Function fromfunction

numpy/_core/numeric.py:1829–1897

Construct an array by executing a function over each coordinate. The resulting array therefore has a value ``fn(x, y, z)`` at coordinate ``(x, y, z)``. Parameters ---------- function : callable The function is called with N parameters, where N is the rank of

(function, shape, *, dtype=float, like=None, **kwargs)

@finalize_array_function_like
@set_module('numpy')
def fromfunction(function, shape, *, dtype=float, like=None, **kwargs):
    """
    Construct an array by executing a function over each coordinate.

    The resulting array therefore has a value ``fn(x, y, z)`` at
    coordinate ``(x, y, z)``.

    Parameters
    ----------
    function : callable
        The function is called with N parameters, where N is the rank of
        `shape`.  Each parameter represents the coordinates of the array
        varying along a specific axis.  For example, if `shape`
        were ``(2, 2)``, then the parameters would be
        ``array([[0, 0], [1, 1]])`` and ``array([[0, 1], [0, 1]])``
    shape : (N,) tuple of ints
        Shape of the output array, which also determines the shape of
        the coordinate arrays passed to `function`.
    dtype : data-type, optional
        Data-type of the coordinate arrays passed to `function`.
        By default, `dtype` is float.
    ${ARRAY_FUNCTION_LIKE}

        .. versionadded:: 1.20.0

    Returns
    -------
    fromfunction : any
        The result of the call to `function` is passed back directly.
        Therefore the shape of `fromfunction` is completely determined by
        `function`.  If `function` returns a scalar value, the shape of
        `fromfunction` would not match the `shape` parameter.

    See Also
    --------
    indices, meshgrid

    Notes
    -----
    Keywords other than `dtype` and `like` are passed to `function`.

    Examples
    --------
    >>> import numpy as np
    >>> np.fromfunction(lambda i, j: i, (2, 2), dtype=np.float64)
    array([[0., 0.],
           [1., 1.]])

    >>> np.fromfunction(lambda i, j: j, (2, 2), dtype=np.float64)
    array([[0., 1.],
           [0., 1.]])

    >>> np.fromfunction(lambda i, j: i == j, (3, 3), dtype=np.int_)
    array([[ True, False, False],
           [False,  True, False],
           [False, False,  True]])

    >>> np.fromfunction(lambda i, j: i + j, (3, 3), dtype=np.int_)