def create_mc2hessian(pdf, Q, Neig, output_dir, name=None, db=None):
X = get_X(pdf, Q, reshape=True)
vec = compress_X(X, Neig)
norm = _pdf_normalization(pdf)
description = {"input_hash": mc2h_input_hash(pdf, Q, Neig)}
save_lincomb(vec, norm, description=description, output_dir=output_dir, name=name)
return hessian_from_lincomb(pdf, vec / norm, folder=output_dir, set_name=name, db=db)
def plot_correlations(results):
for result in results:
pdf = result.pdf
obs = result.obs
Qs = iter(obs.meanQ)
xgrid = pdf.make_xgrid()
fl = pdf.make_flavors()
figure, axarr = plt.subplots(len(fl), sharex=True,
sharey=True,
figsize=(8, len(fl)+3))
for b in result.binlabels:
Q = next(Qs)
X = get_X(pdf, Q=Q, xgrid=xgrid, fl=fl, reshape=True)
values, threshold = bin_corrs_from_X(result._all_vals.ix[b], X)
ind = 0
for f, axis in zip(fl, axarr):
step = len(xgrid)
current_vals = values[ind:ind+step]
ind+=step
line, = axis.plot(xgrid, current_vals)
stacked = np.array([xgrid, current_vals]).T
sel_ranges = split_ranges(stacked, abs(current_vals)>threshold,
filter_falses=True)
for arr in sel_ranges:
x,y = arr.T
axis.plot(x,y, linewidth=3, color=line.get_color())
axis.axvspan(np.min(x), np.max(x), color="#eeeeff")
axis.set_ylim([-1,1])
axis.set_xscale('log')
axis.set_ylabel("$%s$"%PDG_PARTONS[f])
axis.axhline(threshold, c='r', ls='--')
axis.axhline(-threshold, c='r', ls='--')
axarr[0].set_title(str(obs) + "\n")
plt.xlabel("$x$")
figure.subplots_adjust(hspace=0)
plt.setp([a.get_xticklabels() for a in figure.axes[:-1]], visible=False)
yield (obs,pdf), figure
def get_smpdf_lincomb(
pdf, pdf_results, target_error, full_grid=False, correlation_threshold=DEFAULT_CORRELATION_THRESHOLD, Rold=None
):
"""Extract the linear combination that describes the linar part of
the error of the given results with at least `target_error` precision`.
See <paper> for details.
`Rold` is returned so computation can be resumed iteratively (and then
merged) with for example `merge_lincombs`."""
# Estimator= norm**2(rotated)/norm**2(total) which is additive when adding
# eigenvecotors
# Error = (1 - sqrt(1-estimator))
# TODO: Optimize by calculating estimator instead of error?
# target_estimator = 1 - (1-target_error)**2
nxf = len(pdf.make_xgrid()) * len(pdf.make_flavors())
nrep = len(pdf) - 1
max_neig = np.min([nxf, nrep])
# We must divide by norm since we are reproducing the covmat and not XX.T
norm = _pdf_normalization(pdf)
if isinstance(target_error, collections.Container):
total_bins = sum(r.nbins for r in pdf_results)
if len(target_error) != total_bins:
raise ValueError("Incorrect target error specification")
target_error = iter(target_error)
elif isinstance(target_error, numbers.Real):
target_error = itertools.repeat(target_error)
elif not isinstance(target_error, collections.Iterator):
raise ValueError("Target error not understood")
lincomb = np.zeros(shape=(nrep, max_neig))
desc = OrderedDict()
errors = OrderedDict()
index = 0
for result in pdf_results:
obs_desc = OrderedDict()
obs_errors = OrderedDict()
desc[str(result.obs)] = obs_desc
errors[str(result.obs)] = obs_errors
if result.pdf != pdf:
raise ValueError("PDF results must be for %s" % pdf)
for b in result.binlabels:
Xreal = get_X(pdf, Q=result.meanQ[b], reshape=True)
prediction = result._all_vals.ix[b]
original_diffs = prediction - np.mean(prediction)
if Rold is not None:
X = np.dot(Xreal, Rold)
rotated_diffs = np.dot(original_diffs, Rold)
else:
rotated_diffs = original_diffs
X = Xreal
eigs_for_bin = 0
error_val = next(target_error)
# Would be
# while _get_error(rotated_diffs, original_diffs) > error_val
# except that we want to capture current_error
while True:
current_error = _get_error(rotated_diffs, original_diffs)
if current_error < error_val:
break
X = _mask_X(X, rotated_diffs, correlation_threshold=correlation_threshold)
P, R = _pop_eigenvector(X)
if Rold is not None:
P = np.dot(Rold, P)
R = np.dot(Rold, R)
Rold = R
rotated_diffs = np.dot(original_diffs, Rold)
X = np.dot(Xreal, Rold)
lincomb[:, index : index + 1] = P
index += 1
if index == max_neig:
raise TooMuchPrecision(result.obs, b + 1)
eigs_for_bin += 1
if eigs_for_bin:
logging.info(
"Obtained %d eigenvector%s for observable %s, "
"bin %d" % (eigs_for_bin, "s" * (eigs_for_bin > 1), result.obs, b + 1)
)
else:
logging.debug("Observable %s, " "bin %d is already well reproduced." % (result.obs, b + 1))
obs_desc[int(b + 1)] = index
obs_errors[int(b + 1)] = current_error
# Prune extra zeros
lincomb = lincomb[:, :index]
logging.debug("Linear combination has %d eigenvectors" % lincomb.shape[1])
return SMPDFLincombResult(lincomb=lincomb, norm=norm, desc=desc, errors=errors, Rold=Rold)
