multidim-indexing 1.1.0

This repository documents the syntax for multidimensional indexing for Pytorch and Numpy, and offers classes that encapsulates the process and provides additional features on top for data that represents a coordinate grid. You can follow along the code blocks here with the included Jupyter notebook.

Multidimensional Indexing

Suppose we have a multidimensional tensor, which could be a cached voxel grid, or a batch of images (the values are ordered to make clear how the indexing works):

import torch

B = 256  # batch size (optional)
shape = (B, 64, 64)
high = torch.prod(torch.tensor(shape)).to(dtype=torch.long)
data = torch.arange(0, high).reshape(shape)

A key operation on this tensor is to index it for querying and assignment. It is straightforward to index a single value, and particular groupings of dimensions:

# index a single element
print(data[124, 5, 52])

# index all dimensions given the first is index 0 (the following are equivalent)
print(data[0])
print(data[0, :, :])
print(data[0, ...])  # pytorch only syntax

# index all dimensions given the last is index 5 (the following are equivalent)
print(data[..., 5])
print(data[:, :, 5])

It is also straightforward to batch index along a single dimension:

idx = [4, 8, 15, 16, 23, 42]

# index all dimensions given the first follows idx
print(data[idx].shape)  # (len(idx), 64, 64)
print(data[idx, ...].shape)
print(data[idx, :, :].shape)

# index all dimensions given the second follows idx
print(data[:, idx].shape)
print(data[:, idx, :].shape)

It is also reasonable to batch index along multiple dimensions. Note that it does not make sense for idx and idx2 to have different lengths since that would lead to combinations where one is missing a value.

idx = [4, 8, 15, 16, 23, 42]
idx2 = [5, 2, 7, 1, 32, 4]

# index the last dimension when the first two are (4,5), (8,2), (15,7), (16,1), (23,32), and (42,4)
print(data[idx, idx2].shape)  # (len(idx), 64)

It is also common to have a list of entries by their indices that we'd like to batch query.

# indices of 5 entries
idx3 = [[0, 5, 3],
        [2, 7, 5],
        [100, 23, 45],
        [3, 6, 4],
        [4, 2, 1]]

Directly indexing the tensor with a multidimensional index does not do what you want:

print(data[idx3])  # results in an error

Instead, split up the indices by their dimension either manually, or with torch.unbind

# easier to convert it to something that allows column indexing first
idx4 = torch.tensor(idx3)
print(data[idx4[:, 0], idx4[:, 1], idx4[:, 2]])  # returns the 5 entries as desired
print(data[torch.unbind(idx4, -1)])              # can also use unbind

How can it be improved?

Most importantly, it may not be clear why simply doing data[idx3] does not work, and what the correct syntax is. So reading up to here should resolve most questions about indexing with a batch of indices on a multidimensional tensor. This library provides MultidimView variants (torch and numpy) that provide a view for these tensors with features specialized to multidimensional tensor that represent coordinate gridded values:

• direct indexing so data[idx3] does what you want
• optional indexing on values if you specify value ranges
  • value resolution implicitly defined by size of source and value range
• optional safety checking for out of bound values or indices
  • provide default value for out of bound queries instead of throwing an exception

Installation

numpy only

pip install multidim-indexing[numpy]

pytorch only

pip install multidim-indexing[torch]

all

pip install multidim-indexing[all]

Usage

Continuing with data and the indices described before,

from multidim_indexing import torch_view as view

# for numpy, import numpy_view and use NumpyMultidimView

# simple wrapper with bounds checking
data_multi = view.TorchMultidimView(data)
# another view into the data, treating it as a batch of 2 dimensional grid data with X in [-5, 5] and Y in [0, 10]
# can specify value to assign a query if it's out of bounds (defaults to -1)
# note that the invalid value needs to be of the same type as the source, so we can't for example use float('inf') here
data_batch = view.TorchMultidimView(data, value_ranges=[[0, B], [-5, 5], [0, 10]], invalid_value=-1)
# another view into the data, treating it as a 3D grid data with X in [-2.5, 5], Y in [0, 4], and Z in [0, 10]
data_3d = view.TorchMultidimView(data, value_ranges=[[-2.5, 5], [0, 4], [0, 10]])

By default, the nearest grid value is returned. You can instead use linear interpolation like scipy's interpn by setting method='linear' in the constructor.

data_3d = view.TorchMultidimView(data, value_ranges=[[-2.5, 5], [0, 4], [0, 10]], method='linear')

We can then use them like:

# convert index to the corresponding type (pytorch vs numpy)
key = torch.tensor(idx3, dtype=torch.long)
print(data_multi[key])  # returns the 5 entries as desired

# query the other views using grid values
# first, let's try keying the same 2D values across all batches
value_key_per_batch = torch.tensor([[-3.5, 0.2],
                                    [-4, 0.1],
                                    [-7, 0.5],  # this is out of bounds
                                    [3, 2]])
# number of entries to query
N = value_key_per_batch.shape[0]
print(torch.arange(B, dtype=value_key_per_batch.dtype).reshape(B, 1, 1).repeat(1, N, 1).shape)
# make the indices for all batches
value_key_batch = torch.cat(
    (torch.arange(B, dtype=value_key_per_batch.dtype).reshape(B, 1, 1).repeat(1, N, 1),
     value_key_per_batch.repeat(B, 1, 1)), dim=-1)
# keys can have an additional batch indices at the front
print(value_key_batch.shape)  # (B, N, 3)
# these 2 should be the same apart from the first batch index
print(value_key_batch[0:N])
print(value_key_batch[12*N:13*N])

# should see some -1 to indicate invalid value
print(data_batch[value_key_batch]) 

# also there is a shorthand for directly using the per batch indices
print(data_batch[value_key_per_batch.repeat(B,1,1)]) # should be the same as above

value_key_3d = torch.tensor([[-2.5, 0., 0.],  # right on the boundary of validity
                             [-2.51, 0.5, 0],  # out of bounds
                             [5, 4, 10]  # right on the boundary
                             ]
                            )
print(data_3d[value_key_3d])  # (0, -1 for invalid, high - 1)
print(torch.prod(torch.tensor(data.shape)) - 1)
print(high - 1)

The indexing naturally allows setting in addition to querying. Out of bound indices will be ignored.