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from functools import lru_cache
import numpy as np
import torch
try:
import triton
import triton.language as tl
except ImportError:
raise RuntimeError("triton import failed; try `pip install --pre triton`")
@triton.jit
def dtw_kernel(
cost, trace, x, x_stride, cost_stride, trace_stride, N, M, BLOCK_SIZE: tl.constexpr
):
offsets = tl.arange(0, BLOCK_SIZE)
mask = offsets < M
for k in range(1, N + M + 1): # k = i + j
tl.debug_barrier()
p0 = cost + (k - 1) * cost_stride
p1 = cost + k * cost_stride
p2 = cost + k * cost_stride + 1
c0 = tl.load(p0 + offsets, mask=mask)
c1 = tl.load(p1 + offsets, mask=mask)
c2 = tl.load(p2 + offsets, mask=mask)
x_row = tl.load(x + (k - 1) * x_stride + offsets, mask=mask, other=0)
cost_row = x_row + tl.minimum(tl.minimum(c0, c1), c2)
cost_ptr = cost + (k + 1) * cost_stride + 1
tl.store(cost_ptr + offsets, cost_row, mask=mask)
trace_ptr = trace + (k + 1) * trace_stride + 1
tl.store(trace_ptr + offsets, 2, mask=mask & (c2 <= c0) & (c2 <= c1))
tl.store(trace_ptr + offsets, 1, mask=mask & (c1 <= c0) & (c1 <= c2))
tl.store(trace_ptr + offsets, 0, mask=mask & (c0 <= c1) & (c0 <= c2))
@lru_cache(maxsize=None)
def median_kernel(filter_width: int):
@triton.jit
def kernel(
y, x, x_stride, y_stride, BLOCK_SIZE: tl.constexpr
): # x.shape[-1] == filter_width
row_idx = tl.program_id(0)
offsets = tl.arange(0, BLOCK_SIZE)
mask = offsets < y_stride
x_ptr = x + row_idx * x_stride # noqa: F841
y_ptr = y + row_idx * y_stride
LOAD_ALL_ROWS_HERE # noqa: F821
BUBBLESORT_HERE # noqa: F821
tl.store(y_ptr + offsets, MIDDLE_ROW_HERE, mask=mask) # noqa: F821
kernel = triton.JITFunction(kernel.fn)
kernel.src = kernel.src.replace(
" LOAD_ALL_ROWS_HERE",
"\n".join(
[
f" row{i} = tl.load(x_ptr + offsets + {i}, mask=mask)"
for i in range(filter_width)
]
),
)
kernel.src = kernel.src.replace(
" BUBBLESORT_HERE",
"\n\n".join(
[
"\n\n".join(
[
"\n".join(
[
f" smaller = tl.where(row{j} < row{j + 1}, row{j}, row{j + 1})",
f" larger = tl.where(row{j} > row{j + 1}, row{j}, row{j + 1})",
f" row{j} = smaller",
f" row{j + 1} = larger",
]
)
for j in range(filter_width - i - 1)
]
)
for i in range(filter_width // 2 + 1)
]
),
)
kernel.src = kernel.src.replace("MIDDLE_ROW_HERE", f"row{filter_width // 2}")
return kernel
def median_filter_cuda(x: torch.Tensor, filter_width: int):
"""Apply a median filter of given width along the last dimension of x"""
slices = x.contiguous().unfold(-1, filter_width, 1)
grid = np.prod(slices.shape[:-2])
kernel = median_kernel(filter_width)
y = torch.empty_like(slices[..., 0])
BLOCK_SIZE = 1 << (y.stride(-2) - 1).bit_length()
kernel[(grid,)](y, x, x.stride(-2), y.stride(-2), BLOCK_SIZE=BLOCK_SIZE)
return y