# numpy.indices¶

`numpy.``indices`(dimensions, dtype=<class 'int'>, sparse=False)[source]

Return an array representing the indices of a grid.

Compute an array where the subarrays contain index values 0, 1, … varying only along the corresponding axis.

Parameters
dimensionssequence of ints

The shape of the grid.

dtypedtype, optional

Data type of the result.

sparseboolean, optional

Return a sparse representation of the grid instead of a dense representation. Default is False.

New in version 1.17.

Returns
gridone ndarray or tuple of ndarrays
If sparse is False:

Returns one array of grid indices, `grid.shape = (len(dimensions),) + tuple(dimensions)`.

If sparse is True:

Returns a tuple of arrays, with `grid[i].shape = (1, ..., 1, dimensions[i], 1, ..., 1)` with dimensions[i] in the ith place

Notes

The output shape in the dense case is obtained by prepending the number of dimensions in front of the tuple of dimensions, i.e. if dimensions is a tuple `(r0, ..., rN-1)` of length `N`, the output shape is `(N, r0, ..., rN-1)`.

The subarrays `grid[k]` contains the N-D array of indices along the `k-th` axis. Explicitly:

```grid[k, i0, i1, ..., iN-1] = ik
```

Examples

```>>> grid = np.indices((2, 3))
>>> grid.shape
(2, 2, 3)
>>> grid        # row indices
array([[0, 0, 0],
[1, 1, 1]])
>>> grid        # column indices
array([[0, 1, 2],
[0, 1, 2]])
```

The indices can be used as an index into an array.

```>>> x = np.arange(20).reshape(5, 4)
>>> row, col = np.indices((2, 3))
>>> x[row, col]
array([[0, 1, 2],
[4, 5, 6]])
```

Note that it would be more straightforward in the above example to extract the required elements directly with `x[:2, :3]`.

If sparse is set to true, the grid will be returned in a sparse representation.

```>>> i, j = np.indices((2, 3), sparse=True)
>>> i.shape
(2, 1)
>>> j.shape
(1, 3)
>>> i        # row indices
array([,
])
>>> j        # column indices
array([[0, 1, 2]])
```