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mapclass25_6var_tilt.py
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# MAPCLASS is conceived to optimize
# the non-linear aberrations of the
# Final Focus System of CLIC.
#
# Rogelio Tomas,
# February 2006
#
#!/usr/bin/env python2.5
from numpy import *
#from math import *
from string import split
#from LinearAlgebra import *
import sys
#################
def gammln( xx):
#################
g=[0.57236494292474305, 0.0, -0.12078223763524987, -4.4408920985006262e-16, 0.28468287047291829, 0.69314718055994429, 1.2009736023470738, 1.7917594692280547, 2.4537365708424441, 3.1780538303479453, 3.9578139676187165,
4.787491742782044, 5.6625620598571462, 6.5792512120101181, 7.5343642367587762, 8.5251613610654982, 9.5492672573011443, 10.604602902745485, 11.689333420797617, 12.801827480081961, 13.940625219404433, 15.104412573076393,
16.292000476568372, 17.502307845875293, 18.734347511938164, 19.987214495663956, 21.260076156247152, 22.552163853126299, 23.862765841692411, 25.191221182742492, 26.536914491119941, 27.899271383845765, 29.277754515046258,
30.671860106086712, 32.081114895954009, 33.505073450144195, 34.943315776884795, 36.395445208041721, 37.861086508970466, 39.339884187209584]
return g[int(xx/0.5-1)]
#################
def gammln_slow( xx):
#################
cof=[76.18009172947146,-86.50532032941677,24.01409824083091,-1.231739572450155,0.1208650973866179e-2,-0.5395239384953e-5]
y=x=xx
tmp=x+5.5
tmp -= (x+0.5)*log(tmp)
ser=1.000000000190015;
for c in cof:
y=y+1
ser += c/y
return -tmp+log(2.5066282746310005*ser/x)
#########################
class Map_tilt:
#########################
"MAP coefficients from madx-PTC output (fort.18)"
def __init__(self, order=10, theta=0,filename='fort.18'):
ietall=0
self.order=order
xyzd=['x', 'px', 'y', 'py', 'd','s' ]
strord=str(order+1)
for line in open(filename):
if ("etall" in line) :
ietall=ietall+1
exec "self."+xyzd[ietall-1]+"=[]"
exec "self."+xyzd[ietall-1]+"r=1.0*zeros(["+strord+","+strord+","+strord+","+strord+","+strord+","+strord+"])"
sline=split(line)
if (len(sline)==9):
a=[float(sline[1]), int(sline[3]), int(sline[4]), int(sline[5]), int(sline[6]), int(sline[7]), int(sline[8])]
atilt=[cos(theta)*float(sline[1]), int(sline[3]), int(sline[4]), int(sline[5]), int(sline[6]), int(sline[7]), int(sline[8])]
if ((a[1]+a[2]+a[3]+a[4]+a[5]+a[6]) <= self.order ):
if ietall==1:
exec "self."+xyzd[ietall-1]+".append("+str(atilt)+")"
if a[1]+a[2]+a[3]+a[4]+a[5]==0 and a[6]==1:
self.x[-1]=[cos(theta)*float(sline[1])-sin(theta), int(sline[3]), int(sline[4]), int(sline[5]), int(sline[6]), int(sline[7]), int(sline[8])]
else:
exec "self."+xyzd[ietall-1]+".append("+str(a)+")"
exec "self."+xyzd[ietall-1]+"r"+str(a[1:])+" = "+sline[1]
print "Initialized map tilt with # of coefficients in x,px,y,py:", len(self.x),len(self.px), len(self.y), len(self.py), len(self.s)
# print self.x0
# print self.x[:7]
# print self.y0
# print self.x
def comp(self, map2):
if (len(self.x) < len(map2.x)):
print "Self map has fewer elements than map2!!"
print "This gives a wrong result"
chi2=0
for v in self.x:
if v[5]==0: chi2+=(v[0]-map2.xr[v[1],v[2],v[3],v[4],v[5]])**2
for v in self.y:
if v[5]==0: chi2+=(v[0]-map2.yr[v[1],v[2],v[3],v[4],v[5]])**2
for v in self.py:
if v[5]==0: chi2+=(v[0]-map2.pyr[v[1],v[2],v[3],v[4],v[5]])**2
for v in self.px:
if v[5]==0: chi2+=(v[0]-map2.pxr[v[1],v[2],v[3],v[4],v[5]])**2
return chi2
def compc(self, map2):
if (len(self.x) < len(map2.x)):
print "Self map has fewer elements than map2!!"
print "This gives a wrong result"
chi2=0
for v in self.x:
chi2+=(v[0]-map2.xr[v[1],v[2],v[3],v[4],v[5]])**2
for v in self.y:
chi2+=(v[0]-map2.yr[v[1],v[2],v[3],v[4],v[5]])**2
for v in self.py:
chi2+=(v[0]-map2.pyr[v[1],v[2],v[3],v[4],v[5]])**2
for v in self.px:
chi2+=(v[0]-map2.pxr[v[1],v[2],v[3],v[4],v[5]])**2
return chi2
def xf(self, vx,vpx,vy,vpy,vd):
suma=0
for coeff in self.x:
suma += coeff[0]*vx**coeff[1]*vpx**coeff[2]*vy**coeff[3]*vpy**coeff[4]*vd**coeff[5]
return suma
def pxf(self, vx,vpx,vy,vpy,vd):
suma=0
for coeff in self.px:
suma += coeff[0]*vx**coeff[1]*vpx**coeff[2]*vy**coeff[3]*vpy**coeff[4]*vd**coeff[5]
return suma
def yf(self, vx,vpx,vy,vpy,vd):
suma=0
for coeff in self.y:
suma += coeff[0]*vx**coeff[1]*vpx**coeff[2]*vy**coeff[3]*vpy**coeff[4]*vd**coeff[5]
return suma
def pyf(self, vx,vpx,vy,vpy,vd):
suma=0
for coeff in self.py:
suma += coeff[0]*vx**coeff[1]*vpx**coeff[2]*vy**coeff[3]*vpy**coeff[4]*vd**coeff[5]
return suma
def f(self, i):
return [self.xf(i[0],i[1],i[2],i[3],i[4]), self.pxf(i[0],i[1],i[2],i[3],i[4]), self.yf(i[0],i[1],i[2],i[3],i[4]), self.pyf(i[0],i[1],i[2],i[3],i[4]) ]
def offset(self, xory, i):
sx=0
exec 'mapxory=self.'+xory
for coeff1 in mapxory:
jj=coeff1[1]
kk=coeff1[2]
ll=coeff1[3]
mm=coeff1[4]
nn=coeff1[5]
qq=coeff1[6]
if ((jj/2==jj/2.) & (kk/2==kk/2.) & (ll/2==ll/2.) & (mm/2==mm/2.) & (nn/2==nn/2.) & (qq/2==qq/2.)):
sigmaprod=pow(i[0], jj)*pow(i[1], kk)*pow(i[2], ll)*pow(i[3], mm)*pow(i[4]/2., nn)*pow(i[5]/2., qq)
if (sigmaprod >0):
Gammasumln=gammln(0.5+jj/2.)+gammln(0.5+kk/2.)+gammln(0.5+ll/2.)+gammln(0.5+mm/2.)+gammln(0.5+qq/2.)
factor=pow(2, (jj+kk+ll+mm+qq)/2.)/pow(pi, 2.5)/(nn+1)
sx += coeff1[0]*factor*exp(Gammasumln)*sigmaprod
return sx
def offset_z(self, xory, i,z0):
sx=0
exec 'mapxory=self.'+xory
for coeff1 in mapxory:
jj=coeff1[1]
kk=coeff1[2]
ll=coeff1[3]
mm=coeff1[4]
nn=coeff1[5]
qq=coeff1[6]
if ((jj/2==jj/2.) & (kk/2==kk/2.) & (ll/2==ll/2.) & (mm/2==mm/2.) & (nn/2==nn/2.) & (qq/2==qq/2.)):
sigmaprod=pow(i[0], jj)*pow(i[1], kk)*pow(i[2], ll)*pow(i[3], mm)*pow(i[4]/2., nn)
if (sigmaprod >0):
Gammasumln=gammln(0.5+jj/2.)+gammln(0.5+kk/2.)+gammln(0.5+ll/2.)+gammln(0.5+mm/2.)
factor=pow(2, (jj+kk+ll+mm)/2.)/pow(pi, 2.5)/(nn+1)
sx += coeff1[0]*factor*exp(Gammasumln)*sigmaprod*pow(z0,qq)
return sx
def sigma(self, xory, i):
sx2=0
exec 'mapxory=self.'+xory
for coeff1 in mapxory:
for coeff2 in mapxory:
if (coeff1[1:] >= coeff2[1:]):
countfactor=2.0
if (coeff1[1:] == coeff2[1:]):
countfactor=1.0
jj=coeff1[1] + coeff2[1]
kk=coeff1[2] + coeff2[2]
ll=coeff1[3] + coeff2[3]
mm=coeff1[4] + coeff2[4]
nn=coeff1[5] + coeff2[5]
qq=coeff1[6] + coeff2[6]
if ((jj/2==jj/2.) & (kk/2==kk/2.) & (ll/2==ll/2.) & (mm/2==mm/2.) & (nn/2==nn/2.)& (qq/2==qq/2.)):
sigmaprod=pow(i[0], jj)*pow(i[1], kk)*pow(i[2], ll)*pow(i[3], mm)*pow(i[4]/2., nn)*pow(i[5], qq)
if (sigmaprod >0):
Gammasumln=gammln(0.5+jj/2.)+gammln(0.5+kk/2.)+gammln(0.5+ll/2.)+gammln(0.5+mm/2.)+gammln(0.5+qq/2.)
factor= countfactor*pow(2, (jj+kk+ll+mm+qq)/2.)/pow(pi, 2.5)/(nn+1)
sxt = coeff1[0]*coeff2[0]*factor*exp(Gammasumln)*sigmaprod
#print jj,kk,ll,mm,nn,":",coeff1[1],coeff1[2],coeff1[3],coeff1[4],coeff1[5], ":" ,sxt
sx2 += sxt
return sx2
def sigma_z(self, xory, i,z0):
sx2=0
exec 'mapxory=self.'+xory
for coeff1 in mapxory:
for coeff2 in mapxory:
if (coeff1[1:] >= coeff2[1:]):
countfactor=2.0
if (coeff1[1:] == coeff2[1:]):
countfactor=1.0
jj=coeff1[1] + coeff2[1]
kk=coeff1[2] + coeff2[2]
ll=coeff1[3] + coeff2[3]
mm=coeff1[4] + coeff2[4]
nn=coeff1[5] + coeff2[5]
qq=coeff1[6] + coeff2[6]
if ((jj/2==jj/2.) & (kk/2==kk/2.) & (ll/2==ll/2.) & (mm/2==mm/2.) & (nn/2==nn/2.)& (qq/2==qq/2.)):
sigmaprod=pow(i[0], jj)*pow(i[1], kk)*pow(i[2], ll)*pow(i[3], mm)*pow(i[4]/2., nn)
if (sigmaprod >0):
Gammasumln=gammln(0.5+jj/2.)+gammln(0.5+kk/2.)+gammln(0.5+ll/2.)+gammln(0.5+mm/2.)
factor= countfactor*pow(2, (jj+kk+ll+mm)/2.)/pow(pi, 2.5)/(nn+1)
sxt = coeff1[0]*coeff2[0]*factor*exp(Gammasumln)*sigmaprod*pow(z0,qq)
#print jj,kk,ll,mm,nn,":",coeff1[1],coeff1[2],coeff1[3],coeff1[4],coeff1[5], ":" ,sxt
sx2 += sxt
return sx2
def sigma_z_test(self, xory, i,z0):
sx2=0
exec 'mapxory=self.'+xory
for coeff1 in mapxory:
for coeff2 in mapxory:
#if (coeff1[1:] >= coeff2[1:]):
# countfactor=2.0
# if (coeff1[1:] == coeff2[1:]):
countfactor=1.0
jj=coeff1[1] + coeff2[1]
kk=coeff1[2] + coeff2[2]
ll=coeff1[3] + coeff2[3]
mm=coeff1[4] + coeff2[4]
nn=coeff1[5] + coeff2[5]
qq=coeff1[6] + coeff2[6]
if ((jj/2==jj/2.) & (kk/2==kk/2.) & (ll/2==ll/2.) & (mm/2==mm/2.) & (nn/2==nn/2.)):
sigmaprod=pow(i[0], jj)*pow(i[1], kk)*pow(i[2], ll)*pow(i[3], mm)*pow(i[4]/2., nn)
if (sigmaprod >0):
Gammasumln=gammln(0.5+jj/2.)+gammln(0.5+kk/2.)+gammln(0.5+ll/2.)+gammln(0.5+mm/2.)
factor= countfactor*pow(2, (jj+kk+ll+mm)/2.)/pow(pi, 2.5)/(nn+1)
sxt = coeff1[0]*coeff2[0]*factor*exp(Gammasumln)*sigmaprod*pow(z0,qq)
#print jj,kk,ll,mm,nn,":",coeff1[1],coeff1[2],coeff1[3],coeff1[4],coeff1[5], ":" ,sxt
sx2 += sxt
return sx2
def generatelist(self,xory,i):
liste=[]
self.dictmap={}
xyzd=['x', 'px', 'y', 'py', 'd','s']
sx2=0
exec 'mapxory=self.'+xory
exec "self.list"+xory+"=[]"
for coeff1 in mapxory:
for coeff2 in mapxory:
if (coeff1 >= coeff2):
countfactor=2.0
if (coeff1 == coeff2):
countfactor=1.0
jj=coeff1[1] + coeff2[1]
kk=coeff1[2] + coeff2[2]
ll=coeff1[3] + coeff2[3]
mm=coeff1[4] + coeff2[4]
nn=coeff1[5] + coeff2[5]
if ((jj/2==jj/2.) & (kk/2==kk/2.) & (ll/2==ll/2.) & (mm/2==mm/2.) & (nn/2==nn/2.)):
sigmaprod=pow(i[0], jj)*pow(i[1], kk)*pow(i[2], ll)*pow(i[3], mm)*pow(i[4]/2., nn)
if (sigmaprod >0):
Gammasumln=gammln(0.5+jj/2.)+gammln(0.5+kk/2.)+gammln(0.5+ll/2.)+gammln(0.5+mm/2.)
factor=countfactor*pow(2, (jj+kk+ll+mm)/2.)/pow(pi, 2.)/(nn+1)
sxt = coeff1[0]*coeff2[0]*factor*exp(Gammasumln)*sigmaprod
liste.append(xyzd[2]+"_"+str(coeff1[1])+"_"+str(coeff1[2])+"_"+str(coeff1[3])+"_"+str(coeff1[4])+"_"+str(coeff1[5])+'_&_'+str(coeff2[1])+"_"+str(coeff2[2])+"_"+str(coeff2[3])+"_"+str(coeff2[4])+"_"+str(coeff2[5]))
self.dictmap[xyzd[2]+"_"+str(coeff1[1])+"_"+str(coeff1[2])+"_"+str(coeff1[3])+"_"+str(coeff1[4])+"_"+str(coeff1[5])+'_&_'+str(coeff2[1])+"_"+str(coeff2[2])+"_"+str(coeff2[3])+"_"+str(coeff2[4])+"_"+str(coeff2[5])]=sxt
elist=[-abs(sxt),sxt,coeff1[1], coeff1[2],coeff1[3],coeff1[4], coeff1[5],'&', coeff2[1], coeff2[2],coeff2[3],coeff2[4], coeff2[5]]
exec "self.list"+xory+".append(elist)"
# print xyzd[2]+"_"+str(coeff1[1])+"_"+str(coeff1[2])+"_"+str(coeff1[3])+"_"+str(coeff1[4])+"_"+str(coeff1[5])+'_&_'+str(coeff2[1])+"_"+str(coeff2[2])+"_"+str(coeff2[3])+"_"+str(coeff2[4])+"_"+str(coeff2[5]),sxt
exec "self.list"+xory+".sort()"
return liste,self.listy
# return self.dictmap
# return self.listy
############# definition of correlation as in mapclassGaussianDelta25.py is done ####################################
def correlation(self, x1, x2, i):
sx2=0
exec 'mapxory1=self.'+x1
exec 'mapxory2=self.'+x2
for coeff1 in mapxory1:
for coeff2 in mapxory2:
jj=coeff1[1] + coeff2[1]
kk=coeff1[2] + coeff2[2]
ll=coeff1[3] + coeff2[3]
mm=coeff1[4] + coeff2[4]
nn=coeff1[5] + coeff2[5]
if (1==1):
countfactor=1.0
if ((jj/2==jj/2.) & (kk/2==kk/2.) & (ll/2==ll/2.) & (mm/2==mm/2.) & (nn/2==nn/2.)):
sigmaprod=pow(i[0], jj)*pow(i[1], kk)*pow(i[2], ll)*pow(i[3], mm)*pow(i[4]/2., nn)
if (sigmaprod >0):
Gammasumln=gammln(0.5+jj/2.)+gammln(0.5+kk/2.)+gammln(0.5+ll/2.)+gammln(0.5+mm/2.)
factor= countfactor*pow(2, (jj+kk+ll+mm)/2.)/pow(pi, 2.)/(nn+1)
sxt = coeff1[0]*coeff2[0]*factor*exp(Gammasumln)*sigmaprod
#print jj,kk,ll,mm,nn,":",coeff1[1],coeff1[2],coeff1[3],coeff1[4],coeff1[5], ":" ,sxt
sx2 += sxt
return sx2
def correlation3(self, x1, x2, x3, i):
sx2=0
exec 'mapxory1=self.'+x1
exec 'mapxory2=self.'+x2
exec 'mapxory3=self.'+x3
for coeff1 in mapxory1:
for coeff2 in mapxory2:
for coeff3 in mapxory3:
jj=coeff1[1] + coeff2[1]
kk=coeff1[2] + coeff2[2]
ll=coeff1[3] + coeff2[3]
mm=coeff1[4] + coeff2[4]
nn=coeff1[5] + coeff2[5]
countfactor=1.0
if ((jj/2==jj/2.) & (kk/2==kk/2.) & (ll/2==ll/2.) & (mm/2==mm/2.) & (nn/2==nn/2.)):
sigmaprod=pow(i[0], jj)*pow(i[1], kk)*pow(i[2], ll)*pow(i[3], mm)*pow(i[4]/2., nn)
if (sigmaprod >0):
Gammasumln=gammln(0.5+jj/2.)+gammln(0.5+kk/2.)+gammln(0.5+ll/2.)+gammln(0.5+mm/2.)
factor= countfactor*pow(2, (jj+kk+ll+mm)/2.)/pow(pi, 2.)/(nn+1)
sxt = coeff1[0]*coeff2[0]*coeff3[0]*factor*exp(Gammasumln)*sigmaprod
#print jj,kk,ll,mm,nn,":",coeff1[1],coeff1[2],coeff1[3],coeff1[4],coeff1[5], ":" ,sxt
sx2 += sxt
return sx2
############################################
#### some examples of usage #####################
############################################
sigmaFFSstart=[3.9e-6,5.75e-8, 3.76e-7, 1.773e-8,0.01]
#map=Map(4)
#map.generatelist('x',sigmaFFSstart)
#map.generatelist('y',sigmaFFSstart)
#print map.listx[0:9]
#print
#print map.listy[0:20]
#i=[3.9e-6,5.75e-8,3.76e-7,1.773e-8,0]
#print map.offset('x',i), sqrt(map.sigma('x',i)-map.offset('x',i)**2)
#map=Map(1)
#print sqrt(map.sigma('x',sigmaFFSstart)), sqrt(map.sigma('y',sigmaFFSstart))
#map=Map(2)
#print sqrt(map.sigma('x',sigmaFFSstart)), sqrt(map.sigma('y',sigmaFFSstart))
#map=Map(3)
#print sqrt(map.sigma('x',sigmaFFSstart)), sqrt(map.sigma('y',sigmaFFSstart))
#map=Map(4)
#print sqrt(map.sigma('x',sigmaFFSstart)), sqrt(map.sigma('y',sigmaFFSstart))
#map=Map(5)
#print sqrt(map.sigma('x',sigmaFFSstart)), sqrt(map.sigma('y',sigmaFFSstart))
#map=Map(6)
#print sqrt(map.sigma('x',sigmaFFSstart)), sqrt(map.sigma('y',sigmaFFSstart))
#map=Map(7)
#print sqrt(map.sigma('x',sigmaFFSstart)), sqrt(map.sigma('y',sigmaFFSstart))
#map=Map(8)
#print sqrt(map.sigma('x',sigmaFFSstart)), sqrt(map.sigma('y',sigmaFFSstart))