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# numpy.vectorize

class numpy.vectorize(pyfunc=np._NoValue, otypes=None, doc=None, excluded=None, cache=False, signature=None)

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

  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 True, then cache the first function call that determines the number of outputs if otypes is not provided.

    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.

  Methods

  `__call__`(*args, **kwargs) | Call self as a function.

  Returns:
    out callable

      A vectorized function if `pyfunc` was provided, a decorator otherwise.

  See also

  `frompyfunc`

    Takes an arbitrary Python function and returns a ufunc

  Notes

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

  If otypes is not 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.

  References

  [1]

  Generalized universal function API

  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)
      array([3, 4, 1, 2])

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

      >>> vfunc.__doc__
      'Return a-b if a>b, otherwise return a+b'
      >>> vfunc = np.vectorize(myfunc, doc='Vectorized `myfunc`')
      >>> vfunc.__doc__
      'Vectorized `myfunc`'

  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])
      <class 'numpy.int64'>
      >>> vfunc = np.vectorize(myfunc, otypes=[float])
      >>> out = vfunc([1, 2, 3, 4], 2)
      >>> type(out[0])
      <class 'numpy.float64'>

  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])
      array([3, 6])
      >>> vpolyval(p=[1, 2, 3], x=[0, 1])
      array([3, 6])

  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]])
      (array([ 1., -1.]), array([ 0.,  0.]))

  Or for a vectorized convolution:

      >>> convolve = np.vectorize(np.convolve, signature='(n),(m)->(k)')
      >>> convolve(np.eye(4), [1, 2, 1])
      array([[1., 2., 1., 0., 0., 0.],
             [0., 1., 2., 1., 0., 0.],
             [0., 0., 1., 2., 1., 0.],
             [0., 0., 0., 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])
      array([0, 1, 2])
      >>> @np.vectorize(otypes=[float])
      ... def as_float(x):
      ...     return x
      ...
      >>> as_float([0, 1, 2])
      array([0., 1., 2.])