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# numpy.fromfunction

numpy.fromfunction(function, shape, *, dtype=<class '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.

    like array_like, optional

      > Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as `like` supports the `__array_function__` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument.

      Added in version 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=float)
      array([[0., 0.],
             [1., 1.]])

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

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

      >>> np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int)
      array([[0, 1, 2],
             [1, 2, 3],
             [2, 3, 4]])