"""
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 = meshgrid(x, y, sparse=False, indexing='ij')
for i in range(nx):
for j in range(ny):
# treat xv[i,j], yv[i,j]
xv, yv = meshgrid(x, y, sparse=False, indexing='xy')
for i in range(nx):
for j in range(ny):
# treat xv[j,i], yv[j,i]
See Also
--------
index_tricks.mgrid : Construct a multi-dimensional "meshgrid"
using indexing notation.
index_tricks.ogrid : Construct an open multi-dimensional "meshgrid"
using indexing notation.
Examples
--------
>>> nx, ny = (3, 2)
>>> x = np.linspace(0, 1, nx)
>>> y = np.linspace(0, 1, ny)
>>> xv, yv = meshgrid(x, y)
>>> xv
array([[ 0. , 0.5, 1. ],
[ 0. , 0.5, 1. ]])
>>> yv
array([[ 0., 0., 0.],
[ 1., 1., 1.]])
>>> xv, yv = meshgrid(x, y, sparse=True) # make sparse output arrays
>>> xv
array([[ 0. , 0.5, 1. ]])
>>> yv
array([[ 0.],
[ 1.]])
`meshgrid` is very useful to evaluate functions on a grid.
>>> x = np.arange(-5, 5, 0.1)
>>> y = np.arange(-5, 5, 0.1)
>>> xx, yy = meshgrid(x, y, sparse=True)
>>> z = np.sin(xx**2 + yy**2) / (xx**2 + yy**2)
"""
import numpy as np
# Based on scitools meshgrid
[docs]def meshgrid(*xi, **kwargs):
"""Coordinate matrices from two or more 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
----------
xi: 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 a sparse grid is returned in order to conserve memory.
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
-------
ndarray
For vectors `x1`, `x2`,..., 'xn' with lengths ``Ni=len(xi)`` ,
return ``(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.
"""
if len(xi) < 2:
msg = "meshgrid() takes 2 or more arguments (%d given)" % int(len(xi) > 0)
raise ValueError(msg)
args = np.atleast_1d(*xi)
ndim = len(args)
copy_ = kwargs.get("copy", True)
sparse = kwargs.get("sparse", False)
indexing = kwargs.get("indexing", "xy")
if indexing not in ["xy", "ij"]:
raise ValueError("Valid values for `indexing` are 'xy' and 'ij'.")
s0 = (1,) * ndim
output = [x.reshape(s0[:i] + (-1,) + s0[i + 1 : :]) for i, x in enumerate(args)]
shape = [x.size for x in output]
if indexing == "xy":
# switch first and second axis
output[0].shape = (1, -1) + (1,) * (ndim - 2)
output[1].shape = (-1, 1) + (1,) * (ndim - 2)
shape[0], shape[1] = shape[1], shape[0]
if sparse:
if copy_:
return [x.copy() for x in output]
else:
return output
else:
# Return the full N-D matrix (not only the 1-D vector)
if copy_:
mult_fact = np.ones(shape, dtype=int)
return [x * mult_fact for x in output]
else:
return np.broadcast_arrays(*output)
if __name__ == "__main__":
import doctest
doctest.testmod(optionflags=doctest.NORMALIZE_WHITESPACE)
