tip,hfp,hefp,altp,r0,dr,wl + common /data/ plag,plag_errors + common /sys/ sconst + common /errs/ edensp,etep,etip,ehfp,ehefp + end subroutine get_scale + function enorm(n,x) ! in :full_profile_profile:lmdif1.f + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real :: enorm + end function enorm + subroutine fdjac2(fcn,m,n,x,fvec,fjac,ldfjac,iflag,epsfcn,wa) ! in :full_profile_profile:lmdif1.f + use fdjac2__user__routines + external fcn + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + real dimension(ldfjac,n),depend(n) :: fjac + integer, optional,check(shape(fjac,0)==ldfjac),depend(fjac) :: ldfjac=shape(fjac,0) + integer :: iflag + real :: epsfcn + real dimension(m),depend(m) :: wa + end subroutine fdjac2 + subroutine lmdif(fcn,m,n,x,fvec,ftol,xtol,gtol,maxfev,epsfcn,diag,mode,factor,nprint,info,nfev,fjac,ldfjac,ipvt,qtf,wa1,wa2,wa3,wa4) ! in :full_profile_profile:lmdif1.f + use lmdif__user__routines + external fcn + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + real :: ftol + real :: xtol + real :: gtol + integer :: maxfev + real :: epsfcn + real dimension(n),depend(n) :: diag + integer :: mode + real :: factor + integer :: nprint + integer :: info + integer :: nfev + real dimension(ldfjac,n),depend(n) :: fjac + integer, optional,check(shape(fjac,0)==ldfjac),depend(fjac) :: ldfjac=shape(fjac,0) + integer dimension(n),depend(n) :: ipvt + real dimension(n),depend(n) :: qtf + real dimension(n),depend(n) :: wa1 + real dimension(n),depend(n) :: wa2 + real dimension(n),depend(n) :: wa3 + real dimension(m),depend(m) :: wa4 + end subroutine lmdif + subroutine lmpar(n,r,ldr,ipvt,diag,qtb,delta,par,x,sdiag,wa1,wa2) ! in :full_profile_profile:lmdif1.f + integer, optional,check(shape(r,1)==n),depend(r) :: n=shape(r,1) + real dimension(ldr,n) :: r + integer, optional,check(shape(r,0)==ldr),depend(r) :: ldr=shape(r,0) + integer dimension(n),depend(n) :: ipvt + real dimension(n),depend(n) :: diag + real dimension(n),depend(n) :: qtb + real :: delta + real :: par + real dimension(n),depend(n) :: x + real dimension(n),depend(n) :: sdiag + real dimension(n),depend(n) :: wa1 + real dimension(n),depend(n) :: wa2 + end subroutine lmpar + subroutine qrfac(m,n,a,lda,pivot,ipvt,lipvt,rdiag,acnorm,wa) ! in :full_profile_profile:lmdif1.f + integer :: m + integer, optional,check(shape(a,1)==n),depend(a) :: n=shape(a,1) + real dimension(lda,n) :: a + integer, optional,check(shape(a,0)==lda),depend(a) :: lda=shape(a,0) + logical :: pivot + integer dimension(lipvt) :: ipvt + integer, optional,check(len(ipvt)>=lipvt),depend(ipvt) :: lipvt=len(ipvt) + real dimension(n),depend(n) :: rdiag + real dimension(n),depend(n) :: acnorm + real dimension(n),depend(n) :: wa + end subroutine qrfac + subroutine qrsolv(n,r,ldr,ipvt,diag,qtb,x,sdiag,wa) ! in :full_profile_profile:lmdif1.f + integer, optional,check(shape(r,1)==n),depend(r) :: n=shape(r,1) + real dimension(ldr,n) :: r + integer, optional,check(shape(r,0)==ldr),depend(r) :: ldr=shape(r,0) + integer dimension(n),depend(n) :: ipvt + real dimension(n),depend(n) :: diag + real dimension(n),depend(n) :: qtb + real dimension(n),depend(n) :: x + real dimension(n),depend(n) :: sdiag + real dimension(n),depend(n) :: wa + end subroutine qrsolv + function spmpar(i) ! in :full_profile_profile:lmdif1.f + integer :: i + real :: spmpar + end function spmpar + function cdtr1(depth) ! in :full_profile_profile:fitacf.f + real :: depth + real :: cdtr1 + end function cdtr1 + function czte1(zlag,tr) ! in :full_profile_profile:fitacf.f + real :: zlag + real :: tr + real :: czte1 + end function czte1 + subroutine fcn(m,n,x,fvec,iflag) ! in :full_profile_profile:fitacf.f + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + integer :: iflag + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + real dimension(100) :: tau + real dimension(100) :: rho + real dimension(100) :: sigma2 + real dimension(10) :: params + integer dimension(10) :: ifit + real :: chisq + real dimension(10000) :: ev + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /fitter/ tau,rho,sigma2,params,ifit + common /errs/ chisq + common /trans/ ev + end subroutine fcn + function cj_ion(theta,psi) ! in :full_profile_profile:fitacf.f + real :: theta + real :: psi + complex :: cj_ion + end function cj_ion + function cj_electron(theta,phi,psi,alpha) ! in :full_profile_profile:fitacf.f + real :: theta + real :: phi + real :: psi + real :: alpha + integer :: imode + complex :: cj_electron + common /mode/ imode + end function cj_electron + function y_ion(theta,psi) ! in :full_profile_profile:fitacf.f + real :: theta + real :: psi + complex :: y_ion + end function y_ion + function y_electron(theta,phi,psi,alpha) ! in :full_profile_profile:fitacf.f + real :: theta + real :: phi + real :: psi + real :: alpha + complex :: y_electron + end function y_electron + function spect1(omega) ! in :full_profile_profile:fitacf.f + real :: omega + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + integer :: imode + real :: spect1 + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /mode/ imode + end function spect1 + subroutine acf2(wl,tau,te1,ti1,fi1,ven1,vin1,wi1,nion1,alpha1,dens1,bfld1,acf) ! in :full_profile_profile:fitacf.f + real :: wl + real :: tau + real :: te1 + real dimension(nion1) :: ti1 + real dimension(nion1),depend(nion1) :: fi1 + real :: ven1 + real dimension(nion1),depend(nion1) :: vin1 + integer dimension(nion1),depend(nion1) :: wi1 + integer, optional,check(len(ti1)>=nion1),depend(ti1) :: nion1=len(ti1) + real :: alpha1 + real :: dens1 + real :: bfld1 + real :: acf + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + end subroutine acf2 + subroutine gaussq(tau,acf) ! in :full_profile_profile:fitacf.f + real :: tau + real :: acf + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + end subroutine gaussq + subroutine lagp(plag,wl,r0,dr,nl,nrange) ! in :full_profile_profile:lagp.f + real dimension(nl,nrange) :: plag + real :: wl + real :: r0 + real :: dr + integer, optional,check(shape(plag,0)==nl),depend(plag) :: nl=shape(plag,0) + integer, optional,check(shape(plag,1)==nrange),depend(plag) :: nrange=shape(plag,1) + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + real dimension(34) :: ta + real dimension(30,5) :: bcoef + real dimension(85) :: bfld_prof + real dimension(85) :: alpha_prof + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /spline/ ta,bcoef + common /mag/ bfld_prof,alpha_prof + end subroutine lagp + function atanh(x) ! in :full_profile_profile:lagp.f + real :: x + real :: atanh + end function atanh + subroutine get_spline(alt,dens,te,ti,hf,hef) ! in :full_profile_profile:lagp.f + real :: alt + real :: dens + real :: te + real :: ti + real :: hf + real :: hef + real dimension(34) :: ta + real dimension(30,5) :: bcoef + common /spline/ ta,bcoef + end subroutine get_spline + function bvalue(t,bcoef,n,k,x,jderiv) ! in :full_profile_profile:lagp.f + real dimension(n+k),depend(n,k) :: t + real dimension(n) :: bcoef + integer, optional,check(len(bcoef)>=n),depend(bcoef) :: n=len(bcoef) + integer :: k + real :: x + integer :: jderiv + real :: bvalue + end function bvalue + subroutine interv(xt,lxt,x,left,mflag) ! in :full_profile_profile:lagp.f + real dimension(lxt) :: xt + integer, optional,check(len(xt)>=lxt),depend(xt) :: lxt=len(xt) + real :: x + integer :: left + integer :: mflag + end subroutine interv + function r1mach(i) ! in :full_profile_profile:r1mach.f + integer :: i + integer :: cray1 + real :: r1mach + common /d8mach/ cray1 + end function r1mach + end interface +end python module full_profile_profile + +! This file was auto-generated with f2py (version:2). +! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/schainf/Ffiles/arrays.c b/schainf/Ffiles/arrays.c new file mode 100644 index 0000000..2313363 --- /dev/null +++ b/schainf/Ffiles/arrays.c @@ -0,0 +1,67 @@ +float **array2(int m, int n){ + + int i,j; + float **temp; + + temp=(float **)malloc(sizeof(double)*m); + + temp[0]=(float *)malloc(sizeof(double)*m*n); + for(j=1;j $2 +cat $1 | awk -f script2 > $3 \ No newline at end of file diff --git a/schainf/Ffiles/bfmodel/dgrf00 b/schainf/Ffiles/bfmodel/dgrf00 new file mode 100644 index 0000000..429f457 --- /dev/null +++ b/schainf/Ffiles/bfmodel/dgrf00 @@ -0,0 +1,106 @@ + dgrf00 + 13 6371.2 2000.0 + 1 0 -29619.40 0.00 0.00 0.00 DGRF2000 1 + 1 1 -1728.20 5186.10 0.00 0.00 DGRF2000 2 + 2 0 -2267.70 0.00 0.00 0.00 DGRF2000 3 + 2 1 3068.40 -2481.60 0.00 0.00 DGRF2000 4 + 2 2 1670.90 -458.00 0.00 0.00 DGRF2000 5 + 3 0 1339.60 0.00 0.00 0.00 DGRF2000 6 + 3 1 -2288.00 -227.60 0.00 0.00 DGRF2000 7 + 3 2 1252.10 293.40 0.00 0.00 DGRF2000 8 + 3 3 714.50 -491.10 0.00 0.00 DGRF2000 9 + 4 0 932.30 0.00 0.00 0.00 DGRF2000 10 + 4 1 786.80 272.60 0.00 0.00 DGRF2000 11 + 4 2 250.00 -231.90 0.00 0.00 DGRF2000 12 + 4 3 -403.00 119.80 0.00 0.00 DGRF2000 13 + 4 4 111.30 -303.80 0.00 0.00 DGRF2000 14 + 5 0 -218.80 0.00 0.00 0.00 DGRF2000 15 + 5 1 351.40 43.80 0.00 0.00 DGRF2000 16 + 5 2 222.30 171.90 0.00 0.00 DGRF2000 17 + 5 3 -130.40 -133.10 0.00 0.00 DGRF2000 18 + 5 4 -168.60 -39.30 0.00 0.00 DGRF2000 19 + 5 5 -12.90 106.30 0.00 0.00 DGRF2000 20 + 6 0 72.30 0.00 0.00 0.00 DGRF2000 21 + 6 1 68.20 -17.40 0.00 0.00 DGRF2000 22 + 6 2 74.20 63.70 0.00 0.00 DGRF2000 23 + 6 3 -160.90 65.10 0.00 0.00 DGRF2000 24 + 6 4 -5.90 -61.20 0.00 0.00 DGRF2000 25 + 6 5 16.90 0.70 0.00 0.00 DGRF2000 26 + 6 6 -90.40 43.80 0.00 0.00 DGRF2000 27 + 7 0 79.00 0.00 0.00 0.00 DGRF2000 28 + 7 1 -74.00 -64.60 0.00 0.00 DGRF2000 29 + 7 2 0.00 -24.20 0.00 0.00 DGRF2000 30 + 7 3 33.30 6.20 0.00 0.00 DGRF2000 31 + 7 4 9.10 24.00 0.00 0.00 DGRF2000 32 + 7 5 6.90 14.80 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3 33. 6. + 7 4 9. 24. + 7 5 7. 15. + 7 6 8. -25. + 7 7 -2. -6. + 8 0 25. .0 + 8 1 6. 12. + 8 2 -9. -22. + 8 3 -8. 8. + 8 4 -17. -21. + 8 5 9. 15. + 8 6 7. 9. + 8 7 -8. -16. + 8 8 -7. -3. + 9 0 5. .0 + 9 1 9. -20. + 9 2 3. 13. + 9 3 -8. 12. + 9 4 6. -6. + 9 5 -9. -8. + 9 6 -2. 9. + 9 7 9. 4. + 9 8 -4. -8. + 9 9 -8. 5. + 10 0 -2. .0 + 10 1 -6. 1. + 10 2 2. 0. + 10 3 -3. 4. + 10 4 0. 5. + 10 5 4. -6. + 10 6 1. -1. + 10 7 2. -3. + 10 8 4. 0. + 10 9 0. -2. + 10 10 -1. -8. diff --git a/schainf/Ffiles/bfmodel/igrf2000.new b/schainf/Ffiles/bfmodel/igrf2000.new new file mode 100644 index 0000000..530f3bb --- /dev/null +++ b/schainf/Ffiles/bfmodel/igrf2000.new @@ -0,0 +1,67 @@ +igrf2000 +10 6371.2 2000.0 + 1 0 -29615. 0. + 1 1 -1728. 5186. + 2 0 -2267. 0. + 2 1 3072. -2478. + 2 2 1672. -458. + 3 0 1341. 0. + 3 1 -2290. -227. + 3 2 1253. 296. + 3 3 715. -492. + 4 0 935. 0. + 4 1 787. 272. + 4 2 251. -232. + 4 3 -405. 119. + 4 4 110. -304. + 5 0 -217. 0. + 5 1 351. 44. + 5 2 222. 172. + 5 3 -131. 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-227. + 3 2 1253. 296. + 3 3 715. -492. + 4 0 935. 0. + 4 1 787. 272. + 4 2 251. -232. + 4 3 -405. 119. + 4 4 110. -304. + 5 0 -217. 0. + 5 1 351. 44. + 5 2 222. 172. + 5 3 -131. -134. + 5 4 -169. -40. + 5 5 -12. 107. + 6 0 72. 0. + 6 1 68. -17. + 6 2 74. 64. + 6 3 -161. 65. + 6 4 -5. -61. + 6 5 17. 1. + 6 6 -91. 44. + 7 0 79. 0. + 7 1 -74. -65. + 7 2 0. -24. + 7 3 33. 6. + 7 4 9. 24. + 7 5 7. 15. + 7 6 8. -25. + 7 7 -2. -6. + 8 0 25. 0. + 8 1 6. 12. + 8 2 -9. -22. + 8 3 -8. 8. + 8 4 -17. -21. + 8 5 9. 15. + 8 6 7. 9. + 8 7 -8. -16. + 8 8 -7. -3. + 9 0 5. 0. + 9 1 9. -20. + 9 2 3. 13. + 9 3 -8. 12. + 9 4 6. -6. + 9 5 -9. -8. + 9 6 -2. 9. + 9 7 9. 4. + 9 8 -4. -8. + 9 9 -8. 5. +10 0 -2. 0. +10 1 -6. 1. +10 2 2. 0. +10 3 -3. 4. +10 4 0. 5. +10 5 4. -6. +10 6 1. -1. +10 7 2. -3. +10 8 4. 0. +10 9 0. -2. +10 10 -1. -8. diff --git a/schainf/Ffiles/bfmodel/igrf2000s b/schainf/Ffiles/bfmodel/igrf2000s new file mode 100644 index 0000000..fca343a --- /dev/null +++ b/schainf/Ffiles/bfmodel/igrf2000s @@ -0,0 +1,46 @@ + igrf00s + 8 6371.2 2005.0 + 1 0 14.6 0. + 1 1 10.7 -22.5 + 2 0 -12.4 0. + 2 1 1.1 -20.6 + 2 2 -1.1 -9.6 + 3 0 0.7 0. + 3 1 -5.4 6.0 + 3 2 0.9 -0.1 + 3 3 -7.7 -14.2 + 4 0 -1.3 0. + 4 1 1.6 2.1 + 4 2 -7.3 1.3 + 4 3 2.9 5.0 + 4 4 -3.2 0.3 + 5 0 0.0 0. + 5 1 -0.7 -0.1 + 5 2 -2.1 0.6 + 5 3 -2.8 1.7 + 5 4 -0.8 1.9 + 5 5 2.5 0.1 + 6 0 1.0 0. + 6 1 -0.4 -0.2 + 6 2 0.9 -1.4 + 6 3 2.0 0.0 + 6 4 -0.6 -0.8 + 6 5 -0.3 0.0 + 6 6 1.2 0.9 + 7 0 -0.4 0. + 7 1 -0.4 1.1 + 7 2 -0.3 0.0 + 7 3 1.1 0.3 + 7 4 1.1 -0.1 + 7 5 -0.2 -0.6 + 7 6 0.6 -0.7 + 7 7 -0.9 0.2 + 8 0 -0.3 0. + 8 1 0.2 0.1 + 8 2 -0.3 0.0 + 8 3 0.4 0.0 + 8 4 -1.0 0.3 + 8 5 0.3 0.6 + 8 6 -0.5 -0.4 + 8 7 -0.7 0.3 + 8 8 -0.4 0.7 diff --git a/schainf/Ffiles/bfmodel/igrf2000s.new1 b/schainf/Ffiles/bfmodel/igrf2000s.new1 new file mode 100644 index 0000000000000000000000000000000000000000..bd250d8cee9e83ee5070b490cd1c7f9660cabe96 GIT binary patch literal 1217 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zj&qcLwO=;>cb|U*q?=CZXlHvzl2E-yuvf(zZX+-6OU}D3gD?CgGz zwf`po4)9yWZmre+&r0ytCb**s-qr+fZ-O6cz>bioyDlFrD7(qywBhJ&f`iE$foqYV zYg!Eaz(4F8J?r)PM~8+kz%l=r_pA^4!PS{?aPEd5>IhqSz3%J6;n_=MkBoGb&*W~;>a7|qgg@Q8#o4Fnix`sbcPtAt|Q=ba+ z;1&P$Tp$#*73w(}&6}!d-4T!Iv1P$}0*(T%g~x)=ic|KAm>(9t=HWB(*9C4pK|k3a zk%ssu1?Thn4+yNkiT{Zv{$_v1hLg76|6%-5fwfrhXTslO!L66~Jh0b4ZlixYXw=^> mHf^WHRqPN69}&J*f68lj`#r+Ys;jmBt|tEXh5z{9`2PuEBG4lM literal 0 Hc$@1 and from power series when abs(z)<=1. +C +C In most complex variable computation, one must evaluate ele- +C mentary functions. When the magnitude of Z is large, losses +C of significance by argument reduction occur. Consequently, if +C the magnitude of ZETA=(2/3)*Z**(3/2) exceeds U1=SQRT(0.5/UR), +C then losses exceeding half precision are likely and an error +C flag IERR=3 is triggered where UR=R1MACH(4)=UNIT ROUNDOFF. +C Also, if the magnitude of ZETA is larger than U2=0.5/UR, then +C all significance is lost and IERR=4. In order to use the INT +C function, ZETA must be further restricted not to exceed +C U3=I1MACH(9)=LARGEST INTEGER. Thus, the magnitude of ZETA +C must be restricted by MIN(U2,U3). In IEEE arithmetic, U1,U2, +C and U3 are approximately 2.0E+3, 4.2E+6, 2.1E+9 in single +C precision and 4.7E+7, 2.3E+15, 2.1E+9 in double precision. +C This makes U2 limiting is single precision and U3 limiting +C in double precision. This means that the magnitude of Z +C cannot exceed approximately 3.4E+4 in single precision and +C 2.1E+6 in double precision. This also means that one can +C expect to retain, in the worst cases on 32-bit machines, +C no digits in single precision and only 6 digits in double +C precision. +C +C The approximate relative error in the magnitude of a complex +C Bessel function can be expressed as P*10**S where P=MAX(UNIT +C ROUNDOFF,1.0E-18) is the nominal precision and 10**S repre- +C sents the increase in error due to argument reduction in the +C elementary functions. Here, S=MAX(1,ABS(LOG10(ABS(Z))), +C ABS(LOG10(FNU))) approximately (i.e., S=MAX(1,ABS(EXPONENT OF +C ABS(Z),ABS(EXPONENT OF FNU)) ). However, the phase angle may +C have only absolute accuracy. This is most likely to occur +C when one component (in magnitude) is larger than the other by +C several orders of magnitude. If one component is 10**K larger +C than the other, then one can expect only MAX(ABS(LOG10(P))-K, +C 0) significant digits; or, stated another way, when K exceeds +C the exponent of P, no significant digits remain in the smaller +C component. However, the phase angle retains absolute accuracy +C because, in complex arithmetic with precision P, the smaller +C component will not (as a rule) decrease below P times the +C magnitude of the larger component. In these extreme cases, +C the principal phase angle is on the order of +P, -P, PI/2-P, +C or -PI/2+P. +C +C***REFERENCES 1. M. Abramowitz and I. A. Stegun, Handbook of Mathe- +C matical Functions, National Bureau of Standards +C Applied Mathematics Series 55, U. S. Department +C of Commerce, Tenth Printing (1972) or later. +C 2. D. E. Amos, Computation of Bessel Functions of +C Complex Argument and Large Order, Report SAND83-0643, +C Sandia National Laboratories, Albuquerque, NM, May +C 1983. +C 3. D. E. Amos, A Subroutine Package for Bessel Functions +C of a Complex Argument and Nonnegative Order, Report +C SAND85-1018, Sandia National Laboratory, Albuquerque, +C NM, May 1985. +C 4. D. E. Amos, A portable package for Bessel functions +C of a complex argument and nonnegative order, ACM +C Transactions on Mathematical Software, 12 (September +C 1986), pp. 265-273. +C +C***ROUTINES CALLED CACAI, CBKNU, I1MACH, R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 890801 REVISION DATE from Version 3.2 +C 910415 Prologue converted to Version 4.0 format. (BAB) +C 920128 Category corrected. (WRB) +C 920811 Prologue revised. (DWL) +C***END PROLOGUE CAIRY + COMPLEX AI, CONE, CSQ, CY, S1, S2, TRM1, TRM2, Z, ZTA, Z3 + REAL AA, AD, AK, ALIM, ATRM, AZ, AZ3, BK, CK, COEF, C1, C2, DIG, + * DK, D1, D2, ELIM, FID, FNU, RL, R1M5, SFAC, TOL, TTH, ZI, ZR, + * Z3I, Z3R, R1MACH, BB, ALAZ + INTEGER ID, IERR, IFLAG, K, KODE, K1, K2, MR, NN, NZ, I1MACH + DIMENSION CY(1) + DATA TTH, C1, C2, COEF /6.66666666666666667E-01, + * 3.55028053887817240E-01,2.58819403792806799E-01, + * 1.83776298473930683E-01/ + DATA CONE / (1.0E0,0.0E0) / +C***FIRST EXECUTABLE STATEMENT CAIRY + IERR = 0 + NZ=0 + IF (ID.LT.0 .OR. ID.GT.1) IERR=1 + IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 + IF (IERR.NE.0) RETURN + AZ = ABS(Z) + TOL = MAX(R1MACH(4),1.0E-18) + FID = ID + IF (AZ.GT.1.0E0) GO TO 60 +C----------------------------------------------------------------------- +C POWER SERIES FOR ABS(Z).LE.1. +C----------------------------------------------------------------------- + S1 = CONE + S2 = CONE + IF (AZ.LT.TOL) GO TO 160 + AA = AZ*AZ + IF (AA.LT.TOL/AZ) GO TO 40 + TRM1 = CONE + TRM2 = CONE + ATRM = 1.0E0 + Z3 = Z*Z*Z + AZ3 = AZ*AA + AK = 2.0E0 + FID + BK = 3.0E0 - FID - FID + CK = 4.0E0 - FID + DK = 3.0E0 + FID + FID + D1 = AK*DK + D2 = BK*CK + AD = MIN(D1,D2) + AK = 24.0E0 + 9.0E0*FID + BK = 30.0E0 - 9.0E0*FID + Z3R = REAL(Z3) + Z3I = AIMAG(Z3) + DO 30 K=1,25 + TRM1 = TRM1*CMPLX(Z3R/D1,Z3I/D1) + S1 = S1 + TRM1 + TRM2 = TRM2*CMPLX(Z3R/D2,Z3I/D2) + S2 = S2 + TRM2 + ATRM = ATRM*AZ3/AD + D1 = D1 + AK + D2 = D2 + BK + AD = MIN(D1,D2) + IF (ATRM.LT.TOL*AD) GO TO 40 + AK = AK + 18.0E0 + BK = BK + 18.0E0 + 30 CONTINUE + 40 CONTINUE + IF (ID.EQ.1) GO TO 50 + AI = S1*CMPLX(C1,0.0E0) - Z*S2*CMPLX(C2,0.0E0) + IF (KODE.EQ.1) RETURN + ZTA = Z*CSQRT(Z)*CMPLX(TTH,0.0E0) + AI = AI*CEXP(ZTA) + RETURN + 50 CONTINUE + AI = -S2*CMPLX(C2,0.0E0) + IF (AZ.GT.TOL) AI = AI + Z*Z*S1*CMPLX(C1/(1.0E0+FID),0.0E0) + IF (KODE.EQ.1) RETURN + ZTA = Z*CSQRT(Z)*CMPLX(TTH,0.0E0) + AI = AI*CEXP(ZTA) + RETURN +C----------------------------------------------------------------------- +C CASE FOR ABS(Z).GT.1.0 +C----------------------------------------------------------------------- + 60 CONTINUE + FNU = (1.0E0+FID)/3.0E0 +C----------------------------------------------------------------------- +C SET PARAMETERS RELATED TO MACHINE CONSTANTS. +C TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18. +C ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. +C EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND +C EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR +C UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. +C RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. +C DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). +C----------------------------------------------------------------------- + K1 = I1MACH(12) + K2 = I1MACH(13) + R1M5 = R1MACH(5) + K = MIN(ABS(K1),ABS(K2)) + ELIM = 2.303E0*(K*R1M5-3.0E0) + K1 = I1MACH(11) - 1 + AA = R1M5*K1 + DIG = MIN(AA,18.0E0) + AA = AA*2.303E0 + ALIM = ELIM + MAX(-AA,-41.45E0) + RL = 1.2E0*DIG + 3.0E0 + ALAZ=ALOG(AZ) +C----------------------------------------------------------------------- +C TEST FOR RANGE +C----------------------------------------------------------------------- + AA=0.5E0/TOL + BB=I1MACH(9)*0.5E0 + AA=MIN(AA,BB) + AA=AA**TTH + IF (AZ.GT.AA) GO TO 260 + AA=SQRT(AA) + IF (AZ.GT.AA) IERR=3 + CSQ=CSQRT(Z) + ZTA=Z*CSQ*CMPLX(TTH,0.0E0) +C----------------------------------------------------------------------- +C RE(ZTA).LE.0 WHEN RE(Z).LT.0, ESPECIALLY WHEN IM(Z) IS SMALL +C----------------------------------------------------------------------- + IFLAG = 0 + SFAC = 1.0E0 + ZI = AIMAG(Z) + ZR = REAL(Z) + AK = AIMAG(ZTA) + IF (ZR.GE.0.0E0) GO TO 70 + BK = REAL(ZTA) + CK = -ABS(BK) + ZTA = CMPLX(CK,AK) + 70 CONTINUE + IF (ZI.NE.0.0E0) GO TO 80 + IF (ZR.GT.0.0E0) GO TO 80 + ZTA = CMPLX(0.0E0,AK) + 80 CONTINUE + AA = REAL(ZTA) + IF (AA.GE.0.0E0 .AND. ZR.GT.0.0E0) GO TO 100 + IF (KODE.EQ.2) GO TO 90 +C----------------------------------------------------------------------- +C OVERFLOW TEST +C----------------------------------------------------------------------- + IF (AA.GT.(-ALIM)) GO TO 90 + AA = -AA + 0.25E0*ALAZ + IFLAG = 1 + SFAC = TOL + IF (AA.GT.ELIM) GO TO 240 + 90 CONTINUE +C----------------------------------------------------------------------- +C CBKNU AND CACAI RETURN EXP(ZTA)*K(FNU,ZTA) ON KODE=2 +C----------------------------------------------------------------------- + MR = 1 + IF (ZI.LT.0.0E0) MR = -1 + CALL CACAI(ZTA, FNU, KODE, MR, 1, CY, NN, RL, TOL, ELIM, ALIM) + IF (NN.LT.0) GO TO 250 + NZ = NZ + NN + GO TO 120 + 100 CONTINUE + IF (KODE.EQ.2) GO TO 110 +C----------------------------------------------------------------------- +C UNDERFLOW TEST +C----------------------------------------------------------------------- + IF (AA.LT.ALIM) GO TO 110 + AA = -AA - 0.25E0*ALAZ + IFLAG = 2 + SFAC = 1.0E0/TOL + IF (AA.LT.(-ELIM)) GO TO 180 + 110 CONTINUE + CALL CBKNU(ZTA, FNU, KODE, 1, CY, NZ, TOL, ELIM, ALIM) + 120 CONTINUE + S1 = CY(1)*CMPLX(COEF,0.0E0) + IF (IFLAG.NE.0) GO TO 140 + IF (ID.EQ.1) GO TO 130 + AI = CSQ*S1 + RETURN + 130 AI = -Z*S1 + RETURN + 140 CONTINUE + S1 = S1*CMPLX(SFAC,0.0E0) + IF (ID.EQ.1) GO TO 150 + S1 = S1*CSQ + AI = S1*CMPLX(1.0E0/SFAC,0.0E0) + RETURN + 150 CONTINUE + S1 = -S1*Z + AI = S1*CMPLX(1.0E0/SFAC,0.0E0) + RETURN + 160 CONTINUE + AA = 1.0E+3*R1MACH(1) + S1 = CMPLX(0.0E0,0.0E0) + IF (ID.EQ.1) GO TO 170 + IF (AZ.GT.AA) S1 = CMPLX(C2,0.0E0)*Z + AI = CMPLX(C1,0.0E0) - S1 + RETURN + 170 CONTINUE + AI = -CMPLX(C2,0.0E0) + AA = SQRT(AA) + IF (AZ.GT.AA) S1 = Z*Z*CMPLX(0.5E0,0.0E0) + AI = AI + S1*CMPLX(C1,0.0E0) + RETURN + 180 CONTINUE + NZ = 1 + AI = CMPLX(0.0E0,0.0E0) + RETURN + 240 CONTINUE + NZ = 0 + IERR=2 + RETURN + 250 CONTINUE + IF(NN.EQ.(-1)) GO TO 240 + NZ=0 + IERR=5 + RETURN + 260 CONTINUE + IERR=4 + NZ=0 + RETURN + END diff --git a/schainf/Ffiles/casyi.f b/schainf/Ffiles/casyi.f new file mode 100644 index 0000000..fdb2ee2 --- /dev/null +++ b/schainf/Ffiles/casyi.f @@ -0,0 +1,136 @@ +*DECK CASYI + SUBROUTINE CASYI (Z, FNU, KODE, N, Y, NZ, RL, TOL, ELIM, ALIM) +C***BEGIN PROLOGUE CASYI +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBESI and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CASYI-A, ZASYI-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CASYI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY +C MEANS OF THE ASYMPTOTIC EXPANSION FOR LARGE ABS(Z) IN THE +C REGION ABS(Z).GT.MAX(RL,FNU*FNU/2). NZ=0 IS A NORMAL RETURN. +C NZ.LT.0 INDICATES AN OVERFLOW ON KODE=1. +C +C***SEE ALSO CBESI, CBESK +C***ROUTINES CALLED R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CASYI + COMPLEX AK1, CK, CONE, CS1, CS2, CZ, CZERO, DK, EZ, P1, RZ, S2, + * Y, Z + REAL AA, ACZ, AEZ, AK, ALIM, ARG, ARM, ATOL, AZ, BB, BK, DFNU, + * DNU2, ELIM, FDN, FNU, PI, RL, RTPI, RTR1, S, SGN, SQK, TOL, X, + * YY, R1MACH + INTEGER I, IB, IL, INU, J, JL, K, KODE, KODED, M, N, NN, NZ + DIMENSION Y(N) + DATA PI, RTPI /3.14159265358979324E0 , 0.159154943091895336E0 / + DATA CZERO, CONE / (0.0E0,0.0E0), (1.0E0,0.0E0) / +C***FIRST EXECUTABLE STATEMENT CASYI + NZ = 0 + AZ = ABS(Z) + X = REAL(Z) + ARM = 1.0E+3*R1MACH(1) + RTR1 = SQRT(ARM) + IL = MIN(2,N) + DFNU = FNU + (N-IL) +C----------------------------------------------------------------------- +C OVERFLOW TEST +C----------------------------------------------------------------------- + AK1 = CMPLX(RTPI,0.0E0)/Z + AK1 = CSQRT(AK1) + CZ = Z + IF (KODE.EQ.2) CZ = Z - CMPLX(X,0.0E0) + ACZ = REAL(CZ) + IF (ABS(ACZ).GT.ELIM) GO TO 80 + DNU2 = DFNU + DFNU + KODED = 1 + IF ((ABS(ACZ).GT.ALIM) .AND. (N.GT.2)) GO TO 10 + KODED = 0 + AK1 = AK1*CEXP(CZ) + 10 CONTINUE + FDN = 0.0E0 + IF (DNU2.GT.RTR1) FDN = DNU2*DNU2 + EZ = Z*CMPLX(8.0E0,0.0E0) +C----------------------------------------------------------------------- +C WHEN Z IS IMAGINARY, THE ERROR TEST MUST BE MADE RELATIVE TO THE +C FIRST RECIPROCAL POWER SINCE THIS IS THE LEADING TERM OF THE +C EXPANSION FOR THE IMAGINARY PART. +C----------------------------------------------------------------------- + AEZ = 8.0E0*AZ + S = TOL/AEZ + JL = RL+RL + 2 + YY = AIMAG(Z) + P1 = CZERO + IF (YY.EQ.0.0E0) GO TO 20 +C----------------------------------------------------------------------- +C CALCULATE EXP(PI*(0.5+FNU+N-IL)*I) TO MINIMIZE LOSSES OF +C SIGNIFICANCE WHEN FNU OR N IS LARGE +C----------------------------------------------------------------------- + INU = FNU + ARG = (FNU-INU)*PI + INU = INU + N - IL + AK = -SIN(ARG) + BK = COS(ARG) + IF (YY.LT.0.0E0) BK = -BK + P1 = CMPLX(AK,BK) + IF (MOD(INU,2).EQ.1) P1 = -P1 + 20 CONTINUE + DO 50 K=1,IL + SQK = FDN - 1.0E0 + ATOL = S*ABS(SQK) + SGN = 1.0E0 + CS1 = CONE + CS2 = CONE + CK = CONE + AK = 0.0E0 + AA = 1.0E0 + BB = AEZ + DK = EZ + DO 30 J=1,JL + CK = CK*CMPLX(SQK,0.0E0)/DK + CS2 = CS2 + CK + SGN = -SGN + CS1 = CS1 + CK*CMPLX(SGN,0.0E0) + DK = DK + EZ + AA = AA*ABS(SQK)/BB + BB = BB + AEZ + AK = AK + 8.0E0 + SQK = SQK - AK + IF (AA.LE.ATOL) GO TO 40 + 30 CONTINUE + GO TO 90 + 40 CONTINUE + S2 = CS1 + IF (X+X.LT.ELIM) S2 = S2 + P1*CS2*CEXP(-Z-Z) + FDN = FDN + 8.0E0*DFNU + 4.0E0 + P1 = -P1 + M = N - IL + K + Y(M) = S2*AK1 + 50 CONTINUE + IF (N.LE.2) RETURN + NN = N + K = NN - 2 + AK = K + RZ = (CONE+CONE)/Z + IB = 3 + DO 60 I=IB,NN + Y(K) = CMPLX(AK+FNU,0.0E0)*RZ*Y(K+1) + Y(K+2) + AK = AK - 1.0E0 + K = K - 1 + 60 CONTINUE + IF (KODED.EQ.0) RETURN + CK = CEXP(CZ) + DO 70 I=1,NN + Y(I) = Y(I)*CK + 70 CONTINUE + RETURN + 80 CONTINUE + NZ = -1 + RETURN + 90 CONTINUE + NZ=-2 + RETURN + END diff --git a/schainf/Ffiles/caxpy.f b/schainf/Ffiles/caxpy.f new file mode 100644 index 0000000..b0c7f78 --- /dev/null +++ b/schainf/Ffiles/caxpy.f @@ -0,0 +1,139 @@ +*> \brief \b CAXPY +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* SUBROUTINE CAXPY(N,CA,CX,INCX,CY,INCY) +* +* .. Scalar Arguments .. +* COMPLEX CA +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* COMPLEX CX(*),CY(*) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CAXPY constant times a vector plus a vector. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> number of elements in input vector(s) +*> \endverbatim +*> +*> \param[in] CA +*> \verbatim +*> CA is COMPLEX +*> On entry, CA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] CX +*> \verbatim +*> CX is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> storage spacing between elements of CX +*> \endverbatim +*> +*> \param[in,out] CY +*> \verbatim +*> CY is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> storage spacing between elements of CY +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2017 +* +*> \ingroup complex_blas_level1 +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CAXPY(N,CA,CX,INCX,CY,INCY) +* +* -- Reference BLAS level1 routine (version 3.8.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2017 +* +* .. Scalar Arguments .. + COMPLEX CA + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + COMPLEX CX(*),CY(*) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + INTEGER I,IX,IY +* .. +* .. External Functions .. + REAL SCABS1 + EXTERNAL SCABS1 +* .. + IF (N.LE.0) RETURN + IF (SCABS1(CA).EQ.0.0E+0) RETURN + IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN +* +* code for both increments equal to 1 +* + DO I = 1,N + CY(I) = CY(I) + CA*CX(I) + END DO + ELSE +* +* code for unequal increments or equal increments +* not equal to 1 +* + IX = 1 + IY = 1 + IF (INCX.LT.0) IX = (-N+1)*INCX + 1 + IF (INCY.LT.0) IY = (-N+1)*INCY + 1 + DO I = 1,N + CY(IY) = CY(IY) + CA*CX(IX) + IX = IX + INCX + IY = IY + INCY + END DO + END IF +* + RETURN + END diff --git a/schainf/Ffiles/cbesi.f b/schainf/Ffiles/cbesi.f new file mode 100644 index 0000000..f99bd30 --- /dev/null +++ b/schainf/Ffiles/cbesi.f @@ -0,0 +1,261 @@ +*DECK CBESI + SUBROUTINE CBESI (Z, FNU, KODE, N, CY, NZ, IERR) +C***BEGIN PROLOGUE CBESI +C***PURPOSE Compute a sequence of the Bessel functions I(a,z) for +C complex argument z and real nonnegative orders a=b,b+1, +C b+2,... where b>0. A scaling option is available to +C help avoid overflow. +C***LIBRARY SLATEC +C***CATEGORY C10B4 +C***TYPE COMPLEX (CBESI-C, ZBESI-C) +C***KEYWORDS BESSEL FUNCTIONS OF COMPLEX ARGUMENT, I BESSEL FUNCTIONS, +C MODIFIED BESSEL FUNCTIONS +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C On KODE=1, CBESI computes an N-member sequence of complex +C Bessel functions CY(L)=I(FNU+L-1,Z) for real nonnegative +C orders FNU+L-1, L=1,...,N and complex Z in the cut plane +C -pi=0 +C KODE - A parameter to indicate the scaling option +C KODE=1 returns +C CY(L)=I(FNU+L-1,Z), L=1,...,N +C =2 returns +C CY(L)=exp(-abs(X))*I(FNU+L-1,Z), L=1,...,N +C where X=Re(Z) +C N - Number of terms in the sequence, N>=1 +C +C Output +C CY - Result vector of type COMPLEX +C NZ - Number of underflows set to zero +C NZ=0 Normal return +C NZ>0 CY(L)=0, L=N-NZ+1,...,N +C IERR - Error flag +C IERR=0 Normal return - COMPUTATION COMPLETED +C IERR=1 Input error - NO COMPUTATION +C IERR=2 Overflow - NO COMPUTATION +C (Re(Z) too large on KODE=1) +C IERR=3 Precision warning - COMPUTATION COMPLETED +C (Result has half precision or less +C because abs(Z) or FNU+N-1 is large) +C IERR=4 Precision error - NO COMPUTATION +C (Result has no precision because +C abs(Z) or FNU+N-1 is too large) +C IERR=5 Algorithmic error - NO COMPUTATION +C (Termination condition not met) +C +C *Long Description: +C +C The computation of I(a,z) is carried out by the power series +C for small abs(z), the asymptotic expansion for large abs(z), +C the Miller algorithm normalized by the Wronskian and a +C Neumann series for intermediate magnitudes of z, and the +C uniform asymptotic expansions for I(a,z) and J(a,z) for +C large orders a. Backward recurrence is used to generate +C sequences or reduce orders when necessary. +C +C The calculations above are done in the right half plane and +C continued into the left half plane by the formula +C +C I(a,z*exp(t)) = exp(t*a)*I(a,z), Re(z)>0 +C t = i*pi or -i*pi +C +C For negative orders, the formula +C +C I(-a,z) = I(a,z) + (2/pi)*sin(pi*a)*K(a,z) +C +C can be used. However, for large orders close to integers the +C the function changes radically. When a is a large positive +C integer, the magnitude of I(-a,z)=I(a,z) is a large +C negative power of ten. But when a is not an integer, +C K(a,z) dominates in magnitude with a large positive power of +C ten and the most that the second term can be reduced is by +C unit roundoff from the coefficient. Thus, wide changes can +C occur within unit roundoff of a large integer for a. Here, +C large means a>abs(z). +C +C In most complex variable computation, one must evaluate ele- +C mentary functions. When the magnitude of Z or FNU+N-1 is +C large, losses of significance by argument reduction occur. +C Consequently, if either one exceeds U1=SQRT(0.5/UR), then +C losses exceeding half precision are likely and an error flag +C IERR=3 is triggered where UR=R1MACH(4)=UNIT ROUNDOFF. Also, +C if either is larger than U2=0.5/UR, then all significance is +C lost and IERR=4. In order to use the INT function, arguments +C must be further restricted not to exceed the largest machine +C integer, U3=I1MACH(9). Thus, the magnitude of Z and FNU+N-1 +C is restricted by MIN(U2,U3). In IEEE arithmetic, U1,U2, and +C U3 approximate 2.0E+3, 4.2E+6, 2.1E+9 in single precision +C and 4.7E+7, 2.3E+15 and 2.1E+9 in double precision. This +C makes U2 limiting in single precision and U3 limiting in +C double precision. This means that one can expect to retain, +C in the worst cases on IEEE machines, no digits in single pre- +C cision and only 6 digits in double precision. Similar con- +C siderations hold for other machines. +C +C The approximate relative error in the magnitude of a complex +C Bessel function can be expressed as P*10**S where P=MAX(UNIT +C ROUNDOFF,1.0E-18) is the nominal precision and 10**S repre- +C sents the increase in error due to argument reduction in the +C elementary functions. Here, S=MAX(1,ABS(LOG10(ABS(Z))), +C ABS(LOG10(FNU))) approximately (i.e., S=MAX(1,ABS(EXPONENT OF +C ABS(Z),ABS(EXPONENT OF FNU)) ). However, the phase angle may +C have only absolute accuracy. This is most likely to occur +C when one component (in magnitude) is larger than the other by +C several orders of magnitude. If one component is 10**K larger +C than the other, then one can expect only MAX(ABS(LOG10(P))-K, +C 0) significant digits; or, stated another way, when K exceeds +C the exponent of P, no significant digits remain in the smaller +C component. However, the phase angle retains absolute accuracy +C because, in complex arithmetic with precision P, the smaller +C component will not (as a rule) decrease below P times the +C magnitude of the larger component. In these extreme cases, +C the principal phase angle is on the order of +P, -P, PI/2-P, +C or -PI/2+P. +C +C***REFERENCES 1. M. Abramowitz and I. A. Stegun, Handbook of Mathe- +C matical Functions, National Bureau of Standards +C Applied Mathematics Series 55, U. S. Department +C of Commerce, Tenth Printing (1972) or later. +C 2. D. E. Amos, Computation of Bessel Functions of +C Complex Argument, Report SAND83-0086, Sandia National +C Laboratories, Albuquerque, NM, May 1983. +C 3. D. E. Amos, Computation of Bessel Functions of +C Complex Argument and Large Order, Report SAND83-0643, +C Sandia National Laboratories, Albuquerque, NM, May +C 1983. +C 4. D. E. Amos, A Subroutine Package for Bessel Functions +C of a Complex Argument and Nonnegative Order, Report +C SAND85-1018, Sandia National Laboratory, Albuquerque, +C NM, May 1985. +C 5. D. E. Amos, A portable package for Bessel functions +C of a complex argument and nonnegative order, ACM +C Transactions on Mathematical Software, 12 (September +C 1986), pp. 265-273. +C +C***ROUTINES CALLED CBINU, I1MACH, R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 890801 REVISION DATE from Version 3.2 +C 910415 Prologue converted to Version 4.0 format. (BAB) +C 920128 Category corrected. (WRB) +C 920811 Prologue revised. (DWL) +C***END PROLOGUE CBESI + COMPLEX CONE, CSGN, CY, Z, ZN + REAL AA, ALIM, ARG, DIG, ELIM, FNU, FNUL, PI, RL, R1M5, S1, S2, + * TOL, XX, YY, R1MACH, AZ, FN, BB, ASCLE, RTOL, ATOL + INTEGER I, IERR, INU, K, KODE, K1, K2, N, NN, NZ, I1MACH + DIMENSION CY(N) + DATA PI /3.14159265358979324E0/ + DATA CONE / (1.0E0,0.0E0) / +C +C***FIRST EXECUTABLE STATEMENT CBESI + IERR = 0 + NZ=0 + IF (FNU.LT.0.0E0) IERR=1 + IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 + IF (N.LT.1) IERR=1 + IF (IERR.NE.0) RETURN + XX = REAL(Z) + YY = AIMAG(Z) +C----------------------------------------------------------------------- +C SET PARAMETERS RELATED TO MACHINE CONSTANTS. +C TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18. +C ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. +C EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND +C EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR +C UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. +C RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. +C DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). +C FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU. +C----------------------------------------------------------------------- + TOL = MAX(R1MACH(4),1.0E-18) + K1 = I1MACH(12) + K2 = I1MACH(13) + R1M5 = R1MACH(5) + K = MIN(ABS(K1),ABS(K2)) + ELIM = 2.303E0*(K*R1M5-3.0E0) + K1 = I1MACH(11) - 1 + AA = R1M5*K1 + DIG = MIN(AA,18.0E0) + AA = AA*2.303E0 + ALIM = ELIM + MAX(-AA,-41.45E0) + RL = 1.2E0*DIG + 3.0E0 + FNUL = 10.0E0 + 6.0E0*(DIG-3.0E0) + AZ = ABS(Z) +C----------------------------------------------------------------------- +C TEST FOR RANGE +C----------------------------------------------------------------------- + AA = 0.5E0/TOL + BB=I1MACH(9)*0.5E0 + AA=MIN(AA,BB) + IF(AZ.GT.AA) GO TO 140 + FN=FNU+(N-1) + IF(FN.GT.AA) GO TO 140 + AA=SQRT(AA) + IF(AZ.GT.AA) IERR=3 + IF(FN.GT.AA) IERR=3 + ZN = Z + CSGN = CONE + IF (XX.GE.0.0E0) GO TO 40 + ZN = -Z +C----------------------------------------------------------------------- +C CALCULATE CSGN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE +C WHEN FNU IS LARGE +C----------------------------------------------------------------------- + INU = FNU + ARG = (FNU-INU)*PI + IF (YY.LT.0.0E0) ARG = -ARG + S1 = COS(ARG) + S2 = SIN(ARG) + CSGN = CMPLX(S1,S2) + IF (MOD(INU,2).EQ.1) CSGN = -CSGN + 40 CONTINUE + CALL CBINU(ZN, FNU, KODE, N, CY, NZ, RL, FNUL, TOL, ELIM, ALIM) + IF (NZ.LT.0) GO TO 120 + IF (XX.GE.0.0E0) RETURN +C----------------------------------------------------------------------- +C ANALYTIC CONTINUATION TO THE LEFT HALF PLANE +C----------------------------------------------------------------------- + NN = N - NZ + IF (NN.EQ.0) RETURN + RTOL = 1.0E0/TOL + ASCLE = R1MACH(1)*RTOL*1.0E+3 + DO 50 I=1,NN +C CY(I) = CY(I)*CSGN + ZN=CY(I) + AA=REAL(ZN) + BB=AIMAG(ZN) + ATOL=1.0E0 + IF (MAX(ABS(AA),ABS(BB)).GT.ASCLE) GO TO 55 + ZN = ZN*CMPLX(RTOL,0.0E0) + ATOL = TOL + 55 CONTINUE + ZN = ZN*CSGN + CY(I) = ZN*CMPLX(ATOL,0.0E0) + CSGN = -CSGN + 50 CONTINUE + RETURN + 120 CONTINUE + IF(NZ.EQ.(-2)) GO TO 130 + NZ = 0 + IERR=2 + RETURN + 130 CONTINUE + NZ=0 + IERR=5 + RETURN + 140 CONTINUE + NZ=0 + IERR=4 + RETURN + END diff --git a/schainf/Ffiles/cbinu.f b/schainf/Ffiles/cbinu.f new file mode 100644 index 0000000..8f0e830 --- /dev/null +++ b/schainf/Ffiles/cbinu.f @@ -0,0 +1,115 @@ +*DECK CBINU + SUBROUTINE CBINU (Z, FNU, KODE, N, CY, NZ, RL, FNUL, TOL, ELIM, + + ALIM) +C***BEGIN PROLOGUE CBINU +C***SUBSIDIARY +C***PURPOSE Subsidiary to CAIRY, CBESH, CBESI, CBESJ, CBESK and CBIRY +C***LIBRARY SLATEC +C***TYPE ALL (CBINU-A, ZBINU-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CBINU COMPUTES THE I FUNCTION IN THE RIGHT HALF Z PLANE +C +C***SEE ALSO CAIRY, CBESH, CBESI, CBESJ, CBESK, CBIRY +C***ROUTINES CALLED CASYI, CBUNI, CMLRI, CSERI, CUOIK, CWRSK +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CBINU + COMPLEX CW, CY, CZERO, Z + REAL ALIM, AZ, DFNU, ELIM, FNU, FNUL, RL, TOL + INTEGER I, INW, KODE, N, NLAST, NN, NUI, NW, NZ + DIMENSION CY(N), CW(2) + DATA CZERO / (0.0E0,0.0E0) / +C***FIRST EXECUTABLE STATEMENT CBINU + NZ = 0 + AZ = ABS(Z) + NN = N + DFNU = FNU + (N-1) + IF (AZ.LE.2.0E0) GO TO 10 + IF (AZ*AZ*0.25E0.GT.DFNU+1.0E0) GO TO 20 + 10 CONTINUE +C----------------------------------------------------------------------- +C POWER SERIES +C----------------------------------------------------------------------- + CALL CSERI(Z, FNU, KODE, NN, CY, NW, TOL, ELIM, ALIM) + INW = ABS(NW) + NZ = NZ + INW + NN = NN - INW + IF (NN.EQ.0) RETURN + IF (NW.GE.0) GO TO 120 + DFNU = FNU + (NN-1) + 20 CONTINUE + IF (AZ.LT.RL) GO TO 40 + IF (DFNU.LE.1.0E0) GO TO 30 + IF (AZ+AZ.LT.DFNU*DFNU) GO TO 50 +C----------------------------------------------------------------------- +C ASYMPTOTIC EXPANSION FOR LARGE Z +C----------------------------------------------------------------------- + 30 CONTINUE + CALL CASYI(Z, FNU, KODE, NN, CY, NW, RL, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 130 + GO TO 120 + 40 CONTINUE + IF (DFNU.LE.1.0E0) GO TO 70 + 50 CONTINUE +C----------------------------------------------------------------------- +C OVERFLOW AND UNDERFLOW TEST ON I SEQUENCE FOR MILLER ALGORITHM +C----------------------------------------------------------------------- + CALL CUOIK(Z, FNU, KODE, 1, NN, CY, NW, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 130 + NZ = NZ + NW + NN = NN - NW + IF (NN.EQ.0) RETURN + DFNU = FNU+(NN-1) + IF (DFNU.GT.FNUL) GO TO 110 + IF (AZ.GT.FNUL) GO TO 110 + 60 CONTINUE + IF (AZ.GT.RL) GO TO 80 + 70 CONTINUE +C----------------------------------------------------------------------- +C MILLER ALGORITHM NORMALIZED BY THE SERIES +C----------------------------------------------------------------------- + CALL CMLRI(Z, FNU, KODE, NN, CY, NW, TOL) + IF(NW.LT.0) GO TO 130 + GO TO 120 + 80 CONTINUE +C----------------------------------------------------------------------- +C MILLER ALGORITHM NORMALIZED BY THE WRONSKIAN +C----------------------------------------------------------------------- +C----------------------------------------------------------------------- +C OVERFLOW TEST ON K FUNCTIONS USED IN WRONSKIAN +C----------------------------------------------------------------------- + CALL CUOIK(Z, FNU, KODE, 2, 2, CW, NW, TOL, ELIM, ALIM) + IF (NW.GE.0) GO TO 100 + NZ = NN + DO 90 I=1,NN + CY(I) = CZERO + 90 CONTINUE + RETURN + 100 CONTINUE + IF (NW.GT.0) GO TO 130 + CALL CWRSK(Z, FNU, KODE, NN, CY, NW, CW, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 130 + GO TO 120 + 110 CONTINUE +C----------------------------------------------------------------------- +C INCREMENT FNU+NN-1 UP TO FNUL, COMPUTE AND RECUR BACKWARD +C----------------------------------------------------------------------- + NUI = FNUL-DFNU + 1 + NUI = MAX(NUI,0) + CALL CBUNI(Z, FNU, KODE, NN, CY, NW, NUI, NLAST, FNUL, TOL, ELIM, + * ALIM) + IF (NW.LT.0) GO TO 130 + NZ = NZ + NW + IF (NLAST.EQ.0) GO TO 120 + NN = NLAST + GO TO 60 + 120 CONTINUE + RETURN + 130 CONTINUE + NZ = -1 + IF(NW.EQ.(-2)) NZ=-2 + RETURN + END diff --git a/schainf/Ffiles/cbknu.f b/schainf/Ffiles/cbknu.f new file mode 100644 index 0000000..03ff0a1 --- /dev/null +++ b/schainf/Ffiles/cbknu.f @@ -0,0 +1,466 @@ +*DECK CBKNU + SUBROUTINE CBKNU (Z, FNU, KODE, N, Y, NZ, TOL, ELIM, ALIM) +C***BEGIN PROLOGUE CBKNU +C***SUBSIDIARY +C***PURPOSE Subsidiary to CAIRY, CBESH, CBESI and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CBKNU-A, ZBKNU-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CBKNU COMPUTES THE K BESSEL FUNCTION IN THE RIGHT HALF Z PLANE +C +C***SEE ALSO CAIRY, CBESH, CBESI, CBESK +C***ROUTINES CALLED CKSCL, CSHCH, CUCHK, GAMLN, I1MACH, R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CBKNU +C + COMPLEX CCH, CK, COEF, CONE, CRSC, CS, CSCL, CSH, CSR, CSS, CTWO, + * CZ, CZERO, F, FMU, P, PT, P1, P2, Q, RZ, SMU, ST, S1, S2, Y, Z, + * ZD, CELM, CY + REAL AA, AK, ALIM, ASCLE, A1, A2, BB, BK, BRY, CAZ, CC, DNU, + * DNU2, ELIM, ETEST, FC, FHS, FK, FKS, FNU, FPI, G1, G2, HPI, PI, + * P2I, P2M, P2R, RK, RTHPI, R1, S, SPI, TM, TOL, TTH, T1, T2, XX, + * YY, GAMLN, R1MACH, HELIM, ELM, XD, YD, ALAS, AS + INTEGER I, IDUM, IFLAG, INU, K, KFLAG, KK, KMAX, KODE, KODED, N, + * NZ, I1MACH, NW, J, IC, INUB + DIMENSION BRY(3), CC(8), CSS(3), CSR(3), Y(N), CY(2) +C + DATA KMAX / 30 / + DATA R1 / 2.0E0 / + DATA CZERO,CONE,CTWO /(0.0E0,0.0E0),(1.0E0,0.0E0),(2.0E0,0.0E0)/ +C + DATA PI, RTHPI, SPI ,HPI, FPI, TTH / + 1 3.14159265358979324E0, 1.25331413731550025E0, + 2 1.90985931710274403E0, 1.57079632679489662E0, + 3 1.89769999331517738E0, 6.66666666666666666E-01/ +C + DATA CC(1), CC(2), CC(3), CC(4), CC(5), CC(6), CC(7), CC(8)/ + 1 5.77215664901532861E-01, -4.20026350340952355E-02, + 2 -4.21977345555443367E-02, 7.21894324666309954E-03, + 3 -2.15241674114950973E-04, -2.01348547807882387E-05, + 4 1.13302723198169588E-06, 6.11609510448141582E-09/ +C +C***FIRST EXECUTABLE STATEMENT CBKNU + XX = REAL(Z) + YY = AIMAG(Z) + CAZ = ABS(Z) + CSCL = CMPLX(1.0E0/TOL,0.0E0) + CRSC = CMPLX(TOL,0.0E0) + CSS(1) = CSCL + CSS(2) = CONE + CSS(3) = CRSC + CSR(1) = CRSC + CSR(2) = CONE + CSR(3) = CSCL + BRY(1) = 1.0E+3*R1MACH(1)/TOL + BRY(2) = 1.0E0/BRY(1) + BRY(3) = R1MACH(2) + NZ = 0 + IFLAG = 0 + KODED = KODE + RZ = CTWO/Z + INU = FNU+0.5E0 + DNU = FNU - INU + IF (ABS(DNU).EQ.0.5E0) GO TO 110 + DNU2 = 0.0E0 + IF (ABS(DNU).GT.TOL) DNU2 = DNU*DNU + IF (CAZ.GT.R1) GO TO 110 +C----------------------------------------------------------------------- +C SERIES FOR ABS(Z).LE.R1 +C----------------------------------------------------------------------- + FC = 1.0E0 + SMU = CLOG(RZ) + FMU = SMU*CMPLX(DNU,0.0E0) + CALL CSHCH(FMU, CSH, CCH) + IF (DNU.EQ.0.0E0) GO TO 10 + FC = DNU*PI + FC = FC/SIN(FC) + SMU = CSH*CMPLX(1.0E0/DNU,0.0E0) + 10 CONTINUE + A2 = 1.0E0 + DNU +C----------------------------------------------------------------------- +C GAM(1-Z)*GAM(1+Z)=PI*Z/SIN(PI*Z), T1=1/GAM(1-DNU), T2=1/GAM(1+DNU) +C----------------------------------------------------------------------- + T2 = EXP(-GAMLN(A2,IDUM)) + T1 = 1.0E0/(T2*FC) + IF (ABS(DNU).GT.0.1E0) GO TO 40 +C----------------------------------------------------------------------- +C SERIES FOR F0 TO RESOLVE INDETERMINACY FOR SMALL ABS(DNU) +C----------------------------------------------------------------------- + AK = 1.0E0 + S = CC(1) + DO 20 K=2,8 + AK = AK*DNU2 + TM = CC(K)*AK + S = S + TM + IF (ABS(TM).LT.TOL) GO TO 30 + 20 CONTINUE + 30 G1 = -S + GO TO 50 + 40 CONTINUE + G1 = (T1-T2)/(DNU+DNU) + 50 CONTINUE + G2 = 0.5E0*(T1+T2)*FC + G1 = G1*FC + F = CMPLX(G1,0.0E0)*CCH + SMU*CMPLX(G2,0.0E0) + PT = CEXP(FMU) + P = CMPLX(0.5E0/T2,0.0E0)*PT + Q = CMPLX(0.5E0/T1,0.0E0)/PT + S1 = F + S2 = P + AK = 1.0E0 + A1 = 1.0E0 + CK = CONE + BK = 1.0E0 - DNU2 + IF (INU.GT.0 .OR. N.GT.1) GO TO 80 +C----------------------------------------------------------------------- +C GENERATE K(FNU,Z), 0.0D0 .LE. FNU .LT. 0.5D0 AND N=1 +C----------------------------------------------------------------------- + IF (CAZ.LT.TOL) GO TO 70 + CZ = Z*Z*CMPLX(0.25E0,0.0E0) + T1 = 0.25E0*CAZ*CAZ + 60 CONTINUE + F = (F*CMPLX(AK,0.0E0)+P+Q)*CMPLX(1.0E0/BK,0.0E0) + P = P*CMPLX(1.0E0/(AK-DNU),0.0E0) + Q = Q*CMPLX(1.0E0/(AK+DNU),0.0E0) + RK = 1.0E0/AK + CK = CK*CZ*CMPLX(RK,0.0) + S1 = S1 + CK*F + A1 = A1*T1*RK + BK = BK + AK + AK + 1.0E0 + AK = AK + 1.0E0 + IF (A1.GT.TOL) GO TO 60 + 70 CONTINUE + Y(1) = S1 + IF (KODED.EQ.1) RETURN + Y(1) = S1*CEXP(Z) + RETURN +C----------------------------------------------------------------------- +C GENERATE K(DNU,Z) AND K(DNU+1,Z) FOR FORWARD RECURRENCE +C----------------------------------------------------------------------- + 80 CONTINUE + IF (CAZ.LT.TOL) GO TO 100 + CZ = Z*Z*CMPLX(0.25E0,0.0E0) + T1 = 0.25E0*CAZ*CAZ + 90 CONTINUE + F = (F*CMPLX(AK,0.0E0)+P+Q)*CMPLX(1.0E0/BK,0.0E0) + P = P*CMPLX(1.0E0/(AK-DNU),0.0E0) + Q = Q*CMPLX(1.0E0/(AK+DNU),0.0E0) + RK = 1.0E0/AK + CK = CK*CZ*CMPLX(RK,0.0E0) + S1 = S1 + CK*F + S2 = S2 + CK*(P-F*CMPLX(AK,0.0E0)) + A1 = A1*T1*RK + BK = BK + AK + AK + 1.0E0 + AK = AK + 1.0E0 + IF (A1.GT.TOL) GO TO 90 + 100 CONTINUE + KFLAG = 2 + BK = REAL(SMU) + A1 = FNU + 1.0E0 + AK = A1*ABS(BK) + IF (AK.GT.ALIM) KFLAG = 3 + P2 = S2*CSS(KFLAG) + S2 = P2*RZ + S1 = S1*CSS(KFLAG) + IF (KODED.EQ.1) GO TO 210 + F = CEXP(Z) + S1 = S1*F + S2 = S2*F + GO TO 210 +C----------------------------------------------------------------------- +C IFLAG=0 MEANS NO UNDERFLOW OCCURRED +C IFLAG=1 MEANS AN UNDERFLOW OCCURRED- COMPUTATION PROCEEDS WITH +C KODED=2 AND A TEST FOR ON SCALE VALUES IS MADE DURING FORWARD +C RECURSION +C----------------------------------------------------------------------- + 110 CONTINUE + COEF = CMPLX(RTHPI,0.0E0)/CSQRT(Z) + KFLAG = 2 + IF (KODED.EQ.2) GO TO 120 + IF (XX.GT.ALIM) GO TO 290 +C BLANK LINE + A1 = EXP(-XX)*REAL(CSS(KFLAG)) + PT = CMPLX(A1,0.0E0)*CMPLX(COS(YY),-SIN(YY)) + COEF = COEF*PT + 120 CONTINUE + IF (ABS(DNU).EQ.0.5E0) GO TO 300 +C----------------------------------------------------------------------- +C MILLER ALGORITHM FOR ABS(Z).GT.R1 +C----------------------------------------------------------------------- + AK = COS(PI*DNU) + AK = ABS(AK) + IF (AK.EQ.0.0E0) GO TO 300 + FHS = ABS(0.25E0-DNU2) + IF (FHS.EQ.0.0E0) GO TO 300 +C----------------------------------------------------------------------- +C COMPUTE R2=F(E). IF ABS(Z).GE.R2, USE FORWARD RECURRENCE TO +C DETERMINE THE BACKWARD INDEX K. R2=F(E) IS A STRAIGHT LINE ON +C 12.LE.E.LE.60. E IS COMPUTED FROM 2**(-E)=B**(1-I1MACH(11))= +C TOL WHERE B IS THE BASE OF THE ARITHMETIC. +C----------------------------------------------------------------------- + T1 = (I1MACH(11)-1)*R1MACH(5)*3.321928094E0 + T1 = MAX(T1,12.0E0) + T1 = MIN(T1,60.0E0) + T2 = TTH*T1 - 6.0E0 + IF (XX.NE.0.0E0) GO TO 130 + T1 = HPI + GO TO 140 + 130 CONTINUE + T1 = ATAN(YY/XX) + T1 = ABS(T1) + 140 CONTINUE + IF (T2.GT.CAZ) GO TO 170 +C----------------------------------------------------------------------- +C FORWARD RECURRENCE LOOP WHEN ABS(Z).GE.R2 +C----------------------------------------------------------------------- + ETEST = AK/(PI*CAZ*TOL) + FK = 1.0E0 + IF (ETEST.LT.1.0E0) GO TO 180 + FKS = 2.0E0 + RK = CAZ + CAZ + 2.0E0 + A1 = 0.0E0 + A2 = 1.0E0 + DO 150 I=1,KMAX + AK = FHS/FKS + BK = RK/(FK+1.0E0) + TM = A2 + A2 = BK*A2 - AK*A1 + A1 = TM + RK = RK + 2.0E0 + FKS = FKS + FK + FK + 2.0E0 + FHS = FHS + FK + FK + FK = FK + 1.0E0 + TM = ABS(A2)*FK + IF (ETEST.LT.TM) GO TO 160 + 150 CONTINUE + GO TO 310 + 160 CONTINUE + FK = FK + SPI*T1*SQRT(T2/CAZ) + FHS = ABS(0.25E0-DNU2) + GO TO 180 + 170 CONTINUE +C----------------------------------------------------------------------- +C COMPUTE BACKWARD INDEX K FOR ABS(Z).LT.R2 +C----------------------------------------------------------------------- + A2 = SQRT(CAZ) + AK = FPI*AK/(TOL*SQRT(A2)) + AA = 3.0E0*T1/(1.0E0+CAZ) + BB = 14.7E0*T1/(28.0E0+CAZ) + AK = (ALOG(AK)+CAZ*COS(AA)/(1.0E0+0.008E0*CAZ))/COS(BB) + FK = 0.12125E0*AK*AK/CAZ + 1.5E0 + 180 CONTINUE + K = FK +C----------------------------------------------------------------------- +C BACKWARD RECURRENCE LOOP FOR MILLER ALGORITHM +C----------------------------------------------------------------------- + FK = K + FKS = FK*FK + P1 = CZERO + P2 = CMPLX(TOL,0.0E0) + CS = P2 + DO 190 I=1,K + A1 = FKS - FK + A2 = (FKS+FK)/(A1+FHS) + RK = 2.0E0/(FK+1.0E0) + T1 = (FK+XX)*RK + T2 = YY*RK + PT = P2 + P2 = (P2*CMPLX(T1,T2)-P1)*CMPLX(A2,0.0E0) + P1 = PT + CS = CS + P2 + FKS = A1 - FK + 1.0E0 + FK = FK - 1.0E0 + 190 CONTINUE +C----------------------------------------------------------------------- +C COMPUTE (P2/CS)=(P2/ABS(CS))*(CONJG(CS)/ABS(CS)) FOR BETTER +C SCALING +C----------------------------------------------------------------------- + TM = ABS(CS) + PT = CMPLX(1.0E0/TM,0.0E0) + S1 = PT*P2 + CS = CONJG(CS)*PT + S1 = COEF*S1*CS + IF (INU.GT.0 .OR. N.GT.1) GO TO 200 + ZD = Z + IF(IFLAG.EQ.1) GO TO 270 + GO TO 240 + 200 CONTINUE +C----------------------------------------------------------------------- +C COMPUTE P1/P2=(P1/ABS(P2)*CONJG(P2)/ABS(P2) FOR SCALING +C----------------------------------------------------------------------- + TM = ABS(P2) + PT = CMPLX(1.0E0/TM,0.0E0) + P1 = PT*P1 + P2 = CONJG(P2)*PT + PT = P1*P2 + S2 = S1*(CONE+(CMPLX(DNU+0.5E0,0.0E0)-PT)/Z) +C----------------------------------------------------------------------- +C FORWARD RECURSION ON THE THREE TERM RECURSION RELATION WITH +C SCALING NEAR EXPONENT EXTREMES ON KFLAG=1 OR KFLAG=3 +C----------------------------------------------------------------------- + 210 CONTINUE + CK = CMPLX(DNU+1.0E0,0.0E0)*RZ + IF (N.EQ.1) INU = INU - 1 + IF (INU.GT.0) GO TO 220 + IF (N.EQ.1) S1=S2 + ZD = Z + IF(IFLAG.EQ.1) GO TO 270 + GO TO 240 + 220 CONTINUE + INUB = 1 + IF (IFLAG.EQ.1) GO TO 261 + 225 CONTINUE + P1 = CSR(KFLAG) + ASCLE = BRY(KFLAG) + DO 230 I=INUB,INU + ST = S2 + S2 = CK*S2 + S1 + S1 = ST + CK = CK + RZ + IF (KFLAG.GE.3) GO TO 230 + P2 = S2*P1 + P2R = REAL(P2) + P2I = AIMAG(P2) + P2R = ABS(P2R) + P2I = ABS(P2I) + P2M = MAX(P2R,P2I) + IF (P2M.LE.ASCLE) GO TO 230 + KFLAG = KFLAG + 1 + ASCLE = BRY(KFLAG) + S1 = S1*P1 + S2 = P2 + S1 = S1*CSS(KFLAG) + S2 = S2*CSS(KFLAG) + P1 = CSR(KFLAG) + 230 CONTINUE + IF (N.EQ.1) S1 = S2 + 240 CONTINUE + Y(1) = S1*CSR(KFLAG) + IF (N.EQ.1) RETURN + Y(2) = S2*CSR(KFLAG) + IF (N.EQ.2) RETURN + KK = 2 + 250 CONTINUE + KK = KK + 1 + IF (KK.GT.N) RETURN + P1 = CSR(KFLAG) + ASCLE = BRY(KFLAG) + DO 260 I=KK,N + P2 = S2 + S2 = CK*S2 + S1 + S1 = P2 + CK = CK + RZ + P2 = S2*P1 + Y(I) = P2 + IF (KFLAG.GE.3) GO TO 260 + P2R = REAL(P2) + P2I = AIMAG(P2) + P2R = ABS(P2R) + P2I = ABS(P2I) + P2M = MAX(P2R,P2I) + IF (P2M.LE.ASCLE) GO TO 260 + KFLAG = KFLAG + 1 + ASCLE = BRY(KFLAG) + S1 = S1*P1 + S2 = P2 + S1 = S1*CSS(KFLAG) + S2 = S2*CSS(KFLAG) + P1 = CSR(KFLAG) + 260 CONTINUE + RETURN +C----------------------------------------------------------------------- +C IFLAG=1 CASES, FORWARD RECURRENCE ON SCALED VALUES ON UNDERFLOW +C----------------------------------------------------------------------- + 261 CONTINUE + HELIM = 0.5E0*ELIM + ELM = EXP(-ELIM) + CELM = CMPLX(ELM,0.0) + ASCLE = BRY(1) + ZD = Z + XD = XX + YD = YY + IC = -1 + J = 2 + DO 262 I=1,INU + ST = S2 + S2 = CK*S2+S1 + S1 = ST + CK = CK+RZ + AS = ABS(S2) + ALAS = ALOG(AS) + P2R = -XD+ALAS + IF(P2R.LT.(-ELIM)) GO TO 263 + P2 = -ZD+CLOG(S2) + P2R = REAL(P2) + P2I = AIMAG(P2) + P2M = EXP(P2R)/TOL + P1 = CMPLX(P2M,0.0E0)*CMPLX(COS(P2I),SIN(P2I)) + CALL CUCHK(P1,NW,ASCLE,TOL) + IF(NW.NE.0) GO TO 263 + J=3-J + CY(J) = P1 + IF(IC.EQ.(I-1)) GO TO 264 + IC = I + GO TO 262 + 263 CONTINUE + IF(ALAS.LT.HELIM) GO TO 262 + XD = XD-ELIM + S1 = S1*CELM + S2 = S2*CELM + ZD = CMPLX(XD,YD) + 262 CONTINUE + IF(N.EQ.1) S1 = S2 + GO TO 270 + 264 CONTINUE + KFLAG = 1 + INUB = I+1 + S2 = CY(J) + J = 3 - J + S1 = CY(J) + IF(INUB.LE.INU) GO TO 225 + IF(N.EQ.1) S1 = S2 + GO TO 240 + 270 CONTINUE + Y(1) = S1 + IF (N.EQ.1) GO TO 280 + Y(2) = S2 + 280 CONTINUE + ASCLE = BRY(1) + CALL CKSCL(ZD, FNU, N, Y, NZ, RZ, ASCLE, TOL, ELIM) + INU = N - NZ + IF (INU.LE.0) RETURN + KK = NZ + 1 + S1 = Y(KK) + Y(KK) = S1*CSR(1) + IF (INU.EQ.1) RETURN + KK = NZ + 2 + S2 = Y(KK) + Y(KK) = S2*CSR(1) + IF (INU.EQ.2) RETURN + T2 = FNU + (KK-1) + CK = CMPLX(T2,0.0E0)*RZ + KFLAG = 1 + GO TO 250 + 290 CONTINUE +C----------------------------------------------------------------------- +C SCALE BY EXP(Z), IFLAG = 1 CASES +C----------------------------------------------------------------------- + KODED = 2 + IFLAG = 1 + KFLAG = 2 + GO TO 120 +C----------------------------------------------------------------------- +C FNU=HALF ODD INTEGER CASE, DNU=-0.5 +C----------------------------------------------------------------------- + 300 CONTINUE + S1 = COEF + S2 = COEF + GO TO 210 + 310 CONTINUE + NZ=-2 + RETURN + END diff --git a/schainf/Ffiles/cbuni.f b/schainf/Ffiles/cbuni.f new file mode 100644 index 0000000..629851c --- /dev/null +++ b/schainf/Ffiles/cbuni.f @@ -0,0 +1,169 @@ +*DECK CBUNI + SUBROUTINE CBUNI (Z, FNU, KODE, N, Y, NZ, NUI, NLAST, FNUL, TOL, + + ELIM, ALIM) +C***BEGIN PROLOGUE CBUNI +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBESI and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CBUNI-A, ZBUNI-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CBUNI COMPUTES THE I BESSEL FUNCTION FOR LARGE ABS(Z).GT. +C FNUL AND FNU+N-1.LT.FNUL. THE ORDER IS INCREASED FROM +C FNU+N-1 GREATER THAN FNUL BY ADDING NUI AND COMPUTING +C ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR I(FNU,Z) +C ON IFORM=1 AND THE EXPANSION FOR J(FNU,Z) ON IFORM=2 +C +C***SEE ALSO CBESI, CBESK +C***ROUTINES CALLED CUNI1, CUNI2, R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CBUNI + COMPLEX CSCL, CSCR, CY, RZ, ST, S1, S2, Y, Z + REAL ALIM, AX, AY, DFNU, ELIM, FNU, FNUI, FNUL, GNU, TOL, XX, YY, + * ASCLE, BRY, STR, STI, STM, R1MACH + INTEGER I, IFLAG, IFORM, K, KODE, N, NL, NLAST, NUI, NW, NZ + DIMENSION Y(N), CY(2), BRY(3) +C***FIRST EXECUTABLE STATEMENT CBUNI + NZ = 0 + XX = REAL(Z) + YY = AIMAG(Z) + AX = ABS(XX)*1.7321E0 + AY = ABS(YY) + IFORM = 1 + IF (AY.GT.AX) IFORM = 2 + IF (NUI.EQ.0) GO TO 60 + FNUI = NUI + DFNU = FNU + (N-1) + GNU = DFNU + FNUI + IF (IFORM.EQ.2) GO TO 10 +C----------------------------------------------------------------------- +C ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN +C -PI/3.LE.ARG(Z).LE.PI/3 +C----------------------------------------------------------------------- + CALL CUNI1(Z, GNU, KODE, 2, CY, NW, NLAST, FNUL, TOL, ELIM, ALIM) + GO TO 20 + 10 CONTINUE +C----------------------------------------------------------------------- +C ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU +C APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I +C AND HPI=PI/2 +C----------------------------------------------------------------------- + CALL CUNI2(Z, GNU, KODE, 2, CY, NW, NLAST, FNUL, TOL, ELIM, ALIM) + 20 CONTINUE + IF (NW.LT.0) GO TO 50 + IF (NW.NE.0) GO TO 90 + AY = ABS(CY(1)) +C---------------------------------------------------------------------- +C SCALE BACKWARD RECURRENCE, BRY(3) IS DEFINED BUT NEVER USED +C---------------------------------------------------------------------- + BRY(1) = 1.0E+3*R1MACH(1)/TOL + BRY(2) = 1.0E0/BRY(1) + BRY(3) = BRY(2) + IFLAG = 2 + ASCLE = BRY(2) + AX = 1.0E0 + CSCL = CMPLX(AX,0.0E0) + IF (AY.GT.BRY(1)) GO TO 21 + IFLAG = 1 + ASCLE = BRY(1) + AX = 1.0E0/TOL + CSCL = CMPLX(AX,0.0E0) + GO TO 25 + 21 CONTINUE + IF (AY.LT.BRY(2)) GO TO 25 + IFLAG = 3 + ASCLE = BRY(3) + AX = TOL + CSCL = CMPLX(AX,0.0E0) + 25 CONTINUE + AY = 1.0E0/AX + CSCR = CMPLX(AY,0.0E0) + S1 = CY(2)*CSCL + S2 = CY(1)*CSCL + RZ = CMPLX(2.0E0,0.0E0)/Z + DO 30 I=1,NUI + ST = S2 + S2 = CMPLX(DFNU+FNUI,0.0E0)*RZ*S2 + S1 + S1 = ST + FNUI = FNUI - 1.0E0 + IF (IFLAG.GE.3) GO TO 30 + ST = S2*CSCR + STR = REAL(ST) + STI = AIMAG(ST) + STR = ABS(STR) + STI = ABS(STI) + STM = MAX(STR,STI) + IF (STM.LE.ASCLE) GO TO 30 + IFLAG = IFLAG+1 + ASCLE = BRY(IFLAG) + S1 = S1*CSCR + S2 = ST + AX = AX*TOL + AY = 1.0E0/AX + CSCL = CMPLX(AX,0.0E0) + CSCR = CMPLX(AY,0.0E0) + S1 = S1*CSCL + S2 = S2*CSCL + 30 CONTINUE + Y(N) = S2*CSCR + IF (N.EQ.1) RETURN + NL = N - 1 + FNUI = NL + K = NL + DO 40 I=1,NL + ST = S2 + S2 = CMPLX(FNU+FNUI,0.0E0)*RZ*S2 + S1 + S1 = ST + ST = S2*CSCR + Y(K) = ST + FNUI = FNUI - 1.0E0 + K = K - 1 + IF (IFLAG.GE.3) GO TO 40 + STR = REAL(ST) + STI = AIMAG(ST) + STR = ABS(STR) + STI = ABS(STI) + STM = MAX(STR,STI) + IF (STM.LE.ASCLE) GO TO 40 + IFLAG = IFLAG+1 + ASCLE = BRY(IFLAG) + S1 = S1*CSCR + S2 = ST + AX = AX*TOL + AY = 1.0E0/AX + CSCL = CMPLX(AX,0.0E0) + CSCR = CMPLX(AY,0.0E0) + S1 = S1*CSCL + S2 = S2*CSCL + 40 CONTINUE + RETURN + 50 CONTINUE + NZ = -1 + IF(NW.EQ.(-2)) NZ=-2 + RETURN + 60 CONTINUE + IF (IFORM.EQ.2) GO TO 70 +C----------------------------------------------------------------------- +C ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN +C -PI/3.LE.ARG(Z).LE.PI/3 +C----------------------------------------------------------------------- + CALL CUNI1(Z, FNU, KODE, N, Y, NW, NLAST, FNUL, TOL, ELIM, ALIM) + GO TO 80 + 70 CONTINUE +C----------------------------------------------------------------------- +C ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU +C APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I +C AND HPI=PI/2 +C----------------------------------------------------------------------- + CALL CUNI2(Z, FNU, KODE, N, Y, NW, NLAST, FNUL, TOL, ELIM, ALIM) + 80 CONTINUE + IF (NW.LT.0) GO TO 50 + NZ = NW + RETURN + 90 CONTINUE + NLAST = N + RETURN + END diff --git a/schainf/Ffiles/cdotu.f b/schainf/Ffiles/cdotu.f new file mode 100644 index 0000000..c05252c --- /dev/null +++ b/schainf/Ffiles/cdotu.f @@ -0,0 +1,131 @@ +*> \brief \b CDOTU +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* COMPLEX FUNCTION CDOTU(N,CX,INCX,CY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* COMPLEX CX(*),CY(*) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CDOTU forms the dot product of two complex vectors +*> CDOTU = X^T * Y +*> +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> number of elements in input vector(s) +*> \endverbatim +*> +*> \param[in] CX +*> \verbatim +*> CX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> storage spacing between elements of CX +*> \endverbatim +*> +*> \param[in] CY +*> \verbatim +*> CY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> storage spacing between elements of CY +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2017 +* +*> \ingroup complex_blas_level1 +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> \endverbatim +*> +* ===================================================================== + COMPLEX FUNCTION CDOTU(N,CX,INCX,CY,INCY) +* +* -- Reference BLAS level1 routine (version 3.8.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2017 +* +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + COMPLEX CX(*),CY(*) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + COMPLEX CTEMP + INTEGER I,IX,IY +* .. + CTEMP = (0.0,0.0) + CDOTU = (0.0,0.0) + IF (N.LE.0) RETURN + IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN +* +* code for both increments equal to 1 +* + DO I = 1,N + CTEMP = CTEMP + CX(I)*CY(I) + END DO + ELSE +* +* code for unequal increments or equal increments +* not equal to 1 +* + IX = 1 + IY = 1 + IF (INCX.LT.0) IX = (-N+1)*INCX + 1 + IF (INCY.LT.0) IY = (-N+1)*INCY + 1 + DO I = 1,N + CTEMP = CTEMP + CX(IX)*CY(IY) + IX = IX + INCX + IY = IY + INCY + END DO + END IF + CDOTU = CTEMP + RETURN + END diff --git a/schainf/Ffiles/ckscl.f b/schainf/Ffiles/ckscl.f new file mode 100644 index 0000000..8134685 --- /dev/null +++ b/schainf/Ffiles/ckscl.f @@ -0,0 +1,112 @@ +*DECK CKSCL + SUBROUTINE CKSCL (ZR, FNU, N, Y, NZ, RZ, ASCLE, TOL, ELIM) +C***BEGIN PROLOGUE CKSCL +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBKNU, CUNK1 and CUNK2 +C***LIBRARY SLATEC +C***TYPE ALL (CKSCL-A, ZKSCL-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C SET K FUNCTIONS TO ZERO ON UNDERFLOW, CONTINUE RECURRENCE +C ON SCALED FUNCTIONS UNTIL TWO MEMBERS COME ON SCALE, THEN +C RETURN WITH MIN(NZ+2,N) VALUES SCALED BY 1/TOL. +C +C***SEE ALSO CBKNU, CUNK1, CUNK2 +C***ROUTINES CALLED CUCHK +C***REVISION HISTORY (YYMMDD) +C ?????? DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CKSCL + COMPLEX CK, CS, CY, CZERO, RZ, S1, S2, Y, ZR, ZD, CELM + REAL AA, ASCLE, ACS, AS, CSI, CSR, ELIM, FN, FNU, TOL, XX, ZRI, + * ELM, ALAS, HELIM + INTEGER I, IC, K, KK, N, NN, NW, NZ + DIMENSION Y(N), CY(2) + DATA CZERO / (0.0E0,0.0E0) / +C***FIRST EXECUTABLE STATEMENT CUCHK + NZ = 0 + IC = 0 + XX = REAL(ZR) + NN = MIN(2,N) + DO 10 I=1,NN + S1 = Y(I) + CY(I) = S1 + AS = ABS(S1) + ACS = -XX + ALOG(AS) + NZ = NZ + 1 + Y(I) = CZERO + IF (ACS.LT.(-ELIM)) GO TO 10 + CS = -ZR + CLOG(S1) + CSR = REAL(CS) + CSI = AIMAG(CS) + AA = EXP(CSR)/TOL + CS = CMPLX(AA,0.0E0)*CMPLX(COS(CSI),SIN(CSI)) + CALL CUCHK(CS, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 10 + Y(I) = CS + NZ = NZ - 1 + IC = I + 10 CONTINUE + IF (N.EQ.1) RETURN + IF (IC.GT.1) GO TO 20 + Y(1) = CZERO + NZ = 2 + 20 CONTINUE + IF (N.EQ.2) RETURN + IF (NZ.EQ.0) RETURN + FN = FNU + 1.0E0 + CK = CMPLX(FN,0.0E0)*RZ + S1 = CY(1) + S2 = CY(2) + HELIM = 0.5E0*ELIM + ELM = EXP(-ELIM) + CELM = CMPLX(ELM,0.0E0) + ZRI =AIMAG(ZR) + ZD = ZR +C +C FIND TWO CONSECUTIVE Y VALUES ON SCALE. SCALE RECURRENCE IF +C S2 GETS LARGER THAN EXP(ELIM/2) +C + DO 30 I=3,N + KK = I + CS = S2 + S2 = CK*S2 + S1 + S1 = CS + CK = CK + RZ + AS = ABS(S2) + ALAS = ALOG(AS) + ACS = -XX + ALAS + NZ = NZ + 1 + Y(I) = CZERO + IF (ACS.LT.(-ELIM)) GO TO 25 + CS = -ZD + CLOG(S2) + CSR = REAL(CS) + CSI = AIMAG(CS) + AA = EXP(CSR)/TOL + CS = CMPLX(AA,0.0E0)*CMPLX(COS(CSI),SIN(CSI)) + CALL CUCHK(CS, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 25 + Y(I) = CS + NZ = NZ - 1 + IF (IC.EQ.(KK-1)) GO TO 40 + IC = KK + GO TO 30 + 25 CONTINUE + IF(ALAS.LT.HELIM) GO TO 30 + XX = XX-ELIM + S1 = S1*CELM + S2 = S2*CELM + ZD = CMPLX(XX,ZRI) + 30 CONTINUE + NZ = N + IF(IC.EQ.N) NZ=N-1 + GO TO 45 + 40 CONTINUE + NZ = KK - 2 + 45 CONTINUE + DO 50 K=1,NZ + Y(K) = CZERO + 50 CONTINUE + RETURN + END diff --git a/schainf/Ffiles/cmlri.f b/schainf/Ffiles/cmlri.f new file mode 100644 index 0000000..e95dfe7 --- /dev/null +++ b/schainf/Ffiles/cmlri.f @@ -0,0 +1,166 @@ +*DECK CMLRI + SUBROUTINE CMLRI (Z, FNU, KODE, N, Y, NZ, TOL) +C***BEGIN PROLOGUE CMLRI +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBESI and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CMLRI-A, ZMLRI-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CMLRI COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY THE +C MILLER ALGORITHM NORMALIZED BY A NEUMANN SERIES. +C +C***SEE ALSO CBESI, CBESK +C***ROUTINES CALLED GAMLN, R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CMLRI + COMPLEX CK, CNORM, CONE, CTWO, CZERO, PT, P1, P2, RZ, SUM, Y, Z + REAL ACK, AK, AP, AT, AZ, BK, FKAP, FKK, FLAM, FNF, FNU, RHO, + * RHO2, SCLE, TFNF, TOL, TST, X, GAMLN, R1MACH + INTEGER I, IAZ, IDUM, IFNU, INU, ITIME, K, KK, KM, KODE, M, N, NZ + DIMENSION Y(N) + DATA CZERO,CONE,CTWO /(0.0E0,0.0E0),(1.0E0,0.0E0),(2.0E0,0.0E0)/ + SCLE = 1.0E+3*R1MACH(1)/TOL +C***FIRST EXECUTABLE STATEMENT CMLRI + NZ=0 + AZ = ABS(Z) + X = REAL(Z) + IAZ = AZ + IFNU = FNU + INU = IFNU + N - 1 + AT = IAZ + 1.0E0 + CK = CMPLX(AT,0.0E0)/Z + RZ = CTWO/Z + P1 = CZERO + P2 = CONE + ACK = (AT+1.0E0)/AZ + RHO = ACK + SQRT(ACK*ACK-1.0E0) + RHO2 = RHO*RHO + TST = (RHO2+RHO2)/((RHO2-1.0E0)*(RHO-1.0E0)) + TST = TST/TOL +C----------------------------------------------------------------------- +C COMPUTE RELATIVE TRUNCATION ERROR INDEX FOR SERIES +C----------------------------------------------------------------------- + AK = AT + DO 10 I=1,80 + PT = P2 + P2 = P1 - CK*P2 + P1 = PT + CK = CK + RZ + AP = ABS(P2) + IF (AP.GT.TST*AK*AK) GO TO 20 + AK = AK + 1.0E0 + 10 CONTINUE + GO TO 110 + 20 CONTINUE + I = I + 1 + K = 0 + IF (INU.LT.IAZ) GO TO 40 +C----------------------------------------------------------------------- +C COMPUTE RELATIVE TRUNCATION ERROR FOR RATIOS +C----------------------------------------------------------------------- + P1 = CZERO + P2 = CONE + AT = INU + 1.0E0 + CK = CMPLX(AT,0.0E0)/Z + ACK = AT/AZ + TST = SQRT(ACK/TOL) + ITIME = 1 + DO 30 K=1,80 + PT = P2 + P2 = P1 - CK*P2 + P1 = PT + CK = CK + RZ + AP = ABS(P2) + IF (AP.LT.TST) GO TO 30 + IF (ITIME.EQ.2) GO TO 40 + ACK = ABS(CK) + FLAM = ACK + SQRT(ACK*ACK-1.0E0) + FKAP = AP/ABS(P1) + RHO = MIN(FLAM,FKAP) + TST = TST*SQRT(RHO/(RHO*RHO-1.0E0)) + ITIME = 2 + 30 CONTINUE + GO TO 110 + 40 CONTINUE +C----------------------------------------------------------------------- +C BACKWARD RECURRENCE AND SUM NORMALIZING RELATION +C----------------------------------------------------------------------- + K = K + 1 + KK = MAX(I+IAZ,K+INU) + FKK = KK + P1 = CZERO +C----------------------------------------------------------------------- +C SCALE P2 AND SUM BY SCLE +C----------------------------------------------------------------------- + P2 = CMPLX(SCLE,0.0E0) + FNF = FNU - IFNU + TFNF = FNF + FNF + BK = GAMLN(FKK+TFNF+1.0E0,IDUM) - GAMLN(FKK+1.0E0,IDUM) + * -GAMLN(TFNF+1.0E0,IDUM) + BK = EXP(BK) + SUM = CZERO + KM = KK - INU + DO 50 I=1,KM + PT = P2 + P2 = P1 + CMPLX(FKK+FNF,0.0E0)*RZ*P2 + P1 = PT + AK = 1.0E0 - TFNF/(FKK+TFNF) + ACK = BK*AK + SUM = SUM + CMPLX(ACK+BK,0.0E0)*P1 + BK = ACK + FKK = FKK - 1.0E0 + 50 CONTINUE + Y(N) = P2 + IF (N.EQ.1) GO TO 70 + DO 60 I=2,N + PT = P2 + P2 = P1 + CMPLX(FKK+FNF,0.0E0)*RZ*P2 + P1 = PT + AK = 1.0E0 - TFNF/(FKK+TFNF) + ACK = BK*AK + SUM = SUM + CMPLX(ACK+BK,0.0E0)*P1 + BK = ACK + FKK = FKK - 1.0E0 + M = N - I + 1 + Y(M) = P2 + 60 CONTINUE + 70 CONTINUE + IF (IFNU.LE.0) GO TO 90 + DO 80 I=1,IFNU + PT = P2 + P2 = P1 + CMPLX(FKK+FNF,0.0E0)*RZ*P2 + P1 = PT + AK = 1.0E0 - TFNF/(FKK+TFNF) + ACK = BK*AK + SUM = SUM + CMPLX(ACK+BK,0.0E0)*P1 + BK = ACK + FKK = FKK - 1.0E0 + 80 CONTINUE + 90 CONTINUE + PT = Z + IF (KODE.EQ.2) PT = PT - CMPLX(X,0.0E0) + P1 = -CMPLX(FNF,0.0E0)*CLOG(RZ) + PT + AP = GAMLN(1.0E0+FNF,IDUM) + PT = P1 - CMPLX(AP,0.0E0) +C----------------------------------------------------------------------- +C THE DIVISION CEXP(PT)/(SUM+P2) IS ALTERED TO AVOID OVERFLOW +C IN THE DENOMINATOR BY SQUARING LARGE QUANTITIES +C----------------------------------------------------------------------- + P2 = P2 + SUM + AP = ABS(P2) + P1 = CMPLX(1.0E0/AP,0.0E0) + CK = CEXP(PT)*P1 + PT = CONJG(P2)*P1 + CNORM = CK*PT + DO 100 I=1,N + Y(I) = Y(I)*CNORM + 100 CONTINUE + RETURN + 110 CONTINUE + NZ=-2 + RETURN + END diff --git a/schainf/Ffiles/complex.c b/schainf/Ffiles/complex.c new file mode 100644 index 0000000..0ef76dd --- /dev/null +++ b/schainf/Ffiles/complex.c @@ -0,0 +1,134 @@ +#include + +typedef struct FCOMPLEX {float r,i;} fcomplex; + +float Cmod(a) +fcomplex a; +{ float c; + c=a.r*a.r+a.i*a.i; + return c; +} + +fcomplex Cadd(a,b) +fcomplex a,b; +{ fcomplex c; + c.r=a.r+b.r; + c.i=a.i+b.i; + return c; +} + +fcomplex Csub(a,b) +fcomplex a,b; +{ fcomplex c; + c.r=a.r-b.r; + c.i=a.i-b.i; + return c; +} + +fcomplex Cmul(a,b) +fcomplex a,b; +{ fcomplex c; + c.r=a.r*b.r-a.i*b.i; + c.i=a.i*b.r+a.r*b.i; + return c; +} + +fcomplex Complex(re,im) +float re,im; +{ fcomplex c; + c.r=re; + c.i=im; + return c; +} + +fcomplex Conjg(z) +fcomplex z; +{ fcomplex c; + c.r=z.r; + c.i = -z.i; + return c; +} + +fcomplex Cdiv(a,b) +fcomplex a,b; +{ fcomplex c; + float r,den; + if (fabs(b.r) >= fabs(b.i)) { + r=b.i/b.r; + den=b.r+r*b.i; + c.r=(a.r+r*a.i)/den; + c.i=(a.i-r*a.r)/den; + } else { + r=b.r/b.i; + den=b.i+r*b.r; + c.r=(a.r*r+a.i)/den; + c.i=(a.i*r-a.r)/den; + } + return c; +} + +float Cabs(z) +fcomplex z; +{ float x,y,ans,temp; + x=fabs(z.r); + y=fabs(z.i); + if (x == 0.0) + ans=y; + else if (y == 0.0) + ans=x; + else if (x > y) { + temp=y/x; + ans=x*sqrt(1.0+temp*temp); + } else { + temp=x/y; + ans=y*sqrt(1.0+temp*temp); + } + return ans; +} + +fcomplex Csqrt(z) +fcomplex z; +{ fcomplex c; + float x,y,w,r; + if ((z.r == 0.0) && (z.i == 0.0)) { + c.r=0.0; + c.i=0.0; + return c; + } else { + x=fabs(z.r); + y=fabs(z.i); + if (x >= y) { + r=y/x; + w=sqrt(x)*sqrt(0.5*(1.0+sqrt(1.0+r*r))); + } else { + r=x/y; + w=sqrt(y)*sqrt(0.5*(r+sqrt(1.0+r*r))); + } + if (z.r >= 0.0) { + c.r=w; + c.i=z.i/(2.0*w); + } else { + c.i=(z.i >= 0) ? w : -w; + c.r=z.i/(2.0*c.i); + } + return c; + } +} + +fcomplex RCmul(x,a) +float x; +fcomplex a; +{ fcomplex c; + c.r=x*a.r; + c.i=x*a.i; + return c; +} + +fcomplex RCdiv(a,x) +float x; +fcomplex a; +{ fcomplex c; + c.r=a.r/x; + c.i=a.i/x; + return c; +} diff --git a/schainf/Ffiles/complex.h b/schainf/Ffiles/complex.h new file mode 100644 index 0000000..b7091ee --- /dev/null +++ b/schainf/Ffiles/complex.h @@ -0,0 +1,13 @@ +typedef struct FCOMPLEX {float r,i;} fcomplex; + +extern float Cmod(); +extern fcomplex Cadd(); +extern fcomplex Csub(); +extern fcomplex Cmul(); +extern fcomplex Complex(); +extern fcomplex Conjg(); +extern fcomplex Cdiv(); +extern float Cabs(); +extern fcomplex Csqrt(); +extern fcomplex RCmul(); +extern fcomplex RCdiv(); diff --git a/schainf/Ffiles/crati.f b/schainf/Ffiles/crati.f new file mode 100644 index 0000000..e1370c9 --- /dev/null +++ b/schainf/Ffiles/crati.f @@ -0,0 +1,111 @@ +*DECK CRATI + SUBROUTINE CRATI (Z, FNU, N, CY, TOL) +C***BEGIN PROLOGUE CRATI +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBESH, CBESI and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CRATI-A, ZRATI-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CRATI COMPUTES RATIOS OF I BESSEL FUNCTIONS BY BACKWARD +C RECURRENCE. THE STARTING INDEX IS DETERMINED BY FORWARD +C RECURRENCE AS DESCRIBED IN J. RES. OF NAT. BUR. OF STANDARDS-B, +C MATHEMATICAL SCIENCES, VOL 77B, P111-114, SEPTEMBER, 1973, +C BESSEL FUNCTIONS I AND J OF COMPLEX ARGUMENT AND INTEGER ORDER, +C BY D. J. SOOKNE. +C +C***SEE ALSO CBESH, CBESI, CBESK +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CRATI + COMPLEX CDFNU, CONE, CY, CZERO, PT, P1, P2, RZ, T1, Z + REAL AK, AMAGZ, AP1, AP2, ARG, AZ, DFNU, FDNU, FLAM, FNU, FNUP, + * RAP1, RHO, TEST, TEST1, TOL + INTEGER I, ID, IDNU, INU, ITIME, K, KK, MAGZ, N + DIMENSION CY(N) + DATA CZERO, CONE / (0.0E0,0.0E0), (1.0E0,0.0E0) / +C***FIRST EXECUTABLE STATEMENT CRATI + AZ = ABS(Z) + INU = FNU + IDNU = INU + N - 1 + FDNU = IDNU + MAGZ = AZ + AMAGZ = MAGZ+1 + FNUP = MAX(AMAGZ,FDNU) + ID = IDNU - MAGZ - 1 + ITIME = 1 + K = 1 + RZ = (CONE+CONE)/Z + T1 = CMPLX(FNUP,0.0E0)*RZ + P2 = -T1 + P1 = CONE + T1 = T1 + RZ + IF (ID.GT.0) ID = 0 + AP2 = ABS(P2) + AP1 = ABS(P1) +C----------------------------------------------------------------------- +C THE OVERFLOW TEST ON K(FNU+I-1,Z) BEFORE THE CALL TO CBKNX +C GUARANTEES THAT P2 IS ON SCALE. SCALE TEST1 AND ALL SUBSEQUENT +C P2 VALUES BY AP1 TO ENSURE THAT AN OVERFLOW DOES NOT OCCUR +C PREMATURELY. +C----------------------------------------------------------------------- + ARG = (AP2+AP2)/(AP1*TOL) + TEST1 = SQRT(ARG) + TEST = TEST1 + RAP1 = 1.0E0/AP1 + P1 = P1*CMPLX(RAP1,0.0E0) + P2 = P2*CMPLX(RAP1,0.0E0) + AP2 = AP2*RAP1 + 10 CONTINUE + K = K + 1 + AP1 = AP2 + PT = P2 + P2 = P1 - T1*P2 + P1 = PT + T1 = T1 + RZ + AP2 = ABS(P2) + IF (AP1.LE.TEST) GO TO 10 + IF (ITIME.EQ.2) GO TO 20 + AK = ABS(T1)*0.5E0 + FLAM = AK + SQRT(AK*AK-1.0E0) + RHO = MIN(AP2/AP1,FLAM) + TEST = TEST1*SQRT(RHO/(RHO*RHO-1.0E0)) + ITIME = 2 + GO TO 10 + 20 CONTINUE + KK = K + 1 - ID + AK = KK + DFNU = FNU + (N-1) + CDFNU = CMPLX(DFNU,0.0E0) + T1 = CMPLX(AK,0.0E0) + P1 = CMPLX(1.0E0/AP2,0.0E0) + P2 = CZERO + DO 30 I=1,KK + PT = P1 + P1 = RZ*(CDFNU+T1)*P1 + P2 + P2 = PT + T1 = T1 - CONE + 30 CONTINUE + IF (REAL(P1).NE.0.0E0 .OR. AIMAG(P1).NE.0.0E0) GO TO 40 + P1 = CMPLX(TOL,TOL) + 40 CONTINUE + CY(N) = P2/P1 + IF (N.EQ.1) RETURN + K = N - 1 + AK = K + T1 = CMPLX(AK,0.0E0) + CDFNU = CMPLX(FNU,0.0E0)*RZ + DO 60 I=2,N + PT = CDFNU + T1*RZ + CY(K+1) + IF (REAL(PT).NE.0.0E0 .OR. AIMAG(PT).NE.0.0E0) GO TO 50 + PT = CMPLX(TOL,TOL) + 50 CONTINUE + CY(K) = CONE/PT + T1 = T1 - CONE + K = K - 1 + 60 CONTINUE + RETURN + END diff --git a/schainf/Ffiles/cs1s2.f b/schainf/Ffiles/cs1s2.f new file mode 100644 index 0000000..aa60995 --- /dev/null +++ b/schainf/Ffiles/cs1s2.f @@ -0,0 +1,55 @@ +*DECK CS1S2 + SUBROUTINE CS1S2 (ZR, S1, S2, NZ, ASCLE, ALIM, IUF) +C***BEGIN PROLOGUE CS1S2 +C***SUBSIDIARY +C***PURPOSE Subsidiary to CAIRY and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CS1S2-A, ZS1S2-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CS1S2 TESTS FOR A POSSIBLE UNDERFLOW RESULTING FROM THE +C ADDITION OF THE I AND K FUNCTIONS IN THE ANALYTIC CON- +C TINUATION FORMULA WHERE S1=K FUNCTION AND S2=I FUNCTION. +C ON KODE=1 THE I AND K FUNCTIONS ARE DIFFERENT ORDERS OF +C MAGNITUDE, BUT FOR KODE=2 THEY CAN BE OF THE SAME ORDER +C OF MAGNITUDE AND THE MAXIMUM MUST BE AT LEAST ONE +C PRECISION ABOVE THE UNDERFLOW LIMIT. +C +C***SEE ALSO CAIRY, CBESK +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CS1S2 + COMPLEX CZERO, C1, S1, S1D, S2, ZR + REAL AA, ALIM, ALN, ASCLE, AS1, AS2, XX + INTEGER IUF, NZ + DATA CZERO / (0.0E0,0.0E0) / +C***FIRST EXECUTABLE STATEMENT CS1S2 + NZ = 0 + AS1 = ABS(S1) + AS2 = ABS(S2) + AA = REAL(S1) + ALN = AIMAG(S1) + IF (AA.EQ.0.0E0 .AND. ALN.EQ.0.0E0) GO TO 10 + IF (AS1.EQ.0.0E0) GO TO 10 + XX = REAL(ZR) + ALN = -XX - XX + ALOG(AS1) + S1D = S1 + S1 = CZERO + AS1 = 0.0E0 + IF (ALN.LT.(-ALIM)) GO TO 10 + C1 = CLOG(S1D) - ZR - ZR + S1 = CEXP(C1) + AS1 = ABS(S1) + IUF = IUF + 1 + 10 CONTINUE + AA = MAX(AS1,AS2) + IF (AA.GT.ASCLE) RETURN + S1 = CZERO + S2 = CZERO + NZ = 1 + IUF = 0 + RETURN + END diff --git a/schainf/Ffiles/cseri.f b/schainf/Ffiles/cseri.f new file mode 100644 index 0000000..3cf49cc --- /dev/null +++ b/schainf/Ffiles/cseri.f @@ -0,0 +1,164 @@ +*DECK CSERI + SUBROUTINE CSERI (Z, FNU, KODE, N, Y, NZ, TOL, ELIM, ALIM) +C***BEGIN PROLOGUE CSERI +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBESI and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CSERI-A, ZSERI-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CSERI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY +C MEANS OF THE POWER SERIES FOR LARGE ABS(Z) IN THE +C REGION ABS(Z).LE.2*SQRT(FNU+1). NZ=0 IS A NORMAL RETURN. +C NZ.GT.0 MEANS THAT THE LAST NZ COMPONENTS WERE SET TO ZERO +C DUE TO UNDERFLOW. NZ.LT.0 MEANS UNDERFLOW OCCURRED, BUT THE +C CONDITION ABS(Z).LE.2*SQRT(FNU+1) WAS VIOLATED AND THE +C COMPUTATION MUST BE COMPLETED IN ANOTHER ROUTINE WITH N=N-ABS(NZ). +C +C***SEE ALSO CBESI, CBESK +C***ROUTINES CALLED CUCHK, GAMLN, R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CSERI + COMPLEX AK1, CK, COEF, CONE, CRSC, CZ, CZERO, HZ, RZ, S1, S2, W, + * Y, Z + REAL AA, ACZ, AK, ALIM, ARM, ASCLE, ATOL, AZ, DFNU, ELIM, FNU, + * FNUP, RAK1, RS, RTR1, S, SS, TOL, X, GAMLN, R1MACH + INTEGER I, IB, IDUM, IFLAG, IL, K, KODE, L, M, N, NN, NW, NZ + DIMENSION Y(N), W(2) + DATA CZERO, CONE / (0.0E0,0.0E0), (1.0E0,0.0E0) / +C***FIRST EXECUTABLE STATEMENT CSERI + NZ = 0 + AZ = ABS(Z) + IF (AZ.EQ.0.0E0) GO TO 150 + X = REAL(Z) + ARM = 1.0E+3*R1MACH(1) + RTR1 = SQRT(ARM) + CRSC = CMPLX(1.0E0,0.0E0) + IFLAG = 0 + IF (AZ.LT.ARM) GO TO 140 + HZ = Z*CMPLX(0.5E0,0.0E0) + CZ = CZERO + IF (AZ.GT.RTR1) CZ = HZ*HZ + ACZ = ABS(CZ) + NN = N + CK = CLOG(HZ) + 10 CONTINUE + DFNU = FNU + (NN-1) + FNUP = DFNU + 1.0E0 +C----------------------------------------------------------------------- +C UNDERFLOW TEST +C----------------------------------------------------------------------- + AK1 = CK*CMPLX(DFNU,0.0E0) + AK = GAMLN(FNUP,IDUM) + AK1 = AK1 - CMPLX(AK,0.0E0) + IF (KODE.EQ.2) AK1 = AK1 - CMPLX(X,0.0E0) + RAK1 = REAL(AK1) + IF (RAK1.GT.(-ELIM)) GO TO 30 + 20 CONTINUE + NZ = NZ + 1 + Y(NN) = CZERO + IF (ACZ.GT.DFNU) GO TO 170 + NN = NN - 1 + IF (NN.EQ.0) RETURN + GO TO 10 + 30 CONTINUE + IF (RAK1.GT.(-ALIM)) GO TO 40 + IFLAG = 1 + SS = 1.0E0/TOL + CRSC = CMPLX(TOL,0.0E0) + ASCLE = ARM*SS + 40 CONTINUE + AK = AIMAG(AK1) + AA = EXP(RAK1) + IF (IFLAG.EQ.1) AA = AA*SS + COEF = CMPLX(AA,0.0E0)*CMPLX(COS(AK),SIN(AK)) + ATOL = TOL*ACZ/FNUP + IL = MIN(2,NN) + DO 80 I=1,IL + DFNU = FNU + (NN-I) + FNUP = DFNU + 1.0E0 + S1 = CONE + IF (ACZ.LT.TOL*FNUP) GO TO 60 + AK1 = CONE + AK = FNUP + 2.0E0 + S = FNUP + AA = 2.0E0 + 50 CONTINUE + RS = 1.0E0/S + AK1 = AK1*CZ*CMPLX(RS,0.0E0) + S1 = S1 + AK1 + S = S + AK + AK = AK + 2.0E0 + AA = AA*ACZ*RS + IF (AA.GT.ATOL) GO TO 50 + 60 CONTINUE + M = NN - I + 1 + S2 = S1*COEF + W(I) = S2 + IF (IFLAG.EQ.0) GO TO 70 + CALL CUCHK(S2, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 20 + 70 CONTINUE + Y(M) = S2*CRSC + IF (I.NE.IL) COEF = COEF*CMPLX(DFNU,0.0E0)/HZ + 80 CONTINUE + IF (NN.LE.2) RETURN + K = NN - 2 + AK = K + RZ = (CONE+CONE)/Z + IF (IFLAG.EQ.1) GO TO 110 + IB = 3 + 90 CONTINUE + DO 100 I=IB,NN + Y(K) = CMPLX(AK+FNU,0.0E0)*RZ*Y(K+1) + Y(K+2) + AK = AK - 1.0E0 + K = K - 1 + 100 CONTINUE + RETURN +C----------------------------------------------------------------------- +C RECUR BACKWARD WITH SCALED VALUES +C----------------------------------------------------------------------- + 110 CONTINUE +C----------------------------------------------------------------------- +C EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE THE +C UNDERFLOW LIMIT = ASCLE = R1MACH(1)*CSCL*1.0E+3 +C----------------------------------------------------------------------- + S1 = W(1) + S2 = W(2) + DO 120 L=3,NN + CK = S2 + S2 = S1 + CMPLX(AK+FNU,0.0E0)*RZ*S2 + S1 = CK + CK = S2*CRSC + Y(K) = CK + AK = AK - 1.0E0 + K = K - 1 + IF (ABS(CK).GT.ASCLE) GO TO 130 + 120 CONTINUE + RETURN + 130 CONTINUE + IB = L + 1 + IF (IB.GT.NN) RETURN + GO TO 90 + 140 CONTINUE + NZ = N + IF (FNU.EQ.0.0E0) NZ = NZ - 1 + 150 CONTINUE + Y(1) = CZERO + IF (FNU.EQ.0.0E0) Y(1) = CONE + IF (N.EQ.1) RETURN + DO 160 I=2,N + Y(I) = CZERO + 160 CONTINUE + RETURN +C----------------------------------------------------------------------- +C RETURN WITH NZ.LT.0 IF ABS(Z*Z/4).GT.FNU+N-NZ-1 COMPLETE +C THE CALCULATION IN CBINU WITH N=N-ABS(NZ) +C----------------------------------------------------------------------- + 170 CONTINUE + NZ = -NZ + RETURN + END diff --git a/schainf/Ffiles/cshch.f b/schainf/Ffiles/cshch.f new file mode 100644 index 0000000..024e122 --- /dev/null +++ b/schainf/Ffiles/cshch.f @@ -0,0 +1,36 @@ +*DECK CSHCH + SUBROUTINE CSHCH (Z, CSH, CCH) +C***BEGIN PROLOGUE CSHCH +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBESH and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CSHCH-A, ZSHCH-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CSHCH COMPUTES THE COMPLEX HYPERBOLIC FUNCTIONS CSH=SINH(X+I*Y) +C AND CCH=COSH(X+I*Y), WHERE I**2=-1. +C +C***SEE ALSO CBESH, CBESK +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CSHCH + COMPLEX CCH, CSH, Z + REAL CCHI, CCHR, CH, CN, CSHI, CSHR, SH, SN, X, Y +C***FIRST EXECUTABLE STATEMENT CSHCH + X = REAL(Z) + Y = AIMAG(Z) + SH = SINH(X) + CH = COSH(X) + SN = SIN(Y) + CN = COS(Y) + CSHR = SH*CN + CSHI = CH*SN + CSH = CMPLX(CSHR,CSHI) + CCHR = CH*CN + CCHI = SH*SN + CCH = CMPLX(CCHR,CCHI) + RETURN + END diff --git a/schainf/Ffiles/csisl.f b/schainf/Ffiles/csisl.f new file mode 100644 index 0000000..179bf2d --- /dev/null +++ b/schainf/Ffiles/csisl.f @@ -0,0 +1,171 @@ + subroutine csisl(a,lda,n,kpvt,b) + integer lda,n,kpvt(1) + complex a(lda,1),b(1) +c +c csisl solves the complex symmetric system +c a * x = b +c using the factors computed by csifa. +c +c on entry +c +c a complex(lda,n) +c the output from csifa. +c +c lda integer +c the leading dimension of the array a . +c +c n integer +c the order of the matrix a . +c +c kpvt integer(n) +c the pivot vector from csifa. +c +c b complex(n) +c the right hand side vector. +c +c on return +c +c b the solution vector x . +c +c error condition +c +c a division by zero may occur if csico has set rcond .eq. 0.0 +c or csifa has set info .ne. 0 . +c +c to compute inverse(a) * c where c is a matrix +c with p columns +c call csifa(a,lda,n,kpvt,info) +c if (info .ne. 0) go to ... +c do 10 j = 1, p +c call csisl(a,lda,n,kpvt,c(1,j)) +c 10 continue +c +c linpack. this version dated 08/14/78 . +c james bunch, univ. calif. san diego, argonne nat. lab. +c +c subroutines and functions +c +c blas caxpy,cdotu +c fortran iabs +c +c internal variables. +c + complex ak,akm1,bk,bkm1,cdotu,denom,temp + integer k,kp +c +c loop backward applying the transformations and +c d inverse to b. +c + k = n + 10 if (k .eq. 0) go to 80 + if (kpvt(k) .lt. 0) go to 40 +c +c 1 x 1 pivot block. +c + if (k .eq. 1) go to 30 + kp = kpvt(k) + if (kp .eq. k) go to 20 +c +c interchange. +c + temp = b(k) + b(k) = b(kp) + b(kp) = temp + 20 continue +c +c apply the transformation. +c + call caxpy(k-1,b(k),a(1,k),1,b(1),1) + 30 continue +c +c apply d inverse. +c + b(k) = b(k)/a(k,k) + k = k - 1 + go to 70 + 40 continue +c +c 2 x 2 pivot block. +c + if (k .eq. 2) go to 60 + kp = iabs(kpvt(k)) + if (kp .eq. k - 1) go to 50 +c +c interchange. +c + temp = b(k-1) + b(k-1) = b(kp) + b(kp) = temp + 50 continue +c +c apply the transformation. +c + call caxpy(k-2,b(k),a(1,k),1,b(1),1) + call caxpy(k-2,b(k-1),a(1,k-1),1,b(1),1) + 60 continue +c +c apply d inverse. +c + ak = a(k,k)/a(k-1,k) + akm1 = a(k-1,k-1)/a(k-1,k) + bk = b(k)/a(k-1,k) + bkm1 = b(k-1)/a(k-1,k) + denom = ak*akm1 - 1.0e0 + b(k) = (akm1*bk - bkm1)/denom + b(k-1) = (ak*bkm1 - bk)/denom + k = k - 2 + 70 continue + go to 10 + 80 continue +c +c loop forward applying the transformations. +c + k = 1 + 90 if (k .gt. n) go to 160 + if (kpvt(k) .lt. 0) go to 120 +c +c 1 x 1 pivot block. +c + if (k .eq. 1) go to 110 +c +c apply the transformation. +c + b(k) = b(k) + cdotu(k-1,a(1,k),1,b(1),1) + kp = kpvt(k) + if (kp .eq. k) go to 100 +c +c interchange. +c + temp = b(k) + b(k) = b(kp) + b(kp) = temp + 100 continue + 110 continue + k = k + 1 + go to 150 + 120 continue +c +c 2 x 2 pivot block. +c + if (k .eq. 1) go to 140 +c +c apply the transformation. +c + b(k) = b(k) + cdotu(k-1,a(1,k),1,b(1),1) + b(k+1) = b(k+1) + cdotu(k-1,a(1,k+1),1,b(1),1) + kp = iabs(kpvt(k)) + if (kp .eq. k) go to 130 +c +c interchange. +c + temp = b(k) + b(k) = b(kp) + b(kp) = temp + 130 continue + 140 continue + k = k + 2 + 150 continue + go to 90 + 160 continue + return + end diff --git a/schainf/Ffiles/cuchk.f b/schainf/Ffiles/cuchk.f new file mode 100644 index 0000000..5415657 --- /dev/null +++ b/schainf/Ffiles/cuchk.f @@ -0,0 +1,42 @@ +*DECK CUCHK + SUBROUTINE CUCHK (Y, NZ, ASCLE, TOL) +C***BEGIN PROLOGUE CUCHK +C***SUBSIDIARY +C***PURPOSE Subsidiary to SERI, CUOIK, CUNK1, CUNK2, CUNI1, CUNI2 and +C CKSCL +C***LIBRARY SLATEC +C***TYPE ALL (CUCHK-A, ZUCHK-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C Y ENTERS AS A SCALED QUANTITY WHOSE MAGNITUDE IS GREATER THAN +C EXP(-ALIM)=ASCLE=1.0E+3*R1MACH(1)/TOL. THE TEST IS MADE TO SEE +C IF THE MAGNITUDE OF THE REAL OR IMAGINARY PART WOULD UNDER FLOW +C WHEN Y IS SCALED (BY TOL) TO ITS PROPER VALUE. Y IS ACCEPTED +C IF THE UNDERFLOW IS AT LEAST ONE PRECISION BELOW THE MAGNITUDE +C OF THE LARGEST COMPONENT; OTHERWISE THE PHASE ANGLE DOES NOT HAVE +C ABSOLUTE ACCURACY AND AN UNDERFLOW IS ASSUMED. +C +C***SEE ALSO CKSCL, CUNI1, CUNI2, CUNK1, CUNK2, CUOIK, SERI +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C ?????? DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CUCHK +C + COMPLEX Y + REAL ASCLE, SS, ST, TOL, YR, YI + INTEGER NZ +C***FIRST EXECUTABLE STATEMENT CUCHK + NZ = 0 + YR = REAL(Y) + YI = AIMAG(Y) + YR = ABS(YR) + YI = ABS(YI) + ST = MIN(YR,YI) + IF (ST.GT.ASCLE) RETURN + SS = MAX(YR,YI) + ST=ST/TOL + IF (SS.LT.ST) NZ = 1 + RETURN + END diff --git a/schainf/Ffiles/cunhj.f b/schainf/Ffiles/cunhj.f new file mode 100644 index 0000000..603118d --- /dev/null +++ b/schainf/Ffiles/cunhj.f @@ -0,0 +1,658 @@ +*DECK CUNHJ + SUBROUTINE CUNHJ (Z, FNU, IPMTR, TOL, PHI, ARG, ZETA1, ZETA2, + + ASUM, BSUM) +C***BEGIN PROLOGUE CUNHJ +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBESI and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CUNHJ-A, ZUNHJ-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C REFERENCES +C HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ AND I.A. +C STEGUN, AMS55, NATIONAL BUREAU OF STANDARDS, 1965, CHAPTER 9. +C +C ASYMPTOTICS AND SPECIAL FUNCTIONS BY F.W.J. OLVER, ACADEMIC +C PRESS, N.Y., 1974, PAGE 420 +C +C ABSTRACT +C CUNHJ COMPUTES PARAMETERS FOR BESSEL FUNCTIONS C(FNU,Z) = +C J(FNU,Z), Y(FNU,Z) OR H(I,FNU,Z) I=1,2 FOR LARGE ORDERS FNU +C BY MEANS OF THE UNIFORM ASYMPTOTIC EXPANSION +C +C C(FNU,Z)=C1*PHI*( ASUM*AIRY(ARG) + C2*BSUM*DAIRY(ARG) ) +C +C FOR PROPER CHOICES OF C1, C2, AIRY AND DAIRY WHERE AIRY IS +C AN AIRY FUNCTION AND DAIRY IS ITS DERIVATIVE. +C +C (2/3)*FNU*ZETA**1.5 = ZETA1-ZETA2, +C +C ZETA1=0.5*FNU*CLOG((1+W)/(1-W)), ZETA2=FNU*W FOR SCALING +C PURPOSES IN AIRY FUNCTIONS FROM CAIRY OR CBIRY. +C +C MCONJ=SIGN OF AIMAG(Z), BUT IS AMBIGUOUS WHEN Z IS REAL AND +C MUST BE SPECIFIED. IPMTR=0 RETURNS ALL PARAMETERS. IPMTR= +C 1 COMPUTES ALL EXCEPT ASUM AND BSUM. +C +C***SEE ALSO CBESI, CBESK +C***ROUTINES CALLED R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CUNHJ + COMPLEX ARG, ASUM, BSUM, CFNU, CONE, CR, CZERO, DR, P, PHI, + * PRZTH, PTFN, RFN13, RTZTA, RZTH, SUMA, SUMB, TFN, T2, UP, W, W2, + * Z, ZA, ZB, ZC, ZETA, ZETA1, ZETA2, ZTH + REAL ALFA, ANG, AP, AR, ATOL, AW2, AZTH, BETA, BR, BTOL, C, EX1, + * EX2, FNU, FN13, FN23, GAMA, HPI, PI, PP, RFNU, RFNU2, THPI, TOL, + * WI, WR, ZCI, ZCR, ZETAI, ZETAR, ZTHI, ZTHR, ASUMR, ASUMI, BSUMR, + * BSUMI, TEST, TSTR, TSTI, AC, R1MACH + INTEGER IAS, IBS, IPMTR, IS, J, JR, JU, K, KMAX, KP1, KS, L, LR, + * LRP1, L1, L2, M + DIMENSION AR(14), BR(14), C(105), ALFA(180), BETA(210), GAMA(30), + * AP(30), P(30), UP(14), CR(14), DR(14) + DATA AR(1), AR(2), AR(3), AR(4), AR(5), AR(6), AR(7), AR(8), + 1 AR(9), AR(10), AR(11), AR(12), AR(13), AR(14)/ + 2 1.00000000000000000E+00, 1.04166666666666667E-01, + 3 8.35503472222222222E-02, 1.28226574556327160E-01, + 4 2.91849026464140464E-01, 8.81627267443757652E-01, + 5 3.32140828186276754E+00, 1.49957629868625547E+01, + 6 7.89230130115865181E+01, 4.74451538868264323E+02, + 7 3.20749009089066193E+03, 2.40865496408740049E+04, + 8 1.98923119169509794E+05, 1.79190200777534383E+06/ + DATA BR(1), BR(2), BR(3), BR(4), BR(5), BR(6), BR(7), BR(8), + 1 BR(9), BR(10), BR(11), BR(12), BR(13), BR(14)/ + 2 1.00000000000000000E+00, -1.45833333333333333E-01, + 3 -9.87413194444444444E-02, -1.43312053915895062E-01, + 4 -3.17227202678413548E-01, -9.42429147957120249E-01, + 5 -3.51120304082635426E+00, -1.57272636203680451E+01, + 6 -8.22814390971859444E+01, -4.92355370523670524E+02, + 7 -3.31621856854797251E+03, -2.48276742452085896E+04, + 8 -2.04526587315129788E+05, -1.83844491706820990E+06/ + DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10), + 1 C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18), + 2 C(19), C(20), C(21), C(22), C(23), C(24)/ + 3 1.00000000000000000E+00, -2.08333333333333333E-01, + 4 1.25000000000000000E-01, 3.34201388888888889E-01, + 5 -4.01041666666666667E-01, 7.03125000000000000E-02, + 6 -1.02581259645061728E+00, 1.84646267361111111E+00, + 7 -8.91210937500000000E-01, 7.32421875000000000E-02, + 8 4.66958442342624743E+00, -1.12070026162229938E+01, + 9 8.78912353515625000E+00, -2.36408691406250000E+00, + A 1.12152099609375000E-01, -2.82120725582002449E+01, + B 8.46362176746007346E+01, -9.18182415432400174E+01, + C 4.25349987453884549E+01, -7.36879435947963170E+00, + D 2.27108001708984375E-01, 2.12570130039217123E+02, + E -7.65252468141181642E+02, 1.05999045252799988E+03/ + DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32), + 1 C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40), + 2 C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/ + 3 -6.99579627376132541E+02, 2.18190511744211590E+02, + 4 -2.64914304869515555E+01, 5.72501420974731445E-01, + 5 -1.91945766231840700E+03, 8.06172218173730938E+03, + 6 -1.35865500064341374E+04, 1.16553933368645332E+04, + 7 -5.30564697861340311E+03, 1.20090291321635246E+03, + 8 -1.08090919788394656E+02, 1.72772750258445740E+00, + 9 2.02042913309661486E+04, -9.69805983886375135E+04, + A 1.92547001232531532E+05, -2.03400177280415534E+05, + B 1.22200464983017460E+05, -4.11926549688975513E+04, + C 7.10951430248936372E+03, -4.93915304773088012E+02, + D 6.07404200127348304E+00, -2.42919187900551333E+05, + E 1.31176361466297720E+06, -2.99801591853810675E+06/ + DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56), + 1 C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64), + 2 C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/ + 3 3.76327129765640400E+06, -2.81356322658653411E+06, + 4 1.26836527332162478E+06, -3.31645172484563578E+05, + 5 4.52187689813627263E+04, -2.49983048181120962E+03, + 6 2.43805296995560639E+01, 3.28446985307203782E+06, + 7 -1.97068191184322269E+07, 5.09526024926646422E+07, + 8 -7.41051482115326577E+07, 6.63445122747290267E+07, + 9 -3.75671766607633513E+07, 1.32887671664218183E+07, + A -2.78561812808645469E+06, 3.08186404612662398E+05, + B -1.38860897537170405E+04, 1.10017140269246738E+02, + C -4.93292536645099620E+07, 3.25573074185765749E+08, + D -9.39462359681578403E+08, 1.55359689957058006E+09, + E -1.62108055210833708E+09, 1.10684281682301447E+09/ + DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80), + 1 C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88), + 2 C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/ + 3 -4.95889784275030309E+08, 1.42062907797533095E+08, + 4 -2.44740627257387285E+07, 2.24376817792244943E+06, + 5 -8.40054336030240853E+04, 5.51335896122020586E+02, + 6 8.14789096118312115E+08, -5.86648149205184723E+09, + 7 1.86882075092958249E+10, -3.46320433881587779E+10, + 8 4.12801855797539740E+10, -3.30265997498007231E+10, + 9 1.79542137311556001E+10, -6.56329379261928433E+09, + A 1.55927986487925751E+09, -2.25105661889415278E+08, + B 1.73951075539781645E+07, -5.49842327572288687E+05, + C 3.03809051092238427E+03, -1.46792612476956167E+10, + D 1.14498237732025810E+11, -3.99096175224466498E+11, + E 8.19218669548577329E+11, -1.09837515608122331E+12/ + DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104), + 1 C(105)/ + 2 1.00815810686538209E+12, -6.45364869245376503E+11, + 3 2.87900649906150589E+11, -8.78670721780232657E+10, + 4 1.76347306068349694E+10, -2.16716498322379509E+09, + 5 1.43157876718888981E+08, -3.87183344257261262E+06, + 6 1.82577554742931747E+04/ + DATA ALFA(1), ALFA(2), ALFA(3), ALFA(4), ALFA(5), ALFA(6), + 1 ALFA(7), ALFA(8), ALFA(9), ALFA(10), ALFA(11), ALFA(12), + 2 ALFA(13), ALFA(14), ALFA(15), ALFA(16), ALFA(17), ALFA(18), + 3 ALFA(19), ALFA(20), ALFA(21), ALFA(22)/ + 4 -4.44444444444444444E-03, -9.22077922077922078E-04, + 5 -8.84892884892884893E-05, 1.65927687832449737E-04, + 6 2.46691372741792910E-04, 2.65995589346254780E-04, + 7 2.61824297061500945E-04, 2.48730437344655609E-04, + 8 2.32721040083232098E-04, 2.16362485712365082E-04, + 9 2.00738858762752355E-04, 1.86267636637545172E-04, + A 1.73060775917876493E-04, 1.61091705929015752E-04, + B 1.50274774160908134E-04, 1.40503497391269794E-04, + C 1.31668816545922806E-04, 1.23667445598253261E-04, + D 1.16405271474737902E-04, 1.09798298372713369E-04, + E 1.03772410422992823E-04, 9.82626078369363448E-05/ + DATA ALFA(23), ALFA(24), ALFA(25), ALFA(26), ALFA(27), ALFA(28), + 1 ALFA(29), ALFA(30), ALFA(31), ALFA(32), ALFA(33), ALFA(34), + 2 ALFA(35), ALFA(36), ALFA(37), ALFA(38), ALFA(39), ALFA(40), + 3 ALFA(41), ALFA(42), ALFA(43), ALFA(44)/ + 4 9.32120517249503256E-05, 8.85710852478711718E-05, + 5 8.42963105715700223E-05, 8.03497548407791151E-05, + 6 7.66981345359207388E-05, 7.33122157481777809E-05, + 7 7.01662625163141333E-05, 6.72375633790160292E-05, + 8 6.93735541354588974E-04, 2.32241745182921654E-04, + 9 -1.41986273556691197E-05, -1.16444931672048640E-04, + A -1.50803558053048762E-04, -1.55121924918096223E-04, + B -1.46809756646465549E-04, -1.33815503867491367E-04, + C -1.19744975684254051E-04, -1.06184319207974020E-04, + D -9.37699549891194492E-05, -8.26923045588193274E-05, + E -7.29374348155221211E-05, -6.44042357721016283E-05/ + DATA ALFA(45), ALFA(46), ALFA(47), ALFA(48), ALFA(49), ALFA(50), + 1 ALFA(51), ALFA(52), ALFA(53), ALFA(54), ALFA(55), ALFA(56), + 2 ALFA(57), ALFA(58), ALFA(59), ALFA(60), ALFA(61), ALFA(62), + 3 ALFA(63), ALFA(64), ALFA(65), ALFA(66)/ + 4 -5.69611566009369048E-05, -5.04731044303561628E-05, + 5 -4.48134868008882786E-05, -3.98688727717598864E-05, + 6 -3.55400532972042498E-05, -3.17414256609022480E-05, + 7 -2.83996793904174811E-05, -2.54522720634870566E-05, + 8 -2.28459297164724555E-05, -2.05352753106480604E-05, + 9 -1.84816217627666085E-05, -1.66519330021393806E-05, + A -1.50179412980119482E-05, -1.35554031379040526E-05, + B -1.22434746473858131E-05, -1.10641884811308169E-05, + C -3.54211971457743841E-04, -1.56161263945159416E-04, + D 3.04465503594936410E-05, 1.30198655773242693E-04, + E 1.67471106699712269E-04, 1.70222587683592569E-04/ + DATA ALFA(67), ALFA(68), ALFA(69), ALFA(70), ALFA(71), ALFA(72), + 1 ALFA(73), ALFA(74), ALFA(75), ALFA(76), ALFA(77), ALFA(78), + 2 ALFA(79), ALFA(80), ALFA(81), ALFA(82), ALFA(83), ALFA(84), + 3 ALFA(85), ALFA(86), ALFA(87), ALFA(88)/ + 4 1.56501427608594704E-04, 1.36339170977445120E-04, + 5 1.14886692029825128E-04, 9.45869093034688111E-05, + 6 7.64498419250898258E-05, 6.07570334965197354E-05, + 7 4.74394299290508799E-05, 3.62757512005344297E-05, + 8 2.69939714979224901E-05, 1.93210938247939253E-05, + 9 1.30056674793963203E-05, 7.82620866744496661E-06, + A 3.59257485819351583E-06, 1.44040049814251817E-07, + B -2.65396769697939116E-06, -4.91346867098485910E-06, + C -6.72739296091248287E-06, -8.17269379678657923E-06, + D -9.31304715093561232E-06, -1.02011418798016441E-05, + E -1.08805962510592880E-05, -1.13875481509603555E-05/ + DATA ALFA(89), ALFA(90), ALFA(91), ALFA(92), ALFA(93), ALFA(94), + 1 ALFA(95), ALFA(96), ALFA(97), ALFA(98), ALFA(99), ALFA(100), + 2 ALFA(101), ALFA(102), ALFA(103), ALFA(104), ALFA(105), + 3 ALFA(106), ALFA(107), ALFA(108), ALFA(109), ALFA(110)/ + 4 -1.17519675674556414E-05, -1.19987364870944141E-05, + 5 3.78194199201772914E-04, 2.02471952761816167E-04, + 6 -6.37938506318862408E-05, -2.38598230603005903E-04, + 7 -3.10916256027361568E-04, -3.13680115247576316E-04, + 8 -2.78950273791323387E-04, -2.28564082619141374E-04, + 9 -1.75245280340846749E-04, -1.25544063060690348E-04, + A -8.22982872820208365E-05, -4.62860730588116458E-05, + B -1.72334302366962267E-05, 5.60690482304602267E-06, + C 2.31395443148286800E-05, 3.62642745856793957E-05, + D 4.58006124490188752E-05, 5.24595294959114050E-05, + E 5.68396208545815266E-05, 5.94349820393104052E-05/ + DATA ALFA(111), ALFA(112), ALFA(113), ALFA(114), ALFA(115), + 1 ALFA(116), ALFA(117), ALFA(118), ALFA(119), ALFA(120), + 2 ALFA(121), ALFA(122), ALFA(123), ALFA(124), ALFA(125), + 3 ALFA(126), ALFA(127), ALFA(128), ALFA(129), ALFA(130)/ + 4 6.06478527578421742E-05, 6.08023907788436497E-05, + 5 6.01577894539460388E-05, 5.89199657344698500E-05, + 6 5.72515823777593053E-05, 5.52804375585852577E-05, + 7 5.31063773802880170E-05, 5.08069302012325706E-05, + 8 4.84418647620094842E-05, 4.60568581607475370E-05, + 9 -6.91141397288294174E-04, -4.29976633058871912E-04, + A 1.83067735980039018E-04, 6.60088147542014144E-04, + B 8.75964969951185931E-04, 8.77335235958235514E-04, + C 7.49369585378990637E-04, 5.63832329756980918E-04, + D 3.68059319971443156E-04, 1.88464535514455599E-04/ + DATA ALFA(131), ALFA(132), ALFA(133), ALFA(134), ALFA(135), + 1 ALFA(136), ALFA(137), ALFA(138), ALFA(139), ALFA(140), + 2 ALFA(141), ALFA(142), ALFA(143), ALFA(144), ALFA(145), + 3 ALFA(146), ALFA(147), ALFA(148), ALFA(149), ALFA(150)/ + 4 3.70663057664904149E-05, -8.28520220232137023E-05, + 5 -1.72751952869172998E-04, -2.36314873605872983E-04, + 6 -2.77966150694906658E-04, -3.02079514155456919E-04, + 7 -3.12594712643820127E-04, -3.12872558758067163E-04, + 8 -3.05678038466324377E-04, -2.93226470614557331E-04, + 9 -2.77255655582934777E-04, -2.59103928467031709E-04, + A -2.39784014396480342E-04, -2.20048260045422848E-04, + B -2.00443911094971498E-04, -1.81358692210970687E-04, + C -1.63057674478657464E-04, -1.45712672175205844E-04, + D -1.29425421983924587E-04, -1.14245691942445952E-04/ + DATA ALFA(151), ALFA(152), ALFA(153), ALFA(154), ALFA(155), + 1 ALFA(156), ALFA(157), ALFA(158), ALFA(159), ALFA(160), + 2 ALFA(161), ALFA(162), ALFA(163), ALFA(164), ALFA(165), + 3 ALFA(166), ALFA(167), ALFA(168), ALFA(169), ALFA(170)/ + 4 1.92821964248775885E-03, 1.35592576302022234E-03, + 5 -7.17858090421302995E-04, -2.58084802575270346E-03, + 6 -3.49271130826168475E-03, -3.46986299340960628E-03, + 7 -2.82285233351310182E-03, -1.88103076404891354E-03, + 8 -8.89531718383947600E-04, 3.87912102631035228E-06, + 9 7.28688540119691412E-04, 1.26566373053457758E-03, + A 1.62518158372674427E-03, 1.83203153216373172E-03, + B 1.91588388990527909E-03, 1.90588846755546138E-03, + C 1.82798982421825727E-03, 1.70389506421121530E-03, + D 1.55097127171097686E-03, 1.38261421852276159E-03/ + DATA ALFA(171), ALFA(172), ALFA(173), ALFA(174), ALFA(175), + 1 ALFA(176), ALFA(177), ALFA(178), ALFA(179), ALFA(180)/ + 2 1.20881424230064774E-03, 1.03676532638344962E-03, + 3 8.71437918068619115E-04, 7.16080155297701002E-04, + 4 5.72637002558129372E-04, 4.42089819465802277E-04, + 5 3.24724948503090564E-04, 2.20342042730246599E-04, + 6 1.28412898401353882E-04, 4.82005924552095464E-05/ + DATA BETA(1), BETA(2), BETA(3), BETA(4), BETA(5), BETA(6), + 1 BETA(7), BETA(8), BETA(9), BETA(10), BETA(11), BETA(12), + 2 BETA(13), BETA(14), BETA(15), BETA(16), BETA(17), BETA(18), + 3 BETA(19), BETA(20), BETA(21), BETA(22)/ + 4 1.79988721413553309E-02, 5.59964911064388073E-03, + 5 2.88501402231132779E-03, 1.80096606761053941E-03, + 6 1.24753110589199202E-03, 9.22878876572938311E-04, + 7 7.14430421727287357E-04, 5.71787281789704872E-04, + 8 4.69431007606481533E-04, 3.93232835462916638E-04, + 9 3.34818889318297664E-04, 2.88952148495751517E-04, + A 2.52211615549573284E-04, 2.22280580798883327E-04, + B 1.97541838033062524E-04, 1.76836855019718004E-04, + C 1.59316899661821081E-04, 1.44347930197333986E-04, + D 1.31448068119965379E-04, 1.20245444949302884E-04, + E 1.10449144504599392E-04, 1.01828770740567258E-04/ + DATA BETA(23), BETA(24), BETA(25), BETA(26), BETA(27), BETA(28), + 1 BETA(29), BETA(30), BETA(31), BETA(32), BETA(33), BETA(34), + 2 BETA(35), BETA(36), BETA(37), BETA(38), BETA(39), BETA(40), + 3 BETA(41), BETA(42), BETA(43), BETA(44)/ + 4 9.41998224204237509E-05, 8.74130545753834437E-05, + 5 8.13466262162801467E-05, 7.59002269646219339E-05, + 6 7.09906300634153481E-05, 6.65482874842468183E-05, + 7 6.25146958969275078E-05, 5.88403394426251749E-05, + 8 -1.49282953213429172E-03, -8.78204709546389328E-04, + 9 -5.02916549572034614E-04, -2.94822138512746025E-04, + A -1.75463996970782828E-04, -1.04008550460816434E-04, + B -5.96141953046457895E-05, -3.12038929076098340E-05, + C -1.26089735980230047E-05, -2.42892608575730389E-07, + D 8.05996165414273571E-06, 1.36507009262147391E-05, + E 1.73964125472926261E-05, 1.98672978842133780E-05/ + DATA BETA(45), BETA(46), BETA(47), BETA(48), BETA(49), BETA(50), + 1 BETA(51), BETA(52), BETA(53), BETA(54), BETA(55), BETA(56), + 2 BETA(57), BETA(58), BETA(59), BETA(60), BETA(61), BETA(62), + 3 BETA(63), BETA(64), BETA(65), BETA(66)/ + 4 2.14463263790822639E-05, 2.23954659232456514E-05, + 5 2.28967783814712629E-05, 2.30785389811177817E-05, + 6 2.30321976080909144E-05, 2.28236073720348722E-05, + 7 2.25005881105292418E-05, 2.20981015361991429E-05, + 8 2.16418427448103905E-05, 2.11507649256220843E-05, + 9 2.06388749782170737E-05, 2.01165241997081666E-05, + A 1.95913450141179244E-05, 1.90689367910436740E-05, + B 1.85533719641636667E-05, 1.80475722259674218E-05, + C 5.52213076721292790E-04, 4.47932581552384646E-04, + D 2.79520653992020589E-04, 1.52468156198446602E-04, + E 6.93271105657043598E-05, 1.76258683069991397E-05/ + DATA BETA(67), BETA(68), BETA(69), BETA(70), BETA(71), BETA(72), + 1 BETA(73), BETA(74), BETA(75), BETA(76), BETA(77), BETA(78), + 2 BETA(79), BETA(80), BETA(81), BETA(82), BETA(83), BETA(84), + 3 BETA(85), BETA(86), BETA(87), BETA(88)/ + 4 -1.35744996343269136E-05, -3.17972413350427135E-05, + 5 -4.18861861696693365E-05, -4.69004889379141029E-05, + 6 -4.87665447413787352E-05, -4.87010031186735069E-05, + 7 -4.74755620890086638E-05, -4.55813058138628452E-05, + 8 -4.33309644511266036E-05, -4.09230193157750364E-05, + 9 -3.84822638603221274E-05, -3.60857167535410501E-05, + A -3.37793306123367417E-05, -3.15888560772109621E-05, + B -2.95269561750807315E-05, -2.75978914828335759E-05, + C -2.58006174666883713E-05, -2.41308356761280200E-05, + D -2.25823509518346033E-05, -2.11479656768912971E-05, + E -1.98200638885294927E-05, -1.85909870801065077E-05/ + DATA BETA(89), BETA(90), BETA(91), BETA(92), BETA(93), BETA(94), + 1 BETA(95), BETA(96), BETA(97), BETA(98), BETA(99), BETA(100), + 2 BETA(101), BETA(102), BETA(103), BETA(104), BETA(105), + 3 BETA(106), BETA(107), BETA(108), BETA(109), BETA(110)/ + 4 -1.74532699844210224E-05, -1.63997823854497997E-05, + 5 -4.74617796559959808E-04, -4.77864567147321487E-04, + 6 -3.20390228067037603E-04, -1.61105016119962282E-04, + 7 -4.25778101285435204E-05, 3.44571294294967503E-05, + 8 7.97092684075674924E-05, 1.03138236708272200E-04, + 9 1.12466775262204158E-04, 1.13103642108481389E-04, + A 1.08651634848774268E-04, 1.01437951597661973E-04, + B 9.29298396593363896E-05, 8.40293133016089978E-05, + C 7.52727991349134062E-05, 6.69632521975730872E-05, + D 5.92564547323194704E-05, 5.22169308826975567E-05, + E 4.58539485165360646E-05, 4.01445513891486808E-05/ + DATA BETA(111), BETA(112), BETA(113), BETA(114), BETA(115), + 1 BETA(116), BETA(117), BETA(118), BETA(119), BETA(120), + 2 BETA(121), BETA(122), BETA(123), BETA(124), BETA(125), + 3 BETA(126), BETA(127), BETA(128), BETA(129), BETA(130)/ + 4 3.50481730031328081E-05, 3.05157995034346659E-05, + 5 2.64956119950516039E-05, 2.29363633690998152E-05, + 6 1.97893056664021636E-05, 1.70091984636412623E-05, + 7 1.45547428261524004E-05, 1.23886640995878413E-05, + 8 1.04775876076583236E-05, 8.79179954978479373E-06, + 9 7.36465810572578444E-04, 8.72790805146193976E-04, + A 6.22614862573135066E-04, 2.85998154194304147E-04, + B 3.84737672879366102E-06, -1.87906003636971558E-04, + C -2.97603646594554535E-04, -3.45998126832656348E-04, + D -3.53382470916037712E-04, -3.35715635775048757E-04/ + DATA BETA(131), BETA(132), BETA(133), BETA(134), BETA(135), + 1 BETA(136), BETA(137), BETA(138), BETA(139), BETA(140), + 2 BETA(141), BETA(142), BETA(143), BETA(144), BETA(145), + 3 BETA(146), BETA(147), BETA(148), BETA(149), BETA(150)/ + 4 -3.04321124789039809E-04, -2.66722723047612821E-04, + 5 -2.27654214122819527E-04, -1.89922611854562356E-04, + 6 -1.55058918599093870E-04, -1.23778240761873630E-04, + 7 -9.62926147717644187E-05, -7.25178327714425337E-05, + 8 -5.22070028895633801E-05, -3.50347750511900522E-05, + 9 -2.06489761035551757E-05, -8.70106096849767054E-06, + A 1.13698686675100290E-06, 9.16426474122778849E-06, + B 1.56477785428872620E-05, 2.08223629482466847E-05, + C 2.48923381004595156E-05, 2.80340509574146325E-05, + D 3.03987774629861915E-05, 3.21156731406700616E-05/ + DATA BETA(151), BETA(152), BETA(153), BETA(154), BETA(155), + 1 BETA(156), BETA(157), BETA(158), BETA(159), BETA(160), + 2 BETA(161), BETA(162), BETA(163), BETA(164), BETA(165), + 3 BETA(166), BETA(167), BETA(168), BETA(169), BETA(170)/ + 4 -1.80182191963885708E-03, -2.43402962938042533E-03, + 5 -1.83422663549856802E-03, -7.62204596354009765E-04, + 6 2.39079475256927218E-04, 9.49266117176881141E-04, + 7 1.34467449701540359E-03, 1.48457495259449178E-03, + 8 1.44732339830617591E-03, 1.30268261285657186E-03, + 9 1.10351597375642682E-03, 8.86047440419791759E-04, + A 6.73073208165665473E-04, 4.77603872856582378E-04, + B 3.05991926358789362E-04, 1.60315694594721630E-04, + C 4.00749555270613286E-05, -5.66607461635251611E-05, + D -1.32506186772982638E-04, -1.90296187989614057E-04/ + DATA BETA(171), BETA(172), BETA(173), BETA(174), BETA(175), + 1 BETA(176), BETA(177), BETA(178), BETA(179), BETA(180), + 2 BETA(181), BETA(182), BETA(183), BETA(184), BETA(185), + 3 BETA(186), BETA(187), BETA(188), BETA(189), BETA(190)/ + 4 -2.32811450376937408E-04, -2.62628811464668841E-04, + 5 -2.82050469867598672E-04, -2.93081563192861167E-04, + 6 -2.97435962176316616E-04, -2.96557334239348078E-04, + 7 -2.91647363312090861E-04, -2.83696203837734166E-04, + 8 -2.73512317095673346E-04, -2.61750155806768580E-04, + 9 6.38585891212050914E-03, 9.62374215806377941E-03, + A 7.61878061207001043E-03, 2.83219055545628054E-03, + B -2.09841352012720090E-03, -5.73826764216626498E-03, + C -7.70804244495414620E-03, -8.21011692264844401E-03, + D -7.65824520346905413E-03, -6.47209729391045177E-03/ + DATA BETA(191), BETA(192), BETA(193), BETA(194), BETA(195), + 1 BETA(196), BETA(197), BETA(198), BETA(199), BETA(200), + 2 BETA(201), BETA(202), BETA(203), BETA(204), BETA(205), + 3 BETA(206), BETA(207), BETA(208), BETA(209), BETA(210)/ + 4 -4.99132412004966473E-03, -3.45612289713133280E-03, + 5 -2.01785580014170775E-03, -7.59430686781961401E-04, + 6 2.84173631523859138E-04, 1.10891667586337403E-03, + 7 1.72901493872728771E-03, 2.16812590802684701E-03, + 8 2.45357710494539735E-03, 2.61281821058334862E-03, + 9 2.67141039656276912E-03, 2.65203073395980430E-03, + A 2.57411652877287315E-03, 2.45389126236094427E-03, + B 2.30460058071795494E-03, 2.13684837686712662E-03, + C 1.95896528478870911E-03, 1.77737008679454412E-03, + D 1.59690280765839059E-03, 1.42111975664438546E-03/ + DATA GAMA(1), GAMA(2), GAMA(3), GAMA(4), GAMA(5), GAMA(6), + 1 GAMA(7), GAMA(8), GAMA(9), GAMA(10), GAMA(11), GAMA(12), + 2 GAMA(13), GAMA(14), GAMA(15), GAMA(16), GAMA(17), GAMA(18), + 3 GAMA(19), GAMA(20), GAMA(21), GAMA(22)/ + 4 6.29960524947436582E-01, 2.51984209978974633E-01, + 5 1.54790300415655846E-01, 1.10713062416159013E-01, + 6 8.57309395527394825E-02, 6.97161316958684292E-02, + 7 5.86085671893713576E-02, 5.04698873536310685E-02, + 8 4.42600580689154809E-02, 3.93720661543509966E-02, + 9 3.54283195924455368E-02, 3.21818857502098231E-02, + A 2.94646240791157679E-02, 2.71581677112934479E-02, + B 2.51768272973861779E-02, 2.34570755306078891E-02, + C 2.19508390134907203E-02, 2.06210828235646240E-02, + D 1.94388240897880846E-02, 1.83810633800683158E-02, + E 1.74293213231963172E-02, 1.65685837786612353E-02/ + DATA GAMA(23), GAMA(24), GAMA(25), GAMA(26), GAMA(27), GAMA(28), + 1 GAMA(29), GAMA(30)/ + 2 1.57865285987918445E-02, 1.50729501494095594E-02, + 3 1.44193250839954639E-02, 1.38184805735341786E-02, + 4 1.32643378994276568E-02, 1.27517121970498651E-02, + 5 1.22761545318762767E-02, 1.18338262398482403E-02/ + DATA EX1, EX2, HPI, PI, THPI / + 1 3.33333333333333333E-01, 6.66666666666666667E-01, + 2 1.57079632679489662E+00, 3.14159265358979324E+00, + 3 4.71238898038468986E+00/ + DATA CZERO, CONE / (0.0E0,0.0E0), (1.0E0,0.0E0) / +C***FIRST EXECUTABLE STATEMENT CUNHJ + RFNU = 1.0E0/FNU +C ZB = Z*CMPLX(RFNU,0.0E0) +C----------------------------------------------------------------------- +C OVERFLOW TEST (Z/FNU TOO SMALL) +C----------------------------------------------------------------------- + TSTR = REAL(Z) + TSTI = AIMAG(Z) + TEST = R1MACH(1)*1.0E+3 + AC = FNU*TEST + IF (ABS(TSTR).GT.AC .OR. ABS(TSTI).GT.AC) GO TO 15 + AC = 2.0E0*ABS(ALOG(TEST))+FNU + ZETA1 = CMPLX(AC,0.0E0) + ZETA2 = CMPLX(FNU,0.0E0) + PHI=CONE + ARG=CONE + RETURN + 15 CONTINUE + ZB = Z*CMPLX(RFNU,0.0E0) + RFNU2 = RFNU*RFNU +C----------------------------------------------------------------------- +C COMPUTE IN THE FOURTH QUADRANT +C----------------------------------------------------------------------- + FN13 = FNU**EX1 + FN23 = FN13*FN13 + RFN13 = CMPLX(1.0E0/FN13,0.0E0) + W2 = CONE - ZB*ZB + AW2 = ABS(W2) + IF (AW2.GT.0.25E0) GO TO 130 +C----------------------------------------------------------------------- +C POWER SERIES FOR ABS(W2).LE.0.25E0 +C----------------------------------------------------------------------- + K = 1 + P(1) = CONE + SUMA = CMPLX(GAMA(1),0.0E0) + AP(1) = 1.0E0 + IF (AW2.LT.TOL) GO TO 20 + DO 10 K=2,30 + P(K) = P(K-1)*W2 + SUMA = SUMA + P(K)*CMPLX(GAMA(K),0.0E0) + AP(K) = AP(K-1)*AW2 + IF (AP(K).LT.TOL) GO TO 20 + 10 CONTINUE + K = 30 + 20 CONTINUE + KMAX = K + ZETA = W2*SUMA + ARG = ZETA*CMPLX(FN23,0.0E0) + ZA = CSQRT(SUMA) + ZETA2 = CSQRT(W2)*CMPLX(FNU,0.0E0) + ZETA1 = ZETA2*(CONE+ZETA*ZA*CMPLX(EX2,0.0E0)) + ZA = ZA + ZA + PHI = CSQRT(ZA)*RFN13 + IF (IPMTR.EQ.1) GO TO 120 +C----------------------------------------------------------------------- +C SUM SERIES FOR ASUM AND BSUM +C----------------------------------------------------------------------- + SUMB = CZERO + DO 30 K=1,KMAX + SUMB = SUMB + P(K)*CMPLX(BETA(K),0.0E0) + 30 CONTINUE + ASUM = CZERO + BSUM = SUMB + L1 = 0 + L2 = 30 + BTOL = TOL*ABS(BSUM) + ATOL = TOL + PP = 1.0E0 + IAS = 0 + IBS = 0 + IF (RFNU2.LT.TOL) GO TO 110 + DO 100 IS=2,7 + ATOL = ATOL/RFNU2 + PP = PP*RFNU2 + IF (IAS.EQ.1) GO TO 60 + SUMA = CZERO + DO 40 K=1,KMAX + M = L1 + K + SUMA = SUMA + P(K)*CMPLX(ALFA(M),0.0E0) + IF (AP(K).LT.ATOL) GO TO 50 + 40 CONTINUE + 50 CONTINUE + ASUM = ASUM + SUMA*CMPLX(PP,0.0E0) + IF (PP.LT.TOL) IAS = 1 + 60 CONTINUE + IF (IBS.EQ.1) GO TO 90 + SUMB = CZERO + DO 70 K=1,KMAX + M = L2 + K + SUMB = SUMB + P(K)*CMPLX(BETA(M),0.0E0) + IF (AP(K).LT.ATOL) GO TO 80 + 70 CONTINUE + 80 CONTINUE + BSUM = BSUM + SUMB*CMPLX(PP,0.0E0) + IF (PP.LT.BTOL) IBS = 1 + 90 CONTINUE + IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 110 + L1 = L1 + 30 + L2 = L2 + 30 + 100 CONTINUE + 110 CONTINUE + ASUM = ASUM + CONE + PP = RFNU*REAL(RFN13) + BSUM = BSUM*CMPLX(PP,0.0E0) + 120 CONTINUE + RETURN +C----------------------------------------------------------------------- +C ABS(W2).GT.0.25E0 +C----------------------------------------------------------------------- + 130 CONTINUE + W = CSQRT(W2) + WR = REAL(W) + WI = AIMAG(W) + IF (WR.LT.0.0E0) WR = 0.0E0 + IF (WI.LT.0.0E0) WI = 0.0E0 + W = CMPLX(WR,WI) + ZA = (CONE+W)/ZB + ZC = CLOG(ZA) + ZCR = REAL(ZC) + ZCI = AIMAG(ZC) + IF (ZCI.LT.0.0E0) ZCI = 0.0E0 + IF (ZCI.GT.HPI) ZCI = HPI + IF (ZCR.LT.0.0E0) ZCR = 0.0E0 + ZC = CMPLX(ZCR,ZCI) + ZTH = (ZC-W)*CMPLX(1.5E0,0.0E0) + CFNU = CMPLX(FNU,0.0E0) + ZETA1 = ZC*CFNU + ZETA2 = W*CFNU + AZTH = ABS(ZTH) + ZTHR = REAL(ZTH) + ZTHI = AIMAG(ZTH) + ANG = THPI + IF (ZTHR.GE.0.0E0 .AND. ZTHI.LT.0.0E0) GO TO 140 + ANG = HPI + IF (ZTHR.EQ.0.0E0) GO TO 140 + ANG = ATAN(ZTHI/ZTHR) + IF (ZTHR.LT.0.0E0) ANG = ANG + PI + 140 CONTINUE + PP = AZTH**EX2 + ANG = ANG*EX2 + ZETAR = PP*COS(ANG) + ZETAI = PP*SIN(ANG) + IF (ZETAI.LT.0.0E0) ZETAI = 0.0E0 + ZETA = CMPLX(ZETAR,ZETAI) + ARG = ZETA*CMPLX(FN23,0.0E0) + RTZTA = ZTH/ZETA + ZA = RTZTA/W + PHI = CSQRT(ZA+ZA)*RFN13 + IF (IPMTR.EQ.1) GO TO 120 + TFN = CMPLX(RFNU,0.0E0)/W + RZTH = CMPLX(RFNU,0.0E0)/ZTH + ZC = RZTH*CMPLX(AR(2),0.0E0) + T2 = CONE/W2 + UP(2) = (T2*CMPLX(C(2),0.0E0)+CMPLX(C(3),0.0E0))*TFN + BSUM = UP(2) + ZC + ASUM = CZERO + IF (RFNU.LT.TOL) GO TO 220 + PRZTH = RZTH + PTFN = TFN + UP(1) = CONE + PP = 1.0E0 + BSUMR = REAL(BSUM) + BSUMI = AIMAG(BSUM) + BTOL = TOL*(ABS(BSUMR)+ABS(BSUMI)) + KS = 0 + KP1 = 2 + L = 3 + IAS = 0 + IBS = 0 + DO 210 LR=2,12,2 + LRP1 = LR + 1 +C----------------------------------------------------------------------- +C COMPUTE TWO ADDITIONAL CR, DR, AND UP FOR TWO MORE TERMS IN +C NEXT SUMA AND SUMB +C----------------------------------------------------------------------- + DO 160 K=LR,LRP1 + KS = KS + 1 + KP1 = KP1 + 1 + L = L + 1 + ZA = CMPLX(C(L),0.0E0) + DO 150 J=2,KP1 + L = L + 1 + ZA = ZA*T2 + CMPLX(C(L),0.0E0) + 150 CONTINUE + PTFN = PTFN*TFN + UP(KP1) = PTFN*ZA + CR(KS) = PRZTH*CMPLX(BR(KS+1),0.0E0) + PRZTH = PRZTH*RZTH + DR(KS) = PRZTH*CMPLX(AR(KS+2),0.0E0) + 160 CONTINUE + PP = PP*RFNU2 + IF (IAS.EQ.1) GO TO 180 + SUMA = UP(LRP1) + JU = LRP1 + DO 170 JR=1,LR + JU = JU - 1 + SUMA = SUMA + CR(JR)*UP(JU) + 170 CONTINUE + ASUM = ASUM + SUMA + ASUMR = REAL(ASUM) + ASUMI = AIMAG(ASUM) + TEST = ABS(ASUMR) + ABS(ASUMI) + IF (PP.LT.TOL .AND. TEST.LT.TOL) IAS = 1 + 180 CONTINUE + IF (IBS.EQ.1) GO TO 200 + SUMB = UP(LR+2) + UP(LRP1)*ZC + JU = LRP1 + DO 190 JR=1,LR + JU = JU - 1 + SUMB = SUMB + DR(JR)*UP(JU) + 190 CONTINUE + BSUM = BSUM + SUMB + BSUMR = REAL(BSUM) + BSUMI = AIMAG(BSUM) + TEST = ABS(BSUMR) + ABS(BSUMI) + IF (PP.LT.BTOL .AND. TEST.LT.TOL) IBS = 1 + 200 CONTINUE + IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 220 + 210 CONTINUE + 220 CONTINUE + ASUM = ASUM + CONE + BSUM = -BSUM*RFN13/RTZTA + GO TO 120 + END diff --git a/schainf/Ffiles/cuni1.f b/schainf/Ffiles/cuni1.f new file mode 100644 index 0000000..39a3d37 --- /dev/null +++ b/schainf/Ffiles/cuni1.f @@ -0,0 +1,178 @@ +*DECK CUNI1 + SUBROUTINE CUNI1 (Z, FNU, KODE, N, Y, NZ, NLAST, FNUL, TOL, ELIM, + + ALIM) +C***BEGIN PROLOGUE CUNI1 +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBESI and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CUNI1-A, ZUNI1-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CUNI1 COMPUTES I(FNU,Z) BY MEANS OF THE UNIFORM ASYMPTOTIC +C EXPANSION FOR I(FNU,Z) IN -PI/3.LE.ARG Z.LE.PI/3. +C +C FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC +C EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET. +C NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER +C FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL. +C Y(I)=CZERO FOR I=NLAST+1,N +C +C***SEE ALSO CBESI, CBESK +C***ROUTINES CALLED CUCHK, CUNIK, CUOIK, R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CUNI1 + COMPLEX CFN, CONE, CRSC, CSCL, CSR, CSS, CWRK, CZERO, C1, C2, + * PHI, RZ, SUM, S1, S2, Y, Z, ZETA1, ZETA2, CY + REAL ALIM, APHI, ASCLE, BRY, C2I, C2M, C2R, ELIM, FN, FNU, FNUL, + * RS1, TOL, YY, R1MACH + INTEGER I, IFLAG, INIT, K, KODE, M, N, ND, NLAST, NN, NUF, NW, NZ + DIMENSION BRY(3), Y(N), CWRK(16), CSS(3), CSR(3), CY(2) + DATA CZERO, CONE / (0.0E0,0.0E0), (1.0E0,0.0E0) / +C***FIRST EXECUTABLE STATEMENT CUNI1 + NZ = 0 + ND = N + NLAST = 0 +C----------------------------------------------------------------------- +C COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG- +C NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE, +C EXP(ALIM)=EXP(ELIM)*TOL +C----------------------------------------------------------------------- + CSCL = CMPLX(1.0E0/TOL,0.0E0) + CRSC = CMPLX(TOL,0.0E0) + CSS(1) = CSCL + CSS(2) = CONE + CSS(3) = CRSC + CSR(1) = CRSC + CSR(2) = CONE + CSR(3) = CSCL + BRY(1) = 1.0E+3*R1MACH(1)/TOL +C----------------------------------------------------------------------- +C CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER +C----------------------------------------------------------------------- + FN = MAX(FNU,1.0E0) + INIT = 0 + CALL CUNIK(Z, FN, 1, 1, TOL, INIT, PHI, ZETA1, ZETA2, SUM, CWRK) + IF (KODE.EQ.1) GO TO 10 + CFN = CMPLX(FN,0.0E0) + S1 = -ZETA1 + CFN*(CFN/(Z+ZETA2)) + GO TO 20 + 10 CONTINUE + S1 = -ZETA1 + ZETA2 + 20 CONTINUE + RS1 = REAL(S1) + IF (ABS(RS1).GT.ELIM) GO TO 130 + 30 CONTINUE + NN = MIN(2,ND) + DO 80 I=1,NN + FN = FNU + (ND-I) + INIT = 0 + CALL CUNIK(Z, FN, 1, 0, TOL, INIT, PHI, ZETA1, ZETA2, SUM, CWRK) + IF (KODE.EQ.1) GO TO 40 + CFN = CMPLX(FN,0.0E0) + YY = AIMAG(Z) + S1 = -ZETA1 + CFN*(CFN/(Z+ZETA2)) + CMPLX(0.0E0,YY) + GO TO 50 + 40 CONTINUE + S1 = -ZETA1 + ZETA2 + 50 CONTINUE +C----------------------------------------------------------------------- +C TEST FOR UNDERFLOW AND OVERFLOW +C----------------------------------------------------------------------- + RS1 = REAL(S1) + IF (ABS(RS1).GT.ELIM) GO TO 110 + IF (I.EQ.1) IFLAG = 2 + IF (ABS(RS1).LT.ALIM) GO TO 60 +C----------------------------------------------------------------------- +C REFINE TEST AND SCALE +C----------------------------------------------------------------------- + APHI = ABS(PHI) + RS1 = RS1 + ALOG(APHI) + IF (ABS(RS1).GT.ELIM) GO TO 110 + IF (I.EQ.1) IFLAG = 1 + IF (RS1.LT.0.0E0) GO TO 60 + IF (I.EQ.1) IFLAG = 3 + 60 CONTINUE +C----------------------------------------------------------------------- +C SCALE S1 IF ABS(S1).LT.ASCLE +C----------------------------------------------------------------------- + S2 = PHI*SUM + C2R = REAL(S1) + C2I = AIMAG(S1) + C2M = EXP(C2R)*REAL(CSS(IFLAG)) + S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I)) + S2 = S2*S1 + IF (IFLAG.NE.1) GO TO 70 + CALL CUCHK(S2, NW, BRY(1), TOL) + IF (NW.NE.0) GO TO 110 + 70 CONTINUE + M = ND - I + 1 + CY(I) = S2 + Y(M) = S2*CSR(IFLAG) + 80 CONTINUE + IF (ND.LE.2) GO TO 100 + RZ = CMPLX(2.0E0,0.0E0)/Z + BRY(2) = 1.0E0/BRY(1) + BRY(3) = R1MACH(2) + S1 = CY(1) + S2 = CY(2) + C1 = CSR(IFLAG) + ASCLE = BRY(IFLAG) + K = ND - 2 + FN = K + DO 90 I=3,ND + C2 = S2 + S2 = S1 + CMPLX(FNU+FN,0.0E0)*RZ*S2 + S1 = C2 + C2 = S2*C1 + Y(K) = C2 + K = K - 1 + FN = FN - 1.0E0 + IF (IFLAG.GE.3) GO TO 90 + C2R = REAL(C2) + C2I = AIMAG(C2) + C2R = ABS(C2R) + C2I = ABS(C2I) + C2M = MAX(C2R,C2I) + IF (C2M.LE.ASCLE) GO TO 90 + IFLAG = IFLAG + 1 + ASCLE = BRY(IFLAG) + S1 = S1*C1 + S2 = C2 + S1 = S1*CSS(IFLAG) + S2 = S2*CSS(IFLAG) + C1 = CSR(IFLAG) + 90 CONTINUE + 100 CONTINUE + RETURN +C----------------------------------------------------------------------- +C SET UNDERFLOW AND UPDATE PARAMETERS +C----------------------------------------------------------------------- + 110 CONTINUE + IF (RS1.GT.0.0E0) GO TO 120 + Y(ND) = CZERO + NZ = NZ + 1 + ND = ND - 1 + IF (ND.EQ.0) GO TO 100 + CALL CUOIK(Z, FNU, KODE, 1, ND, Y, NUF, TOL, ELIM, ALIM) + IF (NUF.LT.0) GO TO 120 + ND = ND - NUF + NZ = NZ + NUF + IF (ND.EQ.0) GO TO 100 + FN = FNU + (ND-1) + IF (FN.GE.FNUL) GO TO 30 + NLAST = ND + RETURN + 120 CONTINUE + NZ = -1 + RETURN + 130 CONTINUE + IF (RS1.GT.0.0E0) GO TO 120 + NZ = N + DO 140 I=1,N + Y(I) = CZERO + 140 CONTINUE + RETURN + END diff --git a/schainf/Ffiles/cuni2.f b/schainf/Ffiles/cuni2.f new file mode 100644 index 0000000..ffc2bcd --- /dev/null +++ b/schainf/Ffiles/cuni2.f @@ -0,0 +1,225 @@ +*DECK CUNI2 + SUBROUTINE CUNI2 (Z, FNU, KODE, N, Y, NZ, NLAST, FNUL, TOL, ELIM, + + ALIM) +C***BEGIN PROLOGUE CUNI2 +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBESI and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CUNI2-A, ZUNI2-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CUNI2 COMPUTES I(FNU,Z) IN THE RIGHT HALF PLANE BY MEANS OF +C UNIFORM ASYMPTOTIC EXPANSION FOR J(FNU,ZN) WHERE ZN IS Z*I +C OR -Z*I AND ZN IS IN THE RIGHT HALF PLANE ALSO. +C +C FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC +C EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET. +C NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER +C FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL. +C Y(I)=CZERO FOR I=NLAST+1,N +C +C***SEE ALSO CBESI, CBESK +C***ROUTINES CALLED CAIRY, CUCHK, CUNHJ, CUOIK, R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CUNI2 + COMPLEX AI, ARG, ASUM, BSUM, CFN, CI, CID, CIP, CONE, CRSC, CSCL, + * CSR, CSS, CY, CZERO, C1, C2, DAI, PHI, RZ, S1, S2, Y, Z, ZB, + * ZETA1, ZETA2, ZN, ZAR + REAL AARG, AIC, ALIM, ANG, APHI, ASCLE, AY, BRY, CAR, C2I, C2M, + * C2R, ELIM, FN, FNU, FNUL, HPI, RS1, SAR, TOL, YY, R1MACH + INTEGER I, IFLAG, IN, INU, J, K, KODE, N, NAI, ND, NDAI, NLAST, + * NN, NUF, NW, NZ, IDUM + DIMENSION BRY(3), Y(N), CIP(4), CSS(3), CSR(3), CY(2) + DATA CZERO,CONE,CI/(0.0E0,0.0E0),(1.0E0,0.0E0),(0.0E0,1.0E0)/ + DATA CIP(1),CIP(2),CIP(3),CIP(4)/ + 1 (1.0E0,0.0E0), (0.0E0,1.0E0), (-1.0E0,0.0E0), (0.0E0,-1.0E0)/ + DATA HPI, AIC / + 1 1.57079632679489662E+00, 1.265512123484645396E+00/ +C***FIRST EXECUTABLE STATEMENT CUNI2 + NZ = 0 + ND = N + NLAST = 0 +C----------------------------------------------------------------------- +C COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG- +C NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE, +C EXP(ALIM)=EXP(ELIM)*TOL +C----------------------------------------------------------------------- + CSCL = CMPLX(1.0E0/TOL,0.0E0) + CRSC = CMPLX(TOL,0.0E0) + CSS(1) = CSCL + CSS(2) = CONE + CSS(3) = CRSC + CSR(1) = CRSC + CSR(2) = CONE + CSR(3) = CSCL + BRY(1) = 1.0E+3*R1MACH(1)/TOL + YY = AIMAG(Z) +C----------------------------------------------------------------------- +C ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI +C----------------------------------------------------------------------- + ZN = -Z*CI + ZB = Z + CID = -CI + INU = FNU + ANG = HPI*(FNU-INU) + CAR = COS(ANG) + SAR = SIN(ANG) + C2 = CMPLX(CAR,SAR) + ZAR = C2 + IN = INU + N - 1 + IN = MOD(IN,4) + C2 = C2*CIP(IN+1) + IF (YY.GT.0.0E0) GO TO 10 + ZN = CONJG(-ZN) + ZB = CONJG(ZB) + CID = -CID + C2 = CONJG(C2) + 10 CONTINUE +C----------------------------------------------------------------------- +C CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER +C----------------------------------------------------------------------- + FN = MAX(FNU,1.0E0) + CALL CUNHJ(ZN, FN, 1, TOL, PHI, ARG, ZETA1, ZETA2, ASUM, BSUM) + IF (KODE.EQ.1) GO TO 20 + CFN = CMPLX(FNU,0.0E0) + S1 = -ZETA1 + CFN*(CFN/(ZB+ZETA2)) + GO TO 30 + 20 CONTINUE + S1 = -ZETA1 + ZETA2 + 30 CONTINUE + RS1 = REAL(S1) + IF (ABS(RS1).GT.ELIM) GO TO 150 + 40 CONTINUE + NN = MIN(2,ND) + DO 90 I=1,NN + FN = FNU + (ND-I) + CALL CUNHJ(ZN, FN, 0, TOL, PHI, ARG, ZETA1, ZETA2, ASUM, BSUM) + IF (KODE.EQ.1) GO TO 50 + CFN = CMPLX(FN,0.0E0) + AY = ABS(YY) + S1 = -ZETA1 + CFN*(CFN/(ZB+ZETA2)) + CMPLX(0.0E0,AY) + GO TO 60 + 50 CONTINUE + S1 = -ZETA1 + ZETA2 + 60 CONTINUE +C----------------------------------------------------------------------- +C TEST FOR UNDERFLOW AND OVERFLOW +C----------------------------------------------------------------------- + RS1 = REAL(S1) + IF (ABS(RS1).GT.ELIM) GO TO 120 + IF (I.EQ.1) IFLAG = 2 + IF (ABS(RS1).LT.ALIM) GO TO 70 +C----------------------------------------------------------------------- +C REFINE TEST AND SCALE +C----------------------------------------------------------------------- +C----------------------------------------------------------------------- + APHI = ABS(PHI) + AARG = ABS(ARG) + RS1 = RS1 + ALOG(APHI) - 0.25E0*ALOG(AARG) - AIC + IF (ABS(RS1).GT.ELIM) GO TO 120 + IF (I.EQ.1) IFLAG = 1 + IF (RS1.LT.0.0E0) GO TO 70 + IF (I.EQ.1) IFLAG = 3 + 70 CONTINUE +C----------------------------------------------------------------------- +C SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR +C EXPONENT EXTREMES +C----------------------------------------------------------------------- + CALL CAIRY(ARG, 0, 2, AI, NAI, IDUM) + CALL CAIRY(ARG, 1, 2, DAI, NDAI, IDUM) + S2 = PHI*(AI*ASUM+DAI*BSUM) + C2R = REAL(S1) + C2I = AIMAG(S1) + C2M = EXP(C2R)*REAL(CSS(IFLAG)) + S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I)) + S2 = S2*S1 + IF (IFLAG.NE.1) GO TO 80 + CALL CUCHK(S2, NW, BRY(1), TOL) + IF (NW.NE.0) GO TO 120 + 80 CONTINUE + IF (YY.LE.0.0E0) S2 = CONJG(S2) + J = ND - I + 1 + S2 = S2*C2 + CY(I) = S2 + Y(J) = S2*CSR(IFLAG) + C2 = C2*CID + 90 CONTINUE + IF (ND.LE.2) GO TO 110 + RZ = CMPLX(2.0E0,0.0E0)/Z + BRY(2) = 1.0E0/BRY(1) + BRY(3) = R1MACH(2) + S1 = CY(1) + S2 = CY(2) + C1 = CSR(IFLAG) + ASCLE = BRY(IFLAG) + K = ND - 2 + FN = K + DO 100 I=3,ND + C2 = S2 + S2 = S1 + CMPLX(FNU+FN,0.0E0)*RZ*S2 + S1 = C2 + C2 = S2*C1 + Y(K) = C2 + K = K - 1 + FN = FN - 1.0E0 + IF (IFLAG.GE.3) GO TO 100 + C2R = REAL(C2) + C2I = AIMAG(C2) + C2R = ABS(C2R) + C2I = ABS(C2I) + C2M = MAX(C2R,C2I) + IF (C2M.LE.ASCLE) GO TO 100 + IFLAG = IFLAG + 1 + ASCLE = BRY(IFLAG) + S1 = S1*C1 + S2 = C2 + S1 = S1*CSS(IFLAG) + S2 = S2*CSS(IFLAG) + C1 = CSR(IFLAG) + 100 CONTINUE + 110 CONTINUE + RETURN + 120 CONTINUE + IF (RS1.GT.0.0E0) GO TO 140 +C----------------------------------------------------------------------- +C SET UNDERFLOW AND UPDATE PARAMETERS +C----------------------------------------------------------------------- + Y(ND) = CZERO + NZ = NZ + 1 + ND = ND - 1 + IF (ND.EQ.0) GO TO 110 + CALL CUOIK(Z, FNU, KODE, 1, ND, Y, NUF, TOL, ELIM, ALIM) + IF (NUF.LT.0) GO TO 140 + ND = ND - NUF + NZ = NZ + NUF + IF (ND.EQ.0) GO TO 110 + FN = FNU + (ND-1) + IF (FN.LT.FNUL) GO TO 130 +C FN = AIMAG(CID) +C J = NUF + 1 +C K = MOD(J,4) + 1 +C S1 = CIP(K) +C IF (FN.LT.0.0E0) S1 = CONJG(S1) +C C2 = C2*S1 + IN = INU + ND - 1 + IN = MOD(IN,4) + 1 + C2 = ZAR*CIP(IN) + IF (YY.LE.0.0E0)C2=CONJG(C2) + GO TO 40 + 130 CONTINUE + NLAST = ND + RETURN + 140 CONTINUE + NZ = -1 + RETURN + 150 CONTINUE + IF (RS1.GT.0.0E0) GO TO 140 + NZ = N + DO 160 I=1,N + Y(I) = CZERO + 160 CONTINUE + RETURN + END diff --git a/schainf/Ffiles/cunik.f b/schainf/Ffiles/cunik.f new file mode 100644 index 0000000..dd31228 --- /dev/null +++ b/schainf/Ffiles/cunik.f @@ -0,0 +1,198 @@ +*DECK CUNIK + SUBROUTINE CUNIK (ZR, FNU, IKFLG, IPMTR, TOL, INIT, PHI, ZETA1, + + ZETA2, SUM, CWRK) +C***BEGIN PROLOGUE CUNIK +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBESI and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CUNIK-A, ZUNIK-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CUNIK COMPUTES PARAMETERS FOR THE UNIFORM ASYMPTOTIC +C EXPANSIONS OF THE I AND K FUNCTIONS ON IKFLG= 1 OR 2 +C RESPECTIVELY BY +C +C W(FNU,ZR) = PHI*EXP(ZETA)*SUM +C +C WHERE ZETA=-ZETA1 + ZETA2 OR +C ZETA1 - ZETA2 +C +C THE FIRST CALL MUST HAVE INIT=0. SUBSEQUENT CALLS WITH THE +C SAME ZR AND FNU WILL RETURN THE I OR K FUNCTION ON IKFLG= +C 1 OR 2 WITH NO CHANGE IN INIT. CWRK IS A COMPLEX WORK +C ARRAY. IPMTR=0 COMPUTES ALL PARAMETERS. IPMTR=1 COMPUTES PHI, +C ZETA1,ZETA2. +C +C***SEE ALSO CBESI, CBESK +C***ROUTINES CALLED R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CUNIK + COMPLEX CFN, CON, CONE, CRFN, CWRK, CZERO, PHI, S, SR, SUM, T, + * T2, ZETA1, ZETA2, ZN, ZR + REAL AC, C, FNU, RFN, TEST, TOL, TSTR, TSTI, R1MACH + INTEGER I, IKFLG, INIT, IPMTR, J, K, L + DIMENSION C(120), CWRK(16), CON(2) + DATA CZERO, CONE / (0.0E0,0.0E0), (1.0E0,0.0E0) / + DATA CON(1), CON(2) / + 1(3.98942280401432678E-01,0.0E0),(1.25331413731550025E+00,0.0E0)/ + DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10), + 1 C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18), + 2 C(19), C(20), C(21), C(22), C(23), C(24)/ + 3 1.00000000000000000E+00, -2.08333333333333333E-01, + 4 1.25000000000000000E-01, 3.34201388888888889E-01, + 5 -4.01041666666666667E-01, 7.03125000000000000E-02, + 6 -1.02581259645061728E+00, 1.84646267361111111E+00, + 7 -8.91210937500000000E-01, 7.32421875000000000E-02, + 8 4.66958442342624743E+00, -1.12070026162229938E+01, + 9 8.78912353515625000E+00, -2.36408691406250000E+00, + A 1.12152099609375000E-01, -2.82120725582002449E+01, + B 8.46362176746007346E+01, -9.18182415432400174E+01, + C 4.25349987453884549E+01, -7.36879435947963170E+00, + D 2.27108001708984375E-01, 2.12570130039217123E+02, + E -7.65252468141181642E+02, 1.05999045252799988E+03/ + DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32), + 1 C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40), + 2 C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/ + 3 -6.99579627376132541E+02, 2.18190511744211590E+02, + 4 -2.64914304869515555E+01, 5.72501420974731445E-01, + 5 -1.91945766231840700E+03, 8.06172218173730938E+03, + 6 -1.35865500064341374E+04, 1.16553933368645332E+04, + 7 -5.30564697861340311E+03, 1.20090291321635246E+03, + 8 -1.08090919788394656E+02, 1.72772750258445740E+00, + 9 2.02042913309661486E+04, -9.69805983886375135E+04, + A 1.92547001232531532E+05, -2.03400177280415534E+05, + B 1.22200464983017460E+05, -4.11926549688975513E+04, + C 7.10951430248936372E+03, -4.93915304773088012E+02, + D 6.07404200127348304E+00, -2.42919187900551333E+05, + E 1.31176361466297720E+06, -2.99801591853810675E+06/ + DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56), + 1 C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64), + 2 C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/ + 3 3.76327129765640400E+06, -2.81356322658653411E+06, + 4 1.26836527332162478E+06, -3.31645172484563578E+05, + 5 4.52187689813627263E+04, -2.49983048181120962E+03, + 6 2.43805296995560639E+01, 3.28446985307203782E+06, + 7 -1.97068191184322269E+07, 5.09526024926646422E+07, + 8 -7.41051482115326577E+07, 6.63445122747290267E+07, + 9 -3.75671766607633513E+07, 1.32887671664218183E+07, + A -2.78561812808645469E+06, 3.08186404612662398E+05, + B -1.38860897537170405E+04, 1.10017140269246738E+02, + C -4.93292536645099620E+07, 3.25573074185765749E+08, + D -9.39462359681578403E+08, 1.55359689957058006E+09, + E -1.62108055210833708E+09, 1.10684281682301447E+09/ + DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80), + 1 C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88), + 2 C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/ + 3 -4.95889784275030309E+08, 1.42062907797533095E+08, + 4 -2.44740627257387285E+07, 2.24376817792244943E+06, + 5 -8.40054336030240853E+04, 5.51335896122020586E+02, + 6 8.14789096118312115E+08, -5.86648149205184723E+09, + 7 1.86882075092958249E+10, -3.46320433881587779E+10, + 8 4.12801855797539740E+10, -3.30265997498007231E+10, + 9 1.79542137311556001E+10, -6.56329379261928433E+09, + A 1.55927986487925751E+09, -2.25105661889415278E+08, + B 1.73951075539781645E+07, -5.49842327572288687E+05, + C 3.03809051092238427E+03, -1.46792612476956167E+10, + D 1.14498237732025810E+11, -3.99096175224466498E+11, + E 8.19218669548577329E+11, -1.09837515608122331E+12/ + DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104), + 1 C(105), C(106), C(107), C(108), C(109), C(110), C(111), + 2 C(112), C(113), C(114), C(115), C(116), C(117), C(118)/ + 3 1.00815810686538209E+12, -6.45364869245376503E+11, + 4 2.87900649906150589E+11, -8.78670721780232657E+10, + 5 1.76347306068349694E+10, -2.16716498322379509E+09, + 6 1.43157876718888981E+08, -3.87183344257261262E+06, + 7 1.82577554742931747E+04, 2.86464035717679043E+11, + 8 -2.40629790002850396E+12, 9.10934118523989896E+12, + 9 -2.05168994109344374E+13, 3.05651255199353206E+13, + A -3.16670885847851584E+13, 2.33483640445818409E+13, + B -1.23204913055982872E+13, 4.61272578084913197E+12, + C -1.19655288019618160E+12, 2.05914503232410016E+11, + D -2.18229277575292237E+10, 1.24700929351271032E+09/ + DATA C(119), C(120)/ + 1 -2.91883881222208134E+07, 1.18838426256783253E+05/ +C***FIRST EXECUTABLE STATEMENT CUNIK + IF (INIT.NE.0) GO TO 40 +C----------------------------------------------------------------------- +C INITIALIZE ALL VARIABLES +C----------------------------------------------------------------------- + RFN = 1.0E0/FNU + CRFN = CMPLX(RFN,0.0E0) +C T = ZR*CRFN +C----------------------------------------------------------------------- +C OVERFLOW TEST (ZR/FNU TOO SMALL) +C----------------------------------------------------------------------- + TSTR = REAL(ZR) + TSTI = AIMAG(ZR) + TEST = R1MACH(1)*1.0E+3 + AC = FNU*TEST + IF (ABS(TSTR).GT.AC .OR. ABS(TSTI).GT.AC) GO TO 15 + AC = 2.0E0*ABS(ALOG(TEST))+FNU + ZETA1 = CMPLX(AC,0.0E0) + ZETA2 = CMPLX(FNU,0.0E0) + PHI=CONE + RETURN + 15 CONTINUE + T=ZR*CRFN + S = CONE + T*T + SR = CSQRT(S) + CFN = CMPLX(FNU,0.0E0) + ZN = (CONE+SR)/T + ZETA1 = CFN*CLOG(ZN) + ZETA2 = CFN*SR + T = CONE/SR + SR = T*CRFN + CWRK(16) = CSQRT(SR) + PHI = CWRK(16)*CON(IKFLG) + IF (IPMTR.NE.0) RETURN + T2 = CONE/S + CWRK(1) = CONE + CRFN = CONE + AC = 1.0E0 + L = 1 + DO 20 K=2,15 + S = CZERO + DO 10 J=1,K + L = L + 1 + S = S*T2 + CMPLX(C(L),0.0E0) + 10 CONTINUE + CRFN = CRFN*SR + CWRK(K) = CRFN*S + AC = AC*RFN + TSTR = REAL(CWRK(K)) + TSTI = AIMAG(CWRK(K)) + TEST = ABS(TSTR) + ABS(TSTI) + IF (AC.LT.TOL .AND. TEST.LT.TOL) GO TO 30 + 20 CONTINUE + K = 15 + 30 CONTINUE + INIT = K + 40 CONTINUE + IF (IKFLG.EQ.2) GO TO 60 +C----------------------------------------------------------------------- +C COMPUTE SUM FOR THE I FUNCTION +C----------------------------------------------------------------------- + S = CZERO + DO 50 I=1,INIT + S = S + CWRK(I) + 50 CONTINUE + SUM = S + PHI = CWRK(16)*CON(1) + RETURN + 60 CONTINUE +C----------------------------------------------------------------------- +C COMPUTE SUM FOR THE K FUNCTION +C----------------------------------------------------------------------- + S = CZERO + T = CONE + DO 70 I=1,INIT + S = S + T*CWRK(I) + T = -T + 70 CONTINUE + SUM = S + PHI = CWRK(16)*CON(2) + RETURN + END diff --git a/schainf/Ffiles/cuoik.f b/schainf/Ffiles/cuoik.f new file mode 100644 index 0000000..d30b9e8 --- /dev/null +++ b/schainf/Ffiles/cuoik.f @@ -0,0 +1,170 @@ +*DECK CUOIK + SUBROUTINE CUOIK (Z, FNU, KODE, IKFLG, N, Y, NUF, TOL, ELIM, ALIM) +C***BEGIN PROLOGUE CUOIK +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBESH, CBESI and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CUOIK-A, ZUOIK-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CUOIK COMPUTES THE LEADING TERMS OF THE UNIFORM ASYMPTOTIC +C EXPANSIONS FOR THE I AND K FUNCTIONS AND COMPARES THEM +C (IN LOGARITHMIC FORM) TO ALIM AND ELIM FOR OVER AND UNDERFLOW +C WHERE ALIM.LT.ELIM. IF THE MAGNITUDE, BASED ON THE LEADING +C EXPONENTIAL, IS LESS THAN ALIM OR GREATER THAN -ALIM, THEN +C THE RESULT IS ON SCALE. IF NOT, THEN A REFINED TEST USING OTHER +C MULTIPLIERS (IN LOGARITHMIC FORM) IS MADE BASED ON ELIM. HERE +C EXP(-ELIM)=SMALLEST MACHINE NUMBER*1.0E+3 AND EXP(-ALIM)= +C EXP(-ELIM)/TOL +C +C IKFLG=1 MEANS THE I SEQUENCE IS TESTED +C =2 MEANS THE K SEQUENCE IS TESTED +C NUF = 0 MEANS THE LAST MEMBER OF THE SEQUENCE IS ON SCALE +C =-1 MEANS AN OVERFLOW WOULD OCCUR +C IKFLG=1 AND NUF.GT.0 MEANS THE LAST NUF Y VALUES WERE SET TO ZERO +C THE FIRST N-NUF VALUES MUST BE SET BY ANOTHER ROUTINE +C IKFLG=2 AND NUF.EQ.N MEANS ALL Y VALUES WERE SET TO ZERO +C IKFLG=2 AND 0.LT.NUF.LT.N NOT CONSIDERED. Y MUST BE SET BY +C ANOTHER ROUTINE +C +C***SEE ALSO CBESH, CBESI, CBESK +C***ROUTINES CALLED CUCHK, CUNHJ, CUNIK, R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CUOIK + COMPLEX ARG, ASUM, BSUM, CWRK, CZ, CZERO, PHI, SUM, Y, Z, ZB, + * ZETA1, ZETA2, ZN, ZR + REAL AARG, AIC, ALIM, APHI, ASCLE, AX, AY, ELIM, FNN, FNU, GNN, + * GNU, RCZ, TOL, X, YY, R1MACH + INTEGER I, IFORM, IKFLG, INIT, KODE, N, NN, NUF, NW + DIMENSION Y(N), CWRK(16) + DATA CZERO / (0.0E0,0.0E0) / + DATA AIC / 1.265512123484645396E+00 / +C***FIRST EXECUTABLE STATEMENT CUOIK + NUF = 0 + NN = N + X = REAL(Z) + ZR = Z + IF (X.LT.0.0E0) ZR = -Z + ZB = ZR + YY = AIMAG(ZR) + AX = ABS(X)*1.7321E0 + AY = ABS(YY) + IFORM = 1 + IF (AY.GT.AX) IFORM = 2 + GNU = MAX(FNU,1.0E0) + IF (IKFLG.EQ.1) GO TO 10 + FNN = NN + GNN = FNU + FNN - 1.0E0 + GNU = MAX(GNN,FNN) + 10 CONTINUE +C----------------------------------------------------------------------- +C ONLY THE MAGNITUDE OF ARG AND PHI ARE NEEDED ALONG WITH THE +C REAL PARTS OF ZETA1, ZETA2 AND ZB. NO ATTEMPT IS MADE TO GET +C THE SIGN OF THE IMAGINARY PART CORRECT. +C----------------------------------------------------------------------- + IF (IFORM.EQ.2) GO TO 20 + INIT = 0 + CALL CUNIK(ZR, GNU, IKFLG, 1, TOL, INIT, PHI, ZETA1, ZETA2, SUM, + * CWRK) + CZ = -ZETA1 + ZETA2 + GO TO 40 + 20 CONTINUE + ZN = -ZR*CMPLX(0.0E0,1.0E0) + IF (YY.GT.0.0E0) GO TO 30 + ZN = CONJG(-ZN) + 30 CONTINUE + CALL CUNHJ(ZN, GNU, 1, TOL, PHI, ARG, ZETA1, ZETA2, ASUM, BSUM) + CZ = -ZETA1 + ZETA2 + AARG = ABS(ARG) + 40 CONTINUE + IF (KODE.EQ.2) CZ = CZ - ZB + IF (IKFLG.EQ.2) CZ = -CZ + APHI = ABS(PHI) + RCZ = REAL(CZ) +C----------------------------------------------------------------------- +C OVERFLOW TEST +C----------------------------------------------------------------------- + IF (RCZ.GT.ELIM) GO TO 170 + IF (RCZ.LT.ALIM) GO TO 50 + RCZ = RCZ + ALOG(APHI) + IF (IFORM.EQ.2) RCZ = RCZ - 0.25E0*ALOG(AARG) - AIC + IF (RCZ.GT.ELIM) GO TO 170 + GO TO 100 + 50 CONTINUE +C----------------------------------------------------------------------- +C UNDERFLOW TEST +C----------------------------------------------------------------------- + IF (RCZ.LT.(-ELIM)) GO TO 60 + IF (RCZ.GT.(-ALIM)) GO TO 100 + RCZ = RCZ + ALOG(APHI) + IF (IFORM.EQ.2) RCZ = RCZ - 0.25E0*ALOG(AARG) - AIC + IF (RCZ.GT.(-ELIM)) GO TO 80 + 60 CONTINUE + DO 70 I=1,NN + Y(I) = CZERO + 70 CONTINUE + NUF = NN + RETURN + 80 CONTINUE + ASCLE = 1.0E+3*R1MACH(1)/TOL + CZ = CZ + CLOG(PHI) + IF (IFORM.EQ.1) GO TO 90 + CZ = CZ - CMPLX(0.25E0,0.0E0)*CLOG(ARG) - CMPLX(AIC,0.0E0) + 90 CONTINUE + AX = EXP(RCZ)/TOL + AY = AIMAG(CZ) + CZ = CMPLX(AX,0.0E0)*CMPLX(COS(AY),SIN(AY)) + CALL CUCHK(CZ, NW, ASCLE, TOL) + IF (NW.EQ.1) GO TO 60 + 100 CONTINUE + IF (IKFLG.EQ.2) RETURN + IF (N.EQ.1) RETURN +C----------------------------------------------------------------------- +C SET UNDERFLOWS ON I SEQUENCE +C----------------------------------------------------------------------- + 110 CONTINUE + GNU = FNU + (NN-1) + IF (IFORM.EQ.2) GO TO 120 + INIT = 0 + CALL CUNIK(ZR, GNU, IKFLG, 1, TOL, INIT, PHI, ZETA1, ZETA2, SUM, + * CWRK) + CZ = -ZETA1 + ZETA2 + GO TO 130 + 120 CONTINUE + CALL CUNHJ(ZN, GNU, 1, TOL, PHI, ARG, ZETA1, ZETA2, ASUM, BSUM) + CZ = -ZETA1 + ZETA2 + AARG = ABS(ARG) + 130 CONTINUE + IF (KODE.EQ.2) CZ = CZ - ZB + APHI = ABS(PHI) + RCZ = REAL(CZ) + IF (RCZ.LT.(-ELIM)) GO TO 140 + IF (RCZ.GT.(-ALIM)) RETURN + RCZ = RCZ + ALOG(APHI) + IF (IFORM.EQ.2) RCZ = RCZ - 0.25E0*ALOG(AARG) - AIC + IF (RCZ.GT.(-ELIM)) GO TO 150 + 140 CONTINUE + Y(NN) = CZERO + NN = NN - 1 + NUF = NUF + 1 + IF (NN.EQ.0) RETURN + GO TO 110 + 150 CONTINUE + ASCLE = 1.0E+3*R1MACH(1)/TOL + CZ = CZ + CLOG(PHI) + IF (IFORM.EQ.1) GO TO 160 + CZ = CZ - CMPLX(0.25E0,0.0E0)*CLOG(ARG) - CMPLX(AIC,0.0E0) + 160 CONTINUE + AX = EXP(RCZ)/TOL + AY = AIMAG(CZ) + CZ = CMPLX(AX,0.0E0)*CMPLX(COS(AY),SIN(AY)) + CALL CUCHK(CZ, NW, ASCLE, TOL) + IF (NW.EQ.1) GO TO 140 + RETURN + 170 CONTINUE + NUF = -1 + RETURN + END diff --git a/schainf/Ffiles/cwrsk.f b/schainf/Ffiles/cwrsk.f new file mode 100644 index 0000000..887de94 --- /dev/null +++ b/schainf/Ffiles/cwrsk.f @@ -0,0 +1,86 @@ +*DECK CWRSK + SUBROUTINE CWRSK (ZR, FNU, KODE, N, Y, NZ, CW, TOL, ELIM, ALIM) +C***BEGIN PROLOGUE CWRSK +C***SUBSIDIARY +C***PURPOSE Subsidiary to CBESI and CBESK +C***LIBRARY SLATEC +C***TYPE ALL (CWRSK-A, ZWRSK-A) +C***AUTHOR Amos, D. E., (SNL) +C***DESCRIPTION +C +C CWRSK COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY +C NORMALIZING THE I FUNCTION RATIOS FROM CRATI BY THE WRONSKIAN +C +C***SEE ALSO CBESI, CBESK +C***ROUTINES CALLED CBKNU, CRATI, R1MACH +C***REVISION HISTORY (YYMMDD) +C 830501 DATE WRITTEN +C 910415 Prologue converted to Version 4.0 format. (BAB) +C***END PROLOGUE CWRSK + COMPLEX CINU, CSCL, CT, CW, C1, C2, RCT, ST, Y, ZR + REAL ACT, ACW, ALIM, ASCLE, ELIM, FNU, S1, S2, TOL, YY, R1MACH + INTEGER I, KODE, N, NW, NZ + DIMENSION Y(N), CW(2) +C***FIRST EXECUTABLE STATEMENT CWRSK +C----------------------------------------------------------------------- +C I(FNU+I-1,Z) BY BACKWARD RECURRENCE FOR RATIOS +C Y(I)=I(FNU+I,Z)/I(FNU+I-1,Z) FROM CRATI NORMALIZED BY THE +C WRONSKIAN WITH K(FNU,Z) AND K(FNU+1,Z) FROM CBKNU. +C----------------------------------------------------------------------- + NZ = 0 + CALL CBKNU(ZR, FNU, KODE, 2, CW, NW, TOL, ELIM, ALIM) + IF (NW.NE.0) GO TO 50 + CALL CRATI(ZR, FNU, N, Y, TOL) +C----------------------------------------------------------------------- +C RECUR FORWARD ON I(FNU+1,Z) = R(FNU,Z)*I(FNU,Z), +C R(FNU+J-1,Z)=Y(J), J=1,...,N +C----------------------------------------------------------------------- + CINU = CMPLX(1.0E0,0.0E0) + IF (KODE.EQ.1) GO TO 10 + YY = AIMAG(ZR) + S1 = COS(YY) + S2 = SIN(YY) + CINU = CMPLX(S1,S2) + 10 CONTINUE +C----------------------------------------------------------------------- +C ON LOW EXPONENT MACHINES THE K FUNCTIONS CAN BE CLOSE TO BOTH +C THE UNDER AND OVERFLOW LIMITS AND THE NORMALIZATION MUST BE +C SCALED TO PREVENT OVER OR UNDERFLOW. CUOIK HAS DETERMINED THAT +C THE RESULT IS ON SCALE. +C----------------------------------------------------------------------- + ACW = ABS(CW(2)) + ASCLE = 1.0E+3*R1MACH(1)/TOL + CSCL = CMPLX(1.0E0,0.0E0) + IF (ACW.GT.ASCLE) GO TO 20 + CSCL = CMPLX(1.0E0/TOL,0.0E0) + GO TO 30 + 20 CONTINUE + ASCLE = 1.0E0/ASCLE + IF (ACW.LT.ASCLE) GO TO 30 + CSCL = CMPLX(TOL,0.0E0) + 30 CONTINUE + C1 = CW(1)*CSCL + C2 = CW(2)*CSCL + ST = Y(1) +C----------------------------------------------------------------------- +C CINU=CINU*(CONJG(CT)/ABS(CT))*(1.0E0/ABS(CT) PREVENTS +C UNDER- OR OVERFLOW PREMATURELY BY SQUARING ABS(CT) +C----------------------------------------------------------------------- + CT = ZR*(C2+ST*C1) + ACT = ABS(CT) + RCT = CMPLX(1.0E0/ACT,0.0E0) + CT = CONJG(CT)*RCT + CINU = CINU*RCT*CT + Y(1) = CINU*CSCL + IF (N.EQ.1) RETURN + DO 40 I=2,N + CINU = ST*CINU + ST = Y(I) + Y(I) = CINU*CSCL + 40 CONTINUE + RETURN + 50 CONTINUE + NZ = -1 + IF(NW.EQ.(-2)) NZ=-2 + RETURN + END diff --git a/schainf/Ffiles/fitacf.f b/schainf/Ffiles/fitacf.f new file mode 100644 index 0000000..3b7c35d --- /dev/null +++ b/schainf/Ffiles/fitacf.f @@ -0,0 +1,621 @@ + subroutine guess(acf,tau,npts,zero,amin,te,tr) +c +c find zero crossing (zero), depth of minimum (amin), height of maximum +c + real acf(npts),tau(npts) + + zero=0.0 + amin=1.0 + tmin=0.0 + jmin=0 + + do i=npts,2,-1 + if(acf(i)*acf(i-1).lt.0.0) then + zero=(tau(i-1)*acf(i)-tau(i)*acf(i-1))/(acf(i)-acf(i-1)) + end if + if(acf(i).lt.amin) then + amin=acf(i) + jmin=i + end if + end do + + if(jmin.gt.0) then + call parab1(tau(jmin-1),acf(jmin-1),a,b,c) + tmin=-b/(2.0*a) + amin=c+tmin*(b+tmin*a) + end if + + tr=cdtr1(-amin) + te=czte1(zero*1000.0,tr) + return + end + + subroutine parab1(x,y,a,b,c) +C----- + dimension x(3),y(3) + delta=x(1)-x(2) + a=(y(1)-2.*y(2)+y(3))/(2.*delta*delta) + b=(y(1)-y(2))/delta - a*(x(1)+x(2)) + c=y(1)-a*x(1)*x(1)-b*x(1) + return + end + + real function cdtr1(depth) +C-----convert depth to te/ti ratio + dimension tr(4) +C according to the curve published in farley et al 1967 +c modified for 2004 conditions on axis +c data tr/7.31081,3.53286,5.92271,.174/ + data tr/9.5,4.0,8.5,.3/ + data nt/4/ + cdtr1=tr(1) + do i=2,nt + cdtr1=cdtr1*depth + tr(i) + end do + return + end + + real function czte1(zlag,tr) +C-----convert zero crossing point to te +C according to the curve published in farley et al 1967 +c modified for 2004 conditions on axis + dimension dt(4) +c data dt/0.00945025,-0.0774338,.203626,.812397/,nd/4/ + data dt/0.00945025,-0.0774338,.2,0.9/,nd/4/ + data t0/1000./ + tr1=min(abs(tr),5.) + if(zlag .eq. 0)then + czte1=1000000. + else + dt0=dt(1) + do i=2,nd + dt0=dt0*tr1 + dt(i) + end do + czte1=t0*(dt0/zlag)**2 + end if + return + end + + subroutine fit(wl,taup,rhop,covar,cinv,sigma2p,paramp,ebp, + & bfldp,alphap,densp,alt,time,nl,ifitp,ist) +c +c subroutine to fit measured ACF +c wavelength wl (m),lags taup (s), normalized acf rhop, +c experimental variances sigma2p, covariances covar, +c fit parameters params, error bars ebp, magnetic field bfldp (gauss), +c alphap B-field angle (radians), density densp (gcs), +c altitude alt (km), time (LT hours), nl lags +c ifitp determines which parameters are fit (see below) +c + real tol,pi,wl + parameter(nlmax=100,npmax=10,lwa=2000,tol=1.0e-5) + external fcn + + real covar(nl,nl),cinv(nl,nl) + real ev(nlmax*nlmax),ap(nlmax*(nlmax+1)/2) + real fv1(nlmax),fv2(nlmax),det(2),w(nlmax) + + real taup(nl),rhop(nl),sigma2p(nl),paramp(npmax) + real p2(npmax),ebp(npmax),alphap,bfldp,densp + real tau(nlmax),rho(nlmax),sigma2(nlmax),params(npmax) + real fvec(nlmax),wa(lwa),wa2(lwa),eb(npmax) + + integer iwa(npmax),ifitp(npmax),ifit(npmax) + + include 'fitter.h' + common /mode/imode + + common/fitter/tau,rho,sigma2,params,ifit + common/trans/ev +C----- + +c set ifit(1-5) to unity to fit: +c 1 normalization +c 2 Te +c 3 Ti +c 4 H+ +c 5 He+ + + imode=2 +c + pi=4.0*atan(1.0) + ak=2.0*pi/wl + + wi(1)=16 + wi(2)=1 + wi(3)=4 + nion=3 + +c +c invert covariances and find eigenvalues and eigenvectors +c + l = 0 + do 20 j = 1, nl + do 10 i = 1, j + l = l + 1 + ap(l) = covar(i,j) + 10 continue + 20 continue + + call sppfa(ap,nl,info) + call sppdi(ap,nl,det,01) + + l = 0 + do 40 j = 1, nl + do 30 i = 1, j + l = l + 1 + cinv(i,j)=ap(l) + cinv(j,i)=ap(l) + 30 continue + 40 continue + +c +c transformation matrix is inverse (transpose) of eigenvectors +c + + matz=1 + call rs(nl,nl,cinv,w,matz,ev,fv1,fv2,ierr) + + do i=1,nl + sigma2(i)=1.0/w(i) + end do + +c +c extract desired parameters +c + iparm=0 + do i=1,5 + eb(i)=0.0 + if(ifitp(i).eq.1) then + iparm=iparm+1 + p2(iparm)=paramp(i) + end if + ifit(i)=ifitp(i) + params(i)=paramp(i) + end do + np=iparm + + alpha=alphap + dens=densp + do i=1,nl + tau(i)=taup(i) + rho(i)=rhop(i) + sigma2p(i)=sigma2(i) + end do + + bfld=bfldp + +c +c no. equations is no. lags - do nlls fit +c + + call lmdif1(fcn,nl,np,p2,fvec,tol,info,iwa,wa,lwa) + ist=info + +c +c generate error bars here +c + call fdjac2(fcn,nl,np,p2,fvec,wa,nl,iflag,0.0e0,wa2) + + do i=1,np + err=0.0 + do j=1,nl + err=err+(wa(j+(i-1)*nl))**2 + end do + if(err.gt.0.0) eb(i)=sqrt(err**-1) + end do + +c reorder results + iparm=0 + do i=1,5 + if(ifit(i).eq.1) then + iparm=iparm+1 + paramp(i)=p2(iparm) + ebp(i)=eb(iparm) + else + ebp(i)=0.0 + paramp(i)=params(i) + end if + end do + + 9 continue +c write(*,*) dens +c write(*,*) te + + return + end + + + subroutine fcn(m,n,x,fvec,iflag) +c +c provides m functions (fvec) in n variables (x) to minimize +c in least-squares sense +c + + parameter(nlmax=100,npmax=10) + integer m,n,iflag + real fvec(m) + + integer ifit(npmax) + real x(n),fv(nlmax),anorm,params(npmax),ev(nlmax*nlmax) + real tau(nlmax),rho(nlmax),sigma2(nlmax) + real chisq,acf + + include 'fitter.h' + + common/fitter/tau,rho,sigma2,params,ifit + common /errs/ chisq + common /trans/ev + +c 1 0 0 0 0 fit zero lag (otherwise set to default) +c 0 1 0 0 0 fit Te (otherwise default) +c 0 0 1 0 0 fit Ti (otherwise set to Te) +c 0 0 0 1 0 fit H+ (otherwize default) +c 0 0 0 0 1 fit He+ (otherwise default) + + 8 continue + +c +c ignore collisions +c +c write(*,*) "starting fcn" + ven=0.0 + do i=1,3 + vin(i)=0.0 + end do + + iparm=0 + +c +c zero lag normalization constant +c + if(ifit(1).eq.1) then + iparm=iparm+1 + c=x(iparm) + else + c=params(1) + end if +c +c Te +c + if(ifit(2).eq.1) then + iparm=iparm+1 + te=x(iparm) + else + te=params(2) + end if +c +c Ti - default is Te rather than initial value +c + if(ifit(3).eq.1) then + iparm=iparm+1 + do i=1,3 + ti(i)=x(iparm) + end do + else + do i=1,3 + ti(i)=te + end do + params(3)=te + end if + +c three-ion plasma + + nion=3 +c +c composition H+ first +c + fi(1)=1.0 + if(ifit(4).eq.1) then + iparm=iparm+1 + fi(2)=(x(iparm)) + fi(1)=fi(1)-(x(iparm)) + else + fi(2)=params(4) + fi(1)=fi(1)-params(4) + end if +c +c He+ +c + if(ifit(5).eq.1) then + iparm=iparm+1 + fi(3)=(x(iparm)) + fi(1)=fi(1)-(x(iparm)) + else + fi(3)=params(5) + fi(1)=fi(1)-params(5) + end if + +c write(*,*) x,bfld,alpha,dens,ak,m + + call gaussq(0.0,anorm) + anorm=anorm/c + + if(anorm.eq.0.0.or.m.eq.0)return + chisq=0.0 + do i=1,m + call gaussq(tau(i),acf) + fv(i)=(acf/anorm-rho(i)) + end do + +c +c transform to space where s2 is diagonal +c (are i and j transposed below?) +c + do i=1,m + fvec(i)=0.0 + do j=1,m + fvec(i)=fvec(i)+fv(j)*ev(j+(i-1)*m)/sqrt(sigma2(i)) + end do + chisq=chisq+fvec(i)**2 + end do + + chisq=chisq/float(m) + +c write(*,*) fvec +c write(*,*) chisq +c stop + + return + end + +c +c not really fond of above code +c + + + complex function cj_ion(theta,psi) +c + real theta,phi,psi,alpha + complex z + complex*16 zz + z=zz(dcmplx(-theta,psi)) + cj_ion=z*cmplx(0.0,-1.0) + return + end + + complex function cj_electron(theta,phi,psi,alpha) +c +c Theta, phi, and psi are the normalized frequency, gyrofrequency, +c and collision frequency. Alpha is angle between wavevector and +c magnetic field in radians. +c + parameter(nterms=10) + real theta,phi,psi,alpha + real arg + complex cj,cy(0:nterms) + complex z + complex*16 zz + integer m,nz,ierr + integer imode + common/mode/imode +c + if(imode.eq.3) then + + arg=0.5*(sin(alpha)/phi)**2 + +c calculate modified Bessel functions using amos library + + call cbesi(cmplx(arg,0.0),0.0,2,nterms+1,cy,nz,ierr) + + cj=cmplx(0.0,0.0) + + do m=-nterms,nterms + z=zz(dcmplx(-(theta-float(m)*phi)/cos(alpha), + & psi/cos(alpha))) + cj=cj+z*cy(iabs(m)) + end do + + cj_electron=cj*cmplx(0.0,-1.0/cos(alpha)) + + else + + z=zz(dcmplx(-theta/cos(alpha),psi/cos(alpha))) + cj_electron=z*cmplx(0.0,-1.0/cos(alpha)) + cj_electron=cj_electron*(1.0-(sin(alpha)/phi)**2/2.0) + + end if + + return + end + + complex function y_ion(theta,psi) +c + real theta,phi,psi,alpha + complex cj, cj_ion + cj=cj_ion(theta,psi) + y_ion=cj*cmplx(theta,-psi)+cmplx(0.0,1.0) + y_ion=y_ion/(1-psi*cj) + return + end + + complex function y_electron(theta,phi,psi,alpha) +c + real theta,phi,psi,alpha + complex cj, cj_electron + cj=cj_electron(theta,phi,psi,alpha) + y_electron=cj*cmplx(theta,-psi)+cmplx(0.0,1.0) + y_electron=y_electron/(1.0-psi*cj) + return + end + + real function spect1(omega) +c +c Function to generate IS ion-line spectrum +c Provisions for nimax ions +c No provisions for drifts +c +c imode=1 Farley B-field treatment for electrons +c 2 use Mike Sulzer's model for ye +c 3 calculate ye using sums of Bessel functions +c + include 'fitter.h' + + real omega,thetae,thetai(nimax),psie,psii(nimax),phi,p + real tr(nimax),vti(nimax),vte,omegae + real bk,em,e,dlf,dl,pi + real alpha2,densmks,freq + complex ye,yed,yet,yi(nimax),sum1,sum2,sumdl + complex y_ion, y_electron, y_esum + integer i,j,k,imode + common/mode/ imode + data bk,em,e,dlf/1.38e-23,9.1e-31,1.6e-19,4772.9/ + +c fi is ion fraction, wi is ion atomic weight +c dens is electron density (cgs), alpha is angle +c between k and the magnetic field (radians) + + pi=4.0*atan(1.0) + + if(omega.eq.0.0) omega=1.0 + + omegae=e*bfld*1.0e-4/em + densmks=dens*1.0e6 + + sum1=0.0 + sum2=0.0 + + do i=1,nion + tr(i)=te/ti(i) + vti(i)=sqrt(bk*ti(i)/(1.67e-27*wi(i))) + thetai(i)=(omega/ak)/(sqrt(2.0)*vti(i)) + psii(i)=(vin(i)/ak)/(sqrt(2.0)*vti(i)) + yi(i)=y_ion(thetai(i),psii(i)) + sum1=sum1+fi(i)*tr(i)*yi(i) + sum2=sum2+fi(i)*yi(i) + end do + dl=ak**2*dlf*te/densmks +c write(*,fmt='("Before YE")') +c write(*,*) imode +c call exit + + if(imode.eq.1.or.imode.eq.3) then + + vte=sqrt(bk*te/em) + thetae=(omega/ak)/(sqrt(2.0)*vte) + phi=(omegae/ak)/(sqrt(2.0)*vte) + psie=(ven/ak)/(sqrt(2.0)*vte) + ye=y_electron(thetae,phi,psie,alpha) + write(*,fmt='("AFTER YE")') +c call exit + + else if(imode.eq.2) then +c +c use Mike Sulzer's library here: alpha2 is angle off perp in degrees +c + + freq=omega/(2.0*pi) + alpha2=abs(pi/2.0-alpha)*180.0/pi +c write(*,*) "ye: ", ye + call collision(densmks, te, freq, alpha2, ye) +c write(*,fmt='("AFTER COLLISION")') +c call exit + ye=ye*omega+cmplx(0.0,1.0) + + end if + yed=ye+cmplx(0.0,dl) + + p=(cabs(ye))**2*real(sum2)+cabs(sum1+cmplx(0.0,dl))**2*real(ye) + p=p/(cabs(yed+sum1))**2 + spect1=p*2.0e0/(omega*pi) + write(*,*) "spect1:",spect1 + return + end + + subroutine acf2(wl, tau, te1, ti1, fi1, ven1, vin1, wi1, + & alpha1, dens1, bfld1, acf, nion1) +c +c computes autocorrelation function for given plasma parameters +c by integrating real spectrum +c tau in sec., alpha in radians, density in cgs, bfield in cgs +c scattering wavelength (wl) in meters +c + include 'fitter.h' + + real wl,tau,te1,ti1(nion1),fi1(nion1),ven1,vin1(nion1),alpha1, + & dens1,bfld1,acf + real pi + integer nion1 + integer wi1(nion1) + integer i,j,k,imode + common /mode/imode +c + write(*,*) "INITIAL acf:",wl,tau,te1,ti1,fi1,ven1,vin1,wi1,alpha1 + write(*,*) "INITIAL acf:",dens1, bfld1, acf, nion1 +c write(*,fmt='("INIT")') + pi=4.0*atan(1.0) +c +c copy arguments to common block +c + ak=2.0*pi/wl + imode=2 + write(*,*) "imode:",imode + + nion=nion1 + alpha=alpha1 + te=te1 + ven=ven1 +c write(*,fmt='("INIT2")') + do i=1,nion +c write(*,fmt='("INIT2.5")') + ti(i)=ti1(i) + fi(i)=fi1(i) + vin(i)=vin1(i) + wi(i)=wi1(i) + end do +c write(*,fmt='("INIT3")') + dens=dens1 + bfld=bfld1 + +c write(*,*) wl,alpha1,bfld1,dens +c call exit +c write(*,fmt='("Before Gauss")') + call gaussq(tau,acf) + + write(*,*) "FINAL acf:",acf + +c write(*,fmt='("After Gauss")') + return + end + + subroutine gaussq(tau,acf) +c +c Computes cosine or sine transform of given real function +c Uses quadpack, tau in sec. +c + real a,abserr,epsabs,acf,tau,work,chebmo + integer ier,integr,iwork,last,leniw,lenw,limit,limlst, + * lst,maxp1,neval + integer knorm,ksave,momcom,nrmom + dimension iwork(300),work(1625),chebmo(61,25) + external spect1 + include 'fitter.h' +c +c write(*,*) "inside gaussq" + a = 0.0 + b = 2.5e4*ak ! upper integration limit open to debate (was 1.5, now 2.5) + integr = 1 + epsabs = 1.0e-4 + limlst = 50 + limit = 100 + leniw = limit*2+limlst + maxp1 = 61 + lenw = leniw*2+maxp1*25 + +c write(*,*) leniw,lenw + + nrmom=0 + ksave=0 + momcom=0 + write(*,*) "Before qc25f:",acf,imode +c much faster, more robust +c write(*,*) "acf_in: ",acf + call qc25f(spect1,a,b,tau,integr,nrmom,maxp1,ksave,acf, + & abserr,neval,resabs,resasc,momcom,chebmo) +c write(*,*) "acf_out: ",acf +c call qawf(spect1,a,tau,integr,epsabs,acf,abserr,neval, +c & ier,limlst,lst,leniw,maxp1,lenw,iwork,work) + write(*,*) "After qc25f:",acf +c call exit + return + end diff --git a/schainf/Ffiles/fitacf.o b/schainf/Ffiles/fitacf.o new file mode 100644 index 0000000000000000000000000000000000000000..f0fefbe3215131b462c434c3ba09c45ba48ada4d GIT binary patch literal 14336 zc%0>04RBo5b$+}0v9M*{t`SBULo~s_#sx+G!Io2pXtAGpVzgkuvL#oxEK94}!IF)% zYQTw&7->7+kvCC?xR^jwwbM2*!Nk+pR4sP1@(+?hY1WOQ1}h*^L#45X2wOu%qgXxX z-gDo(@9I57nog%Pc{8hf?|08V=iGD7J@?0c(kNTw_xUvO`Lug9yJdf=rFOl9{?68N zwQ@7@f%()(QNE^`iR0)0V{+0=98E(}um37_MGqQ7SMq{6Tz40OFLZCN3Zq-JqR+ePlX7V`dV0I*#=E?FwGieN&Z6i5m@~Ad6Ik_H69E0T` zl^3ZT;bqIk^^J=%^k7%F0bJxH19_a75KPJ@on&z2YP|>|ddTdfjw4Eh~0W$FZ@7%Ce@ybeVNT*^ZURPs4HOH8&K`%3Rj*3Za;@^&}eg751qJl zmmUJr&4WbK!{*4UIBY;6cT5v&0jvch-H08733r3(4`0#u8iy^{l~}IpC?{9F_1k(Y z{eR-E^zVtc`Vi~K@C4JR&|4|;)>9*x(;z<;PqO?}#EJtURwN6c=wL2r8_&?=@A`qX zBhFAQ5f4BKB3Q|s3pRl6A`WY)7xPSI%1(4V!77moY2>J#X zy>axi9z04MLVRQqFg=>6LPHJWqb=WV!VR+QCfQS zpu5Rk2g8!Q-1sR--ZKFeT#oqU3U1bX9LqN=WWv0)p`vl*2Rqvh#}pKmIv9e4IQC z^X_$ecnJJ($m!t_Fg^4+JbWlu4jbm-L*(H@CV6-*_ptf-Jp3_8Zux8v|IZCSp%{K# z!~`0Cd^*Gbjv2+)#>&Kl$b*XrBvFJOg2Y;x22CzNiSgM_x&0K+pcS~F56D{KP+~#t zU^1Wj=X0&|ndwRCy{vQ`Um)4Gr07hLWA9}c8!#)(!#E}MZZLBGGUh8dVx4z!rg0cN z8G%0=he3P;x^Wc!skm`eY^RY4vN`k4xaF9^bb6MKf_6YF>fOVPc?1gtG>1tbYdwJl$T(L-bxoI+(!hcRIuG~0%JW->R<6Fcz< zEoXZKB1X_+IFjSjb~Cvq{raX!CsYkteJ5)f)|-ufq|Q9Nbp z=84k8$?!4OhKyy?;TbONr0WT@Hf^I>+z3N>VQJellwn!n4`4Pl_qNnrldd5&e;SKT_MP4|eJ4Ppe$*)OZ+ng-x(MUIa>Dd<=hclAoZMRso?^`H&sN^L%JuJ9aTUh?TfcjLhjZ2HD8Spgr^XK?4dKZ zi9iINCoENhnTOjz%)gSqJI$v~VZ!~R zaFv{c(>w=PaA8(r8Uj{?S^LX;vAcfaScy?(+!g+ zCKE4Eh&wWYbRn*0y7*VV&ZEVW`cR5VP4m4_xJ9-o99<=Pi08D!J(V&yap!JlCsbK8 zb+5zd^Z)K*wpd~?IVSlnujiM3NGSxH2(wFk&-(!PbwozY+B0Uda&qb;OnfbunWQql zjxVGAzu3hq?Z1d!b_5#p2EKb5Ir3}5+jIo~B^}M_z*;rHo<#7T zP!TzX7shVunuxbX#2_4}(JIfWm5{%mC)@U4L*7Ma$Ea2oJBCc<#7HLt`9F@3;#r3!VoaLOjEW<1Whva=TS-cg*ID2Kd==z&<6M#a?4TT%88QA=2oid(#@%JCEy- zePYPewC^<}Acjocm%WDMcjV!K1D^BcZ}AGD1k#U91Zc6kY4UDDRuX||o( z6|M?z3U3ZqZ#t?Ojw{ShVy@ z93^IXRQh&5toa@f_-@Lbk<$s0GhgFB{FY-Rg|7|#seje%?2N@eAYpwgssB|+|0`C1 z74^UD=zr1b{}%PH&yxEe$`bw0Q~#%$)bAg|Zq|Q{`eTm%omT&Vu%V;>zgT|(Koiv8 zF3Z1ve@0toMhhx|GzIjJ&F{>ZLi5H9pjiO$YNDz0OEhKQ$@q3=GHZW!#v^_v(fz}r zncBybZhaZ9|I&?kh6k=jtH86SU^AI)n@@nsIfRS0;5d))0)_sIgcm9F3khGU;EM?_ zR`3;suT=0b;Ux-QO89C8=kuL0WxgDDcSDAjJq3GMLtEJPUryDH@C#~}CkqG{F}Q{3 zKMeBrJEX!k&9;^N?e)Op#7D?`mC8ROyo)Bfo?QBU!Y@;jd70?{mhexm;q6a}{~^*} z_3w{8^y&7%f8v3k^1%B@pI^=7?HJ)dBfNGNZ;OTS7U5fSdAptFdqH#BUxfC*d(3NC zp)aANGU}n{uRU=5FDR%_>PFtK6G^>(d#t9mzOY`4H5D#dwrH`|7{jtitHW~f60NZg z%Vk=u2+QSKv~bDt;$>R20n6pu)<>~itkvzP$I9K>AJ?=rH$PUbHSdbn^1rb~)mrs^ zWe?sPE~|cU&6-Dyb=B*__m&ye+GDkg@2;=bo~VxQ0J5f?jn!K1*QLf2)!PYUWy8+8 zD6rh#Sg+M?jW%zGo}JD0+V0&@sf#s%nA+X3C=~UzKn*jCMVqR%Xj4;jHB7Iju^9*K z*s;BtbFJA5gJJTEt2OO*G6$OFI`|!-cA@5YqlkmIz?)d!*F7i`_2Oi9@@p+OyYciblLZ5a87jiFn;NuD| zW}`IHf#Dh0Rfui)bQx`K=K*py|0O1P|Np9lTVbKLcOPr-%U zl51=}vVUu?ani3P`UV9T{O8Pc=l_Q@-Stm;(06&@zn1U}iBI+{Cob~Cs#)&z-;{7U z{^JV1j_|+sz|San1>qMIxkCRB61*A-Rt# z^zCHNZ%DWt=T9p1A;RMd|3TvaLxo=O`LPF|a~}A+3jc26|Dgx}k39H%;=#wSyVK|B zPWp>PU#QTF_*~|}XM+b`qwqgQ{I`4Xf6Rl=6CQlx9`sL3xV-NilyJP`i1>L=!WT$* zUcf0=;I{|d`K< z$9yI3bE_p>USDe!J|b^dDSX8JuR-C{N_dOHN95rb75aUIf281IzB8|L$HN}@0}_sU zihZQfgMN>Mqn=xc{$+(;oQHp=(AN>3ljqL=`aE|&%ktd${JDhRDDfHe;QuGryW=AY zF653&INGO#@XWdHeCA8IeEz({123NIquKSJ$|K}8XVduY7@NI;jRrm!e8EfL@ zHc@Me?x-n@MIVo8g>^Nt8m(|^b2Fejd82k`LqoI?`Wkn}qJ{T8P<~f)tfux+8W!DF zUEfsG5Y_&dz5<%E`a)Sk<%0Q6TzxUdFvyhX#rMLkyiC#gXC{pm?=!Sa*_uXNeR1AJ za!mzS-_GtNp6d8+MQ`z``Y$5Puiz;fziS%#D`=nion1),depend(ti1) :: nion1=len(ti1) + real intent(in):: alpha1 + real intent(in):: dens1 + real intent(in):: bfld1 + real intent(in,out):: acf + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + end subroutine acf2 + function spect1(omega) ! in :fitacf_fit_short:fitacf.f + real :: omega + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + integer :: imode + real :: spect1 + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /mode/ imode + end function spect1 + subroutine gaussq(tau,acf) ! in :fitacf_fit_short:fitacf.f + real :: tau + real :: acf + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + end interface +end python module fitacf_acf2 + +! This file was auto-generated with f2py (version:2). +! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/schainf/Ffiles/fitacf_fit_short.f b/schainf/Ffiles/fitacf_fit_short.f new file mode 100644 index 0000000..f62e145 --- /dev/null +++ b/schainf/Ffiles/fitacf_fit_short.f @@ -0,0 +1,544 @@ + + subroutine fit(wl,taup,rhop,covar,cinv,sigma2p,paramp,ebp, + & bfldp,alphap,densp,alt,time,ifitp,ist,nl) +c +c subroutine to fit measured ACF +c wavelength wl (m),lags taup (s), normalized acf rhop, +c experimental variances sigma2p, covariances covar, +c fit parameters params, error bars ebp, magnetic field bfldp (gauss), +c alphap B-field angle (radians), density densp (gcs), +c altitude alt (km), time (LT hours), nl lags +c ifitp determines which parameters are fit (see below) +c + real tol,pi,wl + parameter(nlmax=100,npmax=10,lwa=2000,tol=1.0e-5) + external fcn + + real covar(nl,nl),cinv(nl,nl) + real ev(nlmax*nlmax),ap(nlmax*(nlmax+1)/2) + real fv1(nlmax),fv2(nlmax),det(2),w(nlmax) + + real taup(nl),rhop(nl),sigma2p(nl),paramp(npmax) + real p2(npmax),ebp(npmax),alphap,bfldp,densp + real tau(nlmax),rho(nlmax),sigma2(nlmax),params(npmax) + real fvec(nlmax),wa(lwa),wa2(lwa),eb(npmax) + + integer iwa(npmax),ifitp(npmax),ifit(npmax) + + include 'fitter.h' + common /mode/imode + + common/fitter/tau,rho,sigma2,params,ifit + common/trans/ev +C----- + +c set ifit(1-5) to unity to fit: +c 1 normalization +c 2 Te +c 3 Ti +c 4 H+ +c 5 He+ + + imode=2 +c + pi=4.0*atan(1.0) + ak=2.0*pi/wl + + wi(1)=16 + wi(2)=1 + wi(3)=4 + nion=3 + +c +c invert covariances and find eigenvalues and eigenvectors +c + l = 0 + do 20 j = 1, nl + do 10 i = 1, j + l = l + 1 + ap(l) = covar(i,j) + 10 continue + 20 continue + + call sppfa(ap,nl,info) + call sppdi(ap,nl,det,01) + + l = 0 + do 40 j = 1, nl + do 30 i = 1, j + l = l + 1 + cinv(i,j)=ap(l) + cinv(j,i)=ap(l) + 30 continue + 40 continue + +c +c transformation matrix is inverse (transpose) of eigenvectors +c + + matz=1 + call rs(nl,nl,cinv,w,matz,ev,fv1,fv2,ierr) + + do i=1,nl + sigma2(i)=1.0/w(i) + end do + +c +c extract desired parameters +c + iparm=0 + do i=1,5 + eb(i)=0.0 + if(ifitp(i).eq.1) then + iparm=iparm+1 + p2(iparm)=paramp(i) + end if + ifit(i)=ifitp(i) + params(i)=paramp(i) + end do + np=iparm + + alpha=alphap + dens=densp + do i=1,nl + tau(i)=taup(i) + rho(i)=rhop(i) + sigma2p(i)=sigma2(i) + end do + + bfld=bfldp + +c +c no. equations is no. lags - do nlls fit +c + + call lmdif1(fcn,nl,np,p2,fvec,tol,info,iwa,wa,lwa) + ist=info + +c +c generate error bars here +c + call fdjac2(fcn,nl,np,p2,fvec,wa,nl,iflag,0.0e0,wa2) + + do i=1,np + err=0.0 + do j=1,nl + err=err+(wa(j+(i-1)*nl))**2 + end do + if(err.gt.0.0) eb(i)=sqrt(err**-1) + end do + +c reorder results + iparm=0 + do i=1,5 + if(ifit(i).eq.1) then + iparm=iparm+1 + paramp(i)=p2(iparm) + ebp(i)=eb(iparm) + else + ebp(i)=0.0 + paramp(i)=params(i) + end if + end do + + 9 continue +c write(*,*) dens +c write(*,*) te + + return + end + + + subroutine fcn(m,n,x,fvec,iflag) +c +c provides m functions (fvec) in n variables (x) to minimize +c in least-squares sense +c + + parameter(nlmax=100,npmax=10) + integer m,n,iflag + real fvec(m) + + integer ifit(npmax) + real x(n),fv(nlmax),anorm,params(npmax),ev(nlmax*nlmax) + real tau(nlmax),rho(nlmax),sigma2(nlmax) + real chisq,acf + + include 'fitter.h' + + common/fitter/tau,rho,sigma2,params,ifit + common /errs/ chisq + common /trans/ev + +c 1 0 0 0 0 fit zero lag (otherwise set to default) +c 0 1 0 0 0 fit Te (otherwise default) +c 0 0 1 0 0 fit Ti (otherwise set to Te) +c 0 0 0 1 0 fit H+ (otherwize default) +c 0 0 0 0 1 fit He+ (otherwise default) + + 8 continue + +c +c ignore collisions +c +c write(*,*) "starting fcn" + ven=0.0 + do i=1,3 + vin(i)=0.0 + end do + + iparm=0 + +c +c zero lag normalization constant +c + if(ifit(1).eq.1) then + iparm=iparm+1 + c=x(iparm) + else + c=params(1) + end if +c +c Te +c + if(ifit(2).eq.1) then + iparm=iparm+1 + te=x(iparm) + else + te=params(2) + end if +c +c Ti - default is Te rather than initial value +c + if(ifit(3).eq.1) then + iparm=iparm+1 + do i=1,3 + ti(i)=x(iparm) + end do + else + do i=1,3 + ti(i)=te + end do + params(3)=te + end if + +c three-ion plasma + + nion=3 +c +c composition H+ first +c + fi(1)=1.0 + if(ifit(4).eq.1) then + iparm=iparm+1 + fi(2)=(x(iparm)) + fi(1)=fi(1)-(x(iparm)) + else + fi(2)=params(4) + fi(1)=fi(1)-params(4) + end if +c +c He+ +c + if(ifit(5).eq.1) then + iparm=iparm+1 + fi(3)=(x(iparm)) + fi(1)=fi(1)-(x(iparm)) + else + fi(3)=params(5) + fi(1)=fi(1)-params(5) + end if + +c write(*,*) x,bfld,alpha,dens,ak,m + + call gaussq(0.0,anorm) + anorm=anorm/c + + if(anorm.eq.0.0.or.m.eq.0)return + chisq=0.0 + do i=1,m + call gaussq(tau(i),acf) + fv(i)=(acf/anorm-rho(i)) + end do + +c +c transform to space where s2 is diagonal +c (are i and j transposed below?) +c + do i=1,m + fvec(i)=0.0 + do j=1,m + fvec(i)=fvec(i)+fv(j)*ev(j+(i-1)*m)/sqrt(sigma2(i)) + end do + chisq=chisq+fvec(i)**2 + end do + + chisq=chisq/float(m) + +c write(*,*) fvec +c write(*,*) chisq +c stop + + return + end + +c +c not really fond of above code +c + + + complex function cj_ion(theta,psi) +c + real theta,phi,psi,alpha + complex z + complex*16 zz + z=zz(dcmplx(-theta,psi)) + cj_ion=z*cmplx(0.0,-1.0) + return + end + + complex function cj_electron(theta,phi,psi,alpha) +c +c Theta, phi, and psi are the normalized frequency, gyrofrequency, +c and collision frequency. Alpha is angle between wavevector and +c magnetic field in radians. +c + parameter(nterms=10) + real theta,phi,psi,alpha + real arg + complex cj,cy(0:nterms) + complex z + complex*16 zz + integer m,nz,ierr + integer imode + common/mode/imode +c + if(imode.eq.3) then + + arg=0.5*(sin(alpha)/phi)**2 + +c calculate modified Bessel functions using amos library + + call cbesi(cmplx(arg,0.0),0.0,2,nterms+1,cy,nz,ierr) + + cj=cmplx(0.0,0.0) + + do m=-nterms,nterms + z=zz(dcmplx(-(theta-float(m)*phi)/cos(alpha), + & psi/cos(alpha))) + cj=cj+z*cy(iabs(m)) + end do + + cj_electron=cj*cmplx(0.0,-1.0/cos(alpha)) + + else + + z=zz(dcmplx(-theta/cos(alpha),psi/cos(alpha))) + cj_electron=z*cmplx(0.0,-1.0/cos(alpha)) + cj_electron=cj_electron*(1.0-(sin(alpha)/phi)**2/2.0) + + end if + + return + end + + complex function y_ion(theta,psi) +c + real theta,phi,psi,alpha + complex cj, cj_ion + cj=cj_ion(theta,psi) + y_ion=cj*cmplx(theta,-psi)+cmplx(0.0,1.0) + y_ion=y_ion/(1-psi*cj) + return + end + + complex function y_electron(theta,phi,psi,alpha) +c + real theta,phi,psi,alpha + complex cj, cj_electron + cj=cj_electron(theta,phi,psi,alpha) + y_electron=cj*cmplx(theta,-psi)+cmplx(0.0,1.0) + y_electron=y_electron/(1.0-psi*cj) + return + end + + real function spect1(omega) +c +c Function to generate IS ion-line spectrum +c Provisions for nimax ions +c No provisions for drifts +c +c imode=1 Farley B-field treatment for electrons +c 2 use Mike Sulzer's model for ye +c 3 calculate ye using sums of Bessel functions +c + include 'fitter.h' + + real omega,thetae,thetai(nimax),psie,psii(nimax),phi,p + real tr(nimax),vti(nimax),vte,omegae + real bk,em,e,dlf,dl,pi + real alpha2,densmks,freq + complex ye,yed,yet,yi(nimax),sum1,sum2,sumdl + complex y_ion, y_electron, y_esum + integer i,j,k,imode + common/mode/ imode + data bk,em,e,dlf/1.38e-23,9.1e-31,1.6e-19,4772.9/ + +c fi is ion fraction, wi is ion atomic weight +c dens is electron density (cgs), alpha is angle +c between k and the magnetic field (radians) + + pi=4.0*atan(1.0) + + if(omega.eq.0.0) omega=1.0 + + omegae=e*bfld*1.0e-4/em + densmks=dens*1.0e6 + + sum1=0.0 + sum2=0.0 + + do i=1,nion + tr(i)=te/ti(i) + vti(i)=sqrt(bk*ti(i)/(1.67e-27*wi(i))) + thetai(i)=(omega/ak)/(sqrt(2.0)*vti(i)) + psii(i)=(vin(i)/ak)/(sqrt(2.0)*vti(i)) + yi(i)=y_ion(thetai(i),psii(i)) + sum1=sum1+fi(i)*tr(i)*yi(i) + sum2=sum2+fi(i)*yi(i) + end do + dl=ak**2*dlf*te/densmks +c write(*,fmt='("Before YE")') +c write(*,*) imode +c call exit + + if(imode.eq.1.or.imode.eq.3) then + + vte=sqrt(bk*te/em) + thetae=(omega/ak)/(sqrt(2.0)*vte) + phi=(omegae/ak)/(sqrt(2.0)*vte) + psie=(ven/ak)/(sqrt(2.0)*vte) + ye=y_electron(thetae,phi,psie,alpha) + write(*,fmt='("AFTER YE")') +c call exit + + else if(imode.eq.2) then +c +c use Mike Sulzer's library here: alpha2 is angle off perp in degrees +c + + freq=omega/(2.0*pi) + alpha2=abs(pi/2.0-alpha)*180.0/pi +c write(*,*) "ye: ", ye + call collision(densmks, te, freq, alpha2, ye) +c write(*,fmt='("AFTER COLLISION")') +c call exit + ye=ye*omega+cmplx(0.0,1.0) + + end if + yed=ye+cmplx(0.0,dl) + + p=(cabs(ye))**2*real(sum2)+cabs(sum1+cmplx(0.0,dl))**2*real(ye) + p=p/(cabs(yed+sum1))**2 + spect1=p*2.0e0/(omega*pi) + write(*,*) "spect1:",spect1 + return + end + + subroutine acf2(wl, tau, te1, ti1, fi1, ven1, vin1, wi1, + & alpha1, dens1, bfld1, acf, nion1) +c +c computes autocorrelation function for given plasma parameters +c by integrating real spectrum +c tau in sec., alpha in radians, density in cgs, bfield in cgs +c scattering wavelength (wl) in meters +c + include 'fitter.h' + + real wl,tau,te1,ti1(nion1),fi1(nion1),ven1,vin1(nion1),alpha1, + & dens1,bfld1,acf + real pi + integer nion1 + integer wi1(nion1) + integer i,j,k,imode + common /mode/imode +c + write(*,*) "INITIAL acf:",wl,tau,te1,ti1,fi1,ven1,vin1,wi1,alpha1 + write(*,*) "INITIAL acf:",dens1, bfld1, acf, nion1 +c write(*,fmt='("INIT")') + pi=4.0*atan(1.0) +c +c copy arguments to common block +c + ak=2.0*pi/wl + imode=2 + write(*,*) "imode:",imode + + nion=nion1 + alpha=alpha1 + te=te1 + ven=ven1 +c write(*,fmt='("INIT2")') + do i=1,nion +c write(*,fmt='("INIT2.5")') + ti(i)=ti1(i) + fi(i)=fi1(i) + vin(i)=vin1(i) + wi(i)=wi1(i) + end do +c write(*,fmt='("INIT3")') + dens=dens1 + bfld=bfld1 + +c write(*,*) wl,alpha1,bfld1,dens +c call exit +c write(*,fmt='("Before Gauss")') + call gaussq(tau,acf) + + write(*,*) "FINAL acf:",acf + +c write(*,fmt='("After Gauss")') + return + end + + subroutine gaussq(tau,acf) +c +c Computes cosine or sine transform of given real function +c Uses quadpack, tau in sec. +c + real a,abserr,epsabs,acf,tau,work,chebmo + integer ier,integr,iwork,last,leniw,lenw,limit,limlst, + * lst,maxp1,neval + integer knorm,ksave,momcom,nrmom + dimension iwork(300),work(1625),chebmo(61,25) + external spect1 + include 'fitter.h' +c +c write(*,*) "inside gaussq" + a = 0.0 + b = 2.5e4*ak ! upper integration limit open to debate (was 1.5, now 2.5) + integr = 1 + epsabs = 1.0e-4 + limlst = 50 + limit = 100 + leniw = limit*2+limlst + maxp1 = 61 + lenw = leniw*2+maxp1*25 + +c write(*,*) leniw,lenw + + nrmom=0 + ksave=0 + momcom=0 + write(*,*) "Before qc25f:",acf,imode +c much faster, more robust +c write(*,*) "acf_in: ",acf + call qc25f(spect1,a,b,tau,integr,nrmom,maxp1,ksave,acf, + & abserr,neval,resabs,resasc,momcom,chebmo) +c write(*,*) "acf_out: ",acf +c call qawf(spect1,a,tau,integr,epsabs,acf,abserr,neval, +c & ier,limlst,lst,leniw,maxp1,lenw,iwork,work) + write(*,*) "After qc25f:",acf +c call exit + return + end diff --git a/schainf/Ffiles/fitacf_fit_short.pyf b/schainf/Ffiles/fitacf_fit_short.pyf new file mode 100644 index 0000000..314ac43 --- /dev/null +++ b/schainf/Ffiles/fitacf_fit_short.pyf @@ -0,0 +1,175 @@ +! -*- f90 -*- +! Note: the context of this file is case sensitive. + +python module reader__user__routines + interface ! in : reader.c + subroutine collision_(densmks, te, freq, alpha2, ye) + intent(c) collision_ ! foo is a C function + intent(c) ! all foo arguments are + ! considered as C based + real intent(in) :: densmks(1) ! x is input array + real intent(in) :: te(1) ! y is output array + real intent(in) :: freq(1) ! x is input array + real intent(in) :: alpha2(1) ! y is output array + complex intent(in,out) :: ye(1) ! y is output array + end subroutine foo + end interface +end python module reader +python module lmdif__user__routines + interface lmdif_user_interface + subroutine fcn(m,n,x,fvec,iflag) ! in :fitacf_fit_short:lmdif1.f:lmdif:unknown_interface + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + integer :: iflag + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + real dimension(100) :: tau + real dimension(100) :: rho + real dimension(100) :: sigma2 + real dimension(10) :: params + integer dimension(10) :: ifit + real :: chisq + real dimension(10000) :: ev + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /fitter/ tau,rho,sigma2,params,ifit + common /errs/ chisq + common /trans/ ev + end subroutine fcn + end interface lmdif_user_interface +end python module lmdif__user__routines +python module fitacf_fit_short ! in + interface ! in :fitacf_fit_short + subroutine fit(wl,taup,rhop,covar,cinv,sigma2p,paramp,ebp,bfldp,alphap,densp,alt,time,ifitp,ist,nl) ! in :fitacf_fit_short:fitacf_fit_short.f + real intent(in):: wl + real dimension(nl),intent(in) :: taup + real dimension(nl),depend(nl),intent(in) :: rhop + real intent(in),dimension(nl,nl),depend(nl,nl) :: covar + real intent(in,out),dimension(nl,nl),depend(nl,nl) :: cinv + real intent(in,out),dimension(nl),depend(nl) :: sigma2p + real intent(in,out),dimension(10) :: paramp + real intent(out),dimension(10) :: ebp + real intent(in):: bfldp + real intent(in):: alphap + real intent(in):: densp + real intent(in):: alt + real intent(in):: time + integer intent(in),dimension(10) :: ifitp + integer intent(in,out):: ist + integer intent(in), check(len(taup)>=nl),depend(taup) :: nl=len(taup) + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + integer :: imode + real dimension(100) :: tau + real dimension(100) :: rho + real dimension(100) :: sigma2 + real dimension(10) :: params + integer dimension(10) :: ifit + real dimension(10000) :: ev + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /mode/ imode + common /fitter/ tau,rho,sigma2,params,ifit + common /trans/ ev + end subroutine fit + function spect1(omega) ! in :fitacf_fit_short:fitacf_fit_short.f + real :: omega + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + integer :: imode + real :: spect1 + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /mode/ imode + end function spect1 + subroutine gaussq(tau,acf) ! in :fitacf_fit_short:fitacf_fit_short.f + real :: tau + real :: acf + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + end subroutine gaussq + subroutine lmdif1(fcn,m,n,x,fvec,tol,info,iwa,wa,lwa) ! in :fitacf_fit_short:lmdif1.f + use lmdif__user__routines + external :: fcn + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + real :: tol + integer :: info + integer dimension(n),depend(n) :: iwa + real dimension(lwa) :: wa + integer, optional,check(len(wa)>=lwa),depend(wa) :: lwa=len(wa) + end subroutine lmdif1 + subroutine lmdif(fcn,m,n,x,fvec,ftol,xtol,gtol,maxfev,epsfcn,diag,mode,factor,nprint,info,nfev,fjac,ldfjac,ipvt,qtf,wa1,wa2,wa3,wa4) ! in :fitacf_fit_short:lmdif1.f + use lmdif__user__routines + external :: fcn + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + real :: ftol + real :: xtol + real :: gtol + integer :: maxfev + real :: epsfcn + real dimension(n),depend(n) :: diag + integer :: mode + real :: factor + integer :: nprint + integer :: info + integer :: nfev + real dimension(ldfjac,n),depend(n) :: fjac + integer, optional,check(shape(fjac,0)==ldfjac),depend(fjac) :: ldfjac=shape(fjac,0) + integer dimension(n),depend(n) :: ipvt + real dimension(n),depend(n) :: qtf + real dimension(n),depend(n) :: wa1 + real dimension(n),depend(n) :: wa2 + real dimension(n),depend(n) :: wa3 + real dimension(m),depend(m) :: wa4 + end subroutine lmdif + function spmpar(i) ! in :fitacf_fit_short:lmdif1.f + integer :: i + real :: spmpar + end function spmpar + end interface +end python module fitacf_fit_short + +! This file was auto-generated with f2py (version:2). +! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/schainf/Ffiles/fitter.h b/schainf/Ffiles/fitter.h new file mode 100644 index 0000000..e7d4c9a --- /dev/null +++ b/schainf/Ffiles/fitter.h @@ -0,0 +1,7 @@ +c information needed for spectral computations + + parameter(nimax=10) + integer nion,wi(nimax) + real te,ti(nimax),fi(nimax),ven,vin(nimax),alpha,dens,bfld,ak + common /spec/te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + diff --git a/schainf/Ffiles/fpa.h b/schainf/Ffiles/fpa.h new file mode 100644 index 0000000..40ddeb2 --- /dev/null +++ b/schainf/Ffiles/fpa.h @@ -0,0 +1,12 @@ + parameter(nl=16,nrange=75) ! was 95 + parameter(nstate=5,npen=5) + real plag(nl,nrange+nl),plag_errors(nl,nrange+nl),sconst + real densp(nrange+nl),tep(nrange+nl),trp(nrange+nl), + & tip(nrange+nl),hfp(nrange+nl),hefp(nrange+nl),altp(nrange+nl), + & r0,dr + real edensp(nrange+nl),etep(nrange+nl),etip(nrange+nl), + & ehfp(nrange+nl),ehefp(nrange+nl) + common /fpa/densp,tep,trp,tip,hfp,hefp,altp,r0,dr,wl + 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Hc$@=m),depend(wa) :: m=len(wa) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: wa + integer :: iflag + end subroutine fcn + end interface fdjac2_user_interface +end python module fdjac2__user__routines +python module lmdif__user__routines + interface lmdif_user_interface + subroutine fcn(m,n,x,fvec,iflag) ! in :full_profile:lmdif1.f:lmdif:unknown_interface + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + integer :: iflag + end subroutine fcn + end interface lmdif_user_interface +end python module lmdif__user__routines +python module full_profile ! in + interface ! in :full_profile + subroutine nnlswrap(power,sigma,temp,perror,ut,nhts) ! in :full_profile:full_profile.f + real dimension(nhts) :: power + real dimension(512) :: sigma + real dimension(512) :: temp + real dimension(512) :: perror + real :: ut + integer, optional,check(len(power)>=nhts),depend(power) :: nhts=len(power) + end subroutine nnlswrap + subroutine profile(acf_sum,acf_err,power,en,alag,thb2,bfm2,ote,ete,oti,eti,oph,eph,ophe,ephe,range2,ut,nhts,nacf,ibits,acf_avg,status) ! in :full_profile:full_profile.f + complex dimension(4,nhts,ibits) :: acf_sum + real dimension(nhts,ibits),depend(nhts,ibits) :: acf_err + real dimension(nhts),depend(nhts) :: power + real dimension(nhts),depend(nhts) :: en + real dimension(ibits),depend(ibits) :: alag + real dimension(nhts),depend(nhts) :: thb2 + real dimension(nhts),depend(nhts) :: bfm2 + real dimension(nacf),depend(nacf) :: ote + real dimension(nacf),depend(nacf) :: ete + real dimension(nacf),depend(nacf) :: oti + real dimension(nacf),depend(nacf) :: eti + real dimension(nacf),depend(nacf) :: oph + real dimension(nacf),depend(nacf) :: eph + real dimension(nacf),depend(nacf) :: ophe + real dimension(nacf),depend(nacf) :: ephe + real dimension(nhts),depend(nhts) :: range2 + real :: ut + integer, optional,check(shape(acf_sum,1)==nhts),depend(acf_sum) :: nhts=shape(acf_sum,1) + integer :: nacf + integer, optional,check(shape(acf_sum,2)==ibits),depend(acf_sum) :: ibits=shape(acf_sum,2) + complex dimension(nhts,ibits),depend(nhts,ibits) :: acf_avg + real :: status + real :: chi2 + real dimension(91) :: densp + real dimension(91) :: tep + real dimension(91) :: trp + real dimension(91) :: tip + real dimension(91) :: hfp + real dimension(91) :: hefp + real dimension(91) :: altp + real :: r0 + real :: dr + real :: wl + real dimension(16,91) :: plag + real dimension(16,91) :: plag_errors + real :: sconst + real dimension(91) :: edensp + real dimension(91) :: etep + real dimension(91) :: etip + real dimension(91) :: ehfp + real dimension(91) :: ehefp + real dimension(85) :: bfld_prof + real dimension(85) :: alpha_prof + integer :: imode + real :: uttime + real dimension(34) :: ta + real dimension(30,5) :: bcoef + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + common /chisq/ chi2 + common /fpa/ densp,tep,trp,tip,hfp,hefp,altp,r0,dr,wl + common /data/ plag,plag_errors + common /sys/ sconst + common /errs/ edensp,etep,etip,ehfp,ehefp + common /mag/ bfld_prof,alpha_prof + common /mode/ imode + common /utime/ uttime + common /spline/ ta,bcoef + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + end subroutine profile + subroutine grid ! in :full_profile:full_profile.f + real dimension(34) :: ta + real dimension(30,5) :: bcoef + real dimension(91) :: densp + real dimension(91) :: tep + real dimension(91) :: trp + real dimension(91) :: tip + real dimension(91) :: hfp + real dimension(91) :: hefp + real dimension(91) :: altp + real :: r0 + real :: dr + real :: wl + real dimension(16,91) :: plag + real dimension(16,91) :: plag_errors + real :: sconst + real dimension(91) :: edensp + real dimension(91) :: etep + real dimension(91) :: etip + real dimension(91) :: ehfp + real dimension(91) :: ehefp + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + real :: chi2 + real :: uttime + common /spline/ ta,bcoef + common /fpa/ densp,tep,trp,tip,hfp,hefp,altp,r0,dr,wl + common /data/ plag,plag_errors + common /sys/ sconst + common /errs/ edensp,etep,etip,ehfp,ehefp + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /chisq/ chi2 + common /utime/ uttime + end subroutine grid + subroutine propagate(xe) ! in :full_profile:full_profile.f + real dimension(150) :: xe + real dimension(91) :: densp + real dimension(91) :: tep + real dimension(91) :: trp + real dimension(91) :: tip + real dimension(91) :: hfp + real dimension(91) :: hefp + real dimension(91) :: altp + real :: r0 + real :: dr + real :: wl + real dimension(16,91) :: plag + real dimension(16,91) :: plag_errors + real :: sconst + real dimension(91) :: edensp + real dimension(91) :: etep + real dimension(91) :: etip + real dimension(91) :: ehfp + real dimension(91) :: ehefp + real dimension(34) :: ta + real dimension(30,5) :: bcoef + common /fpa/ densp,tep,trp,tip,hfp,hefp,altp,r0,dr,wl + common /data/ plag,plag_errors + common /sys/ sconst + common /errs/ edensp,etep,etip,ehfp,ehefp + common /spline/ ta,bcoef + end subroutine propagate + subroutine fcn_lpreg(m,n,x,fvec,iflag) ! in :full_profile:full_profile.f + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + integer :: iflag + real dimension(34) :: ta + real dimension(30,5) :: bcoef + real dimension(91) :: densp + real dimension(91) :: tep + real dimension(91) :: trp + real dimension(91) :: tip + real dimension(91) :: hfp + real dimension(91) :: hefp + real dimension(91) :: altp + real :: r0 + real :: dr + real :: wl + real dimension(16,91) :: plag + real dimension(16,91) :: plag_errors + real :: sconst + real dimension(91) :: edensp + real dimension(91) :: etep + real dimension(91) :: etip + real dimension(91) :: ehfp + real dimension(91) :: ehefp + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + real :: chi2 + real :: uttime + common /spline/ ta,bcoef + common /fpa/ densp,tep,trp,tip,hfp,hefp,altp,r0,dr,wl + common /data/ plag,plag_errors + common /sys/ sconst + common /errs/ edensp,etep,etip,ehfp,ehefp + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /chisq/ chi2 + common /utime/ uttime + end subroutine fcn_lpreg + subroutine get_scale(plag2) ! in :full_profile:full_profile.f + real dimension(16,75) :: plag2 + real dimension(91) :: densp + real dimension(91) :: tep + real dimension(91) :: trp + real dimension(91) :: tip + real dimension(91) :: hfp + real dimension(91) :: hefp + real dimension(91) :: altp + real :: r0 + real :: dr + real :: wl + real dimension(16,91) :: plag + real dimension(16,91) :: plag_errors + real :: sconst + real dimension(91) :: edensp + real dimension(91) :: etep + real dimension(91) :: etip + real dimension(91) :: ehfp + real dimension(91) :: ehefp + common /fpa/ densp,tep,trp,tip,hfp,hefp,altp,r0,dr,wl + common /data/ plag,plag_errors + common /sys/ sconst + common /errs/ edensp,etep,etip,ehfp,ehefp + end subroutine get_scale + subroutine lagp(plag,wl,r0,dr,nl,nrange) ! in :full_profile:lagp.f + real dimension(nl,nrange) :: plag + real :: wl + real :: r0 + real :: dr + integer, optional,check(shape(plag,0)==nl),depend(plag) :: nl=shape(plag,0) + integer, optional,check(shape(plag,1)==nrange),depend(plag) :: nrange=shape(plag,1) + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + real dimension(34) :: ta + real dimension(30,5) :: bcoef + real dimension(85) :: bfld_prof + real dimension(85) :: alpha_prof + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /spline/ ta,bcoef + common /mag/ bfld_prof,alpha_prof + end subroutine lagp + subroutine lagp_old(plag,wl,r0,dr,nl,nrange) ! in :full_profile:lagp.f + real dimension(nl,nrange) :: plag + real :: wl + real :: r0 + real :: dr + integer, optional,check(shape(plag,0)==nl),depend(plag) :: nl=shape(plag,0) + integer, optional,check(shape(plag,1)==nrange),depend(plag) :: nrange=shape(plag,1) + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + real dimension(34) :: ta + real dimension(30,5) :: bcoef + real dimension(85) :: bfld_prof + real dimension(85) :: alpha_prof + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /spline/ ta,bcoef + common /mag/ bfld_prof,alpha_prof + end subroutine lagp_old + function atanh(x) ! in :full_profile:lagp.f + real :: x + real :: atanh + end function atanh + subroutine get_spline(alt,dens,te,ti,hf,hef) ! in :full_profile:lagp.f + real :: alt + real :: dens + real :: te + real :: ti + real :: hf + real :: hef + real dimension(34) :: ta + real dimension(30,5) :: bcoef + common /spline/ ta,bcoef + end subroutine get_spline + function bvalue(t,bcoef,n,k,x,jderiv) ! in :full_profile:lagp.f + real dimension(n+k),depend(n,k) :: t + real dimension(n) :: bcoef + integer, optional,check(len(bcoef)>=n),depend(bcoef) :: n=len(bcoef) + integer :: k + real :: x + integer :: jderiv + real :: bvalue + end function bvalue + subroutine interv(xt,lxt,x,left,mflag) ! in :full_profile:lagp.f + real dimension(lxt) :: xt + integer, optional,check(len(xt)>=lxt),depend(xt) :: lxt=len(xt) + real :: x + integer :: left + integer :: mflag + end subroutine interv + subroutine lmdif1(fcn,m,n,x,fvec,tol,info,iwa,wa,lwa) ! in :full_profile:lmdif1.f + use lmdif__user__routines + external fcn + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + real :: tol + integer :: info + integer dimension(n),depend(n) :: iwa + real dimension(lwa) :: wa + integer, optional,check(len(wa)>=lwa),depend(wa) :: lwa=len(wa) + end subroutine lmdif1 + function enorm(n,x) ! in :full_profile:lmdif1.f + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real :: enorm + end function enorm + subroutine fdjac2(fcn,m,n,x,fvec,fjac,ldfjac,iflag,epsfcn,wa) ! in :full_profile:lmdif1.f + use fdjac2__user__routines + external fcn + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + real dimension(ldfjac,n),depend(n) :: fjac + integer, optional,check(shape(fjac,0)==ldfjac),depend(fjac) :: ldfjac=shape(fjac,0) + integer :: iflag + real :: epsfcn + real dimension(m),depend(m) :: wa + end subroutine fdjac2 + subroutine lmdif(fcn,m,n,x,fvec,ftol,xtol,gtol,maxfev,epsfcn,diag,mode,factor,nprint,info,nfev,fjac,ldfjac,ipvt,qtf,wa1,wa2,wa3,wa4) ! in :full_profile:lmdif1.f + use lmdif__user__routines + external fcn + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + real :: ftol + real :: xtol + real :: gtol + integer :: maxfev + real :: epsfcn + real dimension(n),depend(n) :: diag + integer :: mode + real :: factor + integer :: nprint + integer :: info + integer :: nfev + real dimension(ldfjac,n),depend(n) :: fjac + integer, optional,check(shape(fjac,0)==ldfjac),depend(fjac) :: ldfjac=shape(fjac,0) + integer dimension(n),depend(n) :: ipvt + real dimension(n),depend(n) :: qtf + real dimension(n),depend(n) :: wa1 + real dimension(n),depend(n) :: wa2 + real dimension(n),depend(n) :: wa3 + real dimension(m),depend(m) :: wa4 + end subroutine lmdif + subroutine lmpar(n,r,ldr,ipvt,diag,qtb,delta,par,x,sdiag,wa1,wa2) ! in :full_profile:lmdif1.f + integer, optional,check(shape(r,1)==n),depend(r) :: n=shape(r,1) + real dimension(ldr,n) :: r + integer, optional,check(shape(r,0)==ldr),depend(r) :: ldr=shape(r,0) + integer dimension(n),depend(n) :: ipvt + real dimension(n),depend(n) :: diag + real dimension(n),depend(n) :: qtb + real :: delta + real :: par + real dimension(n),depend(n) :: x + real dimension(n),depend(n) :: sdiag + real dimension(n),depend(n) :: wa1 + real dimension(n),depend(n) :: wa2 + end subroutine lmpar + subroutine qrfac(m,n,a,lda,pivot,ipvt,lipvt,rdiag,acnorm,wa) ! in :full_profile:lmdif1.f + integer :: m + integer, optional,check(shape(a,1)==n),depend(a) :: n=shape(a,1) + real dimension(lda,n) :: a + integer, optional,check(shape(a,0)==lda),depend(a) :: lda=shape(a,0) + logical :: pivot + integer dimension(lipvt) :: ipvt + integer, optional,check(len(ipvt)>=lipvt),depend(ipvt) :: lipvt=len(ipvt) + real dimension(n),depend(n) :: rdiag + real dimension(n),depend(n) :: acnorm + real dimension(n),depend(n) :: wa + end subroutine qrfac + subroutine qrsolv(n,r,ldr,ipvt,diag,qtb,x,sdiag,wa) ! in :full_profile:lmdif1.f + integer, optional,check(shape(r,1)==n),depend(r) :: n=shape(r,1) + real dimension(ldr,n) :: r + integer, optional,check(shape(r,0)==ldr),depend(r) :: ldr=shape(r,0) + integer dimension(n),depend(n) :: ipvt + real dimension(n),depend(n) :: diag + real dimension(n),depend(n) :: qtb + real dimension(n),depend(n) :: x + real dimension(n),depend(n) :: sdiag + real dimension(n),depend(n) :: wa + end subroutine qrsolv + function spmpar(i) ! in :full_profile:lmdif1.f + integer :: i + real :: spmpar + end function spmpar + subroutine bndacc(g,mdg,nb,ip,ir,mt,jt) ! in :full_profile:nnls.f + double precision dimension(mdg,*) :: g + integer, optional,check(shape(g,0)==mdg),depend(g) :: mdg=shape(g,0) + integer :: nb + integer :: ip + integer :: ir + integer :: mt + integer :: jt + end subroutine bndacc + subroutine bndsol(mode,g,mdg,nb,ip,ir,x,n,rnorm) ! in :full_profile:nnls.f + integer :: mode + double precision dimension(mdg,*) :: g + integer, optional,check(shape(g,0)==mdg),depend(g) :: mdg=shape(g,0) + integer :: nb + integer :: ip + integer :: ir + double precision dimension(n) :: x + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + double precision :: rnorm + end subroutine bndsol + function diff(x,y) ! in :full_profile:nnls.f + double precision :: x + double precision :: y + double precision :: diff + end function diff + subroutine g1(a,b,cterm,sterm,sig) ! in :full_profile:nnls.f + double precision :: a + double precision :: b + double precision :: cterm + double precision :: sterm + double precision :: sig + end subroutine g1 + subroutine g2(cterm,sterm,x,y) ! in :full_profile:nnls.f + double precision :: cterm + double precision :: sterm + double precision :: x + double precision :: y + end subroutine g2 + function gen2(anoise) ! in :full_profile:nnls.f + double precision :: anoise + double precision :: gen2 + end function gen2 + subroutine h12(mode,lpivot,l1,m,u,iue,up,c,ice,icv,ncv) ! in :full_profile:nnls.f + integer :: mode + integer :: lpivot + integer :: l1 + integer :: m + double precision dimension(iue,*) :: u + integer, optional,check(shape(u,0)==iue),depend(u) :: iue=shape(u,0) + double precision :: up + double precision dimension(*) :: c + integer :: ice + integer :: icv + integer :: ncv + end subroutine h12 + subroutine hfti(a,mda,m,n,b,mdb,nb,tau,krank,rnorm,h,g,ip) ! in :full_profile:nnls.f + double precision dimension(mda,*) :: a + integer, optional,check(shape(a,0)==mda),depend(a) :: mda=shape(a,0) + integer :: m + integer :: n + double precision dimension(mdb,*) :: b + integer, optional,check(shape(b,0)==mdb),depend(b) :: mdb=shape(b,0) + integer :: nb + double precision :: tau + integer :: krank + double precision dimension(*) :: rnorm + double precision dimension(*) :: h + double precision dimension(*) :: g + integer dimension(*) :: ip + end subroutine hfti + subroutine ldp(g,mdg,m,n,h,x,xnorm,w,index_bn,mode) ! in :full_profile:nnls.f + double precision dimension(mdg,*) :: g + integer, optional,check(shape(g,0)==mdg),depend(g) :: mdg=shape(g,0) + integer :: m + integer :: n + double precision dimension(*) :: h + double precision dimension(*) :: x + double precision :: xnorm + double precision dimension(*) :: w + integer dimension(*) :: index_bn + integer :: mode + end subroutine ldp + subroutine mfeout(a,mda,m,n,names,mode,unit,width) ! in :full_profile:nnls.f + double precision dimension(mda,n) :: a + integer, optional,check(shape(a,0)==mda),depend(a) :: mda=shape(a,0) + integer, optional,check(shape(names,0)==m),depend(names) :: m=shape(names,0) + integer, optional,check(shape(a,1)==n),depend(a) :: n=shape(a,1) + character dimension(m,(*)) :: names + integer :: mode + integer :: unit + integer :: width + end subroutine mfeout + subroutine nnls(a,mda,m,n,b,x,rnorm,w,zz,index_bn,mode) ! in :full_profile:nnls.f + double precision dimension(mda,*) :: a + integer, optional,check(shape(a,0)==mda),depend(a) :: mda=shape(a,0) + integer :: m + integer :: n + double precision dimension(*) :: b + double precision dimension(*) :: x + double precision :: rnorm + double precision dimension(*) :: w + double precision dimension(*) :: zz + integer dimension(*) :: index_bn + integer :: mode + end subroutine nnls + subroutine qrbd(ipass,q,e,nn,v,mdv,nrv,c,mdc,ncc) ! in :full_profile:nnls.f + integer :: ipass + double precision dimension(*) :: q + double precision dimension(*) :: e + integer :: nn + double precision dimension(mdv,*) :: v + integer, optional,check(shape(v,0)==mdv),depend(v) :: mdv=shape(v,0) + integer :: nrv + double precision dimension(mdc,*) :: c + integer, optional,check(shape(c,0)==mdc),depend(c) :: mdc=shape(c,0) + integer :: ncc + end subroutine qrbd + subroutine sva(a,mda,m,n,mdata,b,sing,kpvec,names,iscale,d,work) ! in :full_profile:nnls.f + double precision dimension(mda,n) :: a + integer, optional,check(shape(a,0)==mda),depend(a) :: mda=shape(a,0) + integer, optional,check(len(b)>=m),depend(b) :: m=len(b) + integer, optional,check(shape(a,1)==n),depend(a) :: n=shape(a,1) + integer :: mdata + double precision dimension(m) :: b + double precision dimension(n),depend(n) :: sing + integer dimension(4) :: kpvec + character dimension(n,(*)),intent(c),depend(n) :: names + integer :: iscale + double precision dimension(n),depend(n) :: d + double precision dimension(2 * n),depend(n) :: work + end subroutine sva + subroutine svdrs(a,mda,m1,n1,b,mdb,nb,s,work) ! in :full_profile:nnls.f + double precision dimension(mda,*) :: a + integer, optional,check(shape(a,0)==mda),depend(a) :: mda=shape(a,0) + integer :: m1 + integer, optional,check(shape(work,0)==n1),depend(work) :: n1=shape(work,0) + double precision dimension(mdb,*) :: b + integer, optional,check(shape(b,0)==mdb),depend(b) :: mdb=shape(b,0) + integer :: nb + double precision dimension(*) :: s + double precision dimension(n1,2) :: work + end subroutine svdrs + subroutine guess(acf,tau,npts,zero,amin,te,tr) ! in :full_profile:fitacf.f + real dimension(npts) :: acf + real dimension(npts),depend(npts) :: tau + integer, optional,check(len(acf)>=npts),depend(acf) :: npts=len(acf) + real :: zero + real :: amin + real :: te + real :: tr + end subroutine guess + subroutine parab1(x,y,a,b,c) ! in :full_profile:fitacf.f + real dimension(3) :: x + real dimension(3) :: y + real :: a + real :: b + real :: c + end subroutine parab1 + function cdtr1(depth) ! in :full_profile:fitacf.f + real :: depth + real :: cdtr1 + end function cdtr1 + function czte1(zlag,tr) ! in :full_profile:fitacf.f + real :: zlag + real :: tr + real :: czte1 + end function czte1 + subroutine fit(wl,taup,rhop,covar,cinv,sigma2p,paramp,ebp,bfldp,alphap,densp,alt,time,nl,ifitp,ist) ! in :full_profile:fitacf.f + real :: wl + real dimension(nl) :: taup + real dimension(nl),depend(nl) :: rhop + real dimension(nl,nl),depend(nl,nl) :: covar + real dimension(nl,nl),depend(nl,nl) :: cinv + real dimension(nl),depend(nl) :: sigma2p + real dimension(10) :: paramp + real dimension(10) :: ebp + real :: bfldp + real :: alphap + real :: densp + real :: alt + real :: time + integer, optional,check(len(taup)>=nl),depend(taup) :: nl=len(taup) + integer dimension(10) :: ifitp + integer :: ist + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + integer :: imode + real dimension(100) :: tau + real dimension(100) :: rho + real dimension(100) :: sigma2 + real dimension(10) :: params + integer dimension(10) :: ifit + real dimension(10000) :: ev + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /mode/ imode + common /fitter/ tau,rho,sigma2,params,ifit + common /trans/ ev + end subroutine fit + subroutine fcn(m,n,x,fvec,iflag) ! in :full_profile:fitacf.f + integer, optional,check(len(fvec)>=m),depend(fvec) :: m=len(fvec) + integer, optional,check(len(x)>=n),depend(x) :: n=len(x) + real dimension(n) :: x + real dimension(m) :: fvec + integer :: iflag + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + real dimension(100) :: tau + real dimension(100) :: rho + real dimension(100) :: sigma2 + real dimension(10) :: params + integer dimension(10) :: ifit + real :: chisq + real dimension(10000) :: ev + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /fitter/ tau,rho,sigma2,params,ifit + common /errs/ chisq + common /trans/ ev + end subroutine fcn + function cj_ion(theta,psi) ! in :full_profile:fitacf.f + real :: theta + real :: psi + complex :: cj_ion + end function cj_ion + function cj_electron(theta,phi,psi,alpha) ! in :full_profile:fitacf.f + real :: theta + real :: phi + real :: psi + real :: alpha + integer :: imode + complex :: cj_electron + common /mode/ imode + end function cj_electron + function y_ion(theta,psi) ! in :full_profile:fitacf.f + real :: theta + real :: psi + complex :: y_ion + end function y_ion + function y_electron(theta,phi,psi,alpha) ! in :full_profile:fitacf.f + real :: theta + real :: phi + real :: psi + real :: alpha + complex :: y_electron + end function y_electron + function spect1(omega) ! in :full_profile:fitacf.f + real :: omega + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + integer :: imode + real :: spect1 + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + common /mode/ imode + end function spect1 + subroutine acf2(wl,tau,te1,ti1,fi1,ven1,vin1,wi1,nion1,alpha1,dens1,bfld1,acf) ! in :full_profile:fitacf.f + real :: wl + real :: tau + real :: te1 + real dimension(nion1) :: ti1 + real dimension(nion1),depend(nion1) :: fi1 + real :: ven1 + real dimension(nion1),depend(nion1) :: vin1 + integer dimension(nion1),depend(nion1) :: wi1 + integer, optional,check(len(ti1)>=nion1),depend(ti1) :: nion1=len(ti1) + real :: alpha1 + real :: dens1 + real :: bfld1 + real :: acf + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + end subroutine acf2 + subroutine gaussq(tau,acf) ! in :full_profile:fitacf.f + real :: tau + real :: acf + real :: te + real dimension(10) :: ti + real dimension(10) :: fi + real :: ven + real dimension(10) :: vin + real :: alpha + real :: dens + real :: bfld + integer :: nion + integer dimension(10) :: wi + real :: ak + common /spec/ te,ti,fi,ven,vin,alpha,dens,bfld,nion,wi,ak + end subroutine gaussq + function r1mach(i) ! in :full_profile:r1mach.f + integer :: i + integer :: cray1 + real :: r1mach + common /d8mach/ cray1 + end function r1mach + end interface +end python module full_profile + +! This file was auto-generated with f2py (version:2). +! See http://cens.ioc.ee/projects/f2py2e/ diff --git a/schainf/Ffiles/full_profile_profile.f b/schainf/Ffiles/full_profile_profile.f new file mode 100644 index 0000000..5bbba87 --- /dev/null +++ b/schainf/Ffiles/full_profile_profile.f @@ -0,0 +1,646 @@ +c +c $Id: full_profile.f,v 1.3 2013/09/12 19:11:48 daveh Exp daveh $ DLH +c + + subroutine profile(acf_sum,acf_err,power,en,alag,thb2,bfm2, + & ote,ete,oti,eti,oph,eph,ophe,ephe,range2,ut, + & NHTS,NACF,IBITS,acf_avg_real,status) +c + complex acf_sum(4,NHTS,IBITS) + real acf_avg_real(NHTS,IBITS) + real acf_err(NHTS,IBITS),range2(NHTS) + real power(NHTS),en(NHTS),alag(IBITS),thb2(NHTS),bfm2(NHTS) + real ote(NHTS),ete(NHTS),oti(NHTS),eti(NHTS),oph(NHTS),eph(NHTS) + real ophe(NHTS),ephe(NHTS) + integer NHTS,NACF,IBITS + real status(1) + common /chisq/chi2 +c +c arguments above, internal variables below: have to make these match +c + include 'fpa.h' + include 'bfield.h' +c + common /mode/imode + common /utime/uttime +c + include 'spline.h' + include 'fitter.h' +c +c functions to minimize are all lagged profiles plus penalties +c variables to minimize them with are all spline values +c + + parameter(nfun=nrange*nl+nstate*(nspline-2)+npen) + parameter(nvar=nspline*nstate) + parameter(lwa=nfun*nvar+nstate*nvar+nfun) + real fvec(nfun),wa(lwa),xe(nvar) + integer iwa(nvar) +c integer lwa +c + external fcn_lpreg +c + pi=4.0*atan(1.0) + uttime=ut +c write(*,*) "ut: ",ut +c write(*,*) "NHTS: ",NHTS +c write(*,*) "NACF: ",NACF +c write(*,*) "IBITS: ",IBITS +c call exit +c write(*,*) "acf_sum: ", acf_sum(1,111,11) +c write(*,*) "Starting Profile Process" +c set up basic physical parameters +c dens=639747.44 +c dens=509664.781 +c te=3971.98926 +c write(*,*) "acf_sum: ", acf_sum(1,31,2) +c call exit + + wl=3.0 + ak=2.0*pi/wl + +c analysis starts at gate 15 + + ir0=15 + + r0=range2(ir0) + dr=range2(ir0+1)-range2(ir0) + + do i=1,nfield ! nrange+10 memory hole + bfld_prof(i)=bfm2(i+ir0-1) + alpha_prof(i)=thb2(i+ir0-1)*pi/180.0 + end do + + do i=1,nrange+nl ! careful ... check nfield compared to nrange+nl + densp(i)=en(i+ir0-1) + do j=1,nl +c write(*,*) acf_sum(1,i+ir0-1,j) + plag(j,i)=acf_sum(1,i+ir0-1,j) + + plag_errors(j,i)=acf_err(i+ir0-1,j) +c write(*,*) j,i,plag_errors(j,i) + end do + end do +c call exit +c set some fitting conventions +c write(*,*) "plag: ",plag(2,2) + imode=2 + nion=3 + + ven=0.0 + do i=1,nion + vin(i)=0.0 + end do + wi(1)=16 + wi(2)=1 + wi(3)=4 + +c system constant + + sconst=1.0 + +c set up splines: DLH need to modify for different nu. splines + + do i=1,nspline+norder + ta(i)=r0+float(i-1-2)*delr ! 2-knot offset for 4th order spline + end do + +c initial guess - set density, He+ profiles here + + do i=1,nspline ! DLH modify for different no. splines + bcoef(i,1)=log10(abs(densp(1+int(float(i-1)*delr/dr)))) + ! need good guess for density profile + tmp=0.03 + bcoef(i,5)=atanh(2.0*tmp-1.0) ! not so critical + end do + +c write(*,*) bcoef +c call exit + +c grid search for other params to help set initial guess +c could include Ne, He+ in grid search too +c write(*,fmt='("before GRID")') + call grid() +c write(*,fmt='("After GRID")') + write(*,*) "chi2 after grid:",chi2 +c write(*,fmt='("Just After chi")') +c call exit + if(chi2.le.3.5) then + +c write(*,fmt='("After chi")') +c call exit + tol=1.0e-9 + +c call lmdif1(fcn_lpreg,nfun-nl*nl,nvar,bcoef,fvec,tol, +c & info,iwa,wa,lwa) + + info=0 + m=nfun-nl*nl + n=nvar + zero=0.0 + factor=1.0e-2 ! rather small initial step size + + maxfev = 200*(n + 1) + ftol = tol + xtol = tol + gtol = zero + epsfcn = zero + mode = 1 + nprint = 0 + mp5n = m + 5*n +c write(*,*) wa(5*n+1) +c call exit + write(*,*) "before densp:", densp(1),bcoef(1,2) + call lmdif(fcn_lpreg,m,n,bcoef,fvec,ftol,xtol,gtol, + & maxfev,epsfcn,wa(1), + * mode,factor,nprint,info,nfev,wa(mp5n+1),m,iwa, + * wa(n+1),wa(2*n+1),wa(3*n+1),wa(4*n+1),wa(5*n+1)) + +c write(*,fmt='("After lmdif")') +c write(*,*) info + write(*,*) "densp_after:", densp(1),bcoef(1,2) +c call exit + +c +c error handling; evalate solution point first, then Jacobian +c + iflag=0 +c write(*,fmt='("before fcn_lpreg")') + call fcn_lpreg(m,n,bcoef,fvec,iflag) ! common sys constant throughout +c write(*,fmt='("After fcn_lpreg")') + nm1=n*m+1 + call fdjac2(fcn_lpreg,m,n,bcoef,fvec,wa,m,iflag,epsfcn,wa(nm1)) + + do i=1,n + err=0.0 + xe(i)=0.0 + do j=1,m-npen +c do j=2+(nspline-2)*nstate,m-npen ! skip equations unrelated to data + err=err+MIN(wa(j+(i-1)*m)**2,10.0) + end do + if(err.gt.0.0) xe(i)=sqrt(err**(-1)) + end do + + call propagate(xe) + + do i=1,nrange + ete(i+ir0)=etep(i) + eti(i+ir0)=etip(i) + eph(i+ir0)=ehfp(i) + ephe(i+ir0)=ehefp(i) + end do + +c +c output parameters +c + + do i=1,nrange + altp(i)=r0+dr*float(i-1) + call get_spline(altp(i),densp(i),tep(i),tip(i), + & hfp(i),hefp(i)) + ote(i+ir0)=MAX(tep(i),tip(i)) + oti(i+ir0)=tip(i) + oph(i+ir0)=hfp(i) + ophe(i+ir0)=hefp(i) + end do +c +c theoretical lag products and other quantities for plotting +c + + call lagp(plag,wl,r0,dr,nl,nrange) + write(*,*) "plag_plag",REAL(plag(12,58)) + write(*,*) "plag_plag",REAL(plag(12,72)) +c write(*,*) "plag_plag",AIMAG(plag(12,72)) + do i=1,nrange ! + en(i+ir0-1)=densp(i) + do j=1,nl + acf_avg_real(i+ir0-1,j)=REAL(plag(j,i)) +c acf_avg_imag(i+ir0-1,j)=AIMAG(acf_sum(1,i+ir0-1,j)) + end do + end do + write(*,*) "acf",acf_avg_real(72,12) +c write(*,*) "acf",acf_avg_imag(72,12) + end if + status(1)=chi2 + +c write(*,*) "status: ",status + + 5 return + end + + + subroutine grid() +c +c minimize chi-squared statistic through grid search +c just optmize temperature and H+ profiles +c + include 'spline.h' + include 'fpa.h' + include 'fitter.h' +c + real plag2(nl,nrange) + real fvec(nrange*nl) + real chmin,uttime + integer lmin,mmin,nmin + integer iloop,iskip,l1,l2,m1,m2,n1,n2 +c + common /chisq/chi2 + common /utime/uttime +c + chmin=1.0e10 + + do i=1,nrange + altp(i)=r0+dr*float(i-1) + end do + + goto 3 + call newplot(.true.) + call graphinit() + call erase + + call setorigin(6.5,3.5,90.0) + call linearaxis("L",altp(1),altp(nrange),1.5,5.0,2,0.0,50.0) + call linearaxis("B",0.0,5000.0,1.5,5.0,2,0.0,500.0) + call drawaxis("T",2) + call drawaxis("R",2) + call labelaxis("B","(f5.0)",.1,2,0.0,2000.0) + call labelaxis("L","(f5.0)",.1,2,0.0,100.0) + call ctitle("L","Altitude (km)",.125,2) + call ctitle("B","T\\se\\u (K)",.125,2) + + call setorigin(6.5,7.5,90.0) + call linearaxis("L",altp(1),altp(nrange),1.5,5.0,2,0.0,50.0) + call linearaxis("B",0.0,1.0,1.5,5.0,2,0.0,0.25) + call drawaxis("T",2) + call drawaxis("R",2) + call labelaxis("B","(f5.1)",.1,2,0.0,0.5) + call labelaxis("L","(f5.0)",.1,2,0.0,100.0) + call ctitle("B","H\\S+\\U frac.",.125,2) + + 3 continue + + do iloop=1,2 + if(iloop.eq.1) then + l1=2 + l2=26 + m1=2 + m2=10 + n1=2 + n2=16 + iskip=2 + else + l1=lmin-2 + l2=lmin+2 + m1=mmin-2 + m2=mmin+2 + n1=nmin-2 + n2=nmin+2 + iskip=1 + end if + + do l=l1,l2,iskip ! temperature search + do k=1,nspline + + tmp=-2.5+float(k-1)*float(l-1)*1.3e-2 +c if(uttime.ge.2.0.and.uttime.lt.10.0) then +c tmp=-1.5+float(k-1)*float(l-1)*8.0e-3 +c else +c tmp = -0.75 -0.2*float(l) + 3.5e-1*float(k-1) ! was 3.5 +c tmp=-1.5 + 3.0e-2*float(l-1) +c & *(float(k-1)**3.0/float(nspline-1)**2.0) +c end if + + bcoef(k,2)=tmp + if(uttime.ge.10.0.and.uttime.le.14.0) then ! was 10.5 + bcoef(k,3)=tmp-0.1 + else + bcoef(k,3)=tmp-0.02 + end if + end do + + do m=m1,m2,iskip ! H+ scale height search DLH 2015 + + do n=n1,n2,iskip ! H+ crossing height search + + do k=1,nspline + tmp=float(k-nspline/4-n)*(float(m-1)*5.0e-2+0.1) + bcoef(k,4)=tmp + end do + + do i=1,nrange + call get_spline(altp(i),densp(i),tep(i),tip(i), + & hfp(i),hefp(i)) + + end do + + goto 4 + call setorigin(6.5,3.5,90.0) + call setscale("L",altp(1),altp(nrange),1) + call setscale("B",0.0,5000.0,1) + call setclip("L",250.0,1500.0) + call plotline("B,L",tep,altp,nrange,2,0) + + if(l.eq.1) then + call setorigin(6.5,7.5,90.0) + call setscale("L",altp(1),altp(nrange),1) + call setscale("B",0.0,1.0,1) + call setclip("L",250.0,1500.0) + call plotline("B,L",hfp,altp,nrange,2,0) + end if + 4 continue + +c calculate chi-2 +c write(*,*) "wl: ",wl, "r0: ",r0 +c write(*,*) "dr: ",dr,"nl: ",n,"nrange", nrange +c write(*,*) "before lagp inside grid" + call lagp(plag2,wl,r0,dr,nl,nrange) +c write(*,*) "plag2: ",plag2(12,72) +c write(*,*) "plag2: ",plag2 +c call exit + call get_scale(plag2) +c write(*,*) "plag: ",plag(13,70) +c write(*,*) "plag2: ",plag2(13,70) +c write(*,*) "plag_errors: ",plag_errors(13,70) +c write(*,*) "sconst: ",sconst +c call exit +c write(*,*) "cal chi2.1: ", chi2 +c call exit + chi2=0.0 + ipt=0 +c write(*,*) "cal chi2.1: ", chi2 + do j=nl+1,nrange + do i=1,nl + ipt=ipt+1 + fvec(ipt)=(plag(i,j)-plag2(i,j)*sconst)/ + & plag_errors(i,j) +c write(*,*) j,i,plag(i,j),plag2(i,j), +c & plag_errors(i,j),sconst +c call exit + chi2=chi2+fvec(ipt)**2 +c write(*,*) "cal chi2.1: ", chi2 + end do +c call exit + end do +c write(*,*) "cal chi2.2: ", chi2 +c call exit + chi2=sqrt(chi2/float(nrange*nl))!+float(l)*0.005 ! DLH?? + if(chi2.lt.chmin) then + lmin=l + mmin=m + nmin=n + chmin=chi2 + end if + + write(*,*) "A",l,m,n,chi2,chmin,"B" ! best +c call exit +c write(*,fmt='("intermediate")') + end do + end do + end do + + end do +c write(*,fmt='("befire flush")') +c call where() + write(22,*) lmin,mmin,nmin,chmin + call flush(22) +c write(*,fmt='("after flush")') +c best result here + + do k=1,nspline + tmp=-2.5+float(k-1)*float(lmin-1)*1.3e-2 +c if(uttime.ge.2.0.and.uttime.lt.10.0) then +c tmp=-1.5+float(k-1)*float(lmin-1)*8.0e-3 +c else +c tmp = -0.75 -0.2*float(l) + 3.5e-1*float(k-1) ! was 3.5 +c tmp=-1.5 + 3.0e-2*float(lmin-1) ! new family of temps +c & *(float(k-1)**3.0/float(nspline-1)**2.0) +c end if + bcoef(k,2)=tmp + if(uttime.ge.10.0.and.uttime.le.14.0) then ! was 10.5 + bcoef(k,3)=tmp-0.1 + else + bcoef(k,3)=tmp-0.02 + end if + tmp=float(k-nspline/4-nmin)*(float(mmin-1)*5.0e-2+0.1) + bcoef(k,4)=tmp + end do + +c reset system constant + + do i=1,nrange + call get_spline(altp(i),densp(i),tep(i),tip(i), + & hfp(i),hefp(i)) + end do +c write(*,fmt='("------------before lagp------------")') +c write(*,*) chi2 +c call exit + call lagp(plag2,wl,r0,dr,nl,nrange) +c write(*,fmt='("after lagp")') + call get_scale(plag2) +c write(*,*) chi2 + chi2=chmin + return + end + + subroutine propagate(xe) +c +c propagate errors through splines +c + include 'fpa.h' + include 'spline.h' + parameter(nvar=nspline*nstate) + real xe(nvar) + + + do i=1,nrange + + write(*,*) "densp:", densp(i),bcoef(1,2) +c call exit +c + edensp(i)=bvalue(ta,xe(1+0*nspline),nspline,norder,altp(i),0) + & *densp(i)*2.30 + x=bvalue(ta,bcoef(1,2),nspline,norder,altp(i),0) + etep(i)=bvalue(ta,xe(1+1*nspline),nspline,norder,altp(i),0) + & *(t1/2.0)/cosh(x)**2 ! DLH 10/14 was 3500 + + write(*,*) i,altp(i),x, + & bvalue(ta,xe(1+1*nspline),nspline,norder,altp(i),0), + & (3500.0/2.0)/cosh(x)**2,xe(1+i/4+1*nspline) + + x=bvalue(ta,bcoef(1,3),nspline,norder,altp(i),0) + etip(i)=bvalue(ta,xe(1+2*nspline),nspline,norder,altp(i),0) + & *(t1/2.0)/cosh(x)**2 ! DLH 10/14 was 3500 + x=bvalue(ta,bcoef(1,4),nspline,norder,altp(i),0) + ehfp(i)=bvalue(ta,xe(1+3*nspline),nspline,norder,altp(i),0) + & *(1.0/2.0)/cosh(x)**2 + x=bvalue(ta,bcoef(1,5),nspline,norder,altp(i),0) + ehefp(i)=bvalue(ta,xe(1+4*nspline),nspline,norder,altp(i),0) + & *(1.0/2.0)/cosh(x)**2 + + write(*,*) altp(i),edensp(i),etep(i),etip(i),ehfp(i),ehefp(i) +c call exit + end do + +c stop + + return + end + + subroutine fcn_lpreg(m,n,x,fvec,iflag) +c + include 'spline.h' + include 'fpa.h' + include 'fitter.h' +c + integer m,n,iflag,iflaglast + real x(n),fvec(m),pen(nstate+npen) + real plag2(nl,nrange) + real regu(nstate+npen) + data regu/1.0e1,5.0e1,10.0e1,1.0e2,5.0e1, + & 1.0e1,2.0e0,1.0e0,5.0e-3,1.0e0/ + +c 2019 + common /iflaglast/iflaglast + common /chisq/chi2 + common /utime/uttime +c +c write(*,*)uttime," 3 *" + +c zero out, copy over some arrays + +c write(*,*) "Starting fcn_lpreg" + write(*,*) "x:",x(2) + + do j=1,nstate+npen + pen(j)=0.0 + end do + + ipt=0 + do j=1,nstate + do i=1,nspline + ipt=ipt+1 + bcoef(i,j)=x(ipt) +c write(*,*)j,i,bcoef(i,j) + end do + end do + +c populate profiles from splines + write(*,*) "densp1:",densp(1) + do i=1,nrange + altp(i)=r0+dr*float(i-1) +c write(*,*) "densp1:",densp(i) + call get_spline(altp(i),densp(i),tep(i),tip(i), + & hfp(i),hefp(i)) +c write(*,*) "densp2:",densp(i) +c call exit + end do + write(*,*) "densp2:",densp(1) +c regularize spline coefficients, establish boundary conditions +c write(*,*) "After spline_fcn_lpreg" + ipt=0 + do i=2,nspline-1 + do j=1,nstate + + fac=1.2 ! DLH 7/14 could be bendy (or else get spurious He+) + if((uttime.lt.10.0.or.uttime.gt.15.0).and.j.eq.2) fac=4.0 + + ipt=ipt+1 + tmp=(bcoef(i-1,j)-2.*bcoef(i,j)+bcoef(i+1,j)) + fvec(ipt)=tmp*regu(j)*fac + pen(j)=pen(j)+fvec(ipt)**2 + end do + end do + +c rescale for clearer diagnostic (just for printing) + + do i=1,nstate + pen(i)=sqrt(pen(i)/float(nspline)) + end do + +c write(*,*) x + +c compute model prediction error to minimize in LS sense +c write(*,*) "before lagp_fcn_lpreg" + call lagp(plag2,wl,r0,dr,nl,nrange) +c write(*,*) "before lagp_fcn_lpreg" +c adjust system constant + write(*,*) "flgas:",iflag,iflaglast + if(iflag.eq.1.and.iflaglast.eq.2) then + sclast=sconst + call get_scale(plag2) + sconst=0.1*sconst+0.9*sclast + end if + iflaglast=iflag + + chi2=0.0 + do j=nl+1,nrange + do i=1,nl + ipt=ipt+1 + fvec(ipt)=(plag(i,j)-plag2(i,j)*sconst)/plag_errors(i,j) + chi2=chi2+fvec(ipt)**2 + end do + end do + chi2=sqrt(chi2/float(nrange*nl)) + +c add penalties for Tr, composition, He+, lower boundary values, etc. +c have to adjust penalties for different conditions (e.g. sunrise, night) + + do i=1,nrange + pen(nstate+1)=pen(nstate+1)+hefp(i)**2 + + if(tep(i).gt.tip(i)) then ! 3/2015 500 -> 1000 ? + if(uttime.ge.10.0.and.uttime.le.15.0) then ! was 10.5, 14->15 + scale=500.0 ! dlh 7/14 was 1500, but this defeated He+, so 500 + else + scale=50.0 + end if + else + scale=10.0 + end if + + pen(nstate+2)=pen(nstate+2)+((tip(i)-tep(i))/scale)**2 + pen(nstate+3)=pen(nstate+3)+exp((hfp(i)+hefp(i)-1.0)/2.0)**2 + + end do + + pen(nstate+4)=(tip(1)-700.0)**2*float(nrange) ! or 800? + pen(nstate+5)=(hfp(nrange)-1.0)**2*float(nrange) + + do i=1,npen + tmp=sqrt(pen(nstate+i))*regu(nstate+i) + ipt=ipt+1 + fvec(ipt)=tmp + pen(nstate+i)=tmp/sqrt(float(nrange)) + end do + +c write(*,*) "chi2:",chi2," sys const:",sconst, +c & " flag:",iflag," penalties:" +c write(*,*)(pen(i),i=1,5) +c write(*,*)(pen(i),i=6,10) +c write(*,*) "ut:",uttime +c write(*,*) fvec(222) + + return + end + + subroutine get_scale(plag2) +c + include 'fpa.h' + real plag2(nl,nrange) +c + a=0. + b=0. +c do j=3*nrange/4,nrange + do j=nl+1,nrange +c write(*,*) j,plag(1,j),plag2(1,j) + a=a+plag(1,j)*plag2(1,j)/plag_errors(1,j)**2 + b=b+plag(1,j)*plag(1,j)/plag_errors(1,j)**2 + end do + + sconst=b/a + + write(*,*)"sconst_inside_get_scape:",sconst,a,b +c stop + + return + end diff --git a/schainf/Ffiles/full_profile_profile.o b/schainf/Ffiles/full_profile_profile.o new file mode 100644 index 0000000000000000000000000000000000000000..b8d20152869eac98632c77daba10906fdd911ff6 GIT binary patch literal 24072 zc%0>24RlmRmVU33@Ehz721QLY@*_bpqTmWBn#Q!ej6s8d21PnCKO{~_V$wmF(J@Z) zc6i&g#vRf4b4JdHBgcbB&J1uk3Qh+jY2B#NStX9L8wE5m>@gxcL_~V)x8Hr$RZSfA zoSofwPN!adb?>cPw{G3K_1=RAd<8eSbY0_@u3f9yHT#O(Zr|s!zvHx2ZJA*mHkyxQ z8P@%MoxYQpwfX*&H@cq*yLX1ou-mLp*0iASq|s(H_vuE;B$uWcp>z{VFhVJ$(Dxca zUtd9J9IoYC-3GlgLK8?~?K492@m(MOFcH8uy+g(hmGe1eZ6!f749#w@$$^p zW<)peVQZ)FkdrGV#iY|B#6ozs4A 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