def ufuncify(args, expr, **kwargs):
"""
Generates a binary ufunc-like lambda function for numpy arrays
``args``
Either a Symbol or a tuple of symbols. Specifies the argument sequence
for the ufunc-like function.
``expr``
A SymPy expression that defines the element wise operation
``kwargs``
Optional keyword arguments are forwarded to autowrap().
The returned function can only act on one array at a time, as only the
first argument accept arrays as input.
.. Note:: a *proper* numpy ufunc is required to support broadcasting, type
casting and more. The function returned here, may not qualify for
numpy's definition of a ufunc. That why we use the term ufunc-like.
References
==========
[1] http://docs.scipy.org/doc/numpy/reference/ufuncs.html
Examples
========
>>> from sympy.utilities.autowrap import ufuncify
>>> from sympy.abc import x, y
>>> import numpy as np
>>> f = ufuncify([x, y], y + x**2)
>>> f([1, 2, 3], 2)
[ 3. 6. 11.]
>>> a = f(np.arange(5), 3)
>>> isinstance(a, np.ndarray)
True
>>> print a
[ 3. 4. 7. 12. 19.]
"""
y = C.IndexedBase(C.Dummy('y'))
x = C.IndexedBase(C.Dummy('x'))
m = C.Dummy('m', integer=True)
i = C.Dummy('i', integer=True)
i = C.Idx(i, m)
l = C.Lambda(args, expr)
f = implemented_function('f', l)
if isinstance(args, C.Symbol):
args = [args]
else:
args = list(args)
# ensure correct order of arguments
kwargs['args'] = [y, x] + args[1:] + [m]
# first argument accepts an array
args[0] = x[i]
return autowrap(C.Equality(y[i], f(*args)), **kwargs)
def _eval_rewrite_as_Sum(self, arg):
if arg.is_even:
k = C.Dummy("k", integer=True)
j = C.Dummy("j", integer=True)
n = self.args[0] / 2
Em = (S.ImaginaryUnit * C.Sum( C.Sum( C.binomial(k, j) * ((-1)**j * (k - 2*j)**(2*n + 1)) /
(2**k*S.ImaginaryUnit**k * k), (j, 0, k)), (k, 1, 2*n + 1)))
return Em
def ufuncify(args, expr, **kwargs):
"""Generates a binary ufunc-like lambda function for numpy arrays
``args``
Either a Symbol or a tuple of symbols. Specifies the argument sequence
for the ufunc-like function.
``expr``
A Sympy expression that defines the element wise operation
``kwargs``
Optional keyword arguments are forwarded to autowrap().
The returned function can only act on one array at a time, as only the
first argument accept arrays as input.
.. Note:: a *proper* numpy ufunc is required to support broadcasting, type
casting and more. The function returned here, may not qualify for
numpy's definition of a ufunc. That why we use the term ufunc-like.
See http://docs.scipy.org/doc/numpy/reference/ufuncs.html
:Examples:
>>> from sympy.utilities.autowrap import ufuncify
>>> from sympy.abc import x, y, z
>>> f = ufuncify([x, y], y + x**2) # doctest: +SKIP
>>> f([1, 2, 3], 2) # doctest: +SKIP
[2. 5. 10.]
"""
y = C.IndexedBase(C.Dummy('y'))
x = C.IndexedBase(C.Dummy('x'))
m = C.Dummy('m', integer=True)
i = C.Dummy('i', integer=True)
i = C.Idx(i, m)
l = C.Lambda(args, expr)
f = implemented_function('f', l)
if isinstance(args, C.Symbol):
args = [args]
else:
args = list(args)
# first argument accepts an array
args[0] = x[i]
return autowrap(C.Equality(y[i], f(*args)), **kwargs)