Source code for pyhf.tensor.numpy_backend

"""NumPy Tensor Library Module."""
from __future__ import annotations

import logging
from typing import TYPE_CHECKING, Callable, Generic, Mapping, Sequence, TypeVar, Union

import numpy as np

# Needed while numpy lower bound is older than v1.21.0
if TYPE_CHECKING:
    from numpy.typing import ArrayLike, DTypeLike, NBitBase, NDArray
else:
    NBitBase = "NBitBase"

from scipy import special
from scipy.special import gammaln, xlogy
from scipy.stats import norm, poisson

from pyhf.typing import Literal, Shape

T = TypeVar("T", bound=NBitBase)

Tensor = Union["NDArray[np.number[T]]", "NDArray[np.bool_]"]
FloatIntOrBool = Literal["float", "int", "bool"]
log = logging.getLogger(__name__)


class _BasicPoisson:
    def __init__(self, rate: Tensor[T]):
        self.rate = rate

    def sample(self, sample_shape: Shape) -> ArrayLike:
        return poisson(self.rate).rvs(size=sample_shape + self.rate.shape)  # type: ignore[no-any-return]

    def log_prob(self, value: NDArray[np.number[T]]) -> ArrayLike:
        tensorlib: numpy_backend[T] = numpy_backend()
        return tensorlib.poisson_logpdf(value, self.rate)


class _BasicNormal:
    def __init__(self, loc: Tensor[T], scale: Tensor[T]):
        self.loc = loc
        self.scale = scale

    def sample(self, sample_shape: Shape) -> ArrayLike:
        return norm(self.loc, self.scale).rvs(size=sample_shape + self.loc.shape)  # type: ignore[no-any-return]

    def log_prob(self, value: NDArray[np.number[T]]) -> ArrayLike:
        tensorlib: numpy_backend[T] = numpy_backend()
        return tensorlib.normal_logpdf(value, self.loc, self.scale)


[docs] class numpy_backend(Generic[T]): """NumPy backend for pyhf""" __slots__ = ['name', 'precision', 'dtypemap', 'default_do_grad'] #: The array type for numpy array_type = np.ndarray #: The array content type for numpy array_subtype = np.number
[docs] def __init__(self, **kwargs: str): self.name = "numpy" self.precision = kwargs.get("precision", "64b") self.dtypemap: Mapping[ FloatIntOrBool, DTypeLike, # Type[np.floating[T]] | Type[np.integer[T]] | Type[np.bool_], ] = { 'float': np.float64 if self.precision == '64b' else np.float32, 'int': np.int64 if self.precision == '64b' else np.int32, 'bool': np.bool_, } self.default_do_grad: bool = False
[docs] def _setup(self) -> None: """ Run any global setups for the numpy lib. """
[docs] def clip( self, tensor_in: Tensor[T], min_value: np.integer[T] | np.floating[T], max_value: np.integer[T] | np.floating[T], ) -> ArrayLike: """ Clips (limits) the tensor values to be within a specified min and max. Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> a = pyhf.tensorlib.astensor([-2, -1, 0, 1, 2]) >>> pyhf.tensorlib.clip(a, -1, 1) array([-1., -1., 0., 1., 1.]) Args: tensor_in (:obj:`tensor`): The input tensor object min_value (:obj:`scalar` or :obj:`tensor` or :obj:`None`): The minimum value to be clipped to max_value (:obj:`scalar` or :obj:`tensor` or :obj:`None`): The maximum value to be clipped to Returns: NumPy ndarray: A clipped `tensor` """ return np.clip(tensor_in, min_value, max_value)
[docs] def erf(self, tensor_in: Tensor[T]) -> ArrayLike: """ The error function of complex argument. Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> a = pyhf.tensorlib.astensor([-2., -1., 0., 1., 2.]) >>> pyhf.tensorlib.erf(a) array([-0.99532227, -0.84270079, 0. , 0.84270079, 0.99532227]) Args: tensor_in (:obj:`tensor`): The input tensor object Returns: NumPy ndarray: The values of the error function at the given points. """ return special.erf(tensor_in) # type: ignore[no-any-return]
[docs] def erfinv(self, tensor_in: Tensor[T]) -> ArrayLike: """ The inverse of the error function of complex argument. Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> a = pyhf.tensorlib.astensor([-2., -1., 0., 1., 2.]) >>> pyhf.tensorlib.erfinv(pyhf.tensorlib.erf(a)) array([-2., -1., 0., 1., 2.]) Args: tensor_in (:obj:`tensor`): The input tensor object Returns: NumPy ndarray: The values of the inverse of the error function at the given points. """ return special.erfinv(tensor_in) # type: ignore[no-any-return]
[docs] def tile(self, tensor_in: Tensor[T], repeats: int | Sequence[int]) -> ArrayLike: """ Repeat tensor data along a specific dimension Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> a = pyhf.tensorlib.astensor([[1.0], [2.0]]) >>> pyhf.tensorlib.tile(a, (1, 2)) array([[1., 1.], [2., 2.]]) Args: tensor_in (:obj:`tensor`): The tensor to be repeated repeats (:obj:`tensor`): The tuple of multipliers for each dimension Returns: NumPy ndarray: The tensor with repeated axes """ return np.tile(tensor_in, repeats)
[docs] def conditional( self, predicate: NDArray[np.bool_], true_callable: Callable[[], Tensor[T]], false_callable: Callable[[], Tensor[T]], ) -> ArrayLike: """ Runs a callable conditional on the boolean value of the evaluation of a predicate Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> tensorlib = pyhf.tensorlib >>> a = tensorlib.astensor([4]) >>> b = tensorlib.astensor([5]) >>> tensorlib.conditional((a < b)[0], lambda: a + b, lambda: a - b) array([9.]) Args: predicate (:obj:`scalar`): The logical condition that determines which callable to evaluate true_callable (:obj:`callable`): The callable that is evaluated when the :code:`predicate` evaluates to :code:`true` false_callable (:obj:`callable`): The callable that is evaluated when the :code:`predicate` evaluates to :code:`false` Returns: NumPy ndarray: The output of the callable that was evaluated """ return true_callable() if predicate else false_callable()
[docs] def tolist(self, tensor_in: Tensor[T] | list[T]) -> list[T]: try: return tensor_in.tolist() # type: ignore[union-attr,no-any-return] except AttributeError: if isinstance(tensor_in, list): return tensor_in raise
[docs] def outer(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> ArrayLike: return np.outer(tensor_in_1, tensor_in_2) # type: ignore[arg-type]
[docs] def gather(self, tensor: Tensor[T], indices: NDArray[np.integer[T]]) -> ArrayLike: return tensor[indices]
[docs] def boolean_mask(self, tensor: Tensor[T], mask: NDArray[np.bool_]) -> ArrayLike: return tensor[mask]
[docs] def isfinite(self, tensor: Tensor[T]) -> NDArray[np.bool_]: return np.isfinite(tensor)
[docs] def astensor( self, tensor_in: ArrayLike, dtype: FloatIntOrBool = 'float' ) -> ArrayLike: """ Convert to a NumPy array. Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> tensor = pyhf.tensorlib.astensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]) >>> tensor array([[1., 2., 3.], [4., 5., 6.]]) >>> type(tensor) <class 'numpy.ndarray'> Args: tensor_in (Number or Tensor): Tensor object Returns: `numpy.ndarray`: A multi-dimensional, fixed-size homogeneous array. """ try: dtype_obj = self.dtypemap[dtype] except KeyError: log.error( 'Invalid dtype: dtype must be float, int, or bool.', exc_info=True ) raise return np.asarray(tensor_in, dtype=dtype_obj)
[docs] def sum(self, tensor_in: Tensor[T], axis: int | None = None) -> ArrayLike: return np.sum(tensor_in, axis=axis)
[docs] def product(self, tensor_in: Tensor[T], axis: Shape | None = None) -> ArrayLike: return np.prod(tensor_in, axis=axis) # type: ignore[arg-type]
[docs] def abs(self, tensor: Tensor[T]) -> ArrayLike: return np.abs(tensor)
[docs] def ones(self, shape: Shape, dtype: FloatIntOrBool = "float") -> ArrayLike: try: dtype_obj = self.dtypemap[dtype] except KeyError: log.error( f"Invalid dtype: dtype must be one of {list(self.dtypemap)}.", exc_info=True, ) raise return np.ones(shape, dtype=dtype_obj)
[docs] def zeros(self, shape: Shape, dtype: FloatIntOrBool = "float") -> ArrayLike: try: dtype_obj = self.dtypemap[dtype] except KeyError: log.error( f"Invalid dtype: dtype must be one of {list(self.dtypemap)}.", exc_info=True, ) raise return np.zeros(shape, dtype=dtype_obj)
[docs] def power(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> ArrayLike: return np.power(tensor_in_1, tensor_in_2)
[docs] def sqrt(self, tensor_in: Tensor[T]) -> ArrayLike: return np.sqrt(tensor_in)
[docs] def divide(self, tensor_in_1: Tensor[T], tensor_in_2: Tensor[T]) -> ArrayLike: return np.divide(tensor_in_1, tensor_in_2)
[docs] def log(self, tensor_in: Tensor[T]) -> ArrayLike: return np.log(tensor_in)
[docs] def exp(self, tensor_in: Tensor[T]) -> ArrayLike: return np.exp(tensor_in)
[docs] def percentile( self, tensor_in: Tensor[T], q: Tensor[T], axis: None | Shape = None, interpolation: Literal[ "linear", "lower", "higher", "midpoint", "nearest" ] = "linear", ) -> ArrayLike: r""" Compute the :math:`q`-th percentile of the tensor along the specified axis. Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> a = pyhf.tensorlib.astensor([[10, 7, 4], [3, 2, 1]]) >>> pyhf.tensorlib.percentile(a, 50) 3.5 >>> pyhf.tensorlib.percentile(a, 50, axis=1) array([7., 2.]) Args: tensor_in (`tensor`): The tensor containing the data q (:obj:`float` or `tensor`): The :math:`q`-th percentile to compute axis (`number` or `tensor`): The dimensions along which to compute interpolation (:obj:`str`): The interpolation method to use when the desired percentile lies between two data points ``i < j``: - ``'linear'``: ``i + (j - i) * fraction``, where ``fraction`` is the fractional part of the index surrounded by ``i`` and ``j``. - ``'lower'``: ``i``. - ``'higher'``: ``j``. - ``'midpoint'``: ``(i + j) / 2``. - ``'nearest'``: ``i`` or ``j``, whichever is nearest. Returns: NumPy ndarray: The value of the :math:`q`-th percentile of the tensor along the specified axis. .. versionadded:: 0.7.0 """ # see https://github.com/numpy/numpy/issues/22125 return np.percentile(tensor_in, q, axis=axis, interpolation=interpolation) # type: ignore[call-overload,no-any-return]
[docs] def stack(self, sequence: Sequence[Tensor[T]], axis: int = 0) -> ArrayLike: return np.stack(sequence, axis=axis)
[docs] def where( self, mask: NDArray[np.bool_], tensor_in_1: Tensor[T], tensor_in_2: Tensor[T] ) -> ArrayLike: return np.where(mask, tensor_in_1, tensor_in_2)
[docs] def concatenate(self, sequence: Tensor[T], axis: None | int = 0) -> ArrayLike: """ 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 np.concatenate(sequence, axis=axis)
[docs] def simple_broadcast(self, *args: Sequence[Tensor[T]]) -> Sequence[Tensor[T]]: """ Broadcast a sequence of 1 dimensional arrays. Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> pyhf.tensorlib.simple_broadcast( ... pyhf.tensorlib.astensor([1]), ... pyhf.tensorlib.astensor([2, 3, 4]), ... pyhf.tensorlib.astensor([5, 6, 7])) [array([1., 1., 1.]), array([2., 3., 4.]), array([5., 6., 7.])] Args: args (Array of Tensors): Sequence of arrays Returns: list of Tensors: The sequence broadcast together. """ return np.broadcast_arrays(*args)
[docs] def shape(self, tensor: Tensor[T]) -> Shape: return tensor.shape
[docs] def reshape(self, tensor: Tensor[T], newshape: Shape) -> ArrayLike: return np.reshape(tensor, newshape)
[docs] def ravel(self, tensor: Tensor[T]) -> ArrayLike: """ Return a flattened view of the tensor, not a copy. Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> tensor = pyhf.tensorlib.astensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]) >>> pyhf.tensorlib.ravel(tensor) array([1., 2., 3., 4., 5., 6.]) Args: tensor (Tensor): Tensor object Returns: `numpy.ndarray`: A flattened array. """ return np.ravel(tensor)
[docs] def einsum(self, subscripts: str, *operands: Sequence[Tensor[T]]) -> ArrayLike: """ Evaluates the Einstein summation convention on the operands. Using the Einstein summation convention, many common multi-dimensional array operations can be represented in a simple fashion. This function provides a way to compute such summations. The best way to understand this function is to try the examples below, which show how many common NumPy functions can be implemented as calls to einsum. Args: subscripts: str, specifies the subscripts for summation operands: list of array_like, these are the tensors for the operation Returns: tensor: the calculation based on the Einstein summation convention """ return np.einsum(subscripts, *operands) # type: ignore[arg-type,no-any-return]
[docs] def poisson_logpdf(self, n: Tensor[T], lam: Tensor[T]) -> ArrayLike: return xlogy(n, lam) - lam - gammaln(n + 1.0) # type: ignore[no-any-return]
[docs] def poisson(self, n: Tensor[T], lam: Tensor[T]) -> ArrayLike: r""" The continuous 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`. .. note:: Though the p.m.f of the Poisson distribution is not defined for :math:`\lambda = 0`, the limit as :math:`\lambda \to 0` is still defined, which gives a degenerate p.m.f. of .. math:: \lim_{\lambda \to 0} \,\mathrm{Pois}(n | \lambda) = \left\{\begin{array}{ll} 1, & n = 0,\\ 0, & n > 0 \end{array}\right. Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> pyhf.tensorlib.poisson(5., 6.) 0.16062314... >>> values = pyhf.tensorlib.astensor([5., 9.]) >>> rates = pyhf.tensorlib.astensor([6., 8.]) >>> pyhf.tensorlib.poisson(values, rates) array([0.16062314, 0.12407692]) Args: n (:obj:`tensor` or :obj:`float`): The value at which to evaluate the approximation to the Poisson distribution p.m.f. (the observed number of events) lam (:obj:`tensor` or :obj:`float`): The mean of the Poisson distribution p.m.f. (the expected number of events) Returns: NumPy float: Value of the continuous approximation to Poisson(n|lam) """ _n = np.asarray(n) _lam = np.asarray(lam) return np.exp(xlogy(_n, _lam) - _lam - gammaln(_n + 1.0)) # type: ignore[no-any-return,operator]
[docs] def normal_logpdf(self, x: Tensor[T], mu: Tensor[T], sigma: Tensor[T]) -> ArrayLike: # this is much faster than # norm.logpdf(x, loc=mu, scale=sigma) # https://codereview.stackexchange.com/questions/69718/fastest-computation-of-n-likelihoods-on-normal-distributions root2 = np.sqrt(2) root2pi = np.sqrt(2 * np.pi) prefactor = -np.log(sigma * root2pi) summand = -np.square(np.divide((x - mu), (root2 * sigma))) return prefactor + summand # type: ignore[no-any-return]
# def normal_logpdf(self, x, mu, sigma): # return norm.logpdf(x, loc=mu, scale=sigma)
[docs] def normal(self, x: Tensor[T], mu: Tensor[T], sigma: Tensor[T]) -> ArrayLike: 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("numpy") >>> 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]) >>> pyhf.tensorlib.normal(values, means, sigmas) array([0.35206533, 0.46481887]) Args: x (:obj:`tensor` or :obj:`float`): The value at which to evaluate the Normal distribution p.d.f. mu (:obj:`tensor` or :obj:`float`): The mean of the Normal distribution sigma (:obj:`tensor` or :obj:`float`): The standard deviation of the Normal distribution Returns: NumPy float: Value of Normal(x|mu, sigma) """ return norm.pdf(x, loc=mu, scale=sigma) # type: ignore[no-any-return]
[docs] def normal_cdf( self, x: Tensor[T], mu: float | Tensor[T] = 0, sigma: float | Tensor[T] = 1 ) -> ArrayLike: """ The cumulative distribution function for the Normal distribution Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> pyhf.tensorlib.normal_cdf(0.8) 0.78814460... >>> values = pyhf.tensorlib.astensor([0.8, 2.0]) >>> pyhf.tensorlib.normal_cdf(values) array([0.7881446 , 0.97724987]) Args: x (:obj:`tensor` or :obj:`float`): The observed value of the random variable to evaluate the CDF for mu (:obj:`tensor` or :obj:`float`): The mean of the Normal distribution sigma (:obj:`tensor` or :obj:`float`): The standard deviation of the Normal distribution Returns: NumPy float: The CDF """ return norm.cdf(x, loc=mu, scale=sigma) # type: ignore[no-any-return]
[docs] def poisson_dist(self, rate: Tensor[T]) -> _BasicPoisson: r""" The Poisson distribution with rate parameter :code:`rate`. Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> rates = pyhf.tensorlib.astensor([5, 8]) >>> values = pyhf.tensorlib.astensor([4, 9]) >>> poissons = pyhf.tensorlib.poisson_dist(rates) >>> poissons.log_prob(values) array([-1.74030218, -2.0868536 ]) Args: rate (:obj:`tensor` or :obj:`float`): The mean of the Poisson distribution (the expected number of events) Returns: Poisson distribution: The Poisson distribution class """ return _BasicPoisson(rate)
[docs] def normal_dist(self, mu: Tensor[T], sigma: Tensor[T]) -> _BasicNormal: r""" The Normal distribution with mean :code:`mu` and standard deviation :code:`sigma`. Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> 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) >>> normals.log_prob(values) array([-1.41893853, -2.22579135]) Args: mu (:obj:`tensor` or :obj:`float`): The mean of the Normal distribution sigma (:obj:`tensor` or :obj:`float`): The standard deviation of the Normal distribution Returns: Normal distribution: The Normal distribution class """ return _BasicNormal(mu, sigma)
[docs] def to_numpy(self, tensor_in: Tensor[T]) -> ArrayLike: """ Return the input tensor as it already is a :class:`numpy.ndarray`. This API exists only for ``pyhf.tensorlib`` compatibility. Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> tensor = pyhf.tensorlib.astensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]) >>> tensor array([[1., 2., 3.], [4., 5., 6.]]) >>> numpy_ndarray = pyhf.tensorlib.to_numpy(tensor) >>> numpy_ndarray array([[1., 2., 3.], [4., 5., 6.]]) >>> type(numpy_ndarray) <class 'numpy.ndarray'> Args: tensor_in (:obj:`tensor`): The input tensor object. Returns: :class:`numpy.ndarray`: The tensor converted to a NumPy ``ndarray``. """ return tensor_in
[docs] def transpose(self, tensor_in: Tensor[T]) -> ArrayLike: """ Transpose the tensor. Example: >>> import pyhf >>> pyhf.set_backend("numpy") >>> tensor = pyhf.tensorlib.astensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]) >>> tensor array([[1., 2., 3.], [4., 5., 6.]]) >>> pyhf.tensorlib.transpose(tensor) array([[1., 4.], [2., 5.], [3., 6.]]) Args: tensor_in (:obj:`tensor`): The input tensor object. Returns: :class:`numpy.ndarray`: The transpose of the input tensor. .. versionadded:: 0.7.0 """ return tensor_in.transpose()