torch.meshgrid

torch.meshgrid(*tensors, indexing=None)

Creates grids of coordinates specified by the 1D inputs in attr:tensors.

This is helpful when you want to visualize data over some range of inputs. See below for a plotting example.

Given $N$ 1D tensors $T_0 \ldots T_{N-1}$ as inputs with corresponding sizes $S_0 \ldots S_{N-1}$, this creates $N$ N-dimensional tensors $G_0 \ldots G_{N-1}$, each with shape $(S_0, ..., S_{N-1})$ where the output $G_i$ is constructed by expanding $T_i$ to the result shape.

Note

0D inputs are treated equivalently to 1D inputs of a single element.

Warning

torch.meshgrid(*tensors) currently has the same behavior as calling numpy.meshgrid(*arrays, indexing=’ij’).

In the future torch.meshgrid will transition to indexing=’xy’ as the default.

pytorch/pytorch#50276 tracks this issue with the goal of migrating to NumPy’s behavior.

See also

torch.cartesian_prod() has the same effect but it collects the data in a tensor of vectors.

Parameters:

• tensors (list of Tensor) – list of scalars or 1 dimensional tensors. Scalars will be treated as tensors of size $(1,)$ automatically

• indexing (str | None) –

  (str, optional): the indexing mode, either “xy” or “ij”, defaults to “ij”. See warning for future changes.

  If “xy” is selected, the first dimension corresponds to the cardinality of the second input and the second dimension corresponds to the cardinality of the first input.

  If “ij” is selected, the dimensions are in the same order as the cardinality of the inputs.

Returns:

If the input has $N$ tensors of size $S_0 \ldots S_{N-1}`$, then the output will also have $N$ tensors, where each tensor is of shape $(S_0, ..., S_{N-1})$.

Return type:

seq (sequence of Tensors)

Example:

>>> x = torch.tensor([1, 2, 3])
>>> y = torch.tensor([4, 5, 6])

Observe the element-wise pairings across the grid, (1, 4),
(1, 5), ..., (3, 6). This is the same thing as the
cartesian product.
>>> grid_x, grid_y = torch.meshgrid(x, y, indexing='ij')
>>> grid_x
tensor([[1, 1, 1],
        [2, 2, 2],
        [3, 3, 3]])
>>> grid_y
tensor([[4, 5, 6],
        [4, 5, 6],
        [4, 5, 6]])

This correspondence can be seen when these grids are
stacked properly.
>>> torch.equal(torch.cat(tuple(torch.dstack([grid_x, grid_y]))),
...             torch.cartesian_prod(x, y))
True

`torch.meshgrid` is commonly used to produce a grid for
plotting.
>>> import matplotlib.pyplot as plt
>>> xs = torch.linspace(-5, 5, steps=100)
>>> ys = torch.linspace(-5, 5, steps=100)
>>> x, y = torch.meshgrid(xs, ys, indexing='xy')
>>> z = torch.sin(torch.sqrt(x * x + y * y))
>>> ax = plt.axes(projection='3d')
>>> ax.plot_surface(x.numpy(), y.numpy(), z.numpy())
>>> plt.show()