`numpy:vectorize`

source: /numpy/__init__.py

Summary

Returns an object that acts like pyfunc, but takes arrays as input.

Extended Summary

Define a vectorized function which takes a nested sequence of objects or numpy arrays as inputs and returns a single numpy array or a tuple of numpy arrays. The vectorized function evaluates pyfunc over successive tuples of the input arrays like the python map function, except it uses the broadcasting rules of numpy.

The data type of the output of vectorized is determined by calling the function with the first element of the input. This can be avoided by specifying the otypes argument.

Parameters

pyfunc : callable, optional: A python function or method. Can be omitted to produce a decorator with keyword arguments.
otypes : str or list of dtypes, optional: The output data type. It must be specified as either a string of typecode characters or a list of data type specifiers. There should be one data type specifier for each output.
doc : str, optional: The docstring for the function. If None, the docstring will be the pyfunc.__doc__.
excluded : set, optional: Set of strings or integers representing the positional or keyword arguments for which the function will not be vectorized. These will be passed directly to pyfunc unmodified.
cache : bool, optional: If neither otypes nor signature are provided, and cache is True, then cache the number of outputs.
signature : string, optional: Generalized universal function signature, e.g., (m,n),(n)->(m) for vectorized matrix-vector multiplication. If provided, pyfunc will be called with (and expected to return) arrays with shapes given by the size of corresponding core dimensions. By default, pyfunc is assumed to take scalars as input and output.

Returns

out : callable: A vectorized function if pyfunc was provided, a decorator otherwise.

Notes

The vectorize function is provided primarily for convenience, not for performance. The implementation is essentially a for loop.

If neither otypes nor signature are specified, then a call to the function with the first argument will be used to determine the number of outputs. The results of this call will be cached if cache is True to prevent calling the function twice. However, to implement the cache, the original function must be wrapped which will slow down subsequent calls, so only do this if your function is expensive.

The new keyword argument interface and excluded argument support further degrades performance.

Examples

import numpy as np
def myfunc(a, b):
    "Return a-b if a>b, otherwise return a+b"
    if a > b:
        return a - b
    else:
        return a + b

✓

vfunc = np.vectorize(myfunc)
vfunc([1, 2, 3, 4], 2)

✓

The docstring is taken from the input function to `vectorize` unless it is specified:

vfunc.__doc__
vfunc = np.vectorize(myfunc, doc='Vectorized `myfunc`')
vfunc.__doc__

✓

The output type is determined by evaluating the first element of the input, unless it is specified:

out = vfunc([1, 2, 3, 4], 2)
type(out[0])
vfunc = np.vectorize(myfunc, otypes=[float])
out = vfunc([1, 2, 3, 4], 2)
type(out[0])

✓

The `excluded` argument can be used to prevent vectorizing over certain arguments. This can be useful for array-like arguments of a fixed length such as the coefficients for a polynomial as in `polyval`:

def mypolyval(p, x):
    _p = list(p)
    res = _p.pop(0)
    while _p:
        res = res*x + _p.pop(0)
    return res

✓

Here, we exclude the zeroth argument from vectorization whether it is passed by position or keyword.

vpolyval = np.vectorize(mypolyval, excluded={0, 'p'})
vpolyval([1, 2, 3], x=[0, 1])
vpolyval(p=[1, 2, 3], x=[0, 1])

✓

The `signature` argument allows for vectorizing functions that act on non-scalar arrays of fixed length. For example, you can use it for a vectorized calculation of Pearson correlation coefficient and its p-value:

import scipy.stats
pearsonr = np.vectorize(scipy.stats.pearsonr,
                signature='(n),(n)->(),()')

✓

pearsonr([[0, 1, 2, 3]], [[1, 2, 3, 4], [4, 3, 2, 1]])

✗

Or for a vectorized convolution:

convolve = np.vectorize(np.convolve, signature='(n),(m)->(k)')
convolve(np.eye(4), [1, 2, 1])

✓

Decorator syntax is supported. The decorator can be called as a function to provide keyword arguments:

@np.vectorize
def identity(x):
    return x
identity([0, 1, 2])
@np.vectorize(otypes=[float])
def as_float(x):
    return x
as_float([0, 1, 2])

✓

Aliases

numpy.vectorize