def calc_time_series(self):
data = zeros(self.Nbins, 'f')
data.savespace()
# Place the non-pulsed photons
points = randint(0, self.Nbins, self.backgdphot)
for point in points:
data[point] = data[point] + 1.0
# Place the pulsed photons
pulses = randint(0, self.freq, self.pulsedphot)
if pulsetype == 'Sine':
x = arange(10001, typecode='d') * TWOPI / 10000
coscdf = (x + sin(x)) / TWOPI
uvar = random(self.pulsedphot)
phases = take((x + TWOPI * random()) % TWOPI,
searchsorted(coscdf, uvar)) / TWOPI
# plotxy(coscdf, x)
# closeplot()
# hist = histogram(phases, 100, [0.0, TWOPI])
# plotbinned(hist[:,1], hist[:,0])
# closeplot()
elif pulsetype == 'Gaussian':
phases = normal(0.0, width, self.pulsedphot) % 1.0 + random()
points = ((pulses + phases) / self.freq * self.Nbins).astype('i')
for point in points:
data[point] = data[point] + 1.0
# tmp = average(data)
# print 'Average Data = ', tmp
# print ' sqrt(avg) = ', sqrt(tmp)
# print ' StdDev Data = ', standardDeviation(data)
return data
def calc_time_series(self):
data = zeros(self.Nbins, 'f')
data.savespace()
# Place the non-pulsed photons
points = randint(0, self.Nbins, self.backgdphot)
for point in points:
data[point] = data[point] + 1.0
# Place the pulsed photons
pulses = randint(0, self.freq, self.pulsedphot)
if pulsetype=='Sine':
x = arange(10001, typecode='d') * TWOPI/10000
coscdf = (x + sin(x))/TWOPI
uvar = random(self.pulsedphot)
phases = take((x + TWOPI * random()) % TWOPI,
searchsorted(coscdf, uvar)) / TWOPI
# plotxy(coscdf, x)
# closeplot()
# hist = histogram(phases, 100, [0.0, TWOPI])
# plotbinned(hist[:,1], hist[:,0])
# closeplot()
elif pulsetype=='Gaussian':
phases = normal(0.0, width, self.pulsedphot) % 1.0 + random()
points = ((pulses + phases) / self.freq * self.Nbins).astype('i')
for point in points:
data[point] = data[point] + 1.0
# tmp = average(data)
# print 'Average Data = ', tmp
# print ' sqrt(avg) = ', sqrt(tmp)
# print ' StdDev Data = ', standardDeviation(data)
return data
from __future__ import division from scipy import signal, arange, sin, pi from RandomArray import normal from scipy.signal import buttord, butter, lfilter import Interactive dt = 0.001 t = arange(0.0, 10.0, dt) nse = normal(0, 1.4, t.shape) #s = sin(2*pi*t) + nse s = nse lpcf = 3 lpsf = 5 Nyq = 1 / (2 * dt) Rp = 1 Rs = 500 Wp = lpcf / Nyq Ws = lpsf / Nyq d = 0.5 e = 0.0000000001 [n, Wn] = buttord([d - e, d], [d - e - e, d + e], Rp, Rs) [b, a] = butter(n, Wn) xlp = lfilter(b, a, s) Interactive.show(xlp)
parsTrue = array([2.0, -.76, 0.1])
distance = linspace(0, 4, 1000)
def func(pars):
a, alpha, k = pars
return a * exp(alpha * distance) + k
def errfunc(pars):
return data - func(pars) #return the error
# some pseudo data; add some noise
data = func(parsTrue) + normal(0.0, 0.1, distance.shape)
# the intial guess of the params
guess = 1.0, -.4, 0.0
# now solve for the best fit paramters
best, info, ier, mesg = leastsq(errfunc, guess, full_output=1)
print 'true', parsTrue
print 'best', best
print '|err|_l2 =', P.l2norm(parsTrue - best)
# scipy's splrep uses FITPACK's curfit (B-spline interpolation)
print 'Spline smoothing of the data'
sp = splrep(distance, data)
smooth = splev(distance, sp)
from scipy.interpolate import splrep,splev
import pylab as P
parsTrue = array([2.0, -.76, 0.1])
distance = linspace(0, 4, 1000)
def func(pars):
a, alpha, k = pars
return a*exp(alpha*distance) + k
def errfunc(pars):
return data - func(pars) #return the error
# some pseudo data; add some noise
data = func(parsTrue) + normal(0.0, 0.1, distance.shape)
# the intial guess of the params
guess = 1.0, -.4, 0.0
# now solve for the best fit paramters
best, info, ier, mesg = leastsq(errfunc, guess, full_output=1)
print 'true', parsTrue
print 'best', best
print '|err|_l2 =',P.l2norm(parsTrue-best)
# scipy's splrep uses FITPACK's curfit (B-spline interpolation)
print 'Spline smoothing of the data'
sp = splrep(distance,data)
smooth = splev(distance,sp)
from matplotlib.matlab import *
from RandomArray import normal
from Numeric import sin, exp, multiply, absolute, pi
def f(t):
s1 = sin(2 * pi * t)
e1 = exp(-t)
return absolute(multiply(s1, e1)) + .05
t = arange(0.0, 5.0, 0.1)
s = f(t)
nse = multiply(normal(0.0, 0.3, t.shape), s)
plot(t, s + nse, 'b^')
vlines(t, 0, s, color='k')
xlabel('time (s)')
title('Comparison of model with data')
show()
from matplotlib.matlab import *
from RandomArray import normal
from Numeric import sin, exp, multiply, absolute, pi
def f(t):
s1 = sin(2*pi*t)
e1 = exp(-t)
return absolute(multiply(s1,e1))+.05
t = arange(0.0, 5.0, 0.1)
s = f(t)
nse = multiply(normal(0.0, 0.3, t.shape), s)
plot(t, s+nse, 'b^')
vlines(t, 0, s, color='k')
xlabel('time (s)')
title('Comparison of model with data')
show()
