"""Tensorflow Tensor Library Module."""
import logging
import tensorflow as tf
import tensorflow_probability as tfp
log = logging.getLogger(__name__)
[docs]class tensorflow_backend(object):
"""TensorFlow backend for pyhf"""
__slots__ = ['name', 'precision', 'dtypemap', 'default_do_grad']
[docs] def __init__(self, **kwargs):
self.name = 'tensorflow'
self.precision = kwargs.get('precision', '32b')
self.dtypemap = {
'float': tf.float64 if self.precision == '64b' else tf.float32,
'int': tf.int64 if self.precision == '64b' else tf.int32,
'bool': tf.bool,
}
self.default_do_grad = True
def _setup(self):
"""
Run any global setups for the tensorflow lib.
"""
[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
>>> pyhf.set_backend("tensorflow")
>>> a = pyhf.tensorlib.astensor([-2, -1, 0, 1, 2])
>>> t = pyhf.tensorlib.clip(a, -1, 1)
>>> print(t)
tf.Tensor([-1. -1. 0. 1. 1.], shape=(5,), 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
>>> pyhf.set_backend("tensorflow")
>>> a = pyhf.tensorlib.astensor([[1.0], [2.0]])
>>> t = pyhf.tensorlib.tile(a, (1, 2))
>>> print(t)
tf.Tensor(
[[1. 1.]
[2. 2.]], shape=(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
"""
try:
return tf.tile(tensor_in, repeats)
except tf.python.framework.errors_impl.InvalidArgumentError:
shape = tf.shape(tensor_in).numpy().tolist()
diff = len(repeats) - len(shape)
if diff < 0:
raise
return tf.tile(tf.reshape(tensor_in, [1] * diff + shape), 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
>>> pyhf.set_backend("tensorflow")
>>> tensorlib = pyhf.tensorlib
>>> a = tensorlib.astensor([4])
>>> b = tensorlib.astensor([5])
>>> t = tensorlib.conditional((a < b)[0], lambda: a + b, lambda: a - b)
>>> print(t)
tf.Tensor([9.], shape=(1,), 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 tensor_in.numpy().tolist()
except AttributeError:
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.
Example:
>>> import pyhf
>>> pyhf.set_backend("tensorflow")
>>> tensor = pyhf.tensorlib.astensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
>>> tensor
<tf.Tensor: shape=(2, 3), dtype=float32, numpy=
array([[1., 2., 3.],
[4., 5., 6.]], dtype=float32)>
>>> type(tensor)
<class 'tensorflow.python.framework.ops.EagerTensor'>
Args:
tensor_in (Number or Tensor): Tensor object
Returns:
`tf.Tensor`: A symbolic handle to one of the outputs of a `tf.Operation`.
"""
try:
dtype = self.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:
# Use a tensor attribute that isn't meaningless when eager execution is enabled
tensor.device
except AttributeError:
tensor = tf.convert_to_tensor(tensor_in)
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, dtype=self.dtypemap['float'])
[docs] def zeros(self, shape):
return tf.zeros(shape, dtype=self.dtypemap['float'])
[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):
"""
Apply a boolean selection mask to the elements of the input tensors.
Example:
>>> import pyhf
>>> pyhf.set_backend("tensorflow")
>>> t = pyhf.tensorlib.where(
... pyhf.tensorlib.astensor([1, 0, 1], dtype='bool'),
... pyhf.tensorlib.astensor([1, 1, 1]),
... pyhf.tensorlib.astensor([2, 2, 2]),
... )
>>> print(t)
tf.Tensor([1. 2. 1.], shape=(3,), dtype=float32)
Args:
mask (bool): Boolean mask (boolean or tensor object of booleans)
tensor_in_1 (Tensor): Tensor object
tensor_in_2 (Tensor): Tensor object
Returns:
TensorFlow Tensor: The result of the mask being applied to the tensors.
"""
return tf.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
>>> pyhf.set_backend("tensorflow")
>>> b = pyhf.tensorlib.simple_broadcast(
... pyhf.tensorlib.astensor([1]),
... pyhf.tensorlib.astensor([2, 3, 4]),
... pyhf.tensorlib.astensor([5, 6, 7]))
>>> print([str(t) for t in b]) # doctest: +NORMALIZE_WHITESPACE
['tf.Tensor([1. 1. 1.], shape=(3,), dtype=float32)',
'tf.Tensor([2. 3. 4.], shape=(3,), dtype=float32)',
'tf.Tensor([5. 6. 7.], shape=(3,), dtype=float32)']
Args:
args (Array of Tensors): Sequence of arrays
Returns:
list of Tensors: The sequence broadcast together.
"""
max_dim = max(map(tf.size, args))
try:
assert not [arg for arg in args if 1 < tf.size(arg) < max_dim]
except AssertionError as error:
log.error(
'ERROR: The arguments must be of compatible size: 1 or %i', max_dim
)
raise error
return [tf.broadcast_to(arg, (max_dim,)) for arg in args]
[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
>>> pyhf.set_backend("tensorflow")
>>> t = pyhf.tensorlib.poisson_logpdf(5., 6.)
>>> print(t)
tf.Tensor(-1.8286943, shape=(), dtype=float32)
>>> values = pyhf.tensorlib.astensor([5., 9.])
>>> rates = pyhf.tensorlib.astensor([6., 8.])
>>> t = pyhf.tensorlib.poisson_logpdf(values, rates)
>>> print(t)
tf.Tensor([-1.8286943 -2.086854 ], shape=(2,), 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
>>> pyhf.set_backend("tensorflow")
>>> t = pyhf.tensorlib.poisson(5., 6.)
>>> print(t)
tf.Tensor(0.16062315, shape=(), dtype=float32)
>>> values = pyhf.tensorlib.astensor([5., 9.])
>>> rates = pyhf.tensorlib.astensor([6., 8.])
>>> t = pyhf.tensorlib.poisson(values, rates)
>>> print(t)
tf.Tensor([0.16062315 0.12407687], shape=(2,), 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
>>> pyhf.set_backend("tensorflow")
>>> t = pyhf.tensorlib.normal_logpdf(0.5, 0., 1.)
>>> print(t)
tf.Tensor(-1.0439385, shape=(), dtype=float32)
>>> values = pyhf.tensorlib.astensor([0.5, 2.0])
>>> means = pyhf.tensorlib.astensor([0., 2.3])
>>> sigmas = pyhf.tensorlib.astensor([1., 0.8])
>>> t = pyhf.tensorlib.normal_logpdf(values, means, sigmas)
>>> print(t)
tf.Tensor([-1.0439385 -0.7661075], shape=(2,), 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
>>> pyhf.set_backend("tensorflow")
>>> t = pyhf.tensorlib.normal(0.5, 0., 1.)
>>> print(t)
tf.Tensor(0.35206532, shape=(), dtype=float32)
>>> values = pyhf.tensorlib.astensor([0.5, 2.0])
>>> means = pyhf.tensorlib.astensor([0., 2.3])
>>> sigmas = pyhf.tensorlib.astensor([1., 0.8])
>>> t = pyhf.tensorlib.normal(values, means, sigmas)
>>> print(t)
tf.Tensor([0.35206532 0.46481887], shape=(2,), 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=0.0, sigma=1):
"""
Compute the value of cumulative distribution function for the Normal distribution at x.
Example:
>>> import pyhf
>>> pyhf.set_backend("tensorflow")
>>> t = pyhf.tensorlib.normal_cdf(0.8)
>>> print(t)
tf.Tensor(0.7881446, shape=(), dtype=float32)
>>> values = pyhf.tensorlib.astensor([0.8, 2.0])
>>> t = pyhf.tensorlib.normal_cdf(values)
>>> print(t)
tf.Tensor([0.7881446 0.97724986], shape=(2,), 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(
self.astensor(mu, dtype='float'), self.astensor(sigma, dtype='float')
)
return normal.cdf(x)
[docs] def poisson_dist(self, rate):
r"""
Construct a Poisson distribution with rate parameter :code:`rate`.
Example:
>>> import pyhf
>>> pyhf.set_backend("tensorflow")
>>> rates = pyhf.tensorlib.astensor([5, 8])
>>> values = pyhf.tensorlib.astensor([4, 9])
>>> poissons = pyhf.tensorlib.poisson_dist(rates)
>>> t = poissons.log_prob(values)
>>> print(t)
tf.Tensor([-1.7403021 -2.086854 ], shape=(2,), 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"""
Construct a Normal distribution with mean :code:`mu` and standard deviation :code:`sigma`.
Example:
>>> import pyhf
>>> pyhf.set_backend("tensorflow")
>>> 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)
>>> t = normals.log_prob(values)
>>> print(t)
tf.Tensor([-1.4189385 -2.2257915], shape=(2,), 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)