def band_plot(log_likelihood, x_min, x_max, y_min, y_max,
n_sigma=1, steps=20, **kwargs):
r"""This is an alias for `likelihood_contour` which is present for
backward compatibility."""
warnings.warn("The `band_plot` function has been replaced "
"by `likelihood_contour` (or "
"`likelihood_contour_data` in conjunction with `contour`) "
"and might be removed in the future. "
"Please update your code.", FutureWarning)
valid_args = inspect.signature(likelihood_contour_data).parameters.keys()
data_kwargs = {k:v for k,v in kwargs.items() if k in valid_args}
if 'pre_calculated_z' not in kwargs:
contour_kwargs = likelihood_contour_data(log_likelihood,
x_min, x_max, y_min, y_max,
n_sigma, steps, **data_kwargs)
else:
contour_kwargs = {}
nx, ny = kwargs['pre_calculated_z'].shape
_x = np.linspace(x_min, x_max, nx)
_y = np.linspace(y_min, y_max, ny)
x, y = np.meshgrid(_x, _y)
contour_kwargs['x'] = x
contour_kwargs['y'] = y
contour_kwargs['z'] = kwargs['pre_calculated_z']
if isinstance(n_sigma, Number):
contour_kwargs['levels'] = [delta_chi2(n_sigma, dof=2)]
else:
contour_kwargs['levels'] = [delta_chi2(n, dof=2) for n in n_sigma]
valid_args = inspect.signature(contour).parameters.keys()
contour_kwargs.update({k:v for k,v in kwargs.items() if k in valid_args})
contour(**contour_kwargs)
return contour_kwargs['x'], contour_kwargs['y'], contour_kwargs['z']
def likelihood_contour_data(log_likelihood,
x_min,
x_max,
y_min,
y_max,
n_sigma=1,
steps=20,
threads=1,
pool=None):
r"""Generate data required to plot coloured confidence contours (or bands)
given a log likelihood function.
Parameters:
- `log_likelihood`: function returning the logarithm of the likelihood.
Can e.g. be the method of the same name of a FastFit instance.
- `x_min`, `x_max`, `y_min`, `y_max`: data boundaries
- `n_sigma`: plot confidence level corresponding to this number of standard
deviations. Either a number (defaults to 1) or a tuple to plot several
contours.
- `steps`: number of grid steps in each dimension (total computing time is
this number squared times the computing time of one `log_likelihood` call!)
- `threads`: number of threads, defaults to 1. If greater than one,
computation of z values will be done in parallel.
- `pool`: an instance of `multiprocessing.Pool` (or a compatible
implementation, e.g. from `multiprocess` or `schwimmbad`). Overrides the
`threads` argument.
"""
_x = np.linspace(x_min, x_max, steps)
_y = np.linspace(y_min, y_max, steps)
x, y = np.meshgrid(_x, _y)
if threads == 1:
@np.vectorize
def chi2_vect(x, y): # needed for evaluation on meshgrid
return -2 * log_likelihood([x, y])
z = chi2_vect(x, y)
else:
xy = np.array([x, y]).reshape(2, steps**2).T
pool = pool or Pool(threads)
try:
z = -2 * np.array(pool.map(log_likelihood, xy)).reshape(
(steps, steps))
except PicklingError:
pool.close()
raise PicklingError(
"When using more than 1 thread, the "
"log_likelihood function must be picklable; "
"in particular, you cannot use lambda expressions.")
pool.close()
pool.join()
z = z - np.min(z) # subtract the best fit point (on the grid)
# get the correct values for 2D confidence/credibility contours for n sigma
if isinstance(n_sigma, Number):
levels = [delta_chi2(n_sigma, dof=2)]
else:
levels = [delta_chi2(n, dof=2) for n in n_sigma]
return {'x': x, 'y': y, 'z': z, 'levels': levels}
def band_plot(log_likelihood, x_min, x_max, y_min, y_max,
n_sigma=1, steps=20, **kwargs):
r"""This is an alias for `likelihood_contour` which is present for
backward compatibility."""
warnings.warn("The `band_plot` function has been replaced "
"by `likelihood_contour` (or "
"`likelihood_contour_data` in conjunction with `contour`) "
"and might be removed in the future. "
"Please update your code.", FutureWarning)
valid_args = inspect.signature(likelihood_contour_data).parameters.keys()
data_kwargs = {k:v for k,v in kwargs.items() if k in valid_args}
if 'pre_calculated_z' not in kwargs:
contour_kwargs = likelihood_contour_data(log_likelihood,
x_min, x_max, y_min, y_max,
n_sigma, steps, **data_kwargs)
else:
contour_kwargs = {}
nx, ny = kwargs['pre_calculated_z'].shape
_x = np.linspace(x_min, x_max, nx)
_y = np.linspace(y_min, y_max, ny)
x, y = np.meshgrid(_x, _y)
contour_kwargs['x'] = x
contour_kwargs['y'] = y
contour_kwargs['z'] = kwargs['pre_calculated_z']
if isinstance(n_sigma, Number):
contour_kwargs['levels'] = [delta_chi2(n_sigma, dof=2)]
else:
contour_kwargs['levels'] = [delta_chi2(n, dof=2) for n in n_sigma]
valid_args = inspect.signature(contour).parameters.keys()
contour_kwargs.update({k:v for k,v in kwargs.items() if k in valid_args})
contour(**contour_kwargs)
return contour_kwargs['x'], contour_kwargs['y'], contour_kwargs['z']
def likelihood_contour_data(log_likelihood, x_min, x_max, y_min, y_max,
n_sigma=1, steps=20, threads=1, pool=None):
r"""Generate data required to plot coloured confidence contours (or bands)
given a log likelihood function.
Parameters:
- `log_likelihood`: function returning the logarithm of the likelihood.
Can e.g. be the method of the same name of a FastFit instance.
- `x_min`, `x_max`, `y_min`, `y_max`: data boundaries
- `n_sigma`: plot confidence level corresponding to this number of standard
deviations. Either a number (defaults to 1) or a tuple to plot several
contours.
- `steps`: number of grid steps in each dimension (total computing time is
this number squared times the computing time of one `log_likelihood` call!)
- `threads`: number of threads, defaults to 1. If greater than one,
computation of z values will be done in parallel.
- `pool`: an instance of `multiprocessing.Pool` (or a compatible
implementation, e.g. from `multiprocess` or `schwimmbad`). Overrides the
`threads` argument.
"""
_x = np.linspace(x_min, x_max, steps)
_y = np.linspace(y_min, y_max, steps)
x, y = np.meshgrid(_x, _y)
if threads == 1:
@np.vectorize
def chi2_vect(x, y): # needed for evaluation on meshgrid
return -2*log_likelihood([x,y])
z = chi2_vect(x, y)
else:
xy = np.array([x, y]).reshape(2, steps**2).T
pool = pool or Pool(threads)
try:
z = -2*np.array(pool.map(log_likelihood, xy )).reshape((steps, steps))
except PicklingError:
pool.close()
raise PicklingError("When using more than 1 thread, the "
"log_likelihood function must be picklable; "
"in particular, you cannot use lambda expressions.")
pool.close()
pool.join()
z = z - np.min(z) # subtract the best fit point (on the grid)
# get the correct values for 2D confidence/credibility contours for n sigma
if isinstance(n_sigma, Number):
levels = [delta_chi2(n_sigma, dof=2)]
else:
levels = [delta_chi2(n, dof=2) for n in n_sigma]
return {'x': x, 'y': y, 'z': z, 'levels': levels}
def plot(fin, fout, x0=None):
'''
Read data from file and plot it in flavio-style
'''
f = open(fin, 'rt')
_x = []
_y = []
for l in f.readlines():
ls = l.split('\t')
_x.append(float(ls[1]))
_y.append(float(ls[2]))
f.close()
stepx = float('Inf')
stepy = float('Inf')
minx = min(_x)
miny = min(_y)
maxx = max(_x)
maxy = max(_y)
for i in range(0, len(_x)):
if _x[i] != minx:
stepx = min(stepx, _x[i] - minx)
for i in range(0, len(_y)):
if _y[i] != miny:
stepy = min(stepy, _y[i] - miny)
x, y = np.meshgrid(np.arange(minx, maxx, stepx),
np.arange(miny, maxy, stepy))
shape1, shape2 = x.shape
f = open(fin, 'rt')
i = 0
zbs = np.zeros(x.shape)
zDMs = np.zeros(x.shape)
zACP = np.zeros(x.shape)
zglob = np.zeros(x.shape)
for l in f.readlines():
i1 = i % shape1
i2 = i // shape1
i += 1
ls = l.split('\t')
zbs[i1, i2] = float(ls[-4])
zACP[i1, i2] = float(ls[-2])
zDMs[i1, i2] = float(ls[-3])
zglob[i1, i2] = float(ls[-1])
f.close()
zbs = zbs - np.min(zbs)
zDMs = zDMs - np.min(zDMs)
zACP = zACP - np.min(zACP)
zglob = zglob - np.min(zglob)
levels = [delta_chi2(n, dof=2) for n in (1, 2)]
plotbs = {
'x': x,
'y': y,
'z': zbs,
'levels': levels,
'interpolation_factor': 5,
'col': 0,
'label': r'$b \to s \mu^+ \mu^-$'
}
plotDMs = {
'x': x,
'y': y,
'z': zDMs,
'levels': levels,
'interpolation_factor': 5,
'col': 1,
'label': r'$\Delta B_s$'
}
plotACP = {
'x': x,
'y': y,
'z': zACP,
'levels': levels,
'interpolation_factor': 5,
'col': 2,
'label': r'$A_{CP}^{\mathrm{mix}}$'
}
plotglob = {
'x': x,
'y': y,
'z': zglob,
'levels': levels,
'interpolation_factor': 5,
'col': 3,
'label': 'Global'
}
fig = texfig.figure()
#fig = plt.figure()
plt.xlim([-0.15, 0.15])
plt.ylim([-0.15, 0.15])
flavio.plots.contour(**plotbs)
flavio.plots.contour(**plotDMs)
flavio.plots.contour(**plotACP)
flavio.plots.contour(**plotglob)
plt.axhline(0, c='k', lw=0.2)
plt.axvline(0, c='k', lw=0.2)
if x0 is not None:
plt.plot(x0[0], x0[1], marker='x', c='k')
plt.xlabel(r'$\mathrm{Re}\ y^{QL}_{32} y^{QL*}_{22}$')
plt.ylabel(r'$\mathrm{Im}\ y^{QL}_{32} y^{QL*}_{22}$')
#plt.xlabel(r'$\mathrm{Re}\ \lambda^Q_{23}$')
#plt.ylabel(r'$\mathrm{Im}\ \lambda^Q_{23}$')
plt.legend(loc=2, bbox_to_anchor=(1.05, 1))
texfig.savefig(fout)