def gaussian_fit(da, guess=(1, 0, 1), plot=False, title=None):
def gaussian(x, a, x0, sigma):
return a * _np.exp(-0.5 * ((x - x0) / sigma)**2)
#
# def log_gaussian(x, a, x0, sigma):
# return _np.log10(gaussian(x, a, x0, sigma))
#
# if apply_log is True:
# fit_func = log_gaussian
# da = _np.log10(da.copy())
# else:
fit_func = gaussian
x = da.coords[da.dims[0]].values.copy()
y = da.values.copy()
y_max = y.max()
fit_params, _ = _curve_fit(
fit_func, xdata=x, ydata=y / y_max,
p0=guess) #, bounds=([0, -_np.inf, 0], [_np.inf, _np.inf, _np.inf]))
fit_params[0] *= y_max
x_fit = _np.linspace(x.min(), x.max(), 100)
y_fit = _xr.DataArray(gaussian(x_fit, *fit_params),
dims=da.dims,
coords=[x_fit])
if plot is True:
fig, ax = _plt.subplots()
y_fit.plot(ax=ax, label='Fit')
da.plot(ax=ax, label='Raw', linestyle='', marker='x')
ax.set_title(title + '\n' + str(fit_params))
ax.legend()
return fit_params
def rb_decay_rate(dataset,showPlot=False,xlim=None,ylim=None,saveFigPath=None):
"""
Compute the Randomized Benchmarking (RB) decay rate given an data set
containing counts for RB gate strings. Note: currently this function
only works for 1-qubit dataset having SPAM labels 'plus' and 'minus'.
Parameters
----------
dataset : DataSet
The RB data set.
showPlot : bool, optional
Whether to show a plot of the fit to the RB data.
xlim : (xmin,xmax), optional
Specify x-axis limits for plot
ylim : (ymin,ymax), optional
Specify y-axis limits for plot
saveFigPath : string, optional
Pathname to save a plot of the fit to the RB data.
Returns
-------
a,b : float
The best-fit decay curve parameters a and b, as defined in
the rb_decay function.
"""
RBlengths = []
RBsuccesses = []
for key in list(dataset.keys()):
dataLine = dataset[key]
plus = dataLine['plus']
minus = dataLine['minus']
N = plus + minus
RBlengths.append(len(key))
RBsuccesses.append(1 - dataLine['plus']/float(N))
if dataLine['plus']/float(N) > 1:
print(key)
a,b = _curve_fit(rb_decay,RBlengths,RBsuccesses)[0]
if saveFigPath or showPlot:
newplot = _plt.figure()
newplotgca = newplot.gca()
newplotgca.plot(RBlengths,RBsuccesses,'.')
newplotgca.plot(range(max(RBlengths)),
rb_decay(_np.arange(max(RBlengths)),a,b),'+')
newplotgca.set_xlabel('RB sequence length (non-Clifford)')
newplotgca.set_ylabel('Success rate')
newplotgca.set_title('RB success')
if xlim:
_plt.xlim(xlim)
if ylim:
_plt.ylim(ylim)
if saveFigPath:
newplot.savefig(saveFigPath)
return a,b
def __init__(self, f, xdata, ydata, *args, **kwargs):
params, cov = _curve_fit(f, xdata, ydata, *args, **kwargs)
errors = [sp.sqrt(cov[i, i]) for i in range(len(cov))]
if len(sp.where(cov == sp.inf)[0]) > 0:
raise ValueError(
"Fit unsuccessful, provide better initial parameters (p0)")
self.params = params
self.errors = errors
self.xdata = sp.array(xdata)
self.ydata = sp.array(ydata)
self.f = lambda x: f(x, *params)
def _fit_2DGaussian(self, **kwargs):
"""
2D guassian fit function. XP found this code online from
http://stackoverflow.com/questions/21566379/fitting-a-2d-gaussian-function-using-scipy-optimize-curve-fit-valueerror-and-m
Parameters
----------
kwargs
------
rho: float32, the initial guess for amplitude of the gaussian. default(0.3)
x0: int, the initial guess for the column of the peak in pixels. default(300)
y0: int, the initial guess for the row of the peak in pixels. default(250)
w_a: float32, the initial guess for the bigger standard deviation. default(25)
w_b: float32, the initial guess for the smaller standard deviation. default(20)
Background: float32, the initial guess for the offset. default(0.02)
plot: boolean, whether the resultant fit should be plotted. default(False)
"""
rho = kwargs["rho"]
x0 = kwargs["x0"]
y0 = kwargs["y0"]
w_a = kwargs["w_a"]
w_b = kwargs["w_b"]
initial_guess = (rho, x0, y0, w_a, w_b)
# Get the row & column numbers
row_num = len(self.data)
col_num = len(self.data[0])
# Create x and y indices
x = _n.linspace(0, col_num - 1, col_num)
y = _n.linspace(0, row_num - 1, row_num)
x, y = _n.meshgrid(x, y)
# The fitting
popt, pcov = _curve_fit(self._twoD_Gaussian, (x, y), self.data.flatten(), p0=initial_guess)
# Return the fitting parameter results, and convert the position to meters.
self.rho = popt[0]
self.x0 = popt[1]
self.y0 = popt[2]
self.w_a = abs(popt[3])
self.w_b = abs(popt[4])
self.rho_err = _n.sqrt(pcov[0][0])
self.x0_err = _n.sqrt(pcov[1][1])
self.y0_err = _n.sqrt(pcov[2][2])
self.w_a_err = _n.sqrt(pcov[3][3])
self.w_b_err = _n.sqrt(pcov[4][4])
self.w_a_len = 100 * self.pixel_size * self.w_a
self.w_b_len = 100 * self.pixel_size * self.w_b
def compute_diffusion_coefficient(self,
fit_begin=0.1,
fit_end=0.9,
nb_blocks=1,
use_filtered=True):
msd, err = self.msd
block_length = len(msd)
cut_begin = int(block_length * fit_begin)
cut_end = int(block_length * fit_end)
def func(x, m, c):
return m * x + c
popt, pcov = _curve_fit(func,
_np.arange(block_length)[cut_begin:cut_end],
msd[cut_begin:cut_end])
return popt[0] / 6.
def curve_fit(likelihood: Likelihood, x0=None, bounds=None, **kwargs):
"""Use scipy's curve_fit to do LM to find the MAP.
Parameters
----------
likelihood
In this case the likelihood must be a subclass of Chi2.
x0
The initial guess
bounds
A list of tuples of parameters bounds, or False if no bounds are to be set. If
None, use the min/max bounds on each parameter in the likelihood.
"""
def model(x, *p):
return likelihood.reduce_model(params=p)
if x0 is None:
x0 = np.array([apar.fiducial for apar in likelihood.child_active_params])
eps = kwargs.get("options", {}).get("eps", 1e-8)
if bounds is None:
bounds = (
[apar.min + 2 * eps for apar in likelihood.child_active_params],
[apar.max - 2 * eps for apar in likelihood.child_active_params],
)
elif not bounds:
bounds = (-np.inf, np.inf)
res = _curve_fit(
model,
xdata=np.linspace(0, 1, len(likelihood.data)),
ydata=likelihood.data,
p0=x0,
sigma=likelihood.sigma,
bounds=bounds,
**kwargs,
)
return res
def compute_analytic_error_bars(self,
epsilon,
delta,
r_0,
p0=[0.5, 0.5, 0.98]):
"""
Compute error bars on RB fit parameters, including the RB decay rate
using the quasi-analytic methods provided in W&F.
*At present, this method is not fully supported.*
Parameters
----------
epsilon : float
Specifies desired confidence interval half-width for each average
survival probability estimate \hat{F}_m (See W&F Eq. 8).
E.g., epsilon = 0.01 means that the confidence interval width for
\hat{F}_m is 0.02. See `create_K_m_sched` for further details.
delta : float
Specifies desired confidence level for confidence interval
specified by epsilon. delta = 1-0.6827 corresponds to a
confidence level of 1 sigma. (See W&F Eq. 8). The smaller
delta is, the larger each value of K_m will be. See
`create_K_m_sched` for further details.
r_0 : float
Estimate of upper bound of the RB number for the system in
question. The smaller r is, the smaller each value of K_m will be.
However, if the system's actual RB number is larger than r_0, then
the W&F-derived error bars cannot be assumed to be valid. Addition
ally, it is assumed that m_max*r_0 << 1. See `create_K_m_sched`
for further details.
p0 : list, optional
A list of [f,A,B] parameters to seed the RB curve fitting. Usually
the default values are fine.
Returns
-------
None
"""
print("WARNING: ANALYTIC BOOSTRAP ERROR BAR METHOD NOT YET" +
"GUARANTEED TO BE STABLE.")
print("ERROR BARS ONLY FOR ZEROTH ORDER FIT.")
print('Processesing analytic bootstrap, following Wallman and' +
'Flammia.\nThe error bars are reliable if and only if the' +
'schedule for K_m has been chosen appropriately, given:')
print('delta =', delta)
print('epsilon =', epsilon)
print('r_0 =', r_0)
#DEBUG? gstyp_list = ['clifford']
#KENNY: does WF assume clifford-gatestring data?
for gstyp in gstyp_list:
Ns = _np.array(self.dicts[gstyp]['counts'])
sigma_list = _np.sqrt(epsilon**2 + 1. / Ns)
results = _curve_fit(_rbutils.standard_fit_function,
self.dicts[gstyp]['lengths'],
self.dicts[gstyp]['successes'],
p0=p0,
sigma=sigma_list)
self.dicts[gstyp]['WF fit full results'] = results
self.dicts[gstyp]['A_error_WF'] = _np.sqrt(results[1][0, 0])
self.dicts[gstyp]['B_error_WF'] = _np.sqrt(results[1][1, 1])
self.dicts[gstyp]['f_error_WF'] = _np.sqrt(results[1][2, 2])
self.dicts[gstyp]['r_error_WF'] = (self.d-1.)/self.d \
* self.dicts[gstyp]['f_error_WF']
print("Analytic error bars computed. Use print methods to access.")
def custom_least_squares_fit(lengths,
asps,
n,
a=None,
b=None,
seed=None,
rtype='EI'):
"""
Fits RB average success probabilities to the exponential decay a + Bp^m using least-squares fitting.
Parameters
----------
lengths : list
The RB lengths to fit to (the 'm' values in a + Bp^m).
asps : list
The average survival probabilities to fit (the observed P_m values to fit
to P_m = a + Bp^m).
n : int
The number of qubits the data was generated from.
a : float, optional
If not None, a value to fix a to.
b : float, optional
If not None, a value to fix b to.
seed : list, optional
Seeds for variables in the fit, in the order [a,b,p] (with a and/or b dropped if it is set
to a fixed value).
rtype : {'EI','AGI'}, optional
The RB error rate rescaling convention. 'EI' results in RB error rates that are associated
with the entanglement infidelity, which is the error probability with stochastic errors (and
is equal to the diamond distance). 'AGI' results in RB error rates that are associated with
average gate infidelity.
Returns
-------
Dict
The fit results. If item with the key 'success' is False, the fit has failed.
"""
seed_dict = {}
variable = {}
variable['a'] = True
variable['b'] = True
variable['p'] = True
lengths = _np.array(lengths, _np.int64)
asps = _np.array(asps, 'd')
# The fit to do if a fixed value for a is given
if a is not None:
variable['a'] = False
if b is not None:
variable['b'] = False
def curve_to_fit(m, p):
return a + b * p**m
if seed is None:
seed = 0.9
seed_dict['a'] = None
seed_dict['b'] = None
seed_dict['p'] = seed
try:
fitout, junk = _curve_fit(curve_to_fit,
lengths,
asps,
p0=seed,
bounds=([0.], [1.]))
p = fitout
success = True
except:
success = False
else:
def curve_to_fit(m, b, p):
return a + b * p**m
if seed is None:
seed = [1. - a, 0.9]
seed_dict['a'] = None
seed_dict['b'] = 1. - a
seed_dict['p'] = 0.9
try:
fitout, junk = _curve_fit(curve_to_fit,
lengths,
asps,
p0=seed,
bounds=([-_np.inf,
0.], [+_np.inf, 1.]))
b = fitout[0]
p = fitout[1]
success = True
except:
success = False
# The fit to do if a fixed value for a is not given
else:
if b is not None:
variable['b'] = False
def curve_to_fit(m, a, p):
return a + b * p**m
if seed is None:
seed = [1 / 2**n, 0.9]
seed_dict['a'] = 1 / 2**n
seed_dict['b'] = None
seed_dict['p'] = 0.9
try:
fitout, junk = _curve_fit(curve_to_fit,
lengths,
asps,
p0=seed,
bounds=([0., 0.], [1., 1.]))
a = fitout[0]
p = fitout[1]
success = True
except:
success = False
else:
def curve_to_fit(m, a, b, p):
return a + b * p**m
if seed is None:
seed = [1 / 2**n, 1 - 1 / 2**n, 0.9]
seed_dict['a'] = 1 / 2**n
seed_dict['b'] = 1 - 1 / 2**n
seed_dict['p'] = 0.9
try:
fitout, junk = _curve_fit(curve_to_fit,
lengths,
asps,
p0=seed,
bounds=([0., -_np.inf,
0.], [1., +_np.inf, 1.]))
a = fitout[0]
b = fitout[1]
p = fitout[2]
success = True
except:
success = False
estimates = {}
if success:
estimates['a'] = a
estimates['b'] = b
estimates['p'] = p
estimates['r'] = _rbt.p_to_r(p, 2**n, rtype)
results = {}
results['estimates'] = estimates
results['variable'] = variable
results['seed'] = seed_dict
# Todo : fix this.
results['success'] = success
return results
def custom_least_squares_data_fitting(lengths, ASPs, n, A=None, B=None, seed=None, rtype='EI'):
"""
Fits RB average success probabilities to the exponential decay A + Bp^m using least-squares fitting.
Parameters
----------
lengths : list
The RB lengths to fit to (the 'm' values in A + Bp^m).
ASPs : list
The average survival probabilities to fit (the observed P_m values to fit
to P_m = A + Bp^m).
n : int
The number of qubits the data is on..
A : float, optional
If not None, a value to fix A to.
B : float, optional
If not None, a value to fix B to.
seed : list, optional
Seeds for variables in the fit, in the order [A,B,p] (with A and/or B dropped if it is set
to a fixed value).
rtype : {'EI','AGI'}, optional
The RB error rate rescaling convention. 'EI' results in RB error rates that are associated
with the entanglement infidelity, which is the error probability with stochastic errors (and
is equal to the diamond distance). 'AGI' results in RB error rates that are associated with
average gate infidelity.
Returns
-------
Dict
The fit results. If item with the key 'success' is False, the fit has failed.
"""
seed_dict = {}
variable = {}
variable['A'] = True
variable['B'] = True
variable['p'] = True
lengths = _np.array(lengths, int)
ASPs = _np.array(ASPs, 'd')
# The fit to do if a fixed value for A is given
if A is not None:
variable['A'] = False
if B is not None:
variable['B'] = False
def curve_to_fit(m, p):
return A + B * p**m
if seed is None:
seed = 0.9
seed_dict['A'] = None
seed_dict['B'] = None
seed_dict['p'] = seed
try:
fitout, junk = _curve_fit(curve_to_fit, lengths, ASPs, p0=seed, bounds=([0.], [1.]))
p = fitout
success = True
except:
success = False
else:
def curve_to_fit(m, B, p):
return A + B * p**m
if seed is None:
seed = [1. - A, 0.9]
seed_dict['A'] = None
seed_dict['B'] = 1. - A
seed_dict['p'] = 0.9
try:
fitout, junk = _curve_fit(curve_to_fit, lengths, ASPs, p0=seed, bounds=([-_np.inf, 0.], [+_np.inf, 1.]))
B = fitout[0]
p = fitout[1]
success = True
except:
success = False
# The fit to do if a fixed value for A is not given
else:
if B is not None:
variable['B'] = False
def curve_to_fit(m, A, p):
return A + B * p**m
if seed is None:
seed = [1 / 2**n, 0.9]
seed_dict['A'] = 1 / 2**n
seed_dict['B'] = None
seed_dict['p'] = 0.9
try:
fitout, junk = _curve_fit(curve_to_fit, lengths, ASPs, p0=seed, bounds=([0., 0.], [1., 1.]))
A = fitout[0]
p = fitout[1]
success = True
except:
success = False
else:
def curve_to_fit(m, A, B, p):
return A + B * p**m
if seed is None:
seed = [1 / 2**n, 1 - 1 / 2**n, 0.9]
seed_dict['A'] = 1 / 2**n
seed_dict['B'] = 1 - 1 / 2**n
seed_dict['p'] = 0.9
try:
fitout, junk = _curve_fit(curve_to_fit, lengths, ASPs, p0=seed,
bounds=([0., -_np.inf, 0.], [1., +_np.inf, 1.]))
A = fitout[0]
B = fitout[1]
p = fitout[2]
success = True
except:
success = False
estimates = {}
if success:
estimates['A'] = A
estimates['B'] = B
estimates['p'] = p
estimates['r'] = _rbt.p_to_r(p, 2**n)
results = {}
results['estimates'] = estimates
results['variable'] = variable
results['seed'] = seed_dict
# Todo : fix this.
results['success'] = success
return results
def fofRH_from_dry_wet_scattering(scatt_dry, scatt_wet,RH_dry, RH_wet, data_period = 60, return_fits = False, verbose = False):
"""
This function was originally written for ARM's AOS dry wet nephelometer proceedure. Programming will likely be needed to make it work for something else.
Notes
-----
For each RH scan in the wet nephelometer an experimental f_RH curve is created by deviding
scatt_wet by scatt_dry. This curve is then fit by a gamma as well as a kappa parametrizaton.
Here the dry nephelometer is NOT considered as RH = 0 but its actuall RH (averaged over the
time of the scann) is considered. I was hoping that this will eliminated a correlation between
"the ratio" and the dry nephelometer's RH ... it didn't :-(
Parameters
----------
scatt_dry: TimeSeries
scatt_wet: TimeSeries
RH_dry: TimeSeries
RH_wet: TimeSeries
data_period: int,float
measurement frequency. Might only be needed if return_fits = True ... double check
return_fits: bool
If the not just the fit results but also the corresponding curves are going to be returned
Returns
-------
pandas.DataFrame containing the fit results
pandas.DataFrame containing the fit curves (only if retun_fits == True)
"""
# some modification to the kappa function so it can be used in the fit routine later
f_RH_kappa_RH0 = lambda RH0: (lambda RH, k: f_RH_kappa(RH, k, RH0))
f_RH_gamma_RH0 = lambda RH0: (lambda RH, g: f_RH_gamma(RH, g, RH0))
# crate the f(RH)/f(RH0)
# scatt_dry = _timeseries._timeseries(_pd.DataFrame(scatt_dry))
# scatt_dry._data_period = data_period
# scatt_wet = _timeseries._timeseries(_pd.DataFrame(scatt_wet))
# scatt_wet._data_period = data_period
f_RH = scatt_wet / scatt_dry
f_RH.data.columns = ['f_RH']
# f_RH = _timeseries._timeseries(_pd.DataFrame(f_RH, columns=['f_RH']))
# f_RH._data_period = data_period
# get start time for next RH-ramp (it always start a few minutes after the full hour)
start, end = f_RH.get_timespan()
start_first_section = _np.datetime64('{:d}-{:02d}-{:02d} {:02d}:00:00'.format(start.year, start.month, start.day, start.hour))
if (start.minute + start.second + start.microsecond) > 0:
start_first_section += _np.timedelta64(1, 'h')
# select one hour starting with time defined above. Also align/merge dry and wet RH to it
i = -1
fit_res_list = []
results = _pd.DataFrame(columns=['kappa',
'kappa_std',
'f_RH_85_kappa',
'f_RH_85_kappa_std',
# 'f_RH_85_kappa_errp',
# 'f_RH_85_kappa_errm',
'gamma',
'gamma_std',
'f_RH_85_gamma',
'f_RH_85_gamma_std',
'wet_neph_max',
'dry_neph_mean',
'dry_neph_std',
'wet_neph_min'], dtype = _np.float64)
while i < 30:
i += 1
# stop if section end is later than end of file
section_start = start_first_section + _np.timedelta64(i, 'h')
section_end = start_first_section + _np.timedelta64(i, 'h') + _np.timedelta64(45, 'm')
if (end - section_end) < _np.timedelta64(0, 's'):
break
if verbose:
print('================')
print('start of section: ', section_start)
print('end of section: ', section_end)
try:
section = f_RH.zoom_time(section_start, section_end)
except IndexError:
if verbose:
print('section has no data in it!')
results.loc[section_start] = _np.nan
continue
df = section.data.copy().dropna()
if df.shape[0] < 2:
if verbose:
print('no data in section.dropna()!')
results.loc[section_start] = _np.nan
continue
# section = section.merge(out.RH_nephelometer._del_all_columns_but('RH_NephVol_Wet'))
# section = section.merge(out.RH_nephelometer._del_all_columns_but('RH_NephVol_Dry')).data
section = section.merge(RH_wet)
section = section.merge(RH_dry).data
# this is needed to get the best parameterization
dry_neph_mean = section.RH_NephVol_Dry.mean()
dry_neph_std = section.RH_NephVol_Dry.std()
wet_neph_min = section.RH_NephVol_Wet.min()
wet_neph_max = section.RH_NephVol_Wet.max()
# clean up
section.dropna(inplace=True)
section = section[section.f_RH != _np.inf]
section = section[section.f_RH != -_np.inf]
timestamps = section.index.copy()
section.index = section.RH_NephVol_Wet
section.drop('RH_NephVol_Wet', axis=1, inplace=True)
section.drop('RH_NephVol_Dry', axis=1, inplace=True)
# fitting!!
if dry_neph_mean > wet_neph_max:
if verbose:
print('dry_neph_mean > wet_neph_max!!! something wrong with dry neph!!')
results.loc[section_start] = _np.nan
continue
try:
kappa, [k_varience] = _curve_fit(f_RH_kappa_RH0(dry_neph_mean), section.index.values, section.f_RH.values)
# gamma, [varience] = curve_fit(gamma_paramterization, section.index.values, section.f_RH.values)
gamma, [varience] = _curve_fit(f_RH_gamma_RH0(dry_neph_mean), section.index.values, section.f_RH.values)
except:
import pdb
pdb.set_trace()
frame_this = {'kappa': kappa[0],
'kappa_std': _np.sqrt(k_varience[0]),
'f_RH_85_kappa': f_RH_kappa(85, kappa[0]),
'f_RH_85_kappa_std': - f_RH_kappa(85, kappa[0]) + f_RH_kappa(85, kappa[0] + _np.sqrt(k_varience[0])),
# 'f_RH_85_kappa_errp': f_RH_kappa(85, kappa[0] + _np.sqrt(k_varience[0])),
# 'f_RH_85_kappa_errm': f_RH_kappa(85, kappa[0] - _np.sqrt(k_varience[0])),
'gamma': gamma[0],
'gamma_std': _np.sqrt(varience[0]),
'f_RH_85_gamma': f_RH_gamma(85, gamma[0]),
'f_RH_85_gamma_std': - f_RH_gamma(85, gamma[0]) + f_RH_gamma(85, gamma[0] + _np.sqrt(varience[0])),
'dry_neph_mean': dry_neph_mean,
'dry_neph_std': dry_neph_std,
'wet_neph_min': wet_neph_min,
'wet_neph_max': wet_neph_max}
results.loc[section_start] = frame_this
if return_fits:
# plotting preparation
RH = section.index.values
# RH = _np.linspace(0,100,20)
fit = f_RH_gamma_RH0(dry_neph_mean)(RH, gamma)
fit_std_p = f_RH_gamma_RH0(dry_neph_mean)(RH, gamma + _np.sqrt(varience))
fit_std_m = f_RH_gamma_RH0(dry_neph_mean)(RH, gamma - _np.sqrt(varience))
fit_k = f_RH_kappa_RH0(dry_neph_mean)(RH, kappa)
fit_k_std_p = f_RH_kappa_RH0(dry_neph_mean)(RH, kappa + _np.sqrt(k_varience))
fit_k_std_m = f_RH_kappa_RH0(dry_neph_mean)(RH, kappa - _np.sqrt(k_varience))
df['fit_gamma'] = _pd.Series(fit, index=df.index)
df['fit_gamma_stdp'] = _pd.Series(fit_std_p, index=df.index)
df['fit_gamma_stdm'] = _pd.Series(fit_std_m, index=df.index)
df['fit_kappa'] = _pd.Series(fit_k, index=df.index)
df['fit_kappa_stdp'] = _pd.Series(fit_k_std_p, index=df.index)
df['fit_kappa_stdm'] = _pd.Series(fit_k_std_m, index=df.index)
fit_res_list.append(df)
if results.shape[0] == 0:
results.loc[start] = _np.nan
results = _timeseries.TimeSeries(results)
results._data_period = 3600
if return_fits:
fit_res = _pd.concat(fit_res_list).sort_index()
ts = _timeseries.TimeSeries(fit_res)
ts._data_period = data_period
fit_res = ts.close_gaps()
return results, fit_res
else:
return results
def rb_decay_rate(dataset,
showPlot=False,
xlim=None,
ylim=None,
saveFigPath=None):
"""
Compute the Randomized Benchmarking (RB) decay rate given an data set
containing counts for RB gate strings. Note: currently this function
only works for 1-qubit dataset having SPAM labels 'plus' and 'minus'.
Parameters
----------
dataset : DataSet
The RB data set.
showPlot : bool, optional
Whether to show a plot of the fit to the RB data.
xlim : (xmin,xmax), optional
Specify x-axis limits for plot
ylim : (ymin,ymax), optional
Specify y-axis limits for plot
saveFigPath : string, optional
Pathname to save a plot of the fit to the RB data.
Returns
-------
a,b : float
The best-fit decay curve parameters a and b, as defined in
the rb_decay function.
"""
RBlengths = []
RBsuccesses = []
for key in dataset.keys():
dataLine = dataset[key]
plus = dataLine['plus']
minus = dataLine['minus']
N = plus + minus
RBlengths.append(len(key))
RBsuccesses.append(1 - dataLine['plus'] / float(N))
if dataLine['plus'] / float(N) > 1:
print key
a, b = _curve_fit(rb_decay, RBlengths, RBsuccesses)[0]
if saveFigPath or showPlot:
newplot = _plt.figure()
newplotgca = newplot.gca()
newplotgca.plot(RBlengths, RBsuccesses, '.')
newplotgca.plot(xrange(max(RBlengths)),
rb_decay(_np.arange(max(RBlengths)), a, b), '+')
newplotgca.set_xlabel('RB sequence length (non-Clifford)')
newplotgca.set_ylabel('Success rate')
newplotgca.set_title('RB success')
if xlim:
_plt.xlim(xlim)
if ylim:
_plt.ylim(ylim)
if saveFigPath:
newplot.savefig(saveFigPath)
return a, b
def compute_mean_residence_time(self,
nb_blocks=1,
filter_artifacts=False,
per_residue=False,
return_average_time=False,
use_filtered=True):
if use_filtered: results = self.filtered_results
else: results = self.initial_results
def func(x, tau, lamda):
return _np.exp(-(x / tau)**lamda)
all_residence_time = []
all_average_time = []
block_length = int(self.nb_frames / nb_blocks)
xdata = _np.arange(1, block_length + 1)
for run in range(nb_blocks):
s = slice(run * block_length, (run + 1) * block_length, 1)
intervals = {
key: _hf.intervals_binary(results[key][s])
for key in results
}
residence_time = _np.zeros(block_length)
average_time = _np.array([0., 0.])
if per_residue:
residence_time = {}
del_res = []
average_time = {}
for pair in results:
segn, resn, resi, _, _, _ = _hf.deconst_key(pair, True)
residue_key = segn + '-' + resn + '-' + str(resi)
work_intervals = intervals[pair]
interval_lengths = _np.diff(work_intervals,
1).astype(_np.int).flatten()
if filter_artifacts:
interval_lengths = interval_lengths[(interval_lengths <
block_length)]
try:
average_time[residue_key] += _np.array(
[interval_lengths.sum(), interval_lengths.size])
except KeyError:
average_time[residue_key] = _np.array(
[interval_lengths.sum(), interval_lengths.size])
residence_time[residue_key] = _np.zeros(block_length)
for l in interval_lengths:
residence_time[residue_key][:l] += _np.arange(
1, l + 1)[::-1]
for residue_key in residence_time:
residence_time[residue_key] /= _np.arange(
1, block_length + 1)[::-1]
residence_time[residue_key] /= residence_time[residue_key][
0]
if _np.isnan(residence_time[residue_key]).any():
del_res.append(residue_key)
average_time[residue_key] = average_time[residue_key][
0] / average_time[residue_key][1]
try:
(tau,
lamda), pcov = _curve_fit(func,
xdata,
residence_time[residue_key],
p0=(10.0, 0.5))
residence_time[residue_key] = tau / lamda * _gamma(
1 / lamda)
except:
if average_time[residue_key] <= 2.0:
residence_time[residue_key] = 1.0
else:
try:
(tau, lamda), pcov = _curve_fit(
func,
xdata,
residence_time[residue_key],
p0=(block_length, 0.5))
residence_time[
residue_key] = tau / lamda * _gamma(
1 / lamda)
except:
residence_time[residue_key] = block_length
for key in del_res:
del residence_time[key]
else:
for water in results:
work_intervals = intervals[water]
interval_lengths = _np.diff(work_intervals,
1).astype(_np.int).flatten()
if filter_artifacts:
interval_lengths = interval_lengths[(interval_lengths <
block_length)]
average_time += _np.array(
[interval_lengths.sum(), interval_lengths.size])
for l in interval_lengths:
residence_time[:l] += _np.arange(1, l + 1)[::-1]
residence_time /= _np.arange(1, block_length + 1)[::-1]
residence_time /= residence_time[0]
average_time = average_time[0] / average_time[1]
try:
(tau, lamda), pcov = _curve_fit(func,
xdata,
residence_time,
p0=(10.0, 0.5))
residence_time = tau / lamda * _gamma(1 / lamda)
except:
if average_time <= 2.0:
residence_time = 1.0
else:
residence_time = block_length
all_residence_time.append(residence_time)
all_average_time.append(average_time)
if per_residue:
for key in residence_time:
temp_residence_time = []
temp_average_time = []
for residence_dict in all_residence_time:
try:
temp_residence_time.append(residence_dict[key])
except:
pass
for average_dict in all_average_time:
try:
temp_average_time.append(average_time[key])
except:
pass
residence_time[key] = (_np.mean(temp_residence_time),
_np.std(temp_residence_time) /
_np.sqrt(nb_blocks))
average_time[key] = (_np.mean(temp_average_time),
_np.std(temp_average_time) /
_np.sqrt(nb_blocks))
else:
residence_time = (_np.mean(all_residence_time),
_np.std(all_residence_time) /
_np.sqrt(nb_blocks))
average_time = (_np.mean(all_average_time),
_np.std(all_average_time) / _np.sqrt(nb_blocks))
if return_average_time: return residence_time, average_time
else: return residence_time
def calculatePeakDisplacements(intensityProfiles, peakFitSettings, progressReporter = None, pInitial = None, **curveFitKwargs):
"""
Fits an ODM FitFunction to the target Series of intensity profiles.
Parameters
----------
intensityProfiles : pandas.Series of 1D numpy.ndarray
A series of intensityProfiles that will be curve fit
peakFitSettings : ODAFitSettings instance
The curve fit settings to use for curve fitting
progressReporter : ProgressReporter instance
The ProgressReporter to use for displaying progress information.
A StdOutProgressReporter is used by default.
curveFitKwargs : Keyword arguments that will be passed to the curve_fit
function (scipy.optimization).
Returns
-------
A dataframe with the calculated displacements that has the same index as the input
intensity profile Series.
"""
if not progressReporter:
progressReporter = _StdOutProgressReporter()
fitFunction = peakFitSettings.fitFunction
index=intensityProfiles.index
if pInitial is not None:
p0 = pInitial
else:
templateProfile = peakFitSettings.referenceIntensityProfile if peakFitSettings.referenceIntensityProfile is not None else intensityProfiles.iloc[0]
estimatesDict = fitFunction.estimateInitialParameters(templateProfile, **peakFitSettings.estimatorValuesDict)
p0 = estimatesDict.values()
xmin = peakFitSettings.xminBound
xmax = peakFitSettings.xmaxBound
xdata = _np.arange(len(intensityProfiles.iloc[0]))[xmin:xmax]
progress = 0.0
total = len(index)
curveFitResults = total*[None]
for i in range(total):
ydata = intensityProfiles.iloc[i][xmin:xmax]
popt,pcov = _curve_fit(fitFunction,\
xdata = xdata,\
ydata = ydata,\
p0 = p0,**curveFitKwargs)
p0 = popt
curveFitResult = {}
curveFitResult['popt'] = popt
curveFitResult['pcov'] = pcov
curveFitResult['chiSquare'] = _chisquare(ydata,fitFunction(xdata,*popt))[0]
curveFitResult['curveFitResult'] = attrdict.AttrDict(curveFitResult)
curveFitResult['displacement'] = fitFunction.getDisplacement(*popt)
curveFitResults[i] = curveFitResult
progress += 1
progressReporter.progress(progress / total * 100)
df = _pd.DataFrame(index=index,data=curveFitResults)
progressReporter.done()
return df
def graph_it(x,
y,
graph_type=None,
x_error=0,
y_error=0,
title="",
x_title="",
y_title="",
size=(20, 10),
sig_digi=3,
coeff_x=0.8,
coeff_y=0.8,
error_fill_bet=True,
plot_residuals=True,
show_chi=True,
coeff_text=(''),
resid_x_error=0,
resid_y_error=0,
y_scale="",
x_scale="",
extra_code_main='',
extra_code_residuals=''):
"""
Plot and Customize two 1D arrays.
:param x: Horizontal axis data.
:param y: Vertical axis data.
:param graph_type: Formula of fit. Example: lambda x,a,b: a*x+b.
:param x_error: X Error bar size.
:param y_error: Y Error bar size.
:param title: Graphs title.
:param x_title: X axis title.
:param y_title: Y axis title.
:param size: Graphs size.
:param sig_digi: Significant digits length.
:param coeff_x: X position of the legend.
:param coeff_y: Y position of the legend.
:param error_fill_bet: Draws an aura of error freedom around the graph. Default is Off.
:param plot_residuals: Plots the residuals as another graph under the Data graph.
:param show_chi: Show reduced chi-squared result.
:param coeff_text: Tuple of units for graphs legend.
:param resid_x_error: X residuals error bar size.
:param resid_y_error: Y residuals error bar size.
:param y_scale: gets a an array of two iterables, one for for actual rescaling and one for lables,
most commonly use with generatePiAxis().
:param x_scale: gets a an array of two iterables, one for for actual rescaling and one for lables,
most commonly use with generatePiAxis().
:param extra_code_main: Runs extra script after the main graph plot.
:param extra_code_residuals: uns extra script after the residuals graph plot.
:return: A list of guessed parameters given in graph_type.
"""
_plt.rc('text', usetex=False)
fig, ax = _plt.subplots(figsize=size)
tick_fine = 0
x = _np.array(x)
y = _np.array(y)
x_error = _np.array(x_error)
y_error = _np.array(y_error)
graph_dict = {}
if graph_type is not None:
popt, pcov = _curve_fit(graph_type, x, y, maxfev=100000)
sigma_ab = _np.sqrt(_np.diagonal(pcov)) # type: _np.ndarray
x_model = _expand_linspace(x.min(), x.max(), len(x) * 3)
_plt.plot(x_model, graph_type(x_model, *popt), 'black')
_plt.errorbar(x,
y,
xerr=x_error,
yerr=y_error,
fmt='s',
color='b',
visible=False,
alpha=0.6,
capsize=10,
capthick=0.5,
ecolor='k')
if show_chi == True:
if y_error.any() == 0:
print(
"No stat. error data provided, skipping chi squared calculation"
)
else:
chi = _chi_squared(x, y, popt, y_error, graph_type)
title += "\n$\\chi^2 = %s$" % str(chi)
graph_dict['chi2'] = chi
graph_dict['p-value'] = 1 - _chi2.cdf(chi, 1)
if error_fill_bet:
bound_upper = graph_type(x_model, *(popt + sigma_ab))
bound_lower = graph_type(x_model, *(popt - sigma_ab))
# plotting the confidence intervals
_plt.fill_between(x_model,
bound_lower,
bound_upper,
color='midnightblue',
alpha=0.15)
if coeff_text != ():
coeff_text = list(coeff_text)
coeff_text += [''] * (len(popt) - len(coeff_text))
text_res = ""
for i, param in enumerate(popt):
text_res += ((graph_type.__code__.co_varnames[i + 1]) +
str((" = {:." + str(sig_digi) +
"u}").format(_ufloat(popt[i], sigma_ab[i])) +
coeff_text[i] + "\n"))
_plt.text(coeff_x,
coeff_y,
text_res[:-2],
transform=ax.transAxes,
fontsize=20,
bbox=dict(boxstyle='round', facecolor='grey', alpha=0.5),
family='DejaVu Sans')
tick_fine = 1
_plt.scatter(x,
y,
facecolor='red',
marker='s',
edgecolor='black',
s=70,
alpha=1)
_sns.set_style("whitegrid")
ax.set_title(title)
ax.set_ylabel(y_title)
ax.set_xlabel(x_title)
if x_scale != "":
ax.set_xticks(x_scale[0])
ax.set_xticklabels(x_scale[1])
for tick in ax.xaxis.get_major_ticks():
tick.label.set_fontsize(25)
if y_scale != "":
ax.set_yticks(y_scale[0])
ax.set_yticklabels(y_scale[1])
for tick in ax.yaxis.get_major_ticks():
tick.label.set_fontsize(25)
if tick_fine == 1:
ax.set_xlim(x_model.min(), x_model.max())
else:
ax.set_xlim(
_expand_linspace(x.min(), x.max(),
len(x) * 3).min(),
_expand_linspace(x.min(), x.max(),
len(x) * 3).max())
exec(extra_code_main)
graph_dict['main_graph'] = (fig, ax)
if plot_residuals and graph_type is not None:
residuals = y - graph_type(x, *popt)
fig, ax = _plt.subplots(figsize=(20, 5))
_plt.scatter(x,
residuals,
facecolor='red',
marker='s',
edgecolor='black',
s=70,
alpha=1)
ax.errorbar(x,
residuals,
xerr=resid_x_error,
fmt='s',
yerr=residuals * resid_y_error,
marker='s',
visible=False,
alpha=0.6,
capsize=10,
capthick=0.5,
ecolor='k')
ax.set_xlim(x_model.min(), x_model.max())
ax.set_ylim(residuals.min() - _np.abs(residuals.min() * 0.5),
residuals.max() + _np.abs(residuals.max() * 0.5))
ax.set_title("Residuals Plot of " + title)
ax.set_ylabel(y_title)
ax.set_xlabel(x_title)
graph_dict['resid_graph'] = (fig, ax)
_mplcursors.cursor(hover=True)
exec(extra_code_residuals)
if tick_fine == 1:
graph_dict['params'] = [(_ufloat(popt[i], sigma_ab[i]))
for i in range(len(popt))]
return graph_dict
else:
return graph_dict