"""Quadratic Interpolation (Code 2)."""
import logging
import pyhf
from pyhf.tensor.manager import get_backend
from pyhf import events
from pyhf.interpolators import _slow_interpolator_looper
log = logging.getLogger(__name__)
[docs]
class code2:
r"""
The quadratic interpolation and linear extrapolation strategy.
.. math::
\sigma_{sb} (\vec{\alpha}) = \sigma_{sb}^0(\vec{\alpha}) + \underbrace{\sum_{p \in \text{Syst}} I_\text{quad.|lin.} (\alpha_p; \sigma_{sb}^0, \sigma_{psb}^+, \sigma_{psb}^-)}_\text{deltas to calculate}
with
.. math::
I_\text{quad.|lin.}(\alpha; I^0, I^+, I^-) = \begin{cases} (b + 2a)(\alpha - 1) \qquad \alpha \geq 1\\ a\alpha^2 + b\alpha \qquad |\alpha| < 1 \\ (b - 2a)(\alpha + 1) \qquad \alpha < -1 \end{cases}
and
.. math::
a = \frac{1}{2} (I^+ + I^-) - I^0 \qquad \mathrm{and} \qquad b = \frac{1}{2}(I^+ - I^-)
"""
[docs]
def __init__(self, histogramssets, subscribe=True):
"""Quadratic Interpolation."""
default_backend = pyhf.default_backend
self._histogramssets = default_backend.astensor(histogramssets)
# initial shape will be (nsysts, 1)
self.alphasets_shape = (self._histogramssets.shape[0], 1)
# precompute terms that only depend on the histogramssets
self._a = (
0.5 * (self._histogramssets[:, :, 2] + self._histogramssets[:, :, 0])
- self._histogramssets[:, :, 1]
)
self._b = 0.5 * (self._histogramssets[:, :, 2] - self._histogramssets[:, :, 0])
self._b_plus_2a = self._b + 2 * self._a
self._b_minus_2a = self._b - 2 * self._a
self._broadcast_helper = default_backend.ones(default_backend.shape(self._a))
self._precompute()
if subscribe:
events.subscribe('tensorlib_changed')(self._precompute)
[docs]
def _precompute(self):
tensorlib, _ = get_backend()
self.a = tensorlib.astensor(self._a)
self.b = tensorlib.astensor(self._b)
self.b_plus_2a = tensorlib.astensor(self._b_plus_2a)
self.b_minus_2a = tensorlib.astensor(self._b_minus_2a)
# make up the masks correctly
self.broadcast_helper = tensorlib.astensor(self._broadcast_helper)
self.mask_on = tensorlib.ones(self.alphasets_shape)
self.mask_off = tensorlib.zeros(self.alphasets_shape)
[docs]
def _precompute_alphasets(self, alphasets_shape):
if alphasets_shape == self.alphasets_shape:
return
tensorlib, _ = get_backend()
self.alphasets_shape = alphasets_shape
self.mask_on = tensorlib.ones(self.alphasets_shape)
self.mask_off = tensorlib.zeros(self.alphasets_shape)
def __call__(self, alphasets):
"""Compute Interpolated Values."""
tensorlib, _ = get_backend()
self._precompute_alphasets(tensorlib.shape(alphasets))
# select where alpha > 1
where_alphasets_gt1 = tensorlib.where(
alphasets > 1, self.mask_on, self.mask_off
)
# select where alpha >= -1
where_alphasets_not_lt1 = tensorlib.where(
alphasets >= -1, self.mask_on, self.mask_off
)
# s: set under consideration (i.e. the modifier)
# a: alpha variation
# h: histogram affected by modifier
# b: bin of histogram
value_gt1 = tensorlib.einsum(
'sa,shb->shab', alphasets - self.mask_on, self.b_plus_2a
)
value_btwn = tensorlib.einsum(
'sa,sa,shb->shab', alphasets, alphasets, self.a
) + tensorlib.einsum('sa,shb->shab', alphasets, self.b)
value_lt1 = tensorlib.einsum(
'sa,shb->shab', alphasets + self.mask_off, self.b_minus_2a
)
masks_gt1 = tensorlib.astensor(
tensorlib.einsum(
'sa,shb->shab', where_alphasets_gt1, self.broadcast_helper
),
dtype="bool",
)
masks_not_lt1 = tensorlib.astensor(
tensorlib.einsum(
'sa,shb->shab', where_alphasets_not_lt1, self.broadcast_helper
),
dtype="bool",
)
# first, build a result where:
# alpha > 1 : fill with (b+2a)(alpha - 1)
# not(alpha > 1) : fill with (a * alpha^2 + b * alpha)
results_gt1_btwn = tensorlib.where(masks_gt1, value_gt1, value_btwn)
# then, build a result where:
# alpha >= -1 : do nothing (fill with previous result)
# not(alpha >= -1): fill with (b-2a)(alpha + 1)
return tensorlib.where(masks_not_lt1, results_gt1_btwn, value_lt1)
class _slow_code2:
def summand(self, down, nom, up, alpha):
a = 0.5 * (up + down) - nom
b = 0.5 * (up - down)
if alpha > 1:
delta = (b + 2 * a) * (alpha - 1)
elif -1 <= alpha <= 1:
delta = a * alpha * alpha + b * alpha
else:
delta = (b - 2 * a) * (alpha + 1)
return delta
def __init__(self, histogramssets, subscribe=True):
self._histogramssets = histogramssets
def __call__(self, alphasets):
tensorlib, _ = get_backend()
return tensorlib.astensor(
_slow_interpolator_looper(
self._histogramssets, tensorlib.tolist(alphasets), self.summand
)
)