def init(self, X: Union[torch.Tensor, SparseTensor]):
"""Initialize the preconditioner matrix.
This method must be called before the preconditioner can be used.
Parameters
----------
X : MxD tensor
The matrix of Nystroem centers
"""
dtype = X.dtype
eps = self.params.pc_epsilon(X.dtype)
M = X.size(0)
with TicToc("Kernel", debug=self.params.debug):
if isinstance(X, torch.Tensor):
C = create_same_stride((M, M), X, dtype=dtype, device='cpu',
pin_memory=self._use_cuda)
else: # If sparse tensor we need fortran for kernel calculation
C = create_fortran((M, M), dtype=dtype, device='cpu', pin_memory=self._use_cuda)
self.kernel(X, X, out=C, opt=self.params)
self.fC = C.numpy()
if not is_f_contig(C):
self.fC = self.fC.T
with TicToc("Cholesky 1", debug=self.params.debug):
# Compute T: lower(fC) = T.T
inplace_add_diag(self.fC, eps * M)
self.fC = potrf_wrapper(self.fC, clean=False, upper=False,
use_cuda=self._use_cuda, opt=self.params)
# Save the diagonal which will be overwritten when computing A
self.dT = C.diag()
with TicToc("Copy triangular", debug=self.params.debug):
# Copy lower(fC) to upper(fC): upper(fC) = T.
copy_triang(self.fC, upper=False)
if self._use_cuda:
with TicToc("LAUUM", debug=self.params.debug):
# Product upper(fC) @ upper(fC).T : lower(fC) = T @ T.T
self.fC = lauum_wrapper(self.fC, upper=True, use_cuda=self._use_cuda, opt=self.params)
else:
with TicToc("LAUUM", debug=self.params.debug):
# Product lower(fC).T @ lower(fC) : lower(fC) = T @ T.T
self.fC = lauum_wrapper(self.fC, upper=False, use_cuda=self._use_cuda, opt=self.params)
with TicToc("Cholesky 2", debug=self.params.debug):
# lower(fC) = 1/M * [email protected]
self.fC = mul_triang(self.fC, upper=False, preserve_diag=False, multiplier=1 / M)
# lower(fC) = 1/M * [email protected] + lambda * I
inplace_add_diag(self.fC, self._lambda)
# Cholesky on lower(fC) : lower(fC) = A.T
self.fC = potrf_wrapper(self.fC, clean=False, upper=False,
use_cuda=self._use_cuda, opt=self.params)
self.dA = C.diag()
def gen_random_pd(t, dtype, F=False, seed=0):
A = gen_random(t, t, dtype, F, seed)
copy_triang(A, upper=True)
#A += A.T
#A *= 2
#A += 20
A *= 1
A += 2
A.flat[::t + 1] += t*4
return A
def test_up(self, mat, order, dtype):
mat = fix_mat(mat, order=order, dtype=dtype, numpy=True)
mat_up = mat.copy(order="K")
# Upper triangle of mat_low is 0
mat_up[np.tril_indices(self.t, -1)] = 0
copy_triang(mat_up, upper=True)
assert np.sum(mat_up == 0) == 0
np.testing.assert_array_equal(np.triu(mat), np.triu(mat_up))
np.testing.assert_array_equal(np.tril(mat_up), np.triu(mat_up).T)
np.testing.assert_array_equal(np.diag(mat), np.diag(mat_up))
# Reset and try with `upper=False`
mat_up[np.tril_indices(self.t, -1)] = 0
copy_triang(mat_up, upper=False) # Only the diagonal will be set.
np.testing.assert_array_equal(np.diag(mat), np.diag(mat_up))
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 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)
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)
s1_cuda, s2_cuda = s1._as_parameter_, s2._as_parameter_
cublasSetStream(cublas_handle, s1_cuda)
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 block-columns. The single block is a CPU buffer
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).T
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:
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=whole_col_b.data_ptr(),
ldc=max_block_size)
# Run LAUUM on CPU on Abb.T (transpose because LAPACK works in F-order)
# Result will be on upper(uu). So if we copy back to lower(A), we must copy
# back uu.T -- otherwise we should copy back uu directly.
Abb = A[bb.start:bb.end, bb.start:bb.end]
if independent_output:
Abb_np = Abb.T.numpy().copy(order="F") # U\L
copy_triang(Abb_np, upper=True) # L\L
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.T.numpy(),
lower=0,
overwrite_c=False)
# Zeroing must happen if the SYRK output is to be added: otherwise the
# non-processed part of Abb (i.e. upper(Abb) if not independent_output)
# will be multiplied by 2.
if not is_last_row:
zero_triang(uu, upper=False)
Abb.copy_(torch.from_numpy(uu.T))
if not is_last_row:
cuda_memcpy2d_async(dst=temp_bb.data_ptr(),
dpitch=max_block_size * dts,
src=whole_col_b.data_ptr(),
spitch=max_block_size * dts,
width=bb.length * dts,
height=bb.length,
stream=s1_cuda)
s1.synchronize(
) # TODO: Check if failure when this commented out.
if independent_output:
Abb.add_(
torch.triu(temp_bb[:bb.length, :bb.length].T))
else:
Abb.add_(temp_bb[:bb.length, :bb.length])
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)
#s1.synchronize()
# 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 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='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 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:
s1.synchronize()
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=s2_cuda)
s2.synchronize()
def init(self, X: Union[torch.Tensor, SparseTensor], Y: torch.Tensor,
alpha: torch.Tensor, penalty: float, N: int) -> None:
"""Initialize the preconditioner matrix.
This method must be called before the preconditioner becomes usable.
Parameters
----------
X : MxD tensor
Matrix of Nystroem centers
Y : Mx1 tensor
Vector of targets corresponding to the Nystroem centers `X`
alpha : Mx1 tensor
Parameter vector (of the same dimension as `Y`) which gives the current
solution to the optimization problem.
penalty : float
Regularization amount
N : int
Number of points in the full data-set.
Notes
-----
If `debug=True` is present in the options, this method will print a lot of extra
information pertaining timings of the various preconditioner operations. This can be
useful to help understand how the preconditioner works.
"""
if Y.shape[1] != 1:
raise ValueError(
"Logistic preconditioner can only deal with 1D outputs.")
dtype = X.dtype
M = X.size(0)
eps = self.params.pc_epsilon(dtype)
if self.fC is None:
# This is done only at the first iteration of the logistic-falkon algorithm
# It sets the `T` variable from the paper (chol(kMM)) to the upper part of `self.fC`
with TicToc("Kernel", debug=self.params.debug):
if isinstance(X, torch.Tensor):
C = create_same_stride((M, M),
X,
dtype=dtype,
device='cpu',
pin_memory=self._use_cuda)
else: # If sparse tensor we need fortran for kernel calculation
C = create_fortran((M, M),
dtype=dtype,
device='cpu',
pin_memory=self._use_cuda)
self.kernel(X, X, out=C, opt=self.params)
self.fC = C.numpy()
if not is_f_contig(C):
self.fC = self.fC.T
with TicToc("Add diag", debug=self.params.debug):
# Compute T: lower(fC) = T.T
inplace_add_diag(self.fC, eps * M)
with TicToc("Cholesky 1", debug=self.params.debug):
self.fC = potrf_wrapper(self.fC,
clean=True,
upper=False,
use_cuda=self._use_cuda,
opt=self.params)
# Save the diagonal which will be overwritten when computing A
self.dT = C.diag()
with TicToc("Copy triangular", debug=self.params.debug):
# Copy lower(fC) to upper(fC): upper(fC) = T.
copy_triang(self.fC, upper=False)
else:
if not self._use_cuda:
# Copy non-necessary for cuda since LAUUM will do the copying
with TicToc("Copy triangular", debug=self.params.debug):
# Copy upper(fC) to lower(fC): lower(fC) = T.T
copy_triang(self.fC,
upper=True) # does not copy the diagonal
# Setting diagonal necessary for trmm
inplace_set_diag(self.fC, self.dT)
# Compute W
with TicToc("TRMM", debug=self.params.debug):
# T is on upper(fC). Compute T.T @ alpha
alpha = self._trmm(alpha.clone())
with TicToc("W (ddf)", debug=self.params.debug):
W = self.loss.ddf(Y, alpha)
with TicToc("W-Multiply", debug=self.params.debug):
W.sqrt_()
self.fC = vec_mul_triang(self.fC,
W.numpy().reshape(-1),
side=0,
upper=False)
if self._use_cuda:
with TicToc("LAUUM", debug=self.params.debug):
# Product upper(fC) @ upper(fC).T : lower(fC) = T @ T.T
self.fC = lauum_wrapper(self.fC,
upper=True,
use_cuda=self._use_cuda,
opt=self.params)
else:
with TicToc("LAUUM", debug=self.params.debug):
# Product lower(fC).T @ lower(fC) : lower(fC) = T @ T.T
self.fC = lauum_wrapper(self.fC,
upper=False,
use_cuda=self._use_cuda,
opt=self.params)
# NOTE: Here the multiplier is 1/N instead of the more common 1/M!
mul_triang(self.fC, upper=False, preserve_diag=False, multiplier=1 / N)
with TicToc("Add diag", debug=self.params.debug):
# lower(fC) = 1/N * [email protected] + lambda * I
inplace_add_diag(self.fC, penalty)
with TicToc("Cholesky 2", debug=self.params.debug):
# Cholesky on lower(fC) : lower(fC) = A.T
self.fC = potrf_wrapper(self.fC,
clean=False,
upper=False,
use_cuda=self._use_cuda,
opt=self.params)
self.dA = torch.from_numpy(self.fC).diag()