word-level timestamps in transcribe() (#869)

* word-level timestamps in `transcribe()`

* moving to `timing.py`

* numba implementation for dtw, replacing dtw-python

* triton implementation for dtw

* add test for dtw implementations

* triton implementation of median_filter

* a simple word-level timestamps test

* add scipy as dev dependency

* installs an older version of Triton if CUDA < 11.4

* fix broken merge

* loosen nvcc version match regex

* find_alignment() function

* miscellaneous improvements

* skip median filtering when the input is too small

* Expose punctuation options in cli and transcribe() (#973)

* fix merge error

* fix merge error 2

* annotating that word_timestamps is experimental

---------

Co-authored-by: ryanheise <ryan@ryanheise.com>

tests/test_timing.py

@@ -0,0 +1,87 @@
+import pytest
+import numpy as np
+import scipy.ndimage
+import torch
+
+from whisper.timing import dtw_cpu, dtw_cuda, median_filter
+
+
+sizes = [
+    (10, 20), (32, 16), (123, 1500), (234, 189),
+]
+shapes = [
+    (10,), (1, 15),  (4, 5, 345), (6, 12, 240, 512),
+]
+
+
+@pytest.mark.parametrize("N, M", sizes)
+def test_dtw(N: int, M: int):
+    steps = np.concatenate([np.zeros(N - 1), np.ones(M - 1)])
+    np.random.shuffle(steps)
+    x = np.random.random((N, M)).astype(np.float32)
+
+    i, j, k = 0, 0, 0
+    trace = []
+    while True:
+        x[i, j] -= 1
+        trace.append((i, j))
+
+        if k == len(steps):
+            break
+
+        if k + 1 < len(steps) and steps[k] != steps[k + 1]:
+            i += 1
+            j += 1
+            k += 2
+            continue
+
+        if steps[k] == 0:
+            i += 1
+        if steps[k] == 1:
+            j += 1
+        k += 1
+
+    trace = np.array(trace).T
+    dtw_trace = dtw_cpu(x)
+
+    assert np.allclose(trace, dtw_trace)
+
+
+@pytest.mark.requires_cuda
+@pytest.mark.parametrize("N, M", sizes)
+def test_dtw_cuda_equivalence(N: int, M: int):
+    x_numpy = np.random.randn(N, M).astype(np.float32)
+    x_cuda = torch.from_numpy(x_numpy).cuda()
+
+    trace_cpu = dtw_cpu(x_numpy)
+    trace_cuda = dtw_cuda(x_cuda)
+
+    assert np.allclose(trace_cpu, trace_cuda)
+
+
+@pytest.mark.parametrize("shape", shapes)
+def test_median_filter(shape):
+    x = torch.randn(*shape)
+
+    for filter_width in [3, 5, 7, 13]:
+        filtered = median_filter(x, filter_width)
+
+        # using np.pad to reflect-pad, because Scipy's behavior is different near the edges.
+        pad_width = filter_width // 2
+        padded_x = np.pad(x, [(0, 0)] * (x.ndim - 1) + [(pad_width, pad_width)], mode="reflect")
+        scipy_filtered = scipy.ndimage.median_filter(padded_x, [1] * (x.ndim - 1) + [filter_width])
+        scipy_filtered = scipy_filtered[..., pad_width:-pad_width]
+
+        assert np.allclose(filtered, scipy_filtered)
+
+
+@pytest.mark.requires_cuda
+@pytest.mark.parametrize("shape", shapes)
+def test_median_filter_equivalence(shape):
+    x = torch.randn(*shape)
+
+    for filter_width in [3, 5, 7, 13]:
+        filtered_cpu = median_filter(x, filter_width)
+        filtered_gpu = median_filter(x.cuda(), filter_width).cpu()
+
+        assert np.allclose(filtered_cpu, filtered_gpu)