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emittanz.py
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emittanz.py
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from madgui.core.app import init_app
from madgui.core.session import Session
import madgui.util.yaml as yaml
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
#from scipy.stats import moyal
modelPath = '/home/cristopher/HIT/hit_models'
def app(): return init_app([], gui=False)
class EmittanzRechner:
def __init__(self, app):
self.session = Session()
self.loadModel()
self.model = self.session.model()
self.globs = self.model.globals
def loadStrengths(self, filename): self.model.load_strengths(filename)
def loadModel(self): self.session.load_model(modelPath, stdout=False)
def getSecMap(self, initElem, endElem):
return self.model.sectormap(initElem, endElem)
def _buildMats(self, secMaps):
Mx = [[m[0][0]**2,
m[0][1]*m[0][0]*2,
m[0][1]**2]
for m in secMaps
]
My = [[m[2][2]**2,
m[2][3]*m[2][2]*2,
m[2][3]**2]
for m in secMaps]
return Mx, My
def computeTwiss(self, sig11, sig12, sig22):
em2 = sig11*sig22 - sig12**2
if em2 < 0.:
return [0.]*3
beta = sig11/np.sqrt(em2)
alpha = -sig12/np.sqrt(em2)
gamma = sig22/np.sqrt(em2)
return [beta, alpha, gamma]
def computeEmit(self, sig11, sig12, sig22):
em2 = sig11*sig22 - sig12**2
if em2 < 0.:
return 0.
return np.sqrt(em2)
def _solveLinEqs(self, M, x):
Mt = np.transpose(M)
M = np.matmul(np.linalg.inv(np.matmul(Mt,M)), Mt)
return np.matmul(M,x)
def threeMonsMethod(self, data):
"""
@param array data: should have the following structure
[[monitor1, [sigx1 , sigy1]],
[monitor2, [sigx2 , sigy2]],
[monitor3, [sigx3 , sigy3]]]
"""
mes = np.array(data)
mes = np.transpose(mes)
mons = mes[0]
beam = mes[1]
secMaps = [self.getSecMap('hht3$start', mi) for mi in mons]
Mx, My = self._buildMats(secMaps)
x, y = [b[0] for b in beam], [b[1] for b in beam]
solx = self._solveLinEqs(Mx,x)
soly = self._solveLinEqs(My,y)
return self.computeEmit(*solx), self.computeEmit(*soly)
def sample(self, mu, sig, N=1000):
return np.random.normal(mu, sig, N)
def gauss(self, x, mu, sig, A):
return A*np.exp(-(x-mu)**2/(2*sig**2))
def moyal(self, x, mu, sig, A):
return A*np.exp(-( (x-mu)/sig + np.exp(-(x-mu)/sig) )/2)
def _showMonteCarl(self, emx, emy):
print('RESULTS:')
print('emx: {} +- {}'.format(*emx))
print('emy: {} +- {}'.format(*emy))
def _plotTwissx(self, twiss):
twiss = np.transpose(twiss)
plt.figure('Beta_x')
beta = twiss[0]
mask = beta < 200.
beta_masked = beta[mask]
b = plt.hist(beta_masked, bins=100)
x = (b[1][:-1] + b[1][1:])/2
mu = np.mean(beta)
sig = np.std(beta)
A = max(b[0])
popt, pcov = curve_fit(self.moyal, x, b[0], p0=[mu, sig, A])
print('Beta:')
print()
print(popt)
print()
x = np.linspace(0, 100, 200)
plt.plot(x, self.moyal(x, *popt))
plt.figure('Alpha_x')
alf = twiss[1]
alf = alf[twiss[0] < 200.]
a = plt.hist(alf, bins=100)
popt = self.fitData(alf, moyalFit=True)
x = -a[1]
plt.plot(-x, self.moyal(x, *popt))
print('Alpha')
print()
print(popt)
plt.show()
def _plotTwissy(self, twiss):
bety_max = 15.
twiss = np.transpose(twiss)
plt.figure('Beta_x')
beta = twiss[0]
mask = beta < bety_max
beta_masked = beta[mask]
b = plt.hist(beta_masked, bins=100)
x = (b[1][:-1] + b[1][1:])/2
mu = np.mean(beta)
sig = np.std(beta)
A = max(b[0])
popt, pcov = curve_fit(self.moyal, x, b[0], p0=[mu, sig, A])
print('Beta_y:')
print()
print(popt)
print()
x = np.linspace(0, bety_max, 200)
plt.plot(x, self.moyal(x, *popt))
plt.figure('Alpha_y')
alfy_max = 1.
alf = twiss[1]
alf = alf[twiss[1] < alfy_max]
a = plt.hist(alf, bins=100)
x = (a[1][:-1] + a[1][1:])/2
mu = np.mean(alf)
sig = np.std(alf)
A = max(a[0])
popt, pcov = curve_fit(self.moyal, x, a[0], p0=[mu, sig, A])
x = np.linspace(-1., 3, 200)
plt.plot(x, self.moyal(x, *popt))
print('Alpha')
print()
print(popt)
plt.show()
def fitData(self, g, moyalFit=False):
h = plt.hist(g, bins=100)
x = (h[1][:-1] + h[1][1:])/2
y = h[0]
if moyalFit:
x *= -1
mu = np.mean(x)
sig = np.std(x)
A = max(y)
p = [mu, sig, A]
popt, pcov = curve_fit(self.moyal, x, y, p0=p)
else:
mu = np.mean(x)
sig = np.std(x)
A = max(y)
p = [mu, sig, A]
popt, pcov = curve_fit(self.gauss, x, y, p0=p)
return popt
def monteCarl(self, data, unc, plot=False):
mes = np.array(data)
mes = np.transpose(mes)
mons = mes[0]
beam = mes[1]
N = 100000
xSample = [self.sample(beam[i][0], unc[i][0], N)
for i in range(len(beam))]
ySample = [self.sample(beam[i][1], unc[i][1], N)
for i in range(len(beam))]
xSample = np.transpose(xSample)
ySample = np.transpose(ySample)
secMaps = [self.getSecMap('hht3$start', mi) for mi in mons]
Mx, My = self._buildMats(secMaps)
solx = [self._solveLinEqs(Mx, x) for x in xSample]
emx = np.array([self.computeEmit(*sx) for sx in solx])
twx = np.array([self.computeTwiss(*sx) for sx in solx])
soly = [self._solveLinEqs(My, y) for y in ySample]
emy = np.array([self.computeEmit(*sy) for sy in soly])
twy = np.array([self.computeTwiss(*sy) for sy in soly])
twx = twx[emx > 0.]
twy = twy[emy > 0.]
emx = emx[emx > 0.]
emy = emy[emy > 0.]
fitx = self.fitData(emx*1e6)
fity = self.fitData(emy*1e6, moyalFit=True)
self._showMonteCarl(fitx[:2], fity[:2])
self._plotTwissx(twx)
self._plotTwissy(twy)
if plot:
plt.cla()
plt.figure(1)
plt.xlabel(r'$\varepsilon_x$ [mm mrad]')
h = plt.hist(emx*1e6, bins=100, alpha=0.6)
x = np.linspace(0., max(h[1]), 200)
plt.plot(x, self.gauss(x, *fitx))
print('Emx')
print(fitx)
plt.figure(2)
plt.xlabel(r'$\varepsilon_y$ [mm mrad]')
h = plt.hist(emy*1e6, bins=100, alpha=0.6)
x = np.linspace(0., max(h[1]), 200)
x *= -1
plt.plot(-x, self.moyal(x, *fity))
print('Emy')
print(fity)
plt.show()
def intensity8():
homy = "/home/cristopher/HIT/emittanzMess/OrbitResponse/"
messStrengths = homy + "strengths.yml"
fitStrengths = homy + "fit_I8.yml"
emRechner = EmittanzRechner(app())
emRechner.loadStrengths(messStrengths)
emRechner.loadStrengths(fitStrengths)
# These are the measurements
mons = ['h1dg1g', 'h1dg2g', 'h2dg2g', 'h3dg3g',
'g3dg3g', 'g3dg5g']
sigx = np.array([2.118e-3, 2.641e-3, 3.97e-3,
7.54e-3, 1.32e-3, 5.8e-3])**2
sigy = np.array([2.42e-3, 3.975e-3, 6.775e-3,
2.25e-3, 3.36e-3, 2.09e-3])**2
dsig = [[0.13e-3, 0.15e-3],
[0.17e-3, 0.24e-3],
[0.16e-3, 0.33e-3],
[0.34e-3, 0.34e-3],
[0.15e-3, 0.87e-3],
[0.25e-3, 0.08e-3],
]
for i in range(6):
dsig[i][0] *= 2*3*np.sqrt(sigx[i])
dsig[i][1] *= 2*3*np.sqrt(sigy[i])
measurements = [
[mons[i], [sigx[i], sigy[i]]] for i in range(6)
]
for i in range(3, 7):
print()
print('Fitting with {} monitors'.format(i))
print()
m = emRechner.threeMonsMethod(measurements[:i])
print('emx = {} mm mrad'.format(round(m[0]*1e6,4)))
print('emy = {} mm mrad'.format(round(m[1]*1e6,4)))
emRechner.monteCarl(measurements[:i], dsig[:i], plot=True)
def intensity9():
homy = "/home/cristopher/HIT/emittanzMess/OrbitResponse/"
messStrengths = homy + "strengths.yml"
fitStrengths = homy + "fit2_I9.yml"
emRechner = EmittanzRechner(app())
emRechner.loadStrengths(messStrengths)
emRechner.loadStrengths(fitStrengths)
mons = ['h1dg1g', 'h1dg2g', 'h2dg2g', 'h3dg3g',
'g3dg3g', 'g3dg5g']
sigx = np.array([2.06e-3, 2.71e-3, 3.88e-3,
7.898e-3, 4.05e-3, 6.396e-3])**2
sigy = np.array([2.688e-3, 4.63e-3, 9.17e-3,
1.869e-3, 6.67e-3, 2.45e-3])**2
dsig = [[0.11e-3, 0.086e-3],
[0.19e-3, 0.18e-3],
[0.14e-3, 0.2e-3],
[0.836e-3, 1.46e-3],
[0.96e-3, 1.45e-3],
[0.49e-3, 0.71e-3],
]
for i in range(6):
dsig[i][0] *= 2*3*np.sqrt(sigx[i])
dsig[i][1] *= 2*3*np.sqrt(sigy[i])
measurements = [
[mons[i], [sigx[i], sigy[i]]] for i in range(6)
]
for i in range(3, 7):
print()
print('Fitting with {} monitors'.format(i))
print()
m = emRechner.threeMonsMethod(measurements[:i])
print('emx = {} mm mrad'.format(round(m[0]*1e6,4)))
print('emy = {} mm mrad'.format(round(m[1]*1e6,4)))
emRechner.monteCarl(measurements[:i], dsig[:i], plot=True)
intensity8()