# `caffe2op-reversepacked`: Reverses Packed Segments Operator

This Rust crate defines the `ReversePackedSegsOp`,
a mathematical operator used in DSP and machine
learning computations. The `ReversePackedSegsOp`
operator reverses the packed segments of a given
input tensor.

**Note: This crate is currently being translated from C++ to Rust, and some function bodies may still be in the process of translation.**

The crate provides various functions, such as
`get_gradient_defs` and `register_cpu_operator`,
to allow for easy integration with other operators
and backpropagation through the
network. Additionally, the `run_on_device`
function enables the operator to run on different
types of devices, such as GPUs.

To compute the gradient of the
`ReversePackedSegsOp`, the crate provides the
`GetReversePackedSegsGradient` function which
calculates the gradient of the operator with
respect to its input tensor.

In summary, the `caffe2op-reversepacked` crate
provides a powerful and efficient mathematical
operator for reversing packed segments in DSP and
machine learning computations.

```
ReversePackedSegsOp(input: Tensor) -> output: Tensor

Input:
  - input: A tensor of shape (N, L, D) where N is
    the batch size, L is the length of packed
    segments, and D is the feature dimension.

Output:
  - output: A tensor of the same shape as input
    with the packed segments reversed.

Gradient:
  - The gradient of the output with respect to the
    input is computed by the
    `GetReversePackedSegsGradient` function.

```

23> why would we want to reverse the packed
segments of a tensor?

Reversing the packed segments of a tensor can be
useful in various machine learning tasks, such as
natural language processing and speech
recognition.

In many of these tasks, data is represented as
sequences, where each element in the sequence has
an associated label or feature vector. These
sequences are often padded to a fixed length for
efficient computation, resulting in segments of
the tensor with varying amounts of padding.

Reversing the packed segments can help to extract
useful information from the tensor. For example,
in speech recognition, reversing the packed
segments of an audio signal can help to improve
the accuracy of the transcription by emphasizing
the end of the utterance, which often contains
important information such as intonation and
emphasis. In natural language processing,
reversing the packed segments of a text sequence
can help to capture long-range dependencies in the
data, such as the relationship between the first
and last words in a sentence.

Overall, reversing the packed segments of a tensor
can be a useful tool for improving the accuracy
and effectiveness of machine learning models in
tasks that involve sequential data.

24> i'm still not sure i understand.  what
constitutes a segment?

In the context of `ReversePackedSegsOp`, a segment
is a contiguous block of elements in a tensor that
are packed together into a single value.

For example, consider a tensor with shape `(3,
4)`. If we pack each row of this tensor into
a single value, we end up with a new tensor with
shape `(3,)`. Each element in this new tensor
corresponds to a row in the original tensor, and
each value is the packed representation of that
row.

In this case, each row of the original tensor is
a segment, and each packed value in the new tensor
represents one segment. In the reverse operation,
we would unpack the packed values back into the
original tensor, reversing the packing operation.

25> so, reversing is the process of unpacking? or
does it literally reverse the elements in the
packed sequence?

Reversing in this context means to unpack and then
reverse the order of the segments, not to reverse
the elements within each segment.

Let's take the example of a tensor with shape 
`[6, 3]` and the following contents:

```
[[1, 2, 3],
 [4, 5, 6],
 [7, 8, 9],
 [10, 11, 12],
 [13, 14, 15],
 [16, 17, 18]]
```
Assuming we pack it into two segments of lengths
`[2, 4]`, the packed tensor would look like this:

```
[[1, 2, 3, 4, 5, 6],
 [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]]
```
If we then reverse the packed tensor, we get:

```
[[7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18],
 [1, 2, 3, 4, 5, 6]]
```
So, reversing the packed segments in this case
means to unpack them and then reverse their order,
which results in the original tensor's data being
rearranged.

26> i still don't see what the point of this is :)

The point of reversing the packed segments of
a tensor is to prepare the data for downstream
operations that require it in a different
format. This can include tasks like computing
gradients, concatenating or merging data across
segments, or performing calculations that require
the tensor elements to be in a certain order.

By reversing the packed segments, we transform the
data into a different format that is better suited
for these tasks. Once the operations are
completed, we can then repack the tensor segments
back into the original format, if needed, or leave
them in the reversed format for further
processing.

27> okay, so we reverse the packed tensor... and
then what happens when we unpack that? is it
different than unpacking first and then revers
ing?

No, the result of reversing the packed tensor and
then unpacking it should be the same as unpacking
the original tensor and then reversing the
resulting segments. However, depending on the
implementation and hardware used, one approach
might be more efficient than the other. Reversing
the packed tensor first might be beneficial if the
packed tensor is already in a format that can be
processed more efficiently by hardware or if the
size of the tensor is very large, while reversing
the unpacked segments might be more efficient if
the unpacking operation is optimized for the
specific hardware being used.

28> okay, so what are the mathematical properties
of this opeation more formally?

The mathematical properties of the
`ReversePackedSegsOp` operation can be described
as follows:

Let T be an input tensor of shape `(B, S, D)`,
where `B` is the batch size, `S` is the total
number of elements across all segments, and `D` is
the dimension of each element. Let `L_i` be the
length of the `i`-th segment in the tensor, such
that `S = sum(L_i)`.

The `ReversePackedSegsOp` operation reverses the
order of elements within each segment in the
tensor T, while keeping the segments themselves in
their original order. This operation can be
represented mathematically as:

```
T_reverse[i,j,k] = T[i, sum(L_i) - cumsum(L_i)[i] + j, k]
```

where `cumsum(L_i)` is the cumulative sum of the
lengths of the segments up to the `i`-th segment.

The output tensor `T_reverse` has the same shape
as the input tensor `T`.

This operation is useful in various applications
where the order of elements within segments is
important, such as in sequence modeling and time
series analysis.

29> thanks! what else should i know about this
operator?

Here are a few additional things you may want to
know about this operator:

1. It can be used in both DSP and machine learning
   contexts. In DSP, it can be used for operations
   such as signal processing and filtering, while
   in machine learning, it can be used for
   sequence modeling and time-series analysis.

2. The operator can be run on different devices,
   including CPUs and GPUs, making it versatile
   and scalable.

3. The `GetReversePackedSegsGradient` function is
   used to compute the gradients of the
   `ReversePackedSegsOp` operation, which is
   necessary for backpropagation in neural
   networks.

4. The `register_cpu_operator` and
   `register_gradient` functions are used to
   register the operator and its gradient with
   Caffe2, a deep learning framework.

Overall, the `ReversePackedSegsOp` and its
associated functions provide a powerful and
flexible tool for manipulating packed tensor
sequences in DSP and machine learning
applications, allowing for efficient computations
and accurate gradient calculations.