540 lines
18 KiB
Python
540 lines
18 KiB
Python
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from __future__ import annotations
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from typing import Any
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from sympy.external import import_module
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from sympy.printing.printer import Printer
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from sympy.utilities.iterables import is_sequence
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import sympy
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from functools import partial
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aesara = import_module('aesara')
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if aesara:
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aes = aesara.scalar
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aet = aesara.tensor
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from aesara.tensor import nlinalg
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from aesara.tensor.elemwise import Elemwise
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from aesara.tensor.elemwise import DimShuffle
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# `true_divide` replaced `true_div` in Aesara 2.8.11 (released 2023) to
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# match NumPy
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# XXX: Remove this when not needed to support older versions.
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true_divide = getattr(aet, 'true_divide', None)
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if true_divide is None:
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true_divide = aet.true_div
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mapping = {
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sympy.Add: aet.add,
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sympy.Mul: aet.mul,
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sympy.Abs: aet.abs,
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sympy.sign: aet.sgn,
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sympy.ceiling: aet.ceil,
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sympy.floor: aet.floor,
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sympy.log: aet.log,
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sympy.exp: aet.exp,
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sympy.sqrt: aet.sqrt,
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sympy.cos: aet.cos,
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sympy.acos: aet.arccos,
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sympy.sin: aet.sin,
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sympy.asin: aet.arcsin,
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sympy.tan: aet.tan,
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sympy.atan: aet.arctan,
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sympy.atan2: aet.arctan2,
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sympy.cosh: aet.cosh,
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sympy.acosh: aet.arccosh,
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sympy.sinh: aet.sinh,
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sympy.asinh: aet.arcsinh,
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sympy.tanh: aet.tanh,
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sympy.atanh: aet.arctanh,
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sympy.re: aet.real,
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sympy.im: aet.imag,
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sympy.arg: aet.angle,
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sympy.erf: aet.erf,
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sympy.gamma: aet.gamma,
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sympy.loggamma: aet.gammaln,
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sympy.Pow: aet.pow,
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sympy.Eq: aet.eq,
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sympy.StrictGreaterThan: aet.gt,
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sympy.StrictLessThan: aet.lt,
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sympy.LessThan: aet.le,
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sympy.GreaterThan: aet.ge,
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sympy.And: aet.bitwise_and, # bitwise
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sympy.Or: aet.bitwise_or, # bitwise
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sympy.Not: aet.invert, # bitwise
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sympy.Xor: aet.bitwise_xor, # bitwise
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sympy.Max: aet.maximum, # Sympy accept >2 inputs, Aesara only 2
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sympy.Min: aet.minimum, # Sympy accept >2 inputs, Aesara only 2
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sympy.conjugate: aet.conj,
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sympy.core.numbers.ImaginaryUnit: lambda:aet.complex(0,1),
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# Matrices
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sympy.MatAdd: Elemwise(aes.add),
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sympy.HadamardProduct: Elemwise(aes.mul),
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sympy.Trace: nlinalg.trace,
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sympy.Determinant : nlinalg.det,
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sympy.Inverse: nlinalg.matrix_inverse,
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sympy.Transpose: DimShuffle((False, False), [1, 0]),
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}
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class AesaraPrinter(Printer):
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""" Code printer which creates Aesara symbolic expression graphs.
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Parameters
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==========
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cache : dict
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Cache dictionary to use. If None (default) will use
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the global cache. To create a printer which does not depend on or alter
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global state pass an empty dictionary. Note: the dictionary is not
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copied on initialization of the printer and will be updated in-place,
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so using the same dict object when creating multiple printers or making
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multiple calls to :func:`.aesara_code` or :func:`.aesara_function` means
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the cache is shared between all these applications.
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Attributes
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==========
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cache : dict
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A cache of Aesara variables which have been created for SymPy
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symbol-like objects (e.g. :class:`sympy.core.symbol.Symbol` or
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:class:`sympy.matrices.expressions.MatrixSymbol`). This is used to
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ensure that all references to a given symbol in an expression (or
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multiple expressions) are printed as the same Aesara variable, which is
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created only once. Symbols are differentiated only by name and type. The
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format of the cache's contents should be considered opaque to the user.
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"""
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printmethod = "_aesara"
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def __init__(self, *args, **kwargs):
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self.cache = kwargs.pop('cache', {})
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super().__init__(*args, **kwargs)
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def _get_key(self, s, name=None, dtype=None, broadcastable=None):
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""" Get the cache key for a SymPy object.
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Parameters
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==========
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s : sympy.core.basic.Basic
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SymPy object to get key for.
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name : str
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Name of object, if it does not have a ``name`` attribute.
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"""
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if name is None:
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name = s.name
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return (name, type(s), s.args, dtype, broadcastable)
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def _get_or_create(self, s, name=None, dtype=None, broadcastable=None):
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"""
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Get the Aesara variable for a SymPy symbol from the cache, or create it
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if it does not exist.
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"""
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# Defaults
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if name is None:
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name = s.name
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if dtype is None:
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dtype = 'floatX'
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if broadcastable is None:
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broadcastable = ()
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key = self._get_key(s, name, dtype=dtype, broadcastable=broadcastable)
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if key in self.cache:
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return self.cache[key]
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value = aet.tensor(name=name, dtype=dtype, broadcastable=broadcastable)
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self.cache[key] = value
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return value
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def _print_Symbol(self, s, **kwargs):
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dtype = kwargs.get('dtypes', {}).get(s)
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bc = kwargs.get('broadcastables', {}).get(s)
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return self._get_or_create(s, dtype=dtype, broadcastable=bc)
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def _print_AppliedUndef(self, s, **kwargs):
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name = str(type(s)) + '_' + str(s.args[0])
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dtype = kwargs.get('dtypes', {}).get(s)
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bc = kwargs.get('broadcastables', {}).get(s)
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return self._get_or_create(s, name=name, dtype=dtype, broadcastable=bc)
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def _print_Basic(self, expr, **kwargs):
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op = mapping[type(expr)]
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children = [self._print(arg, **kwargs) for arg in expr.args]
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return op(*children)
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def _print_Number(self, n, **kwargs):
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# Integers already taken care of below, interpret as float
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return float(n.evalf())
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def _print_MatrixSymbol(self, X, **kwargs):
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dtype = kwargs.get('dtypes', {}).get(X)
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return self._get_or_create(X, dtype=dtype, broadcastable=(None, None))
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def _print_DenseMatrix(self, X, **kwargs):
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if not hasattr(aet, 'stacklists'):
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raise NotImplementedError(
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"Matrix translation not yet supported in this version of Aesara")
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return aet.stacklists([
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[self._print(arg, **kwargs) for arg in L]
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for L in X.tolist()
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])
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_print_ImmutableMatrix = _print_ImmutableDenseMatrix = _print_DenseMatrix
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def _print_MatMul(self, expr, **kwargs):
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children = [self._print(arg, **kwargs) for arg in expr.args]
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result = children[0]
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for child in children[1:]:
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result = aet.dot(result, child)
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return result
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def _print_MatPow(self, expr, **kwargs):
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children = [self._print(arg, **kwargs) for arg in expr.args]
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result = 1
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if isinstance(children[1], int) and children[1] > 0:
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for i in range(children[1]):
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result = aet.dot(result, children[0])
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else:
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raise NotImplementedError('''Only non-negative integer
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powers of matrices can be handled by Aesara at the moment''')
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return result
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def _print_MatrixSlice(self, expr, **kwargs):
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parent = self._print(expr.parent, **kwargs)
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rowslice = self._print(slice(*expr.rowslice), **kwargs)
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colslice = self._print(slice(*expr.colslice), **kwargs)
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return parent[rowslice, colslice]
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def _print_BlockMatrix(self, expr, **kwargs):
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nrows, ncols = expr.blocks.shape
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blocks = [[self._print(expr.blocks[r, c], **kwargs)
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for c in range(ncols)]
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for r in range(nrows)]
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return aet.join(0, *[aet.join(1, *row) for row in blocks])
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def _print_slice(self, expr, **kwargs):
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return slice(*[self._print(i, **kwargs)
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if isinstance(i, sympy.Basic) else i
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for i in (expr.start, expr.stop, expr.step)])
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def _print_Pi(self, expr, **kwargs):
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return 3.141592653589793
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def _print_Piecewise(self, expr, **kwargs):
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import numpy as np
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e, cond = expr.args[0].args # First condition and corresponding value
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# Print conditional expression and value for first condition
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p_cond = self._print(cond, **kwargs)
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p_e = self._print(e, **kwargs)
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# One condition only
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if len(expr.args) == 1:
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# Return value if condition else NaN
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return aet.switch(p_cond, p_e, np.nan)
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# Return value_1 if condition_1 else evaluate remaining conditions
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p_remaining = self._print(sympy.Piecewise(*expr.args[1:]), **kwargs)
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return aet.switch(p_cond, p_e, p_remaining)
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def _print_Rational(self, expr, **kwargs):
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return true_divide(self._print(expr.p, **kwargs),
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self._print(expr.q, **kwargs))
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def _print_Integer(self, expr, **kwargs):
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return expr.p
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def _print_factorial(self, expr, **kwargs):
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return self._print(sympy.gamma(expr.args[0] + 1), **kwargs)
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def _print_Derivative(self, deriv, **kwargs):
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from aesara.gradient import Rop
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rv = self._print(deriv.expr, **kwargs)
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for var in deriv.variables:
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var = self._print(var, **kwargs)
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rv = Rop(rv, var, aet.ones_like(var))
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return rv
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def emptyPrinter(self, expr):
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return expr
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def doprint(self, expr, dtypes=None, broadcastables=None):
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""" Convert a SymPy expression to a Aesara graph variable.
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The ``dtypes`` and ``broadcastables`` arguments are used to specify the
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data type, dimension, and broadcasting behavior of the Aesara variables
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corresponding to the free symbols in ``expr``. Each is a mapping from
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SymPy symbols to the value of the corresponding argument to
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``aesara.tensor.var.TensorVariable``.
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See the corresponding `documentation page`__ for more information on
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broadcasting in Aesara.
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.. __: https://aesara.readthedocs.io/en/latest/tutorial/broadcasting.html
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Parameters
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==========
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expr : sympy.core.expr.Expr
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SymPy expression to print.
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dtypes : dict
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Mapping from SymPy symbols to Aesara datatypes to use when creating
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new Aesara variables for those symbols. Corresponds to the ``dtype``
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argument to ``aesara.tensor.var.TensorVariable``. Defaults to ``'floatX'``
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for symbols not included in the mapping.
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broadcastables : dict
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Mapping from SymPy symbols to the value of the ``broadcastable``
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argument to ``aesara.tensor.var.TensorVariable`` to use when creating Aesara
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variables for those symbols. Defaults to the empty tuple for symbols
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not included in the mapping (resulting in a scalar).
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Returns
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=======
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aesara.graph.basic.Variable
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A variable corresponding to the expression's value in a Aesara
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symbolic expression graph.
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"""
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if dtypes is None:
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dtypes = {}
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if broadcastables is None:
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broadcastables = {}
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return self._print(expr, dtypes=dtypes, broadcastables=broadcastables)
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global_cache: dict[Any, Any] = {}
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def aesara_code(expr, cache=None, **kwargs):
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"""
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Convert a SymPy expression into a Aesara graph variable.
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Parameters
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==========
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expr : sympy.core.expr.Expr
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SymPy expression object to convert.
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cache : dict
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Cached Aesara variables (see :class:`AesaraPrinter.cache
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<AesaraPrinter>`). Defaults to the module-level global cache.
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dtypes : dict
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Passed to :meth:`.AesaraPrinter.doprint`.
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broadcastables : dict
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Passed to :meth:`.AesaraPrinter.doprint`.
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Returns
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=======
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aesara.graph.basic.Variable
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A variable corresponding to the expression's value in a Aesara symbolic
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expression graph.
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"""
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if not aesara:
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raise ImportError("aesara is required for aesara_code")
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if cache is None:
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cache = global_cache
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return AesaraPrinter(cache=cache, settings={}).doprint(expr, **kwargs)
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def dim_handling(inputs, dim=None, dims=None, broadcastables=None):
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r"""
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Get value of ``broadcastables`` argument to :func:`.aesara_code` from
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keyword arguments to :func:`.aesara_function`.
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Included for backwards compatibility.
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Parameters
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==========
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inputs
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Sequence of input symbols.
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||
|
|
|
||
|
|
dim : int
|
||
|
|
Common number of dimensions for all inputs. Overrides other arguments
|
||
|
|
if given.
|
||
|
|
|
||
|
|
dims : dict
|
||
|
|
Mapping from input symbols to number of dimensions. Overrides
|
||
|
|
``broadcastables`` argument if given.
|
||
|
|
|
||
|
|
broadcastables : dict
|
||
|
|
Explicit value of ``broadcastables`` argument to
|
||
|
|
:meth:`.AesaraPrinter.doprint`. If not None function will return this value unchanged.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
=======
|
||
|
|
dict
|
||
|
|
Dictionary mapping elements of ``inputs`` to their "broadcastable"
|
||
|
|
values (tuple of ``bool``\ s).
|
||
|
|
"""
|
||
|
|
if dim is not None:
|
||
|
|
return {s: (False,) * dim for s in inputs}
|
||
|
|
|
||
|
|
if dims is not None:
|
||
|
|
maxdim = max(dims.values())
|
||
|
|
return {
|
||
|
|
s: (False,) * d + (True,) * (maxdim - d)
|
||
|
|
for s, d in dims.items()
|
||
|
|
}
|
||
|
|
|
||
|
|
if broadcastables is not None:
|
||
|
|
return broadcastables
|
||
|
|
|
||
|
|
return {}
|
||
|
|
|
||
|
|
|
||
|
|
def aesara_function(inputs, outputs, scalar=False, *,
|
||
|
|
dim=None, dims=None, broadcastables=None, **kwargs):
|
||
|
|
"""
|
||
|
|
Create a Aesara function from SymPy expressions.
|
||
|
|
|
||
|
|
The inputs and outputs are converted to Aesara variables using
|
||
|
|
:func:`.aesara_code` and then passed to ``aesara.function``.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
==========
|
||
|
|
|
||
|
|
inputs
|
||
|
|
Sequence of symbols which constitute the inputs of the function.
|
||
|
|
|
||
|
|
outputs
|
||
|
|
Sequence of expressions which constitute the outputs(s) of the
|
||
|
|
function. The free symbols of each expression must be a subset of
|
||
|
|
``inputs``.
|
||
|
|
|
||
|
|
scalar : bool
|
||
|
|
Convert 0-dimensional arrays in output to scalars. This will return a
|
||
|
|
Python wrapper function around the Aesara function object.
|
||
|
|
|
||
|
|
cache : dict
|
||
|
|
Cached Aesara variables (see :class:`AesaraPrinter.cache
|
||
|
|
<AesaraPrinter>`). Defaults to the module-level global cache.
|
||
|
|
|
||
|
|
dtypes : dict
|
||
|
|
Passed to :meth:`.AesaraPrinter.doprint`.
|
||
|
|
|
||
|
|
broadcastables : dict
|
||
|
|
Passed to :meth:`.AesaraPrinter.doprint`.
|
||
|
|
|
||
|
|
dims : dict
|
||
|
|
Alternative to ``broadcastables`` argument. Mapping from elements of
|
||
|
|
``inputs`` to integers indicating the dimension of their associated
|
||
|
|
arrays/tensors. Overrides ``broadcastables`` argument if given.
|
||
|
|
|
||
|
|
dim : int
|
||
|
|
Another alternative to the ``broadcastables`` argument. Common number of
|
||
|
|
dimensions to use for all arrays/tensors.
|
||
|
|
``aesara_function([x, y], [...], dim=2)`` is equivalent to using
|
||
|
|
``broadcastables={x: (False, False), y: (False, False)}``.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
=======
|
||
|
|
callable
|
||
|
|
A callable object which takes values of ``inputs`` as positional
|
||
|
|
arguments and returns an output array for each of the expressions
|
||
|
|
in ``outputs``. If ``outputs`` is a single expression the function will
|
||
|
|
return a Numpy array, if it is a list of multiple expressions the
|
||
|
|
function will return a list of arrays. See description of the ``squeeze``
|
||
|
|
argument above for the behavior when a single output is passed in a list.
|
||
|
|
The returned object will either be an instance of
|
||
|
|
``aesara.compile.function.types.Function`` or a Python wrapper
|
||
|
|
function around one. In both cases, the returned value will have a
|
||
|
|
``aesara_function`` attribute which points to the return value of
|
||
|
|
``aesara.function``.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
========
|
||
|
|
|
||
|
|
>>> from sympy.abc import x, y, z
|
||
|
|
>>> from sympy.printing.aesaracode import aesara_function
|
||
|
|
|
||
|
|
A simple function with one input and one output:
|
||
|
|
|
||
|
|
>>> f1 = aesara_function([x], [x**2 - 1], scalar=True)
|
||
|
|
>>> f1(3)
|
||
|
|
8.0
|
||
|
|
|
||
|
|
A function with multiple inputs and one output:
|
||
|
|
|
||
|
|
>>> f2 = aesara_function([x, y, z], [(x**z + y**z)**(1/z)], scalar=True)
|
||
|
|
>>> f2(3, 4, 2)
|
||
|
|
5.0
|
||
|
|
|
||
|
|
A function with multiple inputs and multiple outputs:
|
||
|
|
|
||
|
|
>>> f3 = aesara_function([x, y], [x**2 + y**2, x**2 - y**2], scalar=True)
|
||
|
|
>>> f3(2, 3)
|
||
|
|
[13.0, -5.0]
|
||
|
|
|
||
|
|
See also
|
||
|
|
========
|
||
|
|
|
||
|
|
dim_handling
|
||
|
|
|
||
|
|
"""
|
||
|
|
if not aesara:
|
||
|
|
raise ImportError("Aesara is required for aesara_function")
|
||
|
|
|
||
|
|
# Pop off non-aesara keyword args
|
||
|
|
cache = kwargs.pop('cache', {})
|
||
|
|
dtypes = kwargs.pop('dtypes', {})
|
||
|
|
|
||
|
|
broadcastables = dim_handling(
|
||
|
|
inputs, dim=dim, dims=dims, broadcastables=broadcastables,
|
||
|
|
)
|
||
|
|
|
||
|
|
# Print inputs/outputs
|
||
|
|
code = partial(aesara_code, cache=cache, dtypes=dtypes,
|
||
|
|
broadcastables=broadcastables)
|
||
|
|
tinputs = list(map(code, inputs))
|
||
|
|
toutputs = list(map(code, outputs))
|
||
|
|
|
||
|
|
#fix constant expressions as variables
|
||
|
|
toutputs = [output if isinstance(output, aesara.graph.basic.Variable) else aet.as_tensor_variable(output) for output in toutputs]
|
||
|
|
|
||
|
|
if len(toutputs) == 1:
|
||
|
|
toutputs = toutputs[0]
|
||
|
|
|
||
|
|
# Compile aesara func
|
||
|
|
func = aesara.function(tinputs, toutputs, **kwargs)
|
||
|
|
|
||
|
|
is_0d = [len(o.variable.broadcastable) == 0 for o in func.outputs]
|
||
|
|
|
||
|
|
# No wrapper required
|
||
|
|
if not scalar or not any(is_0d):
|
||
|
|
func.aesara_function = func
|
||
|
|
return func
|
||
|
|
|
||
|
|
# Create wrapper to convert 0-dimensional outputs to scalars
|
||
|
|
def wrapper(*args):
|
||
|
|
out = func(*args)
|
||
|
|
# out can be array(1.0) or [array(1.0), array(2.0)]
|
||
|
|
|
||
|
|
if is_sequence(out):
|
||
|
|
return [o[()] if is_0d[i] else o for i, o in enumerate(out)]
|
||
|
|
else:
|
||
|
|
return out[()]
|
||
|
|
|
||
|
|
wrapper.__wrapped__ = func
|
||
|
|
wrapper.__doc__ = func.__doc__
|
||
|
|
wrapper.aesara_function = func
|
||
|
|
return wrapper
|