Function meshgrid

numpy/lib/_function_base_impl.py:5063–5213

Return a tuple of coordinate matrices from coordinate vectors. Make N-D coordinate arrays for vectorized evaluations of N-D scalar/vector fields over N-D grids, given one-dimensional coordinate arrays x1, x2,..., xn. Parameters ---------- x1, x2,..., xn : array_like

(*xi, copy=True, sparse=False, indexing='xy')

# Based on scitools meshgrid
@array_function_dispatch(_meshgrid_dispatcher)
def meshgrid(*xi, copy=True, sparse=False, indexing='xy'):
    """
    Return a tuple of coordinate matrices from coordinate vectors.

    Make N-D coordinate arrays for vectorized evaluations of
    N-D scalar/vector fields over N-D grids, given
    one-dimensional coordinate arrays x1, x2,..., xn.

    Parameters
    ----------
    x1, x2,..., xn : array_like
        1-D arrays representing the coordinates of a grid.
    indexing : {'xy', 'ij'}, optional
        Cartesian ('xy', default) or matrix ('ij') indexing of output.
        See Notes for more details.
    sparse : bool, optional
        If True the shape of the returned coordinate array for dimension *i*
        is reduced from ``(N1, ..., Ni, ... Nn)`` to
        ``(1, ..., 1, Ni, 1, ..., 1)``.  These sparse coordinate grids are
        intended to be used with :ref:`basics.broadcasting`.  When all
        coordinates are used in an expression, broadcasting still leads to a
        fully-dimensional result array.

        Default is False.

    copy : bool, optional
        If False, a view into the original arrays are returned in order to
        conserve memory.  Default is True.  Please note that
        ``sparse=False, copy=False`` will likely return non-contiguous
        arrays.  Furthermore, more than one element of a broadcast array
        may refer to a single memory location.  If you need to write to the
        arrays, make copies first.

    Returns
    -------
    X1, X2,..., XN : tuple of ndarrays
        For vectors `x1`, `x2`,..., `xn` with lengths ``Ni=len(xi)``,
        returns ``(N1, N2, N3,..., Nn)`` shaped arrays if indexing='ij'
        or ``(N2, N1, N3,..., Nn)`` shaped arrays if indexing='xy'
        with the elements of `xi` repeated to fill the matrix along
        the first dimension for `x1`, the second for `x2` and so on.

    Notes
    -----
    This function supports both indexing conventions through the indexing
    keyword argument.  Giving the string 'ij' returns a meshgrid with
    matrix indexing, while 'xy' returns a meshgrid with Cartesian indexing.
    In the 2-D case with inputs of length M and N, the outputs are of shape
    (N, M) for 'xy' indexing and (M, N) for 'ij' indexing.  In the 3-D case
    with inputs of length M, N and P, outputs are of shape (N, M, P) for
    'xy' indexing and (M, N, P) for 'ij' indexing.  The difference is
    illustrated by the following code snippet::

        xv, yv = np.meshgrid(x, y, indexing='ij')
        for i in range(nx):
            for j in range(ny):
                # treat xv[i,j], yv[i,j]