def test_lauum(self, dtype, get_mat, expected_lower, expected_upper,
lower):
device = torch.device("cuda:0")
mat = get_mat(order="F", dtype=dtype)
gpu_in = move_tensor(mat, device)
gpu_out = move_tensor(mat, device)
gpu_out.fill_(0.0)
# Run on the GPU
cuda_lauum(n=mat.shape[0],
A=gpu_in,
lda=gpu_in.stride(1),
B=gpu_out,
ldb=gpu_out.stride(1),
lower=lower)
torch.cuda.synchronize(device)
# Compare outputs and print timing info
if lower:
np.testing.assert_allclose(np.tril(expected_lower),
gpu_out.cpu().numpy(),
rtol=self.rtol[dtype])
else:
np.testing.assert_allclose(np.triu(expected_upper),
gpu_out.cpu().numpy(),
rtol=self.rtol[dtype])
def par_lauum_f_lower(A: torch.Tensor,
block_allocs: List[BlockAlloc],
my_rows: List[int],
barrier: threading.Barrier,
device_id: int,
cublas_handle,
independent_output: bool):
N = A.shape[0]
is_cuda = A.device.type == "cuda"
trmm_fn = choose_fn(A.dtype, cublasDtrmm, cublasStrmm, "cuBlas TRMM")
gemm_fn = choose_fn(A.dtype, cublasDgemm, cublasSgemm, "cuBlas GEMM")
syrk_fn = choose_fn(A.dtype, cublasDsyrk, cublasSsyrk, "cuBlas SYRK")
tc_device = torch.device('cuda:%d' % (device_id))
s1 = torch.cuda.Stream(device=tc_device)
s3 = torch.cuda.Stream(device=tc_device)
max_block_size = max(ba.length for ba in block_allocs)
my_rows = sorted(my_rows)
with torch.cuda.device(tc_device), torch.cuda.stream(s1), cublas_stream(cublas_handle, s1._as_parameter_):
# Pre allocate b-col, syrk-out, lauum-out
mem_needed = N * max_block_size + 2 * (max_block_size ** 2)
if not is_cuda:
# Also pre alloc r-col
mem_needed += N * max_block_size
f_gpu = torch.empty(size=(mem_needed,), dtype=A.dtype, device=tc_device)
f_offset = 0
whole_col_b, f_offset = _extract_flat(f_gpu, (N, max_block_size), other=A, offset=f_offset)
syrk_out, f_offset = _extract_flat(f_gpu, (max_block_size, max_block_size), other=A, offset=f_offset)
lauum_out, f_offset = _extract_flat(f_gpu, (max_block_size, max_block_size), other=A, offset=f_offset)
if not is_cuda:
temp_bb = create_fortran((max_block_size, max_block_size), A.dtype, 'cpu', pin_memory=True)
whole_col_r, f_offset = _extract_flat(f_gpu, (N, max_block_size), other=A, offset=f_offset)
syrk_out.fill_(0.0)
for b in range(len(block_allocs)):
bb = block_allocs[b]
# Load col b.
# Instead of loading the whole column only load the last rows
# as necessary by inspecting the minimum value in my_rows which is >= b.
try:
min_row = min([r for r in my_rows if r >= b])
b_start = block_allocs[min_row].start
if is_cuda:
col_b = whole_col_b[b_start:, :bb.length]
col_b.copy_(A[b_start:N, bb.start:bb.end])
else:
col_b: torch.Tensor = copy_to_device(
N - b_start, bb.length, A, b_start, bb.start, whole_col_b, 0, 0, s1)
except ValueError:
pass # No column here
if not independent_output:
# wait for copy to device to succeed. After barrier other threads may modify
# the part of col_b which we need!
s1.synchronize()
barrier.wait()
for r in my_rows:
if r == b:
# SYRK on col_b[bb.length:, :] with output into syrk_out[:bb.length, :bb.length]
# C = beta*C + alpha * op(A) @ op(A).T
if b_start + bb.length < N:
cur_syrk_out = syrk_out[:bb.length, :bb.length]
syrk_fn(cublas_handle, uplo='L', trans='T',
n=bb.length, k=col_b.shape[0] - bb.length,
alpha=1.0, A=col_b[bb.length:, :].data_ptr(), lda=col_b.stride(1),
beta=0.0, C=cur_syrk_out.data_ptr(), ldc=syrk_out.stride(1))
with torch.cuda.stream(s3):
if independent_output:
s1.synchronize() # we need col_b to be loaded
cur_lauum_out = lauum_out[:bb.length, :bb.length]
# Note that col_b[:bb.length, :bb.length] == Abb
if independent_output:
# In the independent output case we need to preserve tril(Abb) instead!
cur_lauum_out.copy_(col_b[:bb.length, :bb.length].T)
else:
# In normal case we need triu(Abb) to be preserved in the upper triangle of lauum_out
cur_lauum_out.copy_(col_b[:bb.length, :bb.length])
# LAUUM on col_b[:bb.length, :bb.length], into lauum_out[:bb.length, :bb.length]
cuda_lauum(n=bb.length, A=col_b[:bb.length, :bb.length], lda=col_b.stride(1),
B=cur_lauum_out, ldb=max_block_size, lower=True)
s1.wait_stream(s3) # all subsequent work will need cur_lauum_out
# Add outputs of SYRK and LAUUM (only if SYRK was performed)
if b_start + bb.length < N:
cur_lauum_out.add_(cur_syrk_out)
# Copy lauum_out into the original matrix, while preserving the other side
# of the triangular matrix. This depends on the `independent_output` flag.
Abb = A[bb.start:bb.end, bb.start:bb.end]
if independent_output:
# cuda and non-cuda cases, since we have different orderings.
Abb.copy_(cur_lauum_out.T)
elif is_cuda:
Abb.copy_(cur_lauum_out)
else:
copy_to_host(bb.length, bb.length, cur_lauum_out, 0, 0, Abb, 0, 0, s=s1)
elif r > b:
br = block_allocs[r]
# Load column r. Since r > b this column will be shorter than column b
if is_cuda: # If col_r is already in GPU no copy needed.
col_r = A[br.start:N, br.start:br.end]
else:
col_r = copy_to_device(N - br.start, br.length, A, br.start, br.start,
whole_col_r, 0, 0, s1)
# Restrict column b to only the last 'r' rows
ccb = col_b[br.start - b_start:, :]
# TRMM on g_r[0:br.length, :] which is triangular (r*r)
# and cur_g_b[0:br.length, :]
# output is a r*b matrix stored in the first rows of ccb
# C = alpha * op(A) @ B -- A triangular
trmm_fn(
handle=cublas_handle,
side='L', uplo='L', trans='T', diag='N',
m=br.length, n=bb.length,
alpha=1.0, A=col_r.data_ptr(), lda=col_r.stride(1),
B=ccb.data_ptr(), ldb=ccb.stride(1),
C=ccb.data_ptr(), ldc=ccb.stride(1))
# GEMM on g_r[br.length:, :].T and cur_g_b[bb.length:, :]
# output is the same r*b matrix as before, outputs need to be summed.
# C = alpha * op(A) @ op(B) + beta * C
if br.end < N:
gemm_fn(handle=cublas_handle,
transa='T', transb='N',
m=br.length, n=bb.length, k=col_r.shape[0] - br.length,
alpha=1.0, A=col_r[br.length:, :].data_ptr(), lda=col_r.stride(1),
B=ccb[br.length:, :].data_ptr(), ldb=ccb.stride(1),
beta=1.0, C=ccb.data_ptr(), ldc=ccb.stride(1))
# Copy back to A[r, b]
if independent_output:
if is_cuda:
A[bb.start:bb.end, br.start:br.end].copy_(ccb[:br.length, :bb.length].T)
else:
_temp_cpu = copy_to_host(br.length, bb.length, ccb, 0, 0, temp_bb, 0, 0, s1)
s1.synchronize() # must wait for data to be onto CPU.
A[bb.start:bb.end, br.start:br.end].copy_(_temp_cpu.T)
elif is_cuda:
A[br.start:br.end, bb.start:bb.end].copy_(ccb[:br.length, :bb.length])
else:
copy_to_host(br.length, bb.length, ccb, 0, 0, A, br.start, bb.start, s1)
s1.synchronize()
def par_lauum_c_lower(A: torch.Tensor,
block_allocs: List[BlockAlloc],
my_rows: List[int],
barrier: threading.Barrier,
device_id: int,
cublas_handle,
independent_output: bool):
N = A.shape[0]
dts = sizeof_dtype(A.dtype)
is_cuda = A.device.type == "cuda"
trmm_fn = choose_fn(A.dtype, cublasDtrmm, cublasStrmm, "cuBlas TRMM")
gemm_fn = choose_fn(A.dtype, cublasDgemm, cublasSgemm, "cuBlas GEMM")
syrk_fn = choose_fn(A.dtype, cublasDsyrk, cublasSsyrk, "cuBlas SYRK")
tc_device = torch.device('cuda:%d' % (device_id))
s1 = torch.cuda.Stream(device=tc_device)
s3 = torch.cuda.Stream(device=tc_device)
s1_cuda = s1._as_parameter_
max_block_size = max(ba.length for ba in block_allocs)
my_rows = sorted(my_rows)
with torch.cuda.device(tc_device), torch.cuda.stream(s1), cublas_stream(cublas_handle, s1_cuda):
if not is_cuda:
temp_bb = create_fortran((max_block_size, max_block_size), A.dtype, 'cpu', pin_memory=True).T
# Pre allocate r-col, b-col, syrk-out, lauum-out
mem_needed = 2 * N * max_block_size + 2 * (max_block_size ** 2)
f_gpu = torch.empty(size=(mem_needed,), dtype=A.dtype, device=tc_device)
whole_col_b = f_gpu[:N * max_block_size]
whole_col_r = f_gpu[N * max_block_size: 2 * N * max_block_size]
syrk_out = extract_fortran(f_gpu, size=(max_block_size, max_block_size), offset=2 * N * max_block_size)
lauum_out = extract_fortran(f_gpu, size=(max_block_size, max_block_size), offset=2 * N * max_block_size + max_block_size ** 2)
syrk_out.fill_(0.0)
for b in range(len(block_allocs)):
bb = block_allocs[b]
# Load col b.
# Instead of loading the whole column only load the last rows
# as necessary by inspecting the minimum value in my_rows which is >= b.
try:
min_row = min([r for r in my_rows if r >= b])
b_start = block_allocs[min_row].start
cuda_memcpy2d_async(
dst=whole_col_b.data_ptr(), dpitch=max_block_size * dts,
src=A[b_start, bb.start].data_ptr(), spitch=A.shape[1] * dts,
width=bb.length * dts, height=N - b_start, stream=s1_cuda)
except ValueError: # all of `my_rows` are smaller than `b`.
pass
if not independent_output:
# wait for copy to device to succeed. After barrier other threads may modify
# the part of col_b which we need!
s1.synchronize()
barrier.wait()
for r in my_rows:
if r < b:
continue
if r == b:
is_last_row = b_start + bb.length == N
# SYRK on g_b[bb.length:, :] with output replacing g_b[:bb.length, :]
# C = beta*C + alpha * op(A) @ op(A).T
if not is_last_row:
syrk_fn(cublas_handle, uplo='U', trans='N',
n=bb.length, k=N - b_start - bb.length,
alpha=1.0, A=whole_col_b[bb.length * max_block_size:].data_ptr(),
lda=max_block_size,
beta=0.0, C=syrk_out.data_ptr(), ldc=max_block_size)
with torch.cuda.stream(s3):
if independent_output:
s1.synchronize() # we need col_b to be loaded
# Lower LAUUM for C-contig is equal to upper LAUUM for F-contig
c_lauum_in = whole_col_b[:bb.length * max_block_size].view(bb.length, max_block_size)[:, :bb.length]
c_lauum_out = lauum_out[:bb.length, :bb.length]
if independent_output:
c_lauum_out.copy_(c_lauum_in)
else:
c_lauum_out.copy_(c_lauum_in.T)
cuda_lauum(n=bb.length, A=c_lauum_in, lda=max_block_size, B=c_lauum_out, ldb=max_block_size, lower=False)
s1.wait_stream(s3) # all subsequent work on s1 will need cur_lauum_out
if not is_last_row:
c_lauum_out.add_(syrk_out[:bb.length, :bb.length])
# copy back whole_col_b into Abb
# Now lauum_out is F-contig, while Abb is C-contig
Abb = A[bb.start:bb.end, bb.start:bb.end]
if independent_output:
Abb.copy_(c_lauum_out)
else:
Abb.copy_(c_lauum_out.T)
else: # r > b
br = block_allocs[r]
# Load column r. Since r > b this column will be shorter than column b
cuda_memcpy2d_async(
dst=whole_col_r.data_ptr(), dpitch=max_block_size * dts,
src=A[br.start, br.start].data_ptr(), spitch=A.shape[1] * dts,
width=br.length * dts, height=N - br.start, stream=s1_cuda)
# Restrict column b to only the last 'r' rows
ccb = whole_col_b[(br.start - b_start) * max_block_size:]
# TRMM on g_r[0:br.length, :] which is triangular (r*r)
# and cur_g_b[0:br.length, :]
# output is a r*b matrix and stored in first rows of ccb
# C = alpha * op(A) @ B -- A triangular
trmm_fn(
handle=cublas_handle,
side='R', uplo='U', trans='T', diag='N',
m=bb.length, n=br.length,
alpha=1.0, A=whole_col_r.data_ptr(), lda=max_block_size,
B=ccb.data_ptr(), ldb=max_block_size,
C=ccb.data_ptr(), ldc=max_block_size)
# GEMM on g_r[br.length:, :].T and cur_g_b[bb.length:, :]
# output is the same r*b matrix as before, outputs need to be summed.
# C = alpha * op(A) @ op(B) + beta * C
if br.end < N:
gemm_fn(handle=cublas_handle, transa='N', transb='T',
m=bb.length, n=br.length, k=N - br.start - br.length,
alpha=1.0,
A=ccb[br.length * max_block_size:].data_ptr(),
lda=max_block_size,
B=whole_col_r[br.length * max_block_size:].data_ptr(),
ldb=max_block_size,
beta=1.0, C=ccb.data_ptr(), ldc=max_block_size)
# Copy back to A[r, b]
if is_cuda:
ccb_square = ccb[:max_block_size * br.length].view(br.length, max_block_size)
if independent_output:
A[bb.start:bb.end, br.start:br.end].copy_(ccb_square[:br.length, :bb.length].T)
else:
A[br.start:br.end, bb.start:bb.end].copy_(ccb_square[:br.length, :bb.length])
elif independent_output:
# Copy must be transposed, copy to temp_bb first.
cublasGetMatrixAsync(
rows=bb.length, cols=br.length, elem_size=dts,
A=ccb.data_ptr(), lda=max_block_size,
B=temp_bb.data_ptr(), ldb=max_block_size, stream=s1_cuda)
s1.synchronize()
A[bb.start:bb.end, br.start:br.end].copy_(temp_bb[:br.length, :bb.length].T)
else:
cublasGetMatrixAsync(
rows=bb.length, cols=br.length, elem_size=dts,
A=ccb.data_ptr(), lda=max_block_size,
B=A[br.start, bb.start].data_ptr(), ldb=A.shape[0],
stream=s1_cuda)
s1.synchronize()
