Source code for sympy.printing.theanocode

from __future__ import print_function, division

from sympy.external import import_module
from sympy.printing.printer import Printer
from sympy.core.compatibility import range, is_sequence
from sympy.utilities.exceptions import SymPyDeprecationWarning
import sympy
from functools import partial


theano = import_module('theano')

if theano:
    ts = theano.scalar
    tt = theano.tensor
    from theano.sandbox import linalg as tlinalg

    mapping = {
            sympy.Add: tt.add,
            sympy.Mul: tt.mul,
            sympy.Abs: tt.abs_,
            sympy.sign: tt.sgn,
            sympy.ceiling: tt.ceil,
            sympy.floor: tt.floor,
            sympy.log: tt.log,
            sympy.exp: tt.exp,
            sympy.sqrt: tt.sqrt,
            sympy.cos: tt.cos,
            sympy.acos: tt.arccos,
            sympy.sin: tt.sin,
            sympy.asin: tt.arcsin,
            sympy.tan: tt.tan,
            sympy.atan: tt.arctan,
            sympy.atan2: tt.arctan2,
            sympy.cosh: tt.cosh,
            sympy.acosh: tt.arccosh,
            sympy.sinh: tt.sinh,
            sympy.asinh: tt.arcsinh,
            sympy.tanh: tt.tanh,
            sympy.atanh: tt.arctanh,
            sympy.re: tt.real,
            sympy.im: tt.imag,
            sympy.arg: tt.angle,
            sympy.erf: tt.erf,
            sympy.gamma: tt.gamma,
            sympy.loggamma: tt.gammaln,
            sympy.Pow: tt.pow,
            sympy.Eq: tt.eq,
            sympy.StrictGreaterThan: tt.gt,
            sympy.StrictLessThan: tt.lt,
            sympy.LessThan: tt.le,
            sympy.GreaterThan: tt.ge,
            sympy.And: tt.and_,
            sympy.Or: tt.or_,
            sympy.Max: tt.maximum,  # Sympy accept >2 inputs, Theano only 2
            sympy.Min: tt.minimum,  # Sympy accept >2 inputs, Theano only 2
            # Matrices
            sympy.MatAdd: tt.Elemwise(ts.add),
            sympy.HadamardProduct: tt.Elemwise(ts.mul),
            sympy.Trace: tlinalg.trace,
            sympy.Determinant : tlinalg.det,
            sympy.Inverse: tlinalg.matrix_inverse,
            sympy.Transpose: tt.DimShuffle((False, False), [1, 0]),
    }


[docs]class TheanoPrinter(Printer): """ Code printer which creates Theano symbolic expression graphs. Parameters ========== cache : dict Cache dictionary to use (see :attr:`cache`). If None (default) will use the global cache. To create a printer which does not depend on or alter global state pass an empty dictionary. Note: the dictionary is not copied on initialization of the printer and will be updated in-place, so using the same dict object when creating multiple printers or making multiple calls to :func:`.theano_code` or :func:`.theano_function` means the cache is shared between all these applications. Attributes ========== cache : dict A cache of Theano variables which have been created for Sympy symbol-like objects (e.g. :class:`sympy.core.symbol.Symbol` or :class:`sympy.matrices.expressions.MatrixSymbol`). This is used to ensure that all references to a given symbol in an expression (or multiple expressions) are printed as the same Theano variable, which is created only once. Symbols are differentiated only by name and type. The format of the cache's contents should be considered opaque to the user. """ printmethod = "_theano" def __init__(self, *args, **kwargs): self.cache = kwargs.pop('cache', dict()) super(TheanoPrinter, self).__init__(*args, **kwargs) def _get_key(self, s, name=None, dtype=None, broadcastable=None): """ Get the cache key for a Sympy object. Parameters ========== s : sympy.core.basic.Basic Sympy object to get key for. name : str Name of object, if it does not have a ``name`` attribute. """ if name is None: name = s.name return (name, type(s), s.args, dtype, broadcastable) def _get_or_create(self, s, name=None, dtype=None, broadcastable=None): """ Get the Theano variable for a Sympy symbol from the cache, or create it if it does not exist. """ # Defaults if name is None: name = s.name if dtype is None: dtype = 'floatX' if broadcastable is None: broadcastable = () key = self._get_key(s, name, dtype=dtype, broadcastable=broadcastable) if key in self.cache: return self.cache[key] value = tt.tensor(name=name, dtype=dtype, broadcastable=broadcastable) self.cache[key] = value return value def _print_Symbol(self, s, **kwargs): dtype = kwargs.get('dtypes', {}).get(s) bc = kwargs.get('broadcastables', {}).get(s) return self._get_or_create(s, dtype=dtype, broadcastable=bc) def _print_AppliedUndef(self, s, **kwargs): name = str(type(s)) + '_' + str(s.args[0]) dtype = kwargs.get('dtypes', {}).get(s) bc = kwargs.get('broadcastables', {}).get(s) return self._get_or_create(s, name=name, dtype=dtype, broadcastable=bc) def _print_Basic(self, expr, **kwargs): op = mapping[type(expr)] children = [self._print(arg, **kwargs) for arg in expr.args] return op(*children) def _print_Number(self, n, **kwargs): # Integers already taken care of below, interpret as float return float(n.evalf()) def _print_MatrixSymbol(self, X, **kwargs): dtype = kwargs.get('dtypes', {}).get(X) return self._get_or_create(X, dtype=dtype, broadcastable=(None, None)) def _print_DenseMatrix(self, X, **kwargs): try: tt.stacklists except AttributeError: raise NotImplementedError( "Matrix translation not yet supported in this version of Theano") return tt.stacklists([ [self._print(arg, **kwargs) for arg in L] for L in X.tolist() ]) _print_ImmutableMatrix = _print_ImmutableDenseMatrix = _print_DenseMatrix def _print_MatMul(self, expr, **kwargs): children = [self._print(arg, **kwargs) for arg in expr.args] result = children[0] for child in children[1:]: result = tt.dot(result, child) return result def _print_MatrixSlice(self, expr, **kwargs): parent = self._print(expr.parent, **kwargs) rowslice = self._print(slice(*expr.rowslice), **kwargs) colslice = self._print(slice(*expr.colslice), **kwargs) return parent[rowslice, colslice] def _print_BlockMatrix(self, expr, **kwargs): nrows, ncols = expr.blocks.shape blocks = [[self._print(expr.blocks[r, c], **kwargs) for c in range(ncols)] for r in range(nrows)] return tt.join(0, *[tt.join(1, *row) for row in blocks]) def _print_slice(self, expr, **kwargs): return slice(*[self._print(i, **kwargs) if isinstance(i, sympy.Basic) else i for i in (expr.start, expr.stop, expr.step)]) def _print_Pi(self, expr, **kwargs): return 3.141592653589793 def _print_Piecewise(self, expr, **kwargs): import numpy as np e, cond = expr.args[0].args # First condition and corresponding value # Print conditional expression and value for first condition p_cond = self._print(cond, **kwargs) p_e = self._print(e, **kwargs) # One condition only if len(expr.args) == 1: # Return value if condition else NaN return tt.switch(p_cond, p_e, np.nan) # Return value_1 if condition_1 else evaluate remaining conditions p_remaining = self._print(sympy.Piecewise(*expr.args[1:]), **kwargs) return tt.switch(p_cond, p_e, p_remaining) def _print_Rational(self, expr, **kwargs): return tt.true_div(self._print(expr.p, **kwargs), self._print(expr.q, **kwargs)) def _print_Integer(self, expr, **kwargs): return expr.p def _print_factorial(self, expr, **kwargs): return self._print(sympy.gamma(expr.args[0] + 1), **kwargs) def _print_Derivative(self, deriv, **kwargs): rv = self._print(deriv.expr, **kwargs) for var in deriv.variables: var = self._print(var, **kwargs) rv = tt.Rop(rv, var, tt.ones_like(var)) return rv def emptyPrinter(self, expr): return expr
[docs] def doprint(self, expr, dtypes=None, broadcastables=None): """ Convert a Sympy expression to a Theano graph variable. The ``dtypes`` and ``broadcastables`` arguments are used to specify the data type, dimension, and broadcasting behavior of the Theano variables corresponding to the free symbols in ``expr``. Each is a mapping from Sympy symbols to the value of the corresponding argument to :func:`theano.tensor.Tensor`. See the corresponding `documentation page`__ for more information on broadcasting in Theano. .. __: http://deeplearning.net/software/theano/tutorial/broadcasting.html Parameters ========== expr : sympy.core.expr.Expr Sympy expression to print. dtypes : dict Mapping from Sympy symbols to Theano datatypes to use when creating new Theano variables for those symbols. Corresponds to the ``dtype`` argument to :func:`theano.tensor.Tensor`. Defaults to ``'floatX'`` for symbols not included in the mapping. broadcastables : dict Mapping from Sympy symbols to the value of the ``broadcastable`` argument to :func:`theano.tensor.Tensor` to use when creating Theano variables for those symbols. Defaults to the empty tuple for symbols not included in the mapping (resulting in a scalar). Returns ======= theano.gof.graph.Variable A variable corresponding to the expression's value in a Theano symbolic expression graph. See Also ======== theano.tensor.Tensor """ if dtypes is None: dtypes = {} if broadcastables is None: broadcastables = {} return self._print(expr, dtypes=dtypes, broadcastables=broadcastables)
global_cache = {}
[docs]def theano_code(expr, cache=None, **kwargs): """ Convert a Sympy expression into a Theano graph variable. Parameters ========== expr : sympy.core.expr.Expr Sympy expression object to convert. cache : dict Cached Theano variables (see :attr:`.TheanoPrinter.cache`). Defaults to the module-level global cache. dtypes : dict Passed to :meth:`.TheanoPrinter.doprint`. broadcastables : dict Passed to :meth:`.TheanoPrinter.doprint`. Returns ======= theano.gof.graph.Variable A variable corresponding to the expression's value in a Theano symbolic expression graph. """ if not theano: raise ImportError("theano is required for theano_code") if cache is None: cache = global_cache return TheanoPrinter(cache=cache, settings={}).doprint(expr, **kwargs)
def dim_handling(inputs, dim=None, dims=None, broadcastables=None): """ Get value of ``broadcastables`` argument to :func:`.theano_code` from keyword arguments to :func:`.theano_function`. Included for backwards compatibility. Parameters ========== inputs Sequence of input symbols. 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:`.TheanoPrinter.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 != None: return broadcastables return {}
[docs]def theano_function(inputs, outputs, squeeze=True, scalar=False, **kwargs): """ Create a Theano function from SymPy expressions. The inputs and outputs are converted to Theano variables using :func:`.theano_code` and then passed to :func:`theano.function`. Parameters ========== inputs Sequence of symbols which constitute the inputs of the function. outputs Expression or sequence of expressions which constitute the outputs(s) of the function. The free symbols of each expression must be a subset of ``inputs``. squeeze : bool If ``outputs`` is a sequence of length one, pass the printed value of the lone element of the sequence to :func:`theano.function` instead of the sequence itself. This has the effect of making a function which returns a single array instead of a list containing one array. This behavior is deprecated and the default value will be changed to False in a future release. To get a function that returns a single scalar : bool Convert 0-dimensional arrays in output to scalars. This will return a Python wrapper function around the Theano function object. cache : dict Cached Theano variables (see :attr:`.TheanoPrinter.cache`). Defaults to the module-level global cache. dtypes : dict Passed to :meth:`.TheanoPrinter.doprint`. broadcastables : dict Passed to :meth:`.TheanoPrinter.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. ``theano_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 :class:`theano.compile.function_module.Function` or a Python wrapper function around one. In both cases, the returned value will have a ``theano_function`` attribute which points to the return value of :func:`theano.function`. Examples ======== >>> from sympy.abc import x, y, z >>> from sympy.printing.theanocode import theano_function A simple function with one input and one output: >>> f1 = theano_function([x], x**2 - 1, scalar=True) >>> f1(3) 8.0 A function with multiple inputs and one output: >>> f2 = theano_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 = theano_function([x, y], [x**2 + y**2, x**2 - y**2], scalar=True) >>> f3(2, 3) [13.0, -5.0] See also ======== theano.function dim_handling """ if not theano: raise ImportError("theano is required for theano_function") # Squeeze output sequence of length one if squeeze and is_sequence(outputs) and len(outputs) == 1: SymPyDeprecationWarning( feature='theano_function() with squeeze=True', issue=14986, deprecated_since_version='1.2.1', useinstead='a single expression as "outputs" (not a list)', ).warn() outputs = outputs[0] # Pop off non-theano keyword args cache = kwargs.pop('cache', {}) dtypes = kwargs.pop('dtypes', {}) broadcastables = dim_handling( inputs, dim=kwargs.pop('dim', None), dims=kwargs.pop('dims', None), broadcastables=kwargs.pop('broadcastables', None), ) # Print inputs/outputs code = partial(theano_code, cache=cache, dtypes=dtypes, broadcastables=broadcastables) tinputs = list(map(code, inputs)) is_seq = is_sequence(outputs) if is_seq: toutputs = list(map(code, outputs)) else: toutputs = code(outputs) # Compile theano func func = theano.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.theano_function = func return func # Create wrapper to convert 0-dimensional outputs to scalars def wrapper(*args): out = func(*args) if not is_seq: return out[()] else: return [o[()] if is_0d[i] else o for i, o in enumerate(out)] wrapper.__wrapped__ = func wrapper.__doc__ = func.__doc__ wrapper.theano_function = func return wrapper