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Optimise as_windowed and apply :reflect padding to the whole input (#17)
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@jonatanklosko
jonatanklosko committed Aug 30, 2023
1 parent 298f8b1 commit 4f1ee15
Showing 1 changed file with 30 additions and 107 deletions.
137 changes: 30 additions & 107 deletions lib/nx_signal.ex
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Original file line number Diff line number Diff line change
Expand Up @@ -172,10 +172,10 @@ defmodule NxSignal do
* `:window_length` - the number of samples in a window
* `:stride` - The number of samples to skip between windows. Defaults to `1`.
* `:padding` - A can be `:reflect` or a valid padding as per `Nx.pad/3` over the
input tensor's shape. Defaults to `:valid`. If `:reflect` or `:zeros`, the first window will be centered
at the start of the signal. For `:reflect`, each incomplete window will be reflected as if it was
periodic (see examples for `as_windowed/2`). For `:zeros`, each incomplete window will be zero-padded.
* `:padding` - Padding mode, can be `:reflect` or a valid padding as per `Nx.pad/3` over the
input tensor's shape. Defaults to `:valid`. If `:reflect` or `:same`, the first window will be centered
at the start of the signal. The padding is applied for the whole input, rather than individual
windows. For `:zeros`, effectively each incomplete window will be zero-padded.
## Examples
Expand Down Expand Up @@ -219,27 +219,29 @@ defmodule NxSignal do
iex> t = Nx.iota({7});
iex> NxSignal.as_windowed(t, window_length: 6, padding: :reflect, stride: 1)
#Nx.Tensor<
s64[7][6]
s64[8][6]
[
[1, 2, 1, 0, 1, 2],
[3, 2, 1, 0, 1, 2],
[2, 1, 0, 1, 2, 3],
[1, 0, 1, 2, 3, 4],
[0, 1, 2, 3, 4, 5],
[1, 2, 3, 4, 5, 6],
[2, 3, 4, 5, 6, 5],
[3, 4, 5, 6, 5, 4]
[3, 4, 5, 6, 5, 4],
[4, 5, 6, 5, 4, 3]
]
>
iex> NxSignal.as_windowed(Nx.iota({10}), window_length: 6, padding: :reflect, stride: 2)
#Nx.Tensor<
s64[5][6]
s64[6][6]
[
[1, 2, 1, 0, 1, 2],
[3, 2, 1, 0, 1, 2],
[1, 0, 1, 2, 3, 4],
[1, 2, 3, 4, 5, 6],
[3, 4, 5, 6, 7, 8],
[5, 6, 7, 8, 9, 8]
[5, 6, 7, 8, 9, 8],
[7, 8, 9, 8, 7, 6]
]
>
"""
Expand All @@ -257,7 +259,7 @@ defmodule NxSignal do

as_windowed_parse_non_reflect_opts(
shape,
Keyword.put(opts, :padding, [{div(window_length, 2), div(window_length, 2) - 1}])
Keyword.put(opts, :padding, [{div(window_length, 2), div(window_length, 2)}])
)
end

Expand Down Expand Up @@ -333,114 +335,34 @@ defmodule NxSignal do
{window_length, stride, padding, output_shape} =
as_windowed_parse_non_reflect_opts(Nx.shape(tensor), opts)

output = Nx.broadcast(Nx.tensor(0, type: tensor.type), output_shape)
{num_windows, _} = Nx.shape(output)

index_template =
Nx.concatenate([Nx.broadcast(0, {window_length, 1}), Nx.iota({window_length, 1})], axis: 1)

{output, _, _, _, _} =
while {output, i = 0, current_window = 0, t = Nx.pad(tensor, 0, padding), index_template},
current_window < num_windows do
indices = index_template + Nx.stack([current_window, 0])
updates = t |> Nx.slice([i], [window_length]) |> Nx.flatten()

updated = Nx.indexed_add(output, indices, updates)
tensor = Nx.pad(tensor, 0, padding)

{updated, i + stride, current_window + 1, t, index_template}
end

output
as_windowed_apply(tensor, stride, output_shape, window_length)
end

defnp as_windowed_reflect_padding(tensor, opts \\ []) do
# current implementation only supports windowing 1D tensors
{window_length, stride, _padding, output_shape} =
as_windowed_parse_reflect_opts(Nx.shape(tensor), opts)

output = Nx.broadcast(Nx.tensor(0, type: tensor.type), output_shape)
{num_windows, _} = Nx.shape(output)

index_template =
Nx.concatenate([Nx.broadcast(0, {window_length, 1}), Nx.iota({window_length, 1})], axis: 1)

leading_window_indices = generate_leading_window_indices(window_length, stride)

trailing_window_indices =
generate_trailing_window_indices(Nx.size(tensor), window_length, stride)

half_window = div(window_length - 1, 2) + 1

{output, _, _, _, _} =
while {output, i = 0, current_window = 0, t = tensor, index_template},
current_window < num_windows do
# Here windows are centered at the current index

cond do
i < half_window ->
# We're indexing before we have a full window on the left

window = Nx.take(t, leading_window_indices[i])

indices = index_template + Nx.stack([current_window, 0])
updated = Nx.indexed_add(output, indices, window)

{updated, i + stride, current_window + 1, t, index_template}

i > Nx.size(t) - half_window ->
# We're indexing after the last full window on the right
window = Nx.take(t, trailing_window_indices[i - (Nx.size(t) - half_window + 1)])

indices = index_template + Nx.stack([current_window, 0])
updated = Nx.indexed_add(output, indices, window)

{updated, i + stride, current_window + 1, t, index_template}

true ->
# Case where we can index a full window
indices = index_template + Nx.stack([current_window, 0])
updates = t |> Nx.slice([i - half_window], [window_length]) |> Nx.flatten()

updated = Nx.indexed_add(output, indices, updates)

{updated, i + stride, current_window + 1, t, index_template}
end
end

# Now we need to handle the tail-end of the windows,
# since they are currently all the same value. We want to apply the tapering-off
# like we did with the initial windows.

output
end

deftransformp generate_leading_window_indices(window_length, stride) do
half_window = div(window_length, 2)
tensor = Nx.reflect(tensor, padding_config: [{half_window, half_window}])

for offset <- 0..half_window//stride do
partial_length = offset + half_window
padding_length = window_length - partial_length

{partial_length}
|> Nx.iota()
|> Nx.reflect(padding_config: [{padding_length, 0}])
end
|> Nx.stack()
as_windowed_apply(tensor, stride, output_shape, window_length)
end

deftransformp generate_trailing_window_indices(tensor_size, window_length, stride) do
min_index = tensor_size - window_length + 1
defnp as_windowed_apply(tensor, stride, output_shape, window_length) do
output = Nx.broadcast(Nx.tensor(0, type: tensor.type), output_shape)
{num_windows, _} = Nx.shape(output)

for {offset, add} <- Enum.with_index(min_index..(tensor_size - 1)//stride) do
partial_length = tensor_size - offset
padding_length = window_length - partial_length
{output, _, _, _} =
while {output, i = 0, current_window = 0, t = tensor}, current_window < num_windows do
window = t |> Nx.slice([i], [window_length])
updated = Nx.put_slice(output, [current_window, 0], Nx.new_axis(window, 0))
{updated, i + stride, current_window + 1, t}
end

{partial_length}
|> Nx.iota()
|> Nx.add(min_index + add - rem(window_length, 2))
|> Nx.reflect(padding_config: [{0, padding_length}])
end
|> Nx.stack()
output
end

@doc """
Expand Down Expand Up @@ -548,15 +470,16 @@ defmodule NxSignal do
iex> Nx.axis_size(z, :frequencies)
16
iex> Nx.axis_size(z, :frames)
5
6
iex> NxSignal.stft_to_mel(z, sampling_rate, fft_length: fft_length, mel_bins: 4)
#Nx.Tensor<
f32[frames: 5][mel: 4]
f32[frames: 6][mel: 4]
[
[0.2900530695915222, 0.17422175407409668, 0.18422472476959229, 0.09807997941970825],
[0.6093881130218506, 0.5647397041320801, 0.4353824257850647, 0.08635270595550537],
[0.7584103345870972, 0.7085014581680298, 0.5636920928955078, 0.179118812084198],
[0.8461772203445435, 0.7952491044998169, 0.6470762491226196, 0.2520409822463989],
[0.908548891544342, 0.8572604656219482, 0.7078656554222107, 0.3086767792701721],
[0.908548891544342, 0.8572604656219482, 0.7078656554222107, 0.3086767792701721]
]
>
Expand Down

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