def sigmaBends2(self, E, s=None, s0=0, n=20):
"""
Returns delta(sigma^2) due to bends (dipoles)
:param float E: energy
:param float s: location of interest along beamline (optional)
:param float s0: start location along beamline (optional)
:param int n: number of intervals for integrations (optional)
"""
if s is None:
s = self.markers[1].S
nELast = len(self.elems) - 1
endPhase = self.markers[1].MUX
ss = self.elems[-1].L
else:
nELast = self.findElem(s)
last = self.elems[nELast]
ss = s - (last.S - last.L)
endPhase = self.getPhase(nELast, ss).MUX
if s0 != 0:
nEFirst = self.findElem(s0)
first = self.elems[nEFirst]
ss0 = s0 - (first.S - first.L)
rangeElems = xrange(nEFirst, len(self.elems))
else:
nEFirst = 0
rangeElems = xrange(len(self.elems))
# Calculates H*G^3 cos(phi)^2 at location s along the beamline
def wrap(nE):
def f(ss):
para = self.getBeta(nE, ss)
disp = self.getDisp(nE, ss)
if disp.DX == 0: return 0
alpha = math.atan(-para.ALFX - para.BETX * disp.DPX / disp.DX)
Phi = (endPhase -
self.getPhase(nE, ss).MUX) * 2 * math.pi + alpha
cosPhi = (math.cos(Phi)**2).real
H = self.getH(nE, ss)
P = abs(e.L / e.ANGLE)
return H.HX * cosPhi / P**3
return f
c2 = 4.13e-11 # m^2(GeV)^-5
coeff = c2 * E**5 * self.markers[1].BETX
total = 0
for i in rangeElems:
e = self.elems[i]
if e.KEYWORD == 'SBEND':
if i == nEFirst:
total += coeff * simpson(wrap(i), ss0, e.L, n)
elif i == nELast:
total += coeff * simpson(wrap(i), 0, ss, n)
else:
total += coeff * simpson(wrap(i), 0, e.L, n)
if i == nELast: return total
def sigmaBends2(self, E, s=None, s0=0, n=20):
"""
Returns delta(sigma^2) due to bends (dipoles)
:param float E: energy
:param float s: location of interest along beamline (optional)
:param float s0: start location along beamline (optional)
:param int n: number of intervals for integrations (optional)
"""
if s is None:
s = self.markers[1].S
nELast = len(self.elems)-1
endPhase = self.markers[1].MUX
ss = self.elems[-1].L
else:
nELast = self.findElem(s)
last = self.elems[nELast]
ss = s - (last.S - last.L)
endPhase = self.getPhase(nELast, ss).MUX
if s0 != 0:
nEFirst = self.findElem(s0)
first = self.elems[nEFirst]
ss0 = s0 - (first.S - first.L)
rangeElems = xrange(nEFirst, len(self.elems))
else:
nEFirst = 0
rangeElems = xrange(len(self.elems))
# Calculates H*G^3 cos(phi)^2 at location s along the beamline
def wrap(nE):
def f(ss):
para = self.getBeta(nE,ss)
disp = self.getDisp(nE,ss)
if disp.DX == 0: return 0
alpha = math.atan(-para.ALFX - para.BETX * disp.DPX / disp.DX)
Phi = (endPhase - self.getPhase(nE,ss).MUX) * 2 * math.pi + alpha
cosPhi = (math.cos(Phi) ** 2).real
H = self.getH(nE, ss)
P = abs(e.L / e.ANGLE)
return H.HX * cosPhi / P**3
return f
c2 = 4.13e-11 # m^2(GeV)^-5
coeff = c2 * E**5 * self.markers[1].BETX
total = 0
for i in rangeElems:
e = self.elems[i]
if e.KEYWORD == 'SBEND':
if i == nEFirst:
total += coeff * simpson(wrap(i), ss0, e.L, n)
elif i == nELast:
total += coeff * simpson(wrap(i), 0, ss, n)
else:
total += coeff * simpson(wrap(i), 0, e.L, n)
if i == nELast: return total
def getChrom(self, s=None, s0=0, n=100):
"""
Calculates chromaticity using -1/4pi * integral (beta*K) ds
:param float s: end location along beamline
:param float s0: start location along beamline (optional)
:param int n: number of intervals for integration (optional)
:returns: chromaticity between s0 and s
"""
if s is None: s = self.markers[1].S
## CHECK: positive/negative signs on K for focus vs. defocus...
## Is this natural chromaticity also because it only considers quadrupoles?
## What about multipole quadrupoles?
def fX(s):
nE = self.findElem(s)
e = self.elems[nE]
ss = s - (e.S - e.L)
bet = self.getBeta(nE, ss)
if e.K1L != 0:
return bet.BETX * -e.K1L / e.L # Correct to make negative?
else:
return 0
def fY(s):
nE = self.findElem(s)
e = self.elems[nE]
ss = s - (e.S - e.L)
bet = self.getBeta(nE, ss)
if e.K1L != 0:
return bet.BETY * e.K1L / e.L
else:
return 0
return dct([('ChromX', -simpson(fX, s0, s, n) / (4 * math.pi)),
('ChromY', -simpson(fY, s0, s, n) / (4 * math.pi))])
def getChrom(self, s=None, s0=0, n=100):
"""
Calculates chromaticity using -1/4pi * integral (beta*K) ds
:param float s: end location along beamline
:param float s0: start location along beamline (optional)
:param int n: number of intervals for integration (optional)
:returns: chromaticity between s0 and s
"""
if s is None: s = self.markers[1].S
## CHECK: positive/negative signs on K for focus vs. defocus...
## Is this natural chromaticity also because it only considers quadrupoles?
## What about multipole quadrupoles?
def fX(s):
nE = self.findElem(s)
e = self.elems[nE]
ss = s - (e.S - e.L)
bet = self.getBeta(nE, ss)
if e.K1L != 0:
return bet.BETX * -e.K1L / e.L # Correct to make negative?
else:
return 0
def fY(s):
nE = self.findElem(s)
e = self.elems[nE]
ss = s - (e.S - e.L)
bet = self.getBeta(nE, ss)
if e.K1L != 0:
return bet.BETY * e.K1L / e.L
else:
return 0
return dct([('ChromX', -simpson(fX, s0, s, n) / (4 * math.pi)),
('ChromY', -simpson(fY, s0, s, n) / (4 * math.pi))])
def sigmaBends(self, E, s=None, s0=0, n=100):
"""
Returns delta(sigma^2) due to bends (dipoles)
:param float E: energy
:param float s: location of interest along beamline (optional)
:param float s0: start location along beamline (optional)
:param int n: number of intervals for integrations (optional)
"""
if s is None:
s = self.markers[1].S
endPhase = self.markers[1].MUX
else:
nE = self.findElem(s)
e = self.elems[nE]
ss = s - (e.S - e.L)
endPhase = self.getPhase(nE, ss)
# Calculates H*G^3 cos(phi)^2 at location s along the beamline
def f(s):
nE = self.findElem(s)
e = self.elems[nE]
# Calculate function only if element is dipole (i.e. ANGLE not 0)
if e.ANGLE != 0:
# ss from beginning of element nE == s from beginning of beamline
ss = s - (e.S - e.L)
para = self.getBeta(nE, ss)
disp = self.getDisp(nE, ss)
alpha = math.atan(-para.ALFX - para.BETX * disp.DPX / disp.DX)
Phi = (endPhase -
self.getPhase(nE, ss).MUX) * 2 * math.pi + alpha
cosPhi = (math.cos(Phi)**2).real
H = self.getH(nE, ss)
P = abs(e.L / e.ANGLE)
return H.HX * cosPhi / P**3
else:
return 0
c2 = 4.13e-11 # m^2(GeV)^-5
coeff = c2 * E**5 * self.markers[1].BETX
return coeff * simpson(f, s0, s, n)
def sigmaBends(self, E, s=None, s0=0, n=100):
"""
Returns delta(sigma^2) due to bends (dipoles)
:param float E: energy
:param float s: location of interest along beamline (optional)
:param float s0: start location along beamline (optional)
:param int n: number of intervals for integrations (optional)
"""
if s is None:
s = self.markers[1].S
endPhase = self.markers[1].MUX
else:
nE = self.findElem(s)
e = self.elems[nE]
ss = s - (e.S - e.L)
endPhase = self.getPhase(nE, ss)
# Calculates H*G^3 cos(phi)^2 at location s along the beamline
def f(s):
nE = self.findElem(s)
e = self.elems[nE]
# Calculate function only if element is dipole (i.e. ANGLE not 0)
if e.ANGLE != 0:
# ss from beginning of element nE == s from beginning of beamline
ss = s - (e.S - e.L)
para = self.getBeta(nE,ss)
disp = self.getDisp(nE,ss)
alpha = math.atan(-para.ALFX - para.BETX * disp.DPX / disp.DX)
Phi = (endPhase - self.getPhase(nE,ss).MUX) * 2 * math.pi + alpha
cosPhi = (math.cos(Phi) ** 2).real
H = self.getH(nE, ss)
P = abs(e.L / e.ANGLE)
return H.HX * cosPhi / P**3
else:
return 0
c2 = 4.13e-11 # m^2(GeV)^-5
coeff = c2 * E**5 * self.markers[1].BETX
return coeff * simpson(f, s0, s, n)
def oide(self, emi=2e-8, gamma=2.9354207436399e-6, betas=None, n=100):
"""
Returns delta(sigma^2) due to Oide Effect
:param float emi: emittance
:param float gamma: Lorentz factor = E/Eo = 1500/0.000511 for CLIC
:param int n: number of intervals for integration (optional)
"""
re = 2.817940325e-15
lame = 3.861592678e-13
if betas is None: betas = self.markers[1].BETY # Reads 6.77249e-5 from FFS
# (betas = 17.92472388e-6 from mathematica nb)
coeff = 110 * re * lame * gamma**5 / (3 * math.sqrt(6 * math.pi))
# Read twiss object in reverse to find first DRIFT and QUADRUPOLE
# to get ls, Lq and Kq
for e in reversed(self.elems):
if e.KEYWORD == 'DRIFT':
ls = e.L
break
for e in reversed(self.elems):
if e.KEYWORD == 'QUADRUPOLE':
# Multiplied by 2 because final quadrupoles split in file
Lq = 2 * e.L
Kq = abs(e.K1L / e.L)
break
c = math.sqrt(Kq) * ls
b = math.sqrt(Kq) * Lq
# Define functions for integration
def f(x):
return math.sin(x) + c * math.cos(x)
def g(y):
return (abs(math.sin(y) + c * math.cos(y))**3) * simpson(f, 0, y, n)**2
integral = simpson(g, 0, b, n)
return coeff * integral * (emi / (betas * gamma))**2.5
def sigmaBends2b(self, E, s=None, s0=0, n=10):
"""
Returns delta(sigma^2) due to bends (dipoles)
:param float E: energy
:param float s: location of interest along beamline (optional)
:param float s0: start location along beamline (optional)
:param int n: number of intervals for integrations (optional)
"""
if s is None:
s = self.markers[1].S
nELast = len(self.elems) - 1
endPhase = self.markers[1].MUX
ss = self.elems[-1].L
else:
nELast = self.findElem(s)
last = self.elems[nELast]
ss = s - (last.S - last.L)
endPhase = self.getPhase(nELast, ss).MUX
if s0 != 0:
nEFirst = self.findElem(s0)
first = self.elems[nEFirst]
ss0 = s0 - (first.S - first.L)
rangeElems = xrange(nEFirst, len(self.elems))
else:
nEFirst = self.findElem(s0)
first = self.elems[nEFirst]
ss0 = s0 - (first.S - first.L)
nEFirst = 0
rangeElems = xrange(len(self.elems))
# Calculates H*G^3 cos(phi)^2 at location s along the beamline
def wrap5(nE, betaxL, dx0, dpx0, dxL, dxpL, E):
def f(ss):
dE = 14.6e-6 * (e.ANGLE / e.L)**2 * ss * E**4
Energie = E - dE
matnE = self.matrixnE(nE, ss)
para = self.getBeta2(nE, ss, matnE)
disp = self.getDisp2(nE, ss, matnE)
etax = disp.DX
etapx = disp.DPX
dphi = (endPhase - self.getPhase(nE, ss).MUX) * 2 * math.pi
dphiT = abs(
self.getPhase(nE, e.L).MUX -
self.getPhase(nE, 0).MUX) * 2 * math.pi
# print dphiT
# fact1 = math.sqrt(betaxL)/math.sqrt(para.BETX) * (etax * math.cos(dphi) + (para.ALFX * etax + para.BETX * etapx)*math.sin(dphi)) - (math.cos(e.ANGLE)*dx0 + e.L/e.ANGLE*math.sin(e.ANGLE)*dpx0)
fact1 = (
math.sqrt(betaxL) / math.sqrt(para.BETX) *
(etax * math.cos(dphi) +
(para.ALFX * etax + para.BETX * etapx) * math.sin(dphi)) -
(dxL)) * (1 - 1 / dphiT)
fact2 = fact1 * fact1
P = abs(e.L / e.ANGLE)
return Energie**5 * fact2 / (P * P * P)
return f
coeff = 4.13e-11 # m^2(GeV)^-5
coeff2 = 2.0 / 3 * 2.8179403267e-15 / ((0.510998928e-3)**3)
# coeff3 = 5*math.sqrt(3)*2.8179403267e-15/(6*197.326963e-18*299792458)
total = 0
total2 = 0
total3 = 0
for i in rangeElems:
e = self.elems[i]
if e.KEYWORD == 'SBEND':
if i == nEFirst:
total += coeff * simpson(
wrap5(i, self.markers[1].BETX, self.markers[0].DX,
self.markers[0].DPX, self.markers[1].DX,
self.markers[1].DPX, E), ss0, e.L, n)
elif i == nELast:
total += coeff * simpson(
wrap5(i, self.markers[1].BETX, self.markers[0].DX,
self.markers[0].DPX, self.markers[1].DX,
self.markers[1].DPX, E), self.mar0, ss, n)
else:
total += coeff * simpson(
wrap5(i, self.markers[1].BETX, self.markers[0].DX,
self.markers[0].DPX, self.markers[1].DX,
self.markers[1].DPX, E), 0, e.L, n)
if i == nELast:
return total
def sigmaBends2a(self, E, s=None, s0=0, n=10):
"""
Returns delta(sigma^2) due to bends (dipoles)
:param float E: energy
:param float s: location of interest along beamline (optional)
:param float s0: start location along beamline (optional)
:param int n: number of intervals for integrations (optional)
"""
if s is None:
s = self.markers[1].S
nELast = len(self.elems) - 1
endPhase = self.markers[1].MUX
ss = self.elems[-1].L
# print "aqui"
else:
nELast = self.findElem(s)
last = self.elems[nELast]
ss = s - (last.S - last.L)
endPhase = self.getPhase(nELast, ss).MUX
if s0 != 0:
nEFirst = self.findElem(s0)
first = self.elems[nEFirst]
ss0 = s0 - (first.S - first.L)
rangeElems = xrange(nEFirst, len(self.elems))
else:
nEFirst = self.findElem(s0)
first = self.elems[nEFirst]
ss0 = s0 - (first.S - first.L)
nEFirst = 0
rangeElems = xrange(len(self.elems))
# Calculates H*G^3 cos(phi)^2 at location s along the beamline
def wrap5(nE, betaxL, dx0, dpx0, dxL, dxpL, E):
def f(ss):
dE = 14.6e-6 * (e.ANGLE / e.L)**2 * ss * E**4
Energie = E - dE
matnE = self.matrixnE(nE, ss)
# print matnE
para = self.getBeta2(nE, ss, matnE)
disp = self.getDisp2(nE, ss, matnE)
etax = disp.DX
# print ss,disp.DX, disp.DPX, dxL, dxpL, para.BETX, betaxL
etapx = disp.DPX
dphi = (endPhase - self.getPhase(nE, ss).MUX) * 2 * math.pi
# fact1 = math.sqrt(betaxL)/math.sqrt(para.BETX) * (etax * math.cos(dphi) + (para.ALFX * etax + para.BETX * etapx)*math.sin(dphi)) - (math.cos(e.ANGLE)*dx0 + e.L/e.ANGLE*math.sin(e.ANGLE)*dpx0)
fact1 = math.sqrt(betaxL) / math.sqrt(
para.BETX) * (etax * math.cos(dphi) +
(para.ALFX * etax + para.BETX * etapx) *
math.sin(dphi)) - (dxL)
fact2 = fact1 * fact1
P = abs(e.L / e.ANGLE)
return Energie**5 * fact2 / (P * P * P)
return f
c2 = 4.13e-11 # m^2(GeV)^-5
coeff = c2
total = 0
for i in rangeElems:
e = self.elems[i]
if e.KEYWORD == 'SBEND' and e.ANGLE != 0:
if i == nEFirst:
# print self.markers[0].DX,self.markers[0].DPX
total += coeff * simpson(
wrap5(i, self.markers[1].BETX, self.markers[0].DX,
self.markers[0].DPX, self.markers[1].DX,
self.markers[1].DPX, E), ss0, e.L, n)
# print "este"
elif i == nELast:
total += coeff * simpson(
wrap5(i, self.markers[1].BETX, self.markers[0].DX,
self.markers[0].DPX, self.markers[1].DX,
self.markers[1].DPX, E), self.mar0, ss, n)
# print "oeste"
else:
total += coeff * simpson(
wrap5(i, self.markers[1].BETX, self.markers[0].DX,
self.markers[0].DPX, self.markers[1].DX,
self.markers[1].DPX, E), 0, e.L, n)
# print "norte"
if i == nELast: return total
def g(y): return (abs(math.sin(y) + c * math.cos(y))**3) * simpson(f, 0, y, n)**2
value = 12 * f(t) * t - 8 * f(t) * t**3
return value
## error of simpson integration as a function of N, step number
def error_simpson(a, b, N):
h = (a - b) / N
threeD_a = threeD_f(a)
threeD_b = threeD_f(b)
return 1 / 90 * h**4 * (f(a) - f(b))
# use simpson integration method to find the integral of e^-x^2 from 0 to x for each x value
step = np.linspace(1, 6000, 501)
In = list(map(lambda n: itg.simpson(f, 0, 3, n),
step)) #find the result of the integral ny taking n steps
error = list(map(lambda n, I: np.abs(error_simpson(0, 3, n)) / I, step,
In)) #compute fractional error
#plot fractional error
plt.plot(step, error, label="Fractional error")
plt.yscale('log') ## plot in log scale
plt.xlabel("Number of bins $N$")
plt.ylabel("log(Fractional error of $J_n(x))$")
plt.title("Fractional error of $E(x)=\int_0^x e^{-t^2} dx$ ")
plt.legend()
plt.savefig('erfError.pdf')
plt.show()
def sigmaBends2b(self, E, s=None, s0=0, n=10):
"""
Returns delta(sigma^2) due to bends (dipoles)
:param float E: energy
:param float s: location of interest along beamline (optional)
:param float s0: start location along beamline (optional)
:param int n: number of intervals for integrations (optional)
"""
if s is None:
s = self.markers[1].S
nELast = len(self.elems)-1
endPhase = self.markers[1].MUX
ss = self.elems[-1].L
else:
nELast = self.findElem(s)
last = self.elems[nELast]
ss = s - (last.S - last.L)
endPhase = self.getPhase(nELast, ss).MUX
if s0 != 0:
nEFirst = self.findElem(s0)
first = self.elems[nEFirst]
ss0 = s0 - (first.S - first.L)
rangeElems = xrange(nEFirst, len(self.elems))
else:
nEFirst = self.findElem(s0)
first = self.elems[nEFirst]
ss0 = s0 - (first.S - first.L)
nEFirst = 0
rangeElems = xrange(len(self.elems))
# Calculates H*G^3 cos(phi)^2 at location s along the beamline
def wrap5(nE,betaxL,dx0,dpx0,dxL,dxpL,E):
def f(ss):
dE = 14.6e-6 * (e.ANGLE/e.L)**2 * ss*E**4
Energie = E - dE
matnE = self.matrixnE(nE,ss)
para = self.getBeta2(nE,ss,matnE)
disp = self.getDisp2(nE,ss, matnE)
etax = disp.DX
etapx = disp.DPX
dphi = (endPhase - self.getPhase(nE,ss).MUX) * 2 * math.pi
dphiT = abs(self.getPhase(nE,e.L).MUX - self.getPhase(nE,0).MUX) * 2 * math.pi
# print dphiT
# fact1 = math.sqrt(betaxL)/math.sqrt(para.BETX) * (etax * math.cos(dphi) + (para.ALFX * etax + para.BETX * etapx)*math.sin(dphi)) - (math.cos(e.ANGLE)*dx0 + e.L/e.ANGLE*math.sin(e.ANGLE)*dpx0)
fact1 = (math.sqrt(betaxL)/math.sqrt(para.BETX) * (etax * math.cos(dphi) + (para.ALFX * etax + para.BETX * etapx)*math.sin(dphi)) - (dxL)) * (1-1/dphiT)
fact2 = fact1 * fact1
P = abs(e.L / e.ANGLE)
return Energie**5*fact2/(P*P*P)
return f
coeff = 4.13e-11 # m^2(GeV)^-5
coeff2 = 2.0/3*2.8179403267e-15/((0.510998928e-3)**3)
# coeff3 = 5*math.sqrt(3)*2.8179403267e-15/(6*197.326963e-18*299792458)
total = 0
total2 =0
total3=0
for i in rangeElems:
e = self.elems[i]
if e.KEYWORD == 'SBEND':
if i == nEFirst:
total += coeff * simpson(wrap5(i,self.markers[1].BETX,self.markers[0].DX, self.markers[0].DPX, self.markers[1].DX, self.markers[1].DPX, E),ss0, e.L, n)
elif i == nELast:
total += coeff * simpson(wrap5(i,self.markers[1].BETX,self.markers[0].DX, self.markers[0].DPX, self.markers[1].DX, self.markers[1].DPX, E), self.mar0, ss, n)
else:
total += coeff * simpson(wrap5(i,self.markers[1].BETX,self.markers[0].DX, self.markers[0].DPX, self.markers[1].DX, self.markers[1].DPX, E), 0, e.L, n)
if i == nELast:
return total
def sigmaBends2a(self, E, s=None, s0=0, n=10):
"""
Returns delta(sigma^2) due to bends (dipoles)
:param float E: energy
:param float s: location of interest along beamline (optional)
:param float s0: start location along beamline (optional)
:param int n: number of intervals for integrations (optional)
"""
if s is None:
s = self.markers[1].S
nELast = len(self.elems)-1
endPhase = self.markers[1].MUX
ss = self.elems[-1].L
# print "aqui"
else:
nELast = self.findElem(s)
last = self.elems[nELast]
ss = s - (last.S - last.L)
endPhase = self.getPhase(nELast, ss).MUX
if s0 != 0:
nEFirst = self.findElem(s0)
first = self.elems[nEFirst]
ss0 = s0 - (first.S - first.L)
rangeElems = xrange(nEFirst, len(self.elems))
else:
nEFirst = self.findElem(s0)
first = self.elems[nEFirst]
ss0 = s0 - (first.S - first.L)
nEFirst = 0
rangeElems = xrange(len(self.elems))
# Calculates H*G^3 cos(phi)^2 at location s along the beamline
def wrap5(nE,betaxL,dx0,dpx0,dxL,dxpL,E):
def f(ss):
dE = 14.6e-6 * (e.ANGLE/e.L)**2 * ss*E**4
Energie = E - dE
matnE = self.matrixnE(nE,ss)
# print matnE
para = self.getBeta2(nE,ss,matnE)
disp = self.getDisp2(nE,ss, matnE)
etax = disp.DX
# print ss,disp.DX, disp.DPX, dxL, dxpL, para.BETX, betaxL
etapx = disp.DPX
dphi = (endPhase - self.getPhase(nE,ss).MUX) * 2 * math.pi
# fact1 = math.sqrt(betaxL)/math.sqrt(para.BETX) * (etax * math.cos(dphi) + (para.ALFX * etax + para.BETX * etapx)*math.sin(dphi)) - (math.cos(e.ANGLE)*dx0 + e.L/e.ANGLE*math.sin(e.ANGLE)*dpx0)
fact1 = math.sqrt(betaxL)/math.sqrt(para.BETX) * (etax * math.cos(dphi) + (para.ALFX * etax + para.BETX * etapx)*math.sin(dphi)) - (dxL)
fact2 = fact1 * fact1
P = abs(e.L / e.ANGLE)
return Energie**5*fact2/(P*P*P)
return f
c2 = 4.13e-11 # m^2(GeV)^-5
coeff = c2
total = 0
for i in rangeElems:
e = self.elems[i]
if e.KEYWORD == 'SBEND' and e.ANGLE!=0:
if i == nEFirst:
# print self.markers[0].DX,self.markers[0].DPX
total += coeff * simpson(wrap5(i,self.markers[1].BETX,self.markers[0].DX, self.markers[0].DPX, self.markers[1].DX, self.markers[1].DPX, E),ss0, e.L, n)
# print "este"
elif i == nELast:
total += coeff * simpson(wrap5(i,self.markers[1].BETX,self.markers[0].DX, self.markers[0].DPX, self.markers[1].DX, self.markers[1].DPX, E), self.mar0, ss, n)
# print "oeste"
else:
total += coeff * simpson(wrap5(i,self.markers[1].BETX,self.markers[0].DX, self.markers[0].DPX, self.markers[1].DX, self.markers[1].DPX, E), 0, e.L, n)
# print "norte"
if i == nELast: return total
def Jm(m, x):
## what is the integrand with m and x
f = f_mx(m, x)
## integrate from 0 to pi, using Simpson's rule with N = 1000
I = itg.simpson(f, 0, np.pi, 1000)
return (1 / np.pi) * I
