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@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Fitting}
@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Version 1: Factorized Beta Distributions}
@
<<Copyleft notice>>=
!
! Copyright (C) 1999-2020 by
! Wolfgang Kilian <kilian@physik.uni-siegen.de>
! Thorsten Ohl <ohl@physik.uni-wuerzburg.de>
! Juergen Reuter <juergen.reuter@desy.de>
! Christian Speckner <cnspeckn@googlemail.com>
!
! WHIZARD is free software; you can redistribute it and/or modify it
! under the terms of the GNU General Public License as published by
! the Free Software Foundation; either version 2, or (at your option)
! any later version.
!
! WHIZARD is distributed in the hope that it will be useful, but
! WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with this program; if not, write to the Free Software
! Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! This file has been stripped of most comments. For documentation, refer
! to the source 'minuit.nw'
<<[[circe1_fit.f90]]>>=
! circe1_fit.f90 -- fitting for circe
<<Copyleft notice>>
module fit_routines
use kinds
implicit none
private
<<[[circe1_fit.f90: public]]>>
contains
<<[[circe1_fit.f90: subroutines]]>>
end module fit_routines
program fit
use kinds
use fit_routines
implicit none
integer :: i, rcode
<<Declare [[NPARAM]]>>
<<Declare parameters>>
<<Declare arguments>>
<<Initialize parameters for [[circe1_fit.f90]]>>
call mninit (5, 6, 7)
<<Load parameters>>
call mnseti ('CIRCE: fit version 1 ')
argv(1) = 1
call mnexcm (fct, 'SET PRINTOUT ', argv, 1, rcode, 0d0)
argv(1) = 1
call mnexcm (fct, 'CALL FCT ', argv, 1, rcode, 0d0)
call mnexcm (fct, 'MIGRAD ', argv, 0, rcode, 0d0)
call mnexcm (fct, 'MINOS ', argv, 0, rcode, 0d0)
argv(1) = 3
call mnexcm (fct, 'CALL FCT ', argv, 1, rcode, 0d0)
call mnexcm (fct, 'STOP ', argv, 0, rcode, 0d0)
end program fit
@ %def fit
@
<<Declare [[NPARAM]]>>=
integer, parameter :: NPARAM = 6
@ %def NPARAM
@
<<Declare parameters>>=
integer, dimension(NPARAM) :: pnum
character(len=10), dimension(NPARAM) :: pname
real(kind=double), dimension(NPARAM) :: pstart, pstep
@
<<Declare arguments>>=
integer, parameter :: ARGC = 10
real(kind=double), dimension(ARGC) :: argv
@
<<Load parameters>>=
do i = 1, NPARAM
call mnparm (pnum(i), pname(i), pstart(i), pstep (i), 0d0, 0d0, rcode)
if (rcode .ne. 0) then
print *, "fit: MINUIT won''t accept parameter ", pnum(i)
stop
endif
end do
@
<<Initialize parameters for [[circe1_fit.f90]]>>=
data pnum / 1, 2, 3, 4, 5, 6 /
data pname / '1_e', 'x_e', '1-x_e', '1_g', 'x_g', '1-x_g' /
data pstart / -1.00, 20.00, 0.20, -1.00, 0.20, 20.00 /
data pstep / 0.01, 0.01, 0.01, 0.01, 0.01, 0.01 /
@
<<[[circe1_fit.f90: public]]>>=
public :: fct
<<[[circe1_fit.f90: subroutines]]>>=
subroutine fct (nx, df, f, a, mode, g)
integer :: nx, mode
real(kind=double) :: f, g
real(kind=double), dimension(:) :: df, a
<<Local variables for [[fct]] (v1)>>
if (mode .eq. 1) then
<<Read input data (v1)>>
else if (mode .eq. 2) then
<<Calculate $\nabla f$>>
end if
<<Calculate $f$ (v1)>>
end if
if (mode .eq. 3) then
<<Write output (v1)>>
end if
end subroutine fct
@ %def fct
@
<<Read input data (v1)>>=
<<Read data from file>>
<<Fixup errors>>
<<Normalize>>
@
<<Read data from file>>=
call gethst ('ee', NDATA, xee, fee, dfee, see, tee, pwr)
call gethst ('eg', NDATA, xeg, feg, dfeg, seg, teg, pwr)
call gethst ('ge', NDATA, xge, fge, dfge, sge, tge, pwr)
call gethst ('gg', NDATA, xgg, fgg, dfgg, sgg, tgg, pwr)
@
<<Local variables for [[fct]] (v1)>>=
integer, parameter :: NDATA = 20
real(kind=double) :: see, tee, dtee
real(kind=double) :: seg, teg, dteg
real(kind=double) :: sge, tge, dtge
real(kind=double) :: sgg, tgg, dtgg
real(kind=double), dimension(2,0:NDATA+1,0:NDATA+1) :: xee, xeg, &
xge, xgg
real(kind=double), dimension(0:NDATA+1,0:NDATA+1) :: fee, dfee, &
feg, dfeg, fge, dfge, fgg, dfgg
real(kind=double) :: pwr
@
<<[[circe1_fit.f90: public]]>>=
public :: gethst
<<[[circe1_fit.f90: subroutines]]>>=
subroutine gethst (tag, ndata, x, f, df, s, t, pwr)
character(len=2) :: tag
integer :: ndata
real(kind=double) :: s, t, pwr
real(kind=double), dimension(2,0:ndata+1,0:ndata+1) :: x
real(kind=double), dimension(0:ndata+1,0:ndata+1) :: f, df
integer :: i, j
open (10, file = 'lumidiff-'//tag//'.dat')
read (10, *) pwr
s = 0d0
<<Read continuum, summing in [[s]]>>
t = s
<<Read single $\delta$, summing in [[t]]>>
<<Read double $\delta$, summing in [[t]]>>
close (10)
end subroutine gethst
@ %def gethst
@
<<Read continuum, summing in [[s]]>>=
do i = 1, ndata
do j = 1, ndata
read (10, *) x(1,i,j), x(2,i,j), f(i,j), df(i,j)
s = s + f(i,j)
end do
end do
@
<<Read single $\delta$, summing in [[t]]>>=
do i = 1, ndata
read (10, *) x(1,i,0), f(i,0), df(i,0), &
f(i,ndata+1), df(i,ndata+1)
x(1,i,ndata+1) = x(1,i,0)
t = t + f(i,0) + f(i,ndata+1)
end do
@
<<Read single $\delta$, summing in [[t]]>>=
do i = 1, ndata
read (10, *) x(2,0,i), f(0,i), df(0,i), &
f(ndata+1,i), df(ndata+1,i)
x(2,ndata+1,i) = x(2,0,i)
t = t + f(0,i) + f(ndata+1,i)
end do
@
<<Read double $\delta$, summing in [[t]]>>=
read (10, *) f(0,0), df(0,0), f(0,ndata+1), df(0,ndata+1)
t = t + f(0,0) + f(0,ndata+1)
read (10, *) f(ndata+1,0), df(ndata+1,0), &
f(ndata+1,ndata+1), df(ndata+1,ndata+1)
t = t + f(ndata+1,0) + f(ndata+1,ndata+1)
@ \texttt{Guinea-Pig} does not provide the full error. A Monte Carlo
study shows that it is a reasonable approximation to rescale the bin
error by suitable factors. These factors are different for eahc
distribution and the factors for the $\delta$-pieces are bigger than
those for the continuum parts. The follows factors are for the
[[slow]] parameter set.
<<Fixup errors>>=
call fixerr (NDATA, dfee, 20d0, 30d0, 40d0)
call fixerr (NDATA, dfeg, 15d0, 20d0, 0d0)
call fixerr (NDATA, dfge, 15d0, 20d0, 0d0)
call fixerr (NDATA, dfgg, 10d0, 0d0, 0d0)
@
<<[[circe1_fit.f90: public]]>>=
public :: fixerr
<<[[circe1_fit.f90: subroutines]]>>=
subroutine fixerr (ndata, df, c, sd, dd)
integer :: ndata
real(kind=double) :: c, sd, dd
real(kind=double), dimension(0:ndata+1,0:ndata+1) :: df
integer :: i, j
do i = 1, NDATA
do j = 1, NDATA
df(i,j) = c * df(i,j)
end do
end do
do i = 1, NDATA
df(0,i) = sd * df(0,i)
df(i,0) = sd * df(i,0)
df(ndata+1,i) = sd * df(ndata+1,i)
df(i,ndata+1) = sd * df(i,ndata+1)
end do
df(0,0) = dd * df(0,0)
df(ndata+1,0) = dd * df(ndata+1,0)
df(0,ndata+1) = dd * df(0,ndata+1)
df(ndata+1,ndata+1) = dd * df(ndata+1,ndata+1)
end subroutine fixerr
@ %def fixerr
@ The error on the integrated luminosity is obtained from adding the
error in channels in quadrature.
<<Normalize>>=
dtee = sumsqu (NDATA, dfee)
dteg = sumsqu (NDATA, dfeg)
dtge = sumsqu (NDATA, dfge)
dtgg = sumsqu (NDATA, dfgg)
@
<<[[circe1_fit.f90: public]]>>=
public :: sumsqu
<<[[circe1_fit.f90: subroutines]]>>=
function sumsqu (ndata, f)
integer :: ndata
real(kind=double) :: sumsqu
real(kind=double), dimension(0:ndata+1,0:ndata+1) :: f
integer :: i, j
real(kind=double) :: s2
s2 = 0
do i = 0, NDATA+1
do j = 0, NDATA+1
s2 = s2 + f(i,j)*f(i,j)
end do
end do
sumsqu = sqrt (s2)
end function sumsqu
@ %def sumsqu
@
<<Normalize>>=
call scale (NDATA, 1d0/tee, fee)
call scale (NDATA, 1d0/tee, dfee)
call scale (NDATA, 1d0/tee, feg)
call scale (NDATA, 1d0/tee, dfeg)
call scale (NDATA, 1d0/tee, fge)
call scale (NDATA, 1d0/tee, dfge)
call scale (NDATA, 1d0/tee, fgg)
call scale (NDATA, 1d0/tee, dfgg)
@
<<[[circe1_fit.f90: public]]>>=
public :: scale
<<[[circe1_fit.f90: subroutines]]>>=
subroutine scale (ndata, s, f)
integer :: ndata
real(kind=double) :: s
real(kind=double), dimension(0:ndata+1,0:ndata+1) :: f
integer :: i, j
do i = 0, NDATA+1
do j = 0, NDATA+1
f(i,j) = s * f(i,j)
end do
end do
end subroutine scale
@ %def scale
@
<<Calculate $\nabla f$>>=
print *, "ERROR: $\nabla f$ n.a."
stop
@ Log-likelihood won't fly, because we can't normalize the likelihood
function for an unbounded parameter range. Let's use good ole
least-squares instead.
<<Calculate $f$ (v1)>>=
f = 0d0
do i = 1, NDATA
do j = 1, NDATA
if (dfee(i,j) .gt. 0d0) then
f = f + ((phie(xee(1,i,j),a) * phie(xee(2,i,j),a) &
- fee(i,j)) / dfee(i,j))**2
end if
if (dfeg(i,j) .gt. 0d0) then
f = f + ((phie(xeg(1,i,j),a) * phig(xeg(2,i,j),a) &
- feg(i,j)) / dfeg(i,j))**2
end if
if (dfge(i,j) .gt. 0d0) then
f = f + ((phig(xge(1,i,j),a) * phie(xge(2,i,j),a) &
- fge(i,j)) / dfge(i,j))**2
end if
if (dfgg(i,j) .gt. 0d0) then
f = f + ((phig(xgg(1,i,j),a) * phig(xgg(2,i,j),a) &
- fgg(i,j)) / dfgg(i,j))**2
end if
end do
end do
@
<<Local variables for [[fct]] (v1)>>=
integer :: i, j
real(kind=double) :: delta
@
<<Calculate $f$ (v1)>>=
if ((a(2) .le. -1d0) .or. (a(3) .le. -1d0/pwr)) then
print *, "warning: discarding out-of-range a2/3: ", a(2), a(3)
<<Give up on $f$>>
else
delta = 1d0 - exp(a(1)) * beta(a(2)+1d0,a(3)+1d0/pwr) * dble(NDATA) / pwr
if (delta .lt. 0d0) then
print *, "warnimg: delta forced to 0 from ", delta
delta = 0d0
end if
@
<<Give up on $f$>>=
f = 1d100
@
<<Calculate $f$ (v1)>>=
do i = 1, NDATA
if (dfee(ndata+1,i) .gt. 0d0) then
f = f + ((delta*phie(xee(2,ndata+1,i),a) &
- fee(ndata+1,i)) / dfee(ndata+1,i))**2
end if
if (dfeg(ndata+1,i) .gt. 0d0) then
f = f + ((delta*phig(xeg(2,ndata+1,i),a) &
- feg(ndata+1,i)) / dfeg(ndata+1,i))**2
end if
if (dfee(i,ndata+1) .gt. 0d0) then
f = f + ((delta*phie(xee(1,i,ndata+1),a) &
- fee(i,ndata+1)) / dfee(i,ndata+1))**2
end if
if (dfge(i,ndata+1) .gt. 0d0) then
f = f + ((delta*phig(xge(1,i,ndata+1),a) &
- fge(i,ndata+1)) / dfge(i,ndata+1))**2
end if
end do
@
<<Calculate $f$ (v1)>>=
if (dfee(ndata+1,ndata+1) .gt. 0d0) then
f = f + ((delta*delta &
- fee(ndata+1,ndata+1)) / dfee(ndata+1,ndata+1))**2
end if
@
<<[[circe1_fit.f90: public]]>>=
public :: phie
<<[[circe1_fit.f90: subroutines]]>>=
function phie (x, a)
real(kind=double) :: x, phie
real(kind=double), dimension(6) :: a
phie = exp (a(1) + a(2)*log(x) + a(3)*log(1d0-x))
end function phie
@ %def phie
@
<<[[circe1_fit.f90: public]]>>=
public :: phig
<<[[circe1_fit.f90: subroutines]]>>=
function phig (x, a)
real(kind=double) :: x, phig
real(kind=double), dimension(6) :: a
phig = exp (a(4) + a(5)*log(x) + a(6)*log(1d0-x))
end function phig
@ %def phig
@
<<Write output (v1)>>=
a1(1) = exp(a(1)) * dble(NDATA) / pwr
a1(2) = a(2)
a1(3) = a(3) - 1d0 + 1d0/pwr
a1(4) = exp(a(4)) * dble(NDATA) / pwr
a1(5) = a(5) - 1d0 + 1d0/pwr
a1(6) = a(6)
open (10, file = 'Parameters')
write (10, 1000) REV, tee / 1D32
write (10, 1001) REV, &
1d0 - a1(1) * beta(a1(2)+1d0,a1(3)+1d0), &
a1(1), a1(2), a1(3), a1(4), a1(5), a1(6), &
a1(4) * beta(a1(5)+1d0,a1(6)+1d0)
1000 format (' data xa5lum(@ENERGY@,@ACC@,', I2, ') / ', E12.5, ' /')
1001 format (' data (xa5(i,@ENERGY@,@ACC@,', I2 ,'),i=0,7) /', /, &
' $ ', 4(E12.5,', '), /, &
' $ ', 3(E12.5,', '), E12.5, ' /')
close (10)
@
<<Local variables for [[fct]] (v1)>>=
<<Declare [[NPARAM]]>>
real(kind=double), dimension(NPARAM) :: a1
integer, parameter :: REV = 1
@ The average elektron energy in the continuum can be calculated
analytically:
\begin{multline}
\left\langle E_{e^\pm} \right\rangle_{\text{cont}}
= E_{\text{beam}} \left\langle x_{e^\pm} \right\rangle_{\text{cont}}
= E_{\text{beam}} \frac{\int\!dx\,x^{a_2}(1-x)^{a_3}x}{B(a_2,a_3)} \\
= E_{\text{beam}} \frac{B(a_2+1,a_3)}{B(a_2,a_3)}
= E_{\text{beam}} \frac{a_2+1}{a_2+a_3+2}
\end{multline}
<<Write output (v1)>>=
delta = 1d0 - a1(1) * beta(a1(2)+1d0,a1(3)+1d0)
print *, '< x_e > = ', delta + (1d0-delta)*(a1(2)+1d0)/(a1(2)+a1(3)+2d0)
@ similarly:
\begin{equation}
\left\langle E_\gamma \right\rangle
= E_{\text{beam}} \frac{a_5+1}{a_5+a_6+2}
\end{equation}
<<Write output (v1)>>=
print *, '< x_g > = ', (a1(5)+1d0)/(a1(5)+a1(6)+2d0)
@ Count the degrees of freedom in [[ndof]]:
<<Write output (v1)>>=
ndof = 0
do i = 0, ndata+1
do j = 0, ndata+1
if (dfee(i,j) .gt. 0d0) ndof = ndof + 1
if (dfeg(i,j) .gt. 0d0) ndof = ndof + 1
if (dfge(i,j) .gt. 0d0) ndof = ndof + 1
if (dfgg(i,j) .gt. 0d0) ndof = ndof + 1
end do
end do
print *, 'CHI2 = ', f / ndof
@
<<Local variables for [[fct]] (v1)>>=
integer :: ndof
@ The error on the luminosity is just the (possibly rescaled) counting
error:
<<Write output (v1)>>=
open (10, file = 'Errors.tex')
write (10, 1099) tee / 1d32, dtee / 1d32, dtee / 1d32
1099 format ('$', F8.2, '_{-', F4.2, '}^{+', F4.2, '}$')
@ After retrieving the error from \texttt{MINUIT}, we have to take
care of the mapping of the parameters
\begin{equation}
a_{1/4}' = e^{a_{1/4}} B(a_{2/5}+1,a_{3/6}+1) N_{\text{bins}} \eta^{-1}
\Longrightarrow \delta a_{1/4}' = a_{1/4}' \delta a_{1/4}
\end{equation}
ignoring the errors in the integral (i.e.~the Beta function).
<<Write output (v1)>>=
call mnerrs (1, eplus, eminus, epara, corr)
ab = a1(1) * beta(a1(2)+1d0,a1(3)+1d0)
write (10, 1100) ab, abs (ab*eminus), abs (ab*eplus)
1100 format ('$', F8.4, '_{-', F6.4, '}^{+', F6.4, '}$')
@
<<Local variables for [[fct]] (v1)>>=
real(kind=double) :: ab
@ The other mappings are even more trivial:
\begin{align}
a_{2/6}' = a_{2/6} - 1 + \eta^{-1}
& \Longrightarrow \delta a_{2/6}' = \delta a_{2/6} &
a_{3/5}' = a_{3/5} - 1 + \eta^{-1}
& \Longrightarrow \delta a_{3/5}' = \delta a_{3/5}
\end{align}
<<Write output (v1)>>=
do i = 2, 3
call mnerrs (i, eplus, eminus, epara, corr)
write (10, 1100) a1(i), abs (eminus), abs (eplus)
end do
call mnerrs (4, eplus, eminus, epara, corr)
ab = a1(4) * beta(a1(5)+1d0,a1(6)+1d0)
write (10, 1100) ab, abs (ab*eminus), abs (ab*eplus)
do i = 5, 6
call mnerrs (i, eplus, eminus, epara, corr)
write (10, 1100) a1(i), abs (eminus), abs (eplus)
end do
close (10)
@
<<Local variables for [[fct]] (v1)>>=
real(kind=double) :: eplus, eminus, epara, corr
integer :: n
@
<<Write output (v1)>>=
do n = 1, 10
call pslice ('ee','x',n,NDATA,xee,fee,dfee,phie,phie,a)
call pslice ('eg','x',n,NDATA,xeg,feg,dfeg,phie,phig,a)
call pslice ('ge','x',n,NDATA,xge,fge,dfge,phig,phie,a)
call pslice ('gg','x',n,NDATA,xgg,fgg,dfgg,phig,phig,a)
call pslice ('ee','y',n,NDATA,xee,fee,dfee,phie,phie,a)
call pslice ('eg','y',n,NDATA,xeg,feg,dfeg,phie,phig,a)
call pslice ('ge','y',n,NDATA,xge,fge,dfge,phig,phie,a)
call pslice ('gg','y',n,NDATA,xgg,fgg,dfgg,phig,phig,a)
end do
call pslice ('ee','x',21,NDATA,xee,fee,dfee,phie,phie,a)
call pslice ('eg','x',21,NDATA,xeg,feg,dfeg,phie,phig,a)
call pslice ('ee','y',21,NDATA,xee,fee,dfee,phie,phie,a)
call pslice ('ge','y',21,NDATA,xge,fge,dfge,phig,phie,a)
@ UNIX Fortran compiler want backslashes escaped:
\index{System dependecies}
<<Write output (v1)>>=
open (10, file = 'Slices.mp4')
write (10,*) "picture eslice[], gslice[];"
do n = 1, NDATA
write (10,*) 'eslice[', n, '] := ', &
'btex $x_{e^\\pm} = ', xee(1,n,1), '$ etex;'
write (10,*) 'gslice[', n, '] := ', &
'btex $x_\\gamma = ', xgg(1,n,1), '$ etex;'
end do
close (10)
@
<<[[circe1_fit.f90: public]]>>=
public :: pslice
<<[[circe1_fit.f90: subroutines]]>>=
subroutine pslice (pp, xy, n, ndata, x, f, df, phi1, phi2, a)
character(len=2) :: pp
character(len=1) :: xy
integer :: n, ndata
real(kind=double), dimension(2,0:ndata+1,0:ndata+1) :: x
real(kind=double), dimension(0:ndata+1,0:ndata+1) :: f, df
real(kind=double), dimension(6) :: a
real(kind=double) :: z
real(kind=double) :: phi1, phi2, d, delta, pwr
external phi1, phi2
integer :: i
character(len=2) digits
write (digits, '(I2.2)') n
open (10, file = 'lumidiff-'//pp//xy//digits//'.dat')
open (11, file = 'lumidiff-'//pp//xy//digits//'.fit')
open (12, file = 'lumidiff-'//pp//xy//digits//'.chi')
if (n .eq. ndata+1) then
pwr = 5d0
delta = 1d0 - exp(a(1))*beta(a(2)+1d0,a(3)+1d0/pwr) &
* dble(NDATA) / pwr
else
delta = 0
end if
if (xy .eq. 'x') then
do i = 1, ndata
if (df(n,i) .gt. 0d0) then
if (pp(2:2) .eq. 'g') then
z = x(2,n,i)
else
z = 1d0 - x(2,n,i)
endif
if (n .eq. ndata+1) then
d = delta*phi2(x(2,n,i),a)
else
d = phi1(x(1,n,i),a)*phi2(x(2,n,i),a)
endif
write (10,*) z, f(n,i), df(n,i)
write (11,*) z, d
write (12,*) z, (f(n,i) - d) / df(n,i)
endif
end do
else if (xy .eq. 'y') then
do i = 1, ndata
if (df(i,n) .gt. 0d0) then
if (pp(1:1) .eq. 'g') then
z = x(1,i,n)
else
z = 1d0 - x(1,i,n)
endif
if (n .eq. ndata+1) then
d = phi1(x(1,i,n),a)*delta
else
d = phi1(x(1,i,n),a)*phi2(x(2,i,n),a)
endif
write (10,*) z, f(i,n), df(i,n)
write (11,*) z, d
write (12,*) z, (f(i,n) - d) / df(i,n)
endif
end do
endif
close (10)
close (11)
close (12)
end subroutine pslice
@ %def pslice
@
<<[[circe1_fit.f90: subroutines]]>>=
function beta (a, b)
real(kind=double) :: a, b, beta
beta = exp (dlgama(a) + dlgama(b) - dlgama(a+b))
contains
function dlgama (x)
real(kind=double) :: dlgama
real(kind=double), dimension(7) :: p1, q1, p2, q2, p3, q3
real(kind=double), dimension(5) :: c, xl
real(kind=double) :: x, y, zero, one, two, half, ap, aq
integer :: i
data ZERO /0.0D0/, ONE /1.0D0/, TWO /2.0D0/, HALF /0.5D0/
data XL /0.0D0,0.5D0,1.5D0,4.0D0,12.0D0/
data p1 /+3.8428736567460D+0, +5.2706893753010D+1, &
+5.5584045723515D+1, -2.1513513573726D+2, &
-2.4587261722292D+2, -5.7500893603041D+1, &
-2.3359098949513D+0/
data q1 /+1.0000000000000D+0, +3.3733047907071D+1, &
+1.9387784034377D+2, +3.0882954973424D+2, &
+1.5006839064891D+2, +2.0106851344334D+1, &
+4.5717420282503D-1/
data p2 /+4.8740201396839D+0, +2.4884525168574D+2, &
+2.1797366058896D+3, +3.7975124011525D+3, &
-1.9778070769842D+3, -3.6929834005591D+3, &
-5.6017773537804D+2/
data q2 /+1.0000000000000D+0, +9.5099917418209D+1, &
+1.5612045277929D+3, +7.2340087928948D+3, &
+1.0459576594059D+4, +4.1699415153200D+3, &
+2.7678583623804D+2/
data p3 /-6.8806240094594D+3, -4.3069969819571D+5, &
-4.7504594653440D+6, -2.9423445930322D+6, &
+3.6321804931543D+7, -3.3567782814546D+6, &
-2.4804369488286D+7/
data q3 /+1.0000000000000D+0, -1.4216829839651D+3, &
-1.5552890280854D+5, -3.4152517108011D+6, &
-2.0969623255804D+7, -3.4544175093344D+7, &
-9.1605582863713D+6/
data c / 1.1224921356561D-1, 7.9591692961204D-2, &
-1.7087794611020D-3, 9.1893853320467D-1, &
1.3469905627879D+0/
if (x .le. xl(1)) then
print *, 'ERROR: DLGAMA non positive argument: ', X
dlgama = zero
end if
if (x .le. xl(2)) then
y = x + one
ap = p1(1)
aq = q1(1)
do i = 2, 7
ap = p1(i) + y * ap
aq = q1(i) + y * aq
end do
y = - log(x) + x * ap / aq
else if (x .le. xl(3)) then
ap = p1(1)
aq = q1(1)
do i = 2, 7
ap = p1(i) + x * ap
aq = q1(i) + x * aq
end do
y = (x - one) * ap / aq
else if (x .le. xl(4)) then
ap = p2(1)
aq = q2(1)
do i = 2, 7
ap = p2(i) + x * ap
aq = q2(i) + x * aq
end do
y = (x-two) * ap / aq
else if (x .le. xl(5)) then
ap = p3(1)
aq = q3(1)
do i = 2, 7
ap = p3(i) + x * ap
aq = q3(i) + x * aq
end do
y = ap / aq
else
y = one / x**2
y = (x-half) * log(x) - x + c(4) + &
(c(1) + y * (c(2) + y * c(3))) / ((c(5) + y) * x)
end if
dlgama = y
end function dlgama
end function beta
@ %def beta
@
<<[[circe1_fit.sh]]>>=
#! /bin/sh
# mode=${2-slow}
mode=${2-fast}
root=`pwd`
indir=${root}/${3-input}
tmpdir=${root}/tmp
outdir=${root}/output
acc="${1-sband350 sband500 sband800 sband1000 sband1600
tesla350 tesla500 tesla800 tesla1000 tesla1600
tesla350-low tesla500-low tesla800-low tesla1000-low tesla1600-low
xband350 xband500 xband800 xband1000 xband1600}"
@
<<[[circe1_fit.sh]]>>=
xmkdir () {
for d in "$@"; do
mkdir $d 2>/dev/null || true
done
}
rm -fr ${tmpdir}
xmkdir ${outdir} ${tmpdir}
@
<<[[circe1_fit.sh]]>>=
cd ${tmpdir}
cat /dev/null >${outdir}/Params.f90
for a in $acc; do
case "$a" in
*1600*) energy=TEV16;;
*1000*) energy=TEV1;;
*800*) energy=GEV800;;
*500*) energy=GEV500;;
*3[56]0*) energy=GEV350;;
*170*) energy=GEV170;;
*90*) energy=GEV090;;
*) energy=GEV500;;
esac
cp ${indir}/${a}_${mode}/lumidiff-??.dat .
${root}/circe1_fit.bin
rm -fr ${outdir}/${a}_${mode}
mkdir ${outdir}/${a}_${mode}
cp Slices.mp4 ${outdir}
cp Errors.tex lumidiff-??x[0-9][0-9].??? ${outdir}/${a}_${mode}
sed -e "s/@ENERGY@/$energy/g" \
-e "s/@ACC@/`echo $a | tr a-z A-Z | tr -cd A-Z`/g" Parameters \
>>${outdir}/Params.f90
done
cd ${root}
rm -fr ${tmpdir}
@
<<[[circe1_fit.sh]]>>=
cat >${outdir}/Params.tex <<'END'
\begin{table}
\begin{center}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{|c||c|c|c|c|}\hline
& \texttt{SBAND} & \texttt{TESLA} & \texttt{TESLA'} & \texttt{XBAND}
\\\hline\hline
END
@
<<[[circe1_fit.sh]]>>=
line () {
for a in $acc; do
case $a in
*350* | *800* | *1000* | *1600*)
;;
*) echo -n ' & '
sed -n $1p ${outdir}/${a}_${mode}/Errors.tex
;;
esac
done
echo '\\\hline'
}
(echo '$\mathcal{L}/\text{fb}^{-1}\upsilon^{-1}$'; line 1
echo '$\int d_{e^\pm}$'; line 2
echo '$x_{e^\pm}^\alpha$'; line 3
echo '$(1-x_{e^\pm})^\alpha$'; line 4
echo '$\int d_\gamma$'; line 5
echo '$x_\gamma^\alpha$'; line 6
echo '$(1-x_\gamma)^\alpha$'; line 7
) >>${outdir}/Params.tex
@
<<[[circe1_fit.sh]]>>=
cat >>${outdir}/Params.tex <<'END'
\end{tabular}
\end{center}
\caption{\label{tab:param}%
Version 1, revision 1997 04 16 of the beam spectra at 500 GeV.
The rows correspond to the luminosity per effective year, the
integral over the continuum and the powers in the factorized Beta
distributions~(\ref{eq:beta}).}
\end{table}
END
@
<<[[circe1_fit.sh]]>>=
cat >>${outdir}/Params.tex <<'END'
\begin{table}
\begin{center}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{|c||c|c|c|c|}\hline
& \texttt{SBAND} & \texttt{TESLA} & \texttt{TESLA'} & \texttt{XBAND}
\\\hline\hline
END
@
<<[[circe1_fit.sh]]>>=
line () {
for a in $acc; do
case $a in
*1000*)
echo -n ' & '
sed -n $1p ${outdir}/${a}_${mode}/Errors.tex
;;
esac
done
echo '\\\hline'
}
(echo '$\mathcal{L}/\text{fb}^{-1}\upsilon^{-1}$'; line 1
echo '$\int d_{e^\pm}$'; line 2
echo '$x_{e^\pm}^\alpha$'; line 3
echo '$(1-x_{e^\pm})^\alpha$'; line 4
echo '$\int d_\gamma$'; line 5
echo '$x_\gamma^\alpha$'; line 6
echo '$(1-x_\gamma)^\alpha$'; line 7
) >>${outdir}/Params.tex
@
<<[[circe1_fit.sh]]>>=
cat >>${outdir}/Params.tex <<'END'
\end{tabular}
\end{center}
\caption{\label{tab:param/TeV}%
Version 1, revision 1997 04 17 of the beam spectra at 1 TeV.}
\end{table}
END
@
<<[[circe1_fit.sh]]>>=
cat >>${outdir}/Params.tex <<'END'
\begin{table}
\begin{center}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{|c||c|c|c|c|}\hline
& 350 GeV & 500 GeV & 800 GeV & 1600 GeV
\\\hline\hline
END
@
<<[[circe1_fit.sh]]>>=
line () {
for a in $acc; do
case $a in
tesla*-low)
;;
tesla1000)
;;
tesla*)
echo -n ' & '
sed -n $1p ${outdir}/${a}_${mode}/Errors.tex
;;
esac
done
echo '\\\hline'
}
(echo '$\mathcal{L}/\text{fb}^{-1}\upsilon^{-1}$'; line 1
echo '$\int d_{e^\pm}$'; line 2
echo '$x_{e^\pm}^\alpha$'; line 3
echo '$(1-x_{e^\pm})^\alpha$'; line 4
echo '$\int d_\gamma$'; line 5
echo '$x_\gamma^\alpha$'; line 6
echo '$(1-x_\gamma)^\alpha$'; line 7
) >>${outdir}/Params.tex
@
<<[[circe1_fit.sh]]>>=
cat >>${outdir}/Params.tex <<'END'
\end{tabular}
\end{center}
\caption{\label{tab:param/Tesla}%
Version 1, revision 1997 04 17 of the beam spectra for TESLA.}
\end{table}
END
exit 0
@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Experimental}
@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Quasi One Dimensional}
<<[[circe1_minuit1.f90]]>>=
! circe1_minuit1.f90 -- fitting for circe
<<Copyleft notice>>
@ We're utilizing the familiar ``\texttt{MINUIT}''
package~\cite{James/Roos:1989:Minuit}.
<<[[circe1_minuit1.f90]]>>=
<<Minuit1 module>>
<<Minuit1 main program>>
@
<<Minuit1 module>>=
module minuit1
use kinds
implicit none
public :: fct
public :: phi
contains
<<Function to minimize>>
<<Function phi1>>
end module minuit1
@ %def minuit1
@
<<Minuit1 main program>>=
program fit
use kinds
use minuit1
implicit none
call minuit (fct, 0d0)
end program fit
@
<<Minuit2 main program>>=
program fit
use kinds
use minuit2
implicit none
call minuit (fct, 0d0)
end program fit
@
<<Function to minimize>>=
subroutine fct (nx, df, f, a, mode, g)
integer, intent(in) :: nx, mode
real(kind=double) :: f, g
real(kind=double), dimension(:) :: df, a
<<Local variables for [[fct]]>>
if (mode .eq. 1) then
<<Read input data>>
else if (mode .eq. 2) then
<<Calculate $\nabla f$>>
end if
<<Calculate $f$>>
if (mode .eq. 3) then
<<Write output>>
end if
end subroutine fct
@ %def fct
@
<<Read input data>>=
open (10, file = 'minuit.data')
do i = 1, NDATA
do j = 1, NDATA
read (10, *) xi(1,i,j), xi(2,i,j), fi(i,j), dfi(i,j)
fi(i,j) = fi(i,j)/1d30
dfi(i,j) = dfi(i,j)/1d30
end do
end do
close (10)
@
<<Local variables for [[fct]]>>=
integer, parameter :: NDATA = 20
real(kind=double) :: chi, chi2
real(kind=double), dimension(2,NDATA,NDATA) :: xi
real(kind=double), dimension(NDATA,NDATA) :: fi, dfi
integer :: i, j, n
@
<<Calculate $f$>>=
f = 0d0
do i = 1, NDATA
do j = 1, NDATA
if (dfi(i,j).gt.0d0) then
f = f + ((phi(xi(1,i,j),xi(2,i,j),a) &
- fi(i,j)) / dfi(i,j))**2
end if
end do
end do
@
<<Write output>>=
chi2 = 0d0
n = 0
open (10, file = 'minuit.fit')
do i = 1, NDATA
do j = 1, NDATA
if (dfi(i,j).gt.0d0) then
chi = (phi(xi(1,i,j),xi(2,i,j),a)-fi(i,j))/dfi(i,j)
write (10,*) xi(1,i,j), xi(2,i,j), &
1d30 * phi(xi(1,i,j),xi(2,i,j),a), &
1d30 * fi(i,j), &
chi
chi2 = chi2 + chi**2
n = n + 1
else
write (10,*) xi(1,i,j), xi(2,i,j), &
1d30 * phi(xi(1,i,j),xi(2,i,j),a), &
1d30 * fi(i,j)
end if
end do
end do
close (10)
print *, 'CHI2 = ', chi2/n
@
<<Function phi1>>=
function phi (e1, e2, a)
real(kind=double) :: e1, e2
real(kind=double), dimension(17) :: a
real(kind=double) :: phi
real(kind=double) :: y1, y2
y1 = e1 / 250d0
y2 = e2 / 250d0
phi = exp ( &
+ a( 1) * 1d0 &
+ a( 2) * log(y1) &
+ a( 3) * log(1d0-y1) &
+ a( 4) * log(-log(y1)) &
+ a( 5) * log(-log(1d0-y1)) &
+ a( 6) * y1 &
+ a( 7) * log(y1)**2 &
+ a( 8) * log(1d0-y1)**2 &
+ a( 9) * log(-log(y1))**2 &
+ a(10) * log(-log(1d0-y1))**2 &
+ a(11) * y1**2 &
+ a(12) / log(y1) &
+ a(13) / log(1d0-y1) &
+ a(14) / log(-log(y1)) &
+ a(15) / log(-log(1d0-y1)) &
+ a(16) / y1 &
+ a(17) / (1d0-y1) &
+ a( 2) * log(y2) &
+ a( 3) * log(1d0-y2) &
+ a( 4) * log(-log(y2)) &
+ a( 5) * log(-log(1d0-y2)) &
+ a( 6) * y2 &
+ a( 7) * log(y2)**2 &
+ a( 8) * log(1d0-y2)**2 &
+ a( 9) * log(-log(y2))**2 &
+ a(10) * log(-log(1d0-y2))**2 &
+ a(11) * y2**2 &
+ a(12) / log(y2) &
+ a(13) / log(1d0-y2) &
+ a(14) / log(-log(y2)) &
+ a(15) / log(-log(1d0-y2)) &
+ a(16) / y2 &
+ a(17) / (1d0-y2) &
)
end function phi
@ %def phi
@
<<[[circe1_minuit1.sh]]>>=
#! /bin/sh
minuit_bin=`pwd`/circe1_minuit1.bin
<<Process arguments>>
(
<<Define parameters>>
<<Fix parameters>>
<<Fix strategy>>
<<Run Minuit>>
) | eval "$minuit_bin $filter"
<<Maybe plot results>>
exit 0
@
<<Process arguments>>=
tmp="$IFS"
IFS=:
args=":$*:"
IFS="$tmp"
@
<<Process arguments>>=
filter="| \
awk '/STATUS=(CONVERGED|CALL LIMIT|FAILED)/ { p=1; print }; \
/@.* \.00000 *fixed/ { next }; \
/EDM=|CHI2|@/ && p { print }' "
@
<<Process arguments>>=
case "$args" in
*:v:*) filter=;;
esac
@
<<Define parameters>>=
cat <<END
set title
CIRCE
parameters
1 '@ 1 ' 0.00 0.01
2 '@ lx ' 0.20 0.01
3 '@ l(1-x) ' 0.20 0.01
4 '@ llx ' 0.00 0.01
5 '@ ll(1-x) ' 0.00 0.01
6 '@ x ' 0.00 0.01
7 '@ lx^2 ' 0.00 0.01
8 '@ l(1-x)^2 ' 0.00 0.01
9 '@ llx^2 ' 0.00 0.01
10 '@ ll(1-x)^2' 0.00 0.01
11 '@ x^2 ' 0.00 0.01
12 '@ 1/lx ' 0.00 0.01
13 '@ 1/l(1-x) ' 0.00 0.01
14 '@ 1/llx ' 0.00 0.01
15 '@ 1/ll(1-x)' 0.00 0.01
16 '@ 1/x ' 0.00 0.01
17 '@ 1/(1-x) ' 0.00 0.01
END
@
<<Fix parameters>>=
for p in 1 2 3 4 5 6 7 8 9 10 \
11 12 13 14 15 16 17; do
case "$args" in
*:$p=*:*) val=`echo "$args" | sed 's/.*:'"$p"'=\\([0-9.-]*\\):.*/\\1/'`;
echo set parameter $p $val;
echo fix $p;;
*:$p:*) ;;
*) echo fix $p;;
esac
done
@
<<Fix strategy>>=
case "$args" in
*:S0:*) echo set strategy 0;;
*:S1:*) echo set strategy 1;;
*:S2:*) echo set strategy 2;;
esac
@
<<Run Minuit>>=
cat <<END
migrat 10000 0.01
stop
END
@
<<Maybe plot results>>=
case "$args" in
*:p:*) awk '$5 != "" { print $1, $2, $5 }' minuit.fit > chi2
awk '$5 != "" { print $1, $5 }' minuit.fit > chix
awk '$5 != "" { print $2, $5 }' minuit.fit > chiy
gnuplot -geometry -0+0 plot2 >/dev/null 2>&1
esac
@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Quasi Two Dimensional}
<<[[circe1_minuit2.f90]]>>=
! minuit2.f90 -- fitting for circe
<<Copyleft notice>>
@
<<[[circe1_minuit2.f90]]>>=
<<Minuit2 module>>
<<Minuit2 main program>>
@
<<Minuit2 module>>=
module minuit2
use kinds
implicit none
public :: fct
public :: phi
contains
<<Function to minimize>>
<<Function phi2>>
end module minuit2
@ %def minuit2
@
<<Function phi2>>=
function phi (e1, e2, a)
real(kind=double) :: e1, e2
real(kind=double), dimension(33) :: a
real(kind=double) :: phi
real(kind=double) :: y1, y2
y1 = e1 / 250d0
y2 = e2 / 250d0
phi = exp ( &
+ a( 1) * 1d0 &
+ a( 2) * log(y1) &
+ a( 3) * log(1d0-y1) &
+ a( 4) * log(-log(y1)) &
+ a( 5) * log(-log(1d0-y1)) &
+ a( 6) * y1 &
+ a( 7) * log(y1)**2 &
+ a( 8) * log(1d0-y1)**2 &
+ a( 9) * log(-log(y1))**2 &
+ a(10) * log(-log(1d0-y1))**2 &
+ a(11) * y1**2 &
+ a(12) / log(y1) &
+ a(13) / log(1d0-y1) &
+ a(14) / log(-log(y1)) &
+ a(15) / log(-log(1d0-y1)) &
+ a(16) / y1 &
+ a(17) / (1d0-y1) &
+ a(18) * log(y2) &
+ a(19) * log(1d0-y2) &
+ a(20) * log(-log(y2)) &
+ a(21) * log(-log(1d0-y2)) &
+ a(22) * y2 &
+ a(23) * log(y2)**2 &
+ a(24) * log(1d0-y2)**2 &
+ a(25) * log(-log(y2))**2 &
+ a(26) * log(-log(1d0-y2))**2 &
+ a(27) * y2**2 &
+ a(28) / log(y2) &
+ a(29) / log(1d0-y2) &
+ a(30) / log(-log(y2)) &
+ a(31) / log(-log(1d0-y2)) &
+ a(32) / y2 &
+ a(33) / (1d0-y2) &
)
end function phi
@ %def phi
@
<<[[circe1_minuit2.sh]]>>=
#! /bin/sh
minuit_bin=`pwd`/circe1_minuit2.bin
<<Process arguments>>
(
<<Define parameters (2dim)>>
<<Fix parameters (2dim)>>
<<Fix strategy>>
<<Run Minuit>>
) | eval "$minuit_bin $filter"
<<Maybe plot results>>
exit 0
@
<<Define parameters (2dim)>>=
cat <<END
set title
CIRCE
parameters
1 '@ 1 ' 0.00 0.01
2 '@ lx ' 0.20 0.01
3 '@ l(1-x) ' 0.20 0.01
4 '@ llx ' 0.00 0.01
5 '@ ll(1-x) ' 0.00 0.01
6 '@ x ' 0.00 0.01
7 '@ lx^2 ' 0.00 0.01
8 '@ l(1-x)^2 ' 0.00 0.01
9 '@ llx^2 ' 0.00 0.01
10 '@ ll(1-x)^2' 0.00 0.01
11 '@ x^2 ' 0.00 0.01
12 '@ 1/lx ' 0.00 0.01
13 '@ 1/l(1-x) ' 0.00 0.01
14 '@ 1/llx ' 0.00 0.01
15 '@ 1/ll(1-x)' 0.00 0.01
16 '@ 1/x ' 0.00 0.01
17 '@ 1/(1-x) ' 0.00 0.01
18 '@ ly ' 0.20 0.01
19 '@ l(1-y) ' 0.20 0.01
20 '@ lly ' 0.00 0.01
21 '@ ll(1-y) ' 0.00 0.01
22 '@ y ' 0.00 0.01
23 '@ ly^2 ' 0.00 0.01
24 '@ l(1-y)^2 ' 0.00 0.01
25 '@ lly^2 ' 0.00 0.01
26 '@ ll(1-y)^2' 0.00 0.01
27 '@ y^2 ' 0.00 0.01
28 '@ 1/ly ' 0.00 0.01
29 '@ 1/l(1-y) ' 0.00 0.01
30 '@ 1/lly ' 0.00 0.01
31 '@ 1/ll(1-y)' 0.00 0.01
32 '@ 1/y ' 0.00 0.01
33 '@ 1/(1-y) ' 0.00 0.01
END
@
<<Fix parameters (2dim)>>=
for p in 1 2 3 4 5 6 7 8 9 10 \
11 12 13 14 15 16 17 18 19 20 \
21 22 23 24 25 26 27 28 29 30 \
31 32 33; do
case "$args" in
*:$p=*:*) val=`echo "$args" | sed 's/.*:'"$p"'=\\([0-9.-]*\\):.*/\\1/'`;
echo set parameter $p $val;
echo fix $p;;
*:$p:*) ;;
*) echo fix $p;;
esac
done
@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Version 2}
@
% Local Variables:
% mode:noweb
% noweb-doc-mode:latex-mode
% noweb-code-mode:fortran-mode
% indent-tabs-mode:nil
% page-delimiter:"^@ %%%.*\n"
% End:

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