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]
lauum_fn = choose_fn(A.dtype, scll.dlauum, scll.slauum, "Lapack LAUUM")
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)
s2 = torch.cuda.Stream(device=tc_device)
cublasSetStream(cublas_handle, 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):
# Preallocate 2 columns
whole_col_b = create_fortran((A.shape[0], max_block_size), A.dtype,
tc_device)
whole_col_r = create_fortran((A.shape[0], max_block_size), A.dtype,
tc_device)
temp_bb = create_fortran((max_block_size, max_block_size),
A.dtype,
'cpu',
pin_memory=True)
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
col_b = 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:
barrier.wait()
for r in my_rows:
if r < b:
continue
if r == b:
# SYRK on g_b[bb.length:, :] with output replacing g_b[:bb.length, :]
# C = beta*C + alpha * op(A) @ op(A).T
if b_start + bb.length < N:
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=col_b.data_ptr(),
ldc=col_b.stride(1))
# CPU LAUUM on A[bb.start:bb.end, bb.start:bb.end]. This is a bit messy, should do cleanup.
Abb = A[bb.start:bb.end, bb.start:bb.end] # L\U
if independent_output:
Abb_np = Abb.numpy().copy(order="F")
# Make symmetric: L\L
copy_triang(Abb_np, upper=False)
uu, info = lauum_fn(Abb_np, lower=1,
overwrite_c=True) # LAU\L
Abb.copy_(torch.from_numpy(uu.T)) # L\LAU
else:
uu, info = lauum_fn(Abb.numpy(),
lower=1,
overwrite_c=False) # LAU\L
if b_start + bb.length < N:
zero_triang(uu, upper=True)
Abb.copy_(torch.from_numpy(uu))
if b_start + bb.length < N:
# It is IMPORTANT to do the copy on s1 and then sync it.
tbb = copy_to_host(bb.length, bb.length, col_b, 0, 0,
temp_bb, 0, 0, s1)
s1.synchronize()
if independent_output:
Abb.add_(torch.triu(tbb.T))
else:
Abb.add_(tbb)
else: # r > b
br = block_allocs[r]
# Load column r. Since r > b this column will be shorter than column b
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 and should be stored in a separate g_out block
# Could store output in the first rows of g_b
# 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:
_temp_cpu = copy_to_host(br.length, bb.length, ccb, 0,
0, temp_bb, 0, 0, s1)
s1.synchronize()
A[bb.start:bb.end, br.start:br.end].copy_(_temp_cpu.T)
else:
s1.synchronize()
copy_to_host(br.length, bb.length, ccb, 0, 0, A,
br.start, bb.start, s2)
s2.synchronize()
def _ic_cholesky(A, upper, device, cusolver_handle):
"""Cholesky factorization of matrix `A` on the GPU
Uses the cuSOLVER library for implementation of the POTRF function.
Parameters:
-----------
A : [n, n] CPU or GPU array (column-contiguous)
The (positive definite) matrix which should be factorized
upper : bool
Whether we need to factorize the upper of lower portion of `A`. The other side
of the matrix will not be touched.
device : int
The GPU device on which to run the factorization
cusolver_handle
Pointer to the cuSOLVER context, which needs to be initialized before calling
the function.
Returns:
--------
A : [n, n] CPU or GPU array (column-contiguous)
The factorization of A which overwrites the upper (or lower) triangular part
of the matrix A. This is not a copy of the original matrix.
"""
# Check library initialization
if cusolver_handle is None:
raise RuntimeError("CuSolver must be initialized "
"before running in-core Cholesky.")
if not is_f_contig(A):
raise RuntimeError("Cholesky input must be F-contiguous")
uplo = 'U' if upper else 'L'
n = A.shape[0]
tc_device = torch.device("cuda:%d" % (device))
# Choose functions by dtype
potrf_buf_size = choose_fn(A.dtype, cusolverDnDpotrf_bufferSize,
cusolverDnSpotrf_bufferSize,
"POTRF Buffer size")
potrf_fn = choose_fn(A.dtype, cusolverDnDpotrf, cusolverDnSpotrf, "POTRF")
# noinspection PyUnresolvedReferences
with torch.cuda.device(tc_device):
# Copy A to device memory
if A.is_cuda:
Agpu = A
else:
Agpu = create_fortran(A.shape, A.dtype, tc_device)
copy_to_device(n, n, A, 0, 0, Agpu, 0, 0)
# Create workspace buffer
potrf_bsize = potrf_buf_size(handle=cusolver_handle,
uplo=uplo,
n=n,
A=Agpu.data_ptr(),
lda=n)
potrf_wspace = create_fortran((potrf_bsize, ), A.dtype, tc_device)
dev_info = torch.tensor(4, dtype=torch.int32, device=tc_device)
# Run cholesky
potrf_fn(handle=cusolver_handle,
uplo=uplo,
n=n,
A=Agpu.data_ptr(),
lda=n,
workspace=potrf_wspace.data_ptr(),
Lwork=potrf_bsize,
devInfo=dev_info)
torch.cuda.synchronize()
# Copy back to CPU
if not A.is_cuda:
copy_to_host(n, n, Agpu, 0, 0, A, 0, 0)
del Agpu
del potrf_wspace, dev_info
return A
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_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_):
# Preallocate 2 columns
if not is_cuda:
whole_col_b = create_fortran((A.shape[0], max_block_size), A.dtype,
tc_device)
whole_col_r = create_fortran((A.shape[0], max_block_size), A.dtype,
tc_device)
syrk_out = create_fortran((max_block_size, max_block_size), A.dtype,
tc_device)
lauum_out = create_fortran((max_block_size, max_block_size), A.dtype,
tc_device)
temp_bb = create_fortran((max_block_size, max_block_size),
A.dtype,
'cpu',
pin_memory=True)
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: torch.Tensor = 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:
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):
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_lower(n=bb.length,
A=col_b[:bb.length, :bb.length],
lda=col_b.stride(1),
B=cur_lauum_out,
ldb=max_block_size)
s3.synchronize()
# Add outputs of SYRK and LAUUM (only if SYRK was performed)
if b_start + bb.length < N:
s1.synchronize()
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:
Abb.copy_(cur_lauum_out.T)
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:
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 and should be stored in a separate g_out block
# Could store output in the first rows of g_b
# 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()
A[bb.start:bb.end,
br.start:br.end].copy_(_temp_cpu.T)
elif not is_cuda:
copy_to_host(br.length, bb.length, ccb, 0, 0, A,
br.start, bb.start, s1)
s1.synchronize()
