import logging
import tensorflow as tf
import tensorflow_probability as tfp
log = logging.getLogger(__name__)
[docs]class tensorflow_backend(object):
"""TensorFlow backend for pyhf"""
[docs] def __init__(self, **kwargs):
self.session = kwargs.get('session')
self.name = 'tensorflow'
[docs] def clip(self, tensor_in, min_value, max_value):
"""
Clips (limits) the tensor values to be within a specified min and max.
Example:
>>> import pyhf
>>> import tensorflow as tf
>>> sess = tf.compat.v1.Session()
...
>>> pyhf.set_backend("tensorflow", _session=sess)
>>> a = pyhf.tensorlib.astensor([-2, -1, 0, 1, 2])
>>> with sess.as_default():
... sess.run(pyhf.tensorlib.clip(a, -1, 1))
...
array([-1., -1., 0., 1., 1.], dtype=float32)
Args:
tensor_in (`tensor`): The input tensor object
min_value (`scalar` or `tensor` or `None`): The minimum value to be cliped to
max_value (`scalar` or `tensor` or `None`): The maximum value to be cliped to
Returns:
TensorFlow Tensor: A clipped `tensor`
"""
if min_value is None:
min_value = tf.reduce_min(tensor_in)
if max_value is None:
max_value = tf.reduce_max(tensor_in)
return tf.clip_by_value(tensor_in, min_value, max_value)
[docs] def tile(self, tensor_in, repeats):
"""
Repeat tensor data along a specific dimension
Example:
>>> import pyhf
>>> import tensorflow as tf
>>> sess = tf.compat.v1.Session()
...
>>> pyhf.set_backend("tensorflow", _session=sess)
>>> a = pyhf.tensorlib.astensor([[1.0], [2.0]])
>>> with sess.as_default():
... sess.run(pyhf.tensorlib.tile(a, (1, 2)))
...
array([[1., 1.],
[2., 2.]], dtype=float32)
Args:
tensor_in (`Tensor`): The tensor to be repeated
repeats (`Tensor`): The tuple of multipliers for each dimension
Returns:
TensorFlow Tensor: The tensor with repeated axes
"""
return tf.tile(tensor_in, repeats)
[docs] def conditional(self, predicate, true_callable, false_callable):
"""
Runs a callable conditional on the boolean value of the evaulation of a predicate
Example:
>>> import pyhf
>>> import tensorflow as tf
>>> sess = tf.compat.v1.Session()
...
>>> pyhf.set_backend("tensorflow", _session=sess)
>>> tensorlib = pyhf.tensorlib
>>> a = tensorlib.astensor([4])
>>> b = tensorlib.astensor([5])
>>> compare = tensorlib.conditional((a < b)[0], lambda: a + b, lambda: a - b)
>>> with sess.as_default():
... sess.run(compare)
...
array([9.], dtype=float32)
Args:
predicate (`scalar`): The logical condition that determines which callable to evaluate
true_callable (`callable`): The callable that is evaluated when the :code:`predicate` evalutes to :code:`true`
false_callable (`callable`): The callable that is evaluated when the :code:`predicate` evalutes to :code:`false`
Returns:
TensorFlow Tensor: The output of the callable that was evaluated
"""
return tf.cond(predicate, true_callable, false_callable)
[docs] def tolist(self, tensor_in):
try:
return self.session.run(tensor_in).tolist()
except AttributeError as err:
if isinstance(tensor_in, list):
return tensor_in
if "no attribute 'run'" in str(err):
raise RuntimeError(
'evaluation of tensor requested via .tolist() but no session defined'
)
raise
except RuntimeError as err:
# if no tensor operations have been added to the graph, but we want
# to pass-through a list, then we need to catch the runtime error
# First, see if the input tensor is just a vanilla python list and
# return it instead
if "graph is empty" in str(err) and isinstance(tensor_in, list):
return tensor_in
raise
except TypeError:
# if a tensor operation has been added to the graph, but we want to
# pass-through a list, we need to catch the type error
if isinstance(tensor_in, list):
return tensor_in
raise
[docs] def outer(self, tensor_in_1, tensor_in_2):
tensor_in_1 = (
tensor_in_1
if tensor_in_1.dtype != tf.bool
else tf.cast(tensor_in_1, tf.float32)
)
tensor_in_1 = (
tensor_in_1
if tensor_in_2.dtype != tf.bool
else tf.cast(tensor_in_2, tf.float32)
)
return tf.einsum('i,j->ij', tensor_in_1, tensor_in_2)
[docs] def gather(self, tensor, indices):
return tf.compat.v2.gather(tensor, indices)
[docs] def boolean_mask(self, tensor, mask):
return tf.boolean_mask(tensor, mask)
[docs] def isfinite(self, tensor):
return tf.math.is_finite(tensor)
[docs] def astensor(self, tensor_in, dtype='float'):
"""
Convert to a TensorFlow Tensor.
Args:
tensor_in (Number or Tensor): Tensor object
Returns:
`tf.Tensor`: A symbolic handle to one of the outputs of a `tf.Operation`.
"""
dtypemap = {'float': tf.float32, 'int': tf.int32, 'bool': tf.bool}
try:
dtype = dtypemap[dtype]
except KeyError:
log.error('Invalid dtype: dtype must be float, int, or bool.')
raise
tensor = tensor_in
# If already a tensor then done
try:
tensor.op
except AttributeError:
tensor = tf.convert_to_tensor(tensor_in)
# Ensure non-empty tensor shape for consistency
try:
tensor.shape[0]
except IndexError:
tensor = tf.reshape(tensor, [1])
if tensor.dtype is not dtype:
tensor = tf.cast(tensor, dtype)
return tensor
[docs] def sum(self, tensor_in, axis=None):
return (
tf.reduce_sum(tensor_in)
if (axis is None or tensor_in.shape == tf.TensorShape([]))
else tf.reduce_sum(tensor_in, axis)
)
[docs] def product(self, tensor_in, axis=None):
return (
tf.reduce_prod(tensor_in)
if axis is None
else tf.reduce_prod(tensor_in, axis)
)
[docs] def abs(self, tensor):
return tf.abs(tensor)
[docs] def ones(self, shape):
return tf.ones(shape)
[docs] def zeros(self, shape):
return tf.zeros(shape)
[docs] def power(self, tensor_in_1, tensor_in_2):
return tf.pow(tensor_in_1, tensor_in_2)
[docs] def sqrt(self, tensor_in):
return tf.sqrt(tensor_in)
[docs] def shape(self, tensor):
return tuple(map(int, tensor.shape))
[docs] def reshape(self, tensor, newshape):
return tf.reshape(tensor, newshape)
[docs] def divide(self, tensor_in_1, tensor_in_2):
return tf.divide(tensor_in_1, tensor_in_2)
[docs] def log(self, tensor_in):
return tf.math.log(tensor_in)
[docs] def exp(self, tensor_in):
return tf.exp(tensor_in)
[docs] def stack(self, sequence, axis=0):
return tf.stack(sequence, axis=axis)
[docs] def where(self, mask, tensor_in_1, tensor_in_2):
return tf.compat.v2.where(mask, tensor_in_1, tensor_in_2)
[docs] def concatenate(self, sequence, axis=0):
"""
Join a sequence of arrays along an existing axis.
Args:
sequence: sequence of tensors
axis: dimension along which to concatenate
Returns:
output: the concatenated tensor
"""
return tf.concat(sequence, axis=axis)
[docs] def simple_broadcast(self, *args):
"""
Broadcast a sequence of 1 dimensional arrays.
Example:
>>> import pyhf
>>> import tensorflow as tf
>>> sess = tf.compat.v1.Session()
...
>>> pyhf.set_backend("tensorflow", _session=sess)
>>> tf.Session().run(pyhf.tensorlib.simple_broadcast(
... pyhf.tensorlib.astensor([1]),
... pyhf.tensorlib.astensor([2, 3, 4]),
... pyhf.tensorlib.astensor([5, 6, 7])))
[array([1., 1., 1.], dtype=float32), array([2., 3., 4.], dtype=float32), array([5., 6., 7.], dtype=float32)]
Args:
args (Array of Tensors): Sequence of arrays
Returns:
list of Tensors: The sequence broadcast together.
"""
max_dim = max(map(lambda arg: arg.shape[0], args))
try:
assert not [arg for arg in args if 1 < arg.shape[0] < max_dim]
except AssertionError as error:
log.error(
'ERROR: The arguments must be of compatible size: 1 or %i', max_dim
)
raise error
broadcast = [
arg
if arg.shape[0] > 1
else tf.tile(tf.slice(arg, [0], [1]), tf.stack([max_dim]))
for arg in args
]
return broadcast
[docs] def einsum(self, subscripts, *operands):
"""
A generalized contraction between tensors of arbitrary dimension.
This function returns a tensor whose elements are defined by equation,
which is written in a shorthand form inspired by the Einstein summation
convention.
Args:
subscripts: str, specifies the subscripts for summation
operands: list of array_like, these are the tensors for the operation
Returns:
TensorFlow Tensor: the calculation based on the Einstein summation convention
"""
return tf.einsum(subscripts, *operands)
[docs] def poisson_logpdf(self, n, lam):
r"""
The log of the continous approximation, using :math:`n! = \Gamma\left(n+1\right)`,
to the probability mass function of the Poisson distribution evaluated
at :code:`n` given the parameter :code:`lam`.
Example:
>>> import pyhf
>>> import tensorflow as tf
>>> sess = tf.compat.v1.Session()
>>> pyhf.set_backend("tensorflow", _session=sess)
...
>>> with sess.as_default():
... sess.run(pyhf.tensorlib.poisson_logpdf(5., 6.))
...
-1.8286943
>>> values = pyhf.tensorlib.astensor([5., 9.])
>>> rates = pyhf.tensorlib.astensor([6., 8.])
>>> with sess.as_default():
... sess.run(pyhf.tensorlib.poisson_logpdf(values, rates))
...
array([-1.8286943, -2.086854 ], dtype=float32)
Args:
n (`tensor` or `float`): The value at which to evaluate the approximation to the Poisson distribution p.m.f.
(the observed number of events)
lam (`tensor` or `float`): The mean of the Poisson distribution p.m.f.
(the expected number of events)
Returns:
TensorFlow Tensor: Value of the continous approximation to log(Poisson(n|lam))
"""
return tfp.distributions.Poisson(lam).log_prob(n)
[docs] def poisson(self, n, lam):
r"""
The continous approximation, using :math:`n! = \Gamma\left(n+1\right)`,
to the probability mass function of the Poisson distribution evaluated
at :code:`n` given the parameter :code:`lam`.
Example:
>>> import pyhf
>>> import tensorflow as tf
>>> sess = tf.compat.v1.Session()
>>> pyhf.set_backend("tensorflow", _session=sess)
...
>>> with sess.as_default():
... sess.run(pyhf.tensorlib.poisson(5., 6.))
...
0.16062315
>>> values = pyhf.tensorlib.astensor([5., 9.])
>>> rates = pyhf.tensorlib.astensor([6., 8.])
>>> with sess.as_default():
... sess.run(pyhf.tensorlib.poisson(values, rates))
...
array([0.16062315, 0.12407687], dtype=float32)
Args:
n (`tensor` or `float`): The value at which to evaluate the approximation to the Poisson distribution p.m.f.
(the observed number of events)
lam (`tensor` or `float`): The mean of the Poisson distribution p.m.f.
(the expected number of events)
Returns:
TensorFlow Tensor: Value of the continous approximation to Poisson(n|lam)
"""
return tf.exp(tfp.distributions.Poisson(lam).log_prob(n))
[docs] def normal_logpdf(self, x, mu, sigma):
r"""
The log of the probability density function of the Normal distribution evaluated
at :code:`x` given parameters of mean of :code:`mu` and standard deviation
of :code:`sigma`.
Example:
>>> import pyhf
>>> import tensorflow as tf
>>> sess = tf.compat.v1.Session()
>>> pyhf.set_backend("tensorflow", _session=sess)
...
>>> with sess.as_default():
... sess.run(pyhf.tensorlib.normal_logpdf(0.5, 0., 1.))
...
-1.0439385
>>> values = pyhf.tensorlib.astensor([0.5, 2.0])
>>> means = pyhf.tensorlib.astensor([0., 2.3])
>>> sigmas = pyhf.tensorlib.astensor([1., 0.8])
>>> with sess.as_default():
... sess.run(pyhf.tensorlib.normal_logpdf(values, means, sigmas))
...
array([-1.0439385, -0.7661075], dtype=float32)
Args:
x (`tensor` or `float`): The value at which to evaluate the Normal distribution p.d.f.
mu (`tensor` or `float`): The mean of the Normal distribution
sigma (`tensor` or `float`): The standard deviation of the Normal distribution
Returns:
TensorFlow Tensor: Value of log(Normal(x|mu, sigma))
"""
normal = tfp.distributions.Normal(mu, sigma)
return normal.log_prob(x)
[docs] def normal(self, x, mu, sigma):
r"""
The probability density function of the Normal distribution evaluated
at :code:`x` given parameters of mean of :code:`mu` and standard deviation
of :code:`sigma`.
Example:
>>> import pyhf
>>> import tensorflow as tf
>>> sess = tf.compat.v1.Session()
>>> pyhf.set_backend("tensorflow", _session=sess)
...
>>> with sess.as_default():
... sess.run(pyhf.tensorlib.normal(0.5, 0., 1.))
...
0.35206532
>>> values = pyhf.tensorlib.astensor([0.5, 2.0])
>>> means = pyhf.tensorlib.astensor([0., 2.3])
>>> sigmas = pyhf.tensorlib.astensor([1., 0.8])
>>> with sess.as_default():
... sess.run(pyhf.tensorlib.normal(values, means, sigmas))
...
array([0.35206532, 0.46481887], dtype=float32)
Args:
x (`tensor` or `float`): The value at which to evaluate the Normal distribution p.d.f.
mu (`tensor` or `float`): The mean of the Normal distribution
sigma (`tensor` or `float`): The standard deviation of the Normal distribution
Returns:
TensorFlow Tensor: Value of Normal(x|mu, sigma)
"""
normal = tfp.distributions.Normal(mu, sigma)
return normal.prob(x)
[docs] def normal_cdf(self, x, mu=0, sigma=1):
"""
The cumulative distribution function for the Normal distribution
Example:
>>> import pyhf
>>> import tensorflow as tf
>>> sess = tf.compat.v1.Session()
...
>>> pyhf.set_backend("tensorflow", _session=sess)
>>> with sess.as_default():
... sess.run(pyhf.tensorlib.normal_cdf(0.8))
...
0.7881446
>>> values = pyhf.tensorlib.astensor([0.8, 2.0])
>>> with sess.as_default():
... sess.run(pyhf.tensorlib.normal_cdf(values))
...
array([0.7881446 , 0.97724986], dtype=float32)
Args:
x (`tensor` or `float`): The observed value of the random variable to evaluate the CDF for
mu (`tensor` or `float`): The mean of the Normal distribution
sigma (`tensor` or `float`): The standard deviation of the Normal distribution
Returns:
TensorFlow Tensor: The CDF
"""
normal = tfp.distributions.Normal(mu, sigma)
return normal.cdf(x)
[docs] def poisson_dist(self, rate):
r"""
The Poisson distribution with rate parameter :code:`rate`.
Example:
>>> import pyhf
>>> import tensorflow as tf
>>> sess = tf.compat.v1.Session()
...
>>> pyhf.set_backend("tensorflow", _session=sess)
>>> rates = pyhf.tensorlib.astensor([5, 8])
>>> values = pyhf.tensorlib.astensor([4, 9])
>>> poissons = pyhf.tensorlib.poisson_dist(rates)
>>> with sess.as_default():
... sess.run(poissons.log_prob(values))
...
array([-1.7403021, -2.086854 ], dtype=float32)
Args:
rate (`tensor` or `float`): The mean of the Poisson distribution (the expected number of events)
Returns:
TensorFlow Probability Poisson distribution: The Poisson distribution class
"""
return tfp.distributions.Poisson(rate)
[docs] def normal_dist(self, mu, sigma):
r"""
The Normal distribution with mean :code:`mu` and standard deviation :code:`sigma`.
Example:
>>> import pyhf
>>> import tensorflow as tf
>>> sess = tf.compat.v1.Session()
...
>>> pyhf.set_backend("tensorflow", _session=sess)
>>> means = pyhf.tensorlib.astensor([5, 8])
>>> stds = pyhf.tensorlib.astensor([1, 0.5])
>>> values = pyhf.tensorlib.astensor([4, 9])
>>> normals = pyhf.tensorlib.normal_dist(means, stds)
>>> with sess.as_default():
... sess.run(normals.log_prob(values))
...
array([-1.4189385, -2.2257915], dtype=float32)
Args:
mu (`tensor` or `float`): The mean of the Normal distribution
sigma (`tensor` or `float`): The standard deviation of the Normal distribution
Returns:
TensorFlow Probability Normal distribution: The Normal distribution class
"""
return tfp.distributions.Normal(mu, sigma)