def test_report_ci(confidence_interval, capsys):
"""Verify that the CI report is printed when using report_ci."""
report_ci(confidence_interval)
captured = capsys.readouterr()
assert len(captured.out) > 250
for par in confidence_interval.keys():
assert par in captured.out
for interval in ['99.73', '95.45', '68.27', '_BEST_']:
assert interval in captured.out
def test_ci():
np.random.seed(1)
p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.33)
p_true.add('shift', value=0.123)
p_true.add('decay', value=0.010)
def residual(pars, x, data=None):
amp = pars['amp']
per = pars['period']
shift = pars['shift']
decay = pars['decay']
if abs(shift) > pi / 2:
shift = shift - np.sign(shift) * pi
model = amp * np.sin(shift + x / per) * np.exp(-x * x * decay * decay)
if data is None:
return model
return model - data
n = 2500
xmin = 0.
xmax = 250.0
noise = np.random.normal(scale=0.7215, size=n)
x = np.linspace(xmin, xmax, n)
data = residual(p_true, x) + noise
fit_params = Parameters()
fit_params.add('amp', value=13.0)
fit_params.add('period', value=4)
fit_params.add('shift', value=0.1)
fit_params.add('decay', value=0.02)
out = minimize(residual, fit_params, args=(x,), kws={'data': data})
fit = residual(fit_params, x)
print( ' N fev = ', out.nfev)
print( out.chisqr, out.redchi, out.nfree)
report_errors(fit_params)
ci, tr = conf_interval(out, sigmas=[0.674], trace=True)
report_ci(ci)
for p in out.params:
diff1 = ci[p][1][1] - ci[p][0][1]
diff2 = ci[p][2][1] - ci[p][1][1]
stderr = out.params[p].stderr
assert(abs(diff1 - stderr) / stderr < 0.05)
assert(abs(diff2 - stderr) / stderr < 0.05)
def confidence_intervals(self, p_names=None, sigmas=(1, 2, 3)):
"""Prints a confidence intervals.
Parameters
----------
p_names : {list, None}, optional
Names of the parameters for which the confidence intervals are calculated. If None (default),
the confidence intervals are calculated for every parameter.
sigmas : {list, tuple}, optional
The sigma-levels to find (default is [1, 2, 3]). See Note below.
Note
----
The values for sigma are taken as the number of standard deviations for a normal distribution
and converted to probabilities. That is, the default sigma=[1, 2, 3] will use probabilities of
0.6827, 0.9545, and 0.9973. If any of the sigma values is less than 1, that will be interpreted
as a probability. That is, a value of 1 and 0.6827 will give the same results, within precision.
"""
ci = conf_interval(self.minimizer, self.result, p_names=p_names, sigmas=sigmas)
report_ci(ci)
fit_params.add('amp', value=13.0)
fit_params.add('period', value=2)
fit_params.add('shift', value=0.0)
fit_params.add('decay', value=0.02)
out = minimize(residual, fit_params, args=(x,), kws={'data':data})
fit = residual(fit_params, x)
print( ' N fev = ', out.nfev)
print( out.chisqr, out.redchi, out.nfree)
report_fit(fit_params)
#ci=calc_ci(out)
ci, tr = conf_interval(out, trace=True)
report_ci(ci)
if HASPYLAB:
names=fit_params.keys()
i=0
gs=pylab.GridSpec(4,4)
sx={}
sy={}
for fixed in names:
j=0
for free in names:
if j in sx and i in sy:
ax=pylab.subplot(gs[i,j],sharex=sx[j],sharey=sy[i])
elif i in sy:
ax=pylab.subplot(gs[i,j],sharey=sy[i])
sx[j]=ax
fit_params.add('decay', value=0.02)
###############################################################################
# Set-up the minimizer and perform the fit using ``leastsq`` algorithm, and
# show the report:
mini = Minimizer(residual, fit_params, fcn_args=(x, ), fcn_kws={'data': data})
out = mini.leastsq()
fit = residual(out.params, x)
report_fit(out)
###############################################################################
# Calculate the confidence intervals for parameters and display the results:
ci, tr = conf_interval(mini, out, trace=True)
report_ci(ci)
names = out.params.keys()
i = 0
gs = plt.GridSpec(4, 4)
sx = {}
sy = {}
for fixed in names:
j = 0
for free in names:
if j in sx and i in sy:
ax = plt.subplot(gs[i, j], sharex=sx[j], sharey=sy[i])
elif i in sy:
ax = plt.subplot(gs[i, j], sharey=sy[i])
sx[j] = ax
elif j in sx:
np.save('2014_04_13_freq.npy',y)
## assume quantum projection noise
yerr = np.arcsin(1/np.sqrt(4*100)/0.35)/(2*np.pi*ramsey_time)
params = lmfit.Parameters()
params.add('A', value = 0, vary = True) ##cos ### -3 cXZ sin 2 chi: 7 +- 23 mHz
params.add('B', value = 0, vary = True) ##sin ### -3 cYZ sin 2 chi: 32 +- 56 mHz
params.add('C', value = 0, vary = True) ##cos2 ### -1.5 (cXX-cYY) sin^2 chi: 15 +- 22 mHz
params.add('D', value = 0, vary = True) ##sin2 ### -3 cXY sin^2 chi: 8 +- 20 mHz
params.add('offset', value = 0.069818)
result = lmfit.minimize(cosine_fit, params, args = (x, y, yerr))
fit_values = y + result.residual
lmfit.report_errors(params)
print "Reduced chi-squared = ", result.redchi
ci = lmfit.conf_interval(result)
lmfit.report_ci(ci)
x_plot = np.linspace(x.min(),x.max()+100000,1000)
figure = pyplot.figure(1)
figure.clf()
pyplot.plot(x,y,'o')
pyplot.plot(x_plot,cosine_model(params,x_plot),linewidth = 3.0)
pyplot.show()
## assume quantum projection noise
yerr = np.arcsin(1 / np.sqrt(4 * 100) / 0.35) / (2 * np.pi * ramsey_time)
params = lmfit.Parameters()
params.add('A', value=0, vary=True) ##cos ### -3 cXZ sin 2 chi: 7 +- 23 mHz
params.add('B', value=0, vary=True) ##sin ### -3 cYZ sin 2 chi: 32 +- 56 mHz
params.add('C', value=0,
vary=True) ##cos2 ### -1.5 (cXX-cYY) sin^2 chi: 15 +- 22 mHz
params.add('D', value=0, vary=True) ##sin2 ### -3 cXY sin^2 chi: 8 +- 20 mHz
params.add('offset', value=0.069818)
result = lmfit.minimize(cosine_fit, params, args=(x, y, yerr))
fit_values = y + result.residual
lmfit.report_errors(params)
print "Reduced chi-squared = ", result.redchi
ci = lmfit.conf_interval(result)
lmfit.report_ci(ci)
x_plot = np.linspace(x.min(), x.max() + 100000, 1000)
figure = pyplot.figure(1)
figure.clf()
pyplot.plot(x, y, 'o')
pyplot.plot(x_plot, cosine_model(params, x_plot), linewidth=3.0)
pyplot.show()
