def _make_fast_matvec(A):
matvec = None
if csr.isspmatrix_csr(A) and cusparse.check_availability('spmv'):
handle = device.get_cusparse_handle()
op_a = _cusparse.CUSPARSE_OPERATION_NON_TRANSPOSE
alpha = numpy.array(1.0, A.dtype)
beta = numpy.array(0.0, A.dtype)
cuda_dtype = _dtype.to_cuda_dtype(A.dtype)
alg = _cusparse.CUSPARSE_MV_ALG_DEFAULT
x = cupy.empty((A.shape[0], ), dtype=A.dtype)
y = cupy.empty((A.shape[0], ), dtype=A.dtype)
desc_A = cusparse.SpMatDescriptor.create(A)
desc_x = cusparse.DnVecDescriptor.create(x)
desc_y = cusparse.DnVecDescriptor.create(y)
buff_size = _cusparse.spMV_bufferSize(handle, op_a, alpha.ctypes.data,
desc_A.desc, desc_x.desc,
beta.ctypes.data, desc_y.desc,
cuda_dtype, alg)
buff = cupy.empty(buff_size, cupy.int8)
del x, desc_x, y, desc_y
def matvec(x):
y = cupy.empty_like(x)
desc_x = cusparse.DnVecDescriptor.create(x)
desc_y = cusparse.DnVecDescriptor.create(y)
_cusparse.spMV(handle, op_a, alpha.ctypes.data, desc_A.desc,
desc_x.desc, beta.ctypes.data, desc_y.desc,
cuda_dtype, alg, buff.data.ptr)
return y
return matvec
def __init__(self, A, V, alpha, beta, update_impl='fast'):
assert A.ndim == V.ndim == 2
assert alpha.ndim == beta.ndim == 1
assert A.dtype == V.dtype == alpha.dtype
assert A.dtype.char.lower() == beta.dtype.char
assert A.shape[0] == A.shape[1] == V.shape[1]
assert V.shape[0] == alpha.shape[0] == beta.shape[0]
self.A = A
self.V = V
self.alpha = alpha
self.beta = beta
self.n = V.shape[1]
self.ncv = V.shape[0]
self.update_impl = update_impl
if self.update_impl != 'fast':
return
self.cublas_handle = device.get_cublas_handle()
self.cublas_pointer_mode = _cublas.getPointerMode(self.cublas_handle)
if A.dtype.char == 'f':
self.dotc = _cublas.sdot
self.nrm2 = _cublas.snrm2
self.gemm = _cublas.sgemm
elif A.dtype.char == 'd':
self.dotc = _cublas.ddot
self.nrm2 = _cublas.dnrm2
self.gemm = _cublas.dgemm
elif A.dtype.char == 'F':
self.dotc = _cublas.cdotc
self.nrm2 = _cublas.scnrm2
self.gemm = _cublas.cgemm
elif A.dtype.char == 'D':
self.dotc = _cublas.zdotc
self.nrm2 = _cublas.dznrm2
self.gemm = _cublas.zgemm
else:
raise TypeError('invalid dtype ({})'.format(A.dtype))
if csr.isspmatrix_csr(A) and cusparse.check_availability('spmv'):
self.cusparse_handle = device.get_cusparse_handle()
self.spmv_op_a = _cusparse.CUSPARSE_OPERATION_NON_TRANSPOSE
self.spmv_alpha = numpy.array(1.0, A.dtype)
self.spmv_beta = numpy.array(0.0, A.dtype)
self.spmv_cuda_dtype = cusparse._dtype_to_DataType(A.dtype)
self.spmv_alg = _cusparse.CUSPARSE_MV_ALG_DEFAULT
else:
self.cusparse_handle = None
self.v = cupy.empty((self.n, ), dtype=A.dtype)
self.u = cupy.empty((self.n, ), dtype=A.dtype)
self.uu = cupy.empty((self.ncv, ), dtype=A.dtype)
def _lanczos_fast(A, n, ncv):
cublas_handle = device.get_cublas_handle()
cublas_pointer_mode = _cublas.getPointerMode(cublas_handle)
if A.dtype.char == 'f':
dotc = _cublas.sdot
nrm2 = _cublas.snrm2
gemm = _cublas.sgemm
elif A.dtype.char == 'd':
dotc = _cublas.ddot
nrm2 = _cublas.dnrm2
gemm = _cublas.dgemm
elif A.dtype.char == 'F':
dotc = _cublas.cdotc
nrm2 = _cublas.scnrm2
gemm = _cublas.cgemm
elif A.dtype.char == 'D':
dotc = _cublas.zdotc
nrm2 = _cublas.dznrm2
gemm = _cublas.zgemm
else:
raise TypeError('invalid dtype ({})'.format(A.dtype))
cusparse_handle = None
if csr.isspmatrix_csr(A) and cusparse.check_availability('spmv'):
cusparse_handle = device.get_cusparse_handle()
spmv_op_a = _cusparse.CUSPARSE_OPERATION_NON_TRANSPOSE
spmv_alpha = numpy.array(1.0, A.dtype)
spmv_beta = numpy.array(0.0, A.dtype)
spmv_cuda_dtype = _dtype.to_cuda_dtype(A.dtype)
spmv_alg = _cusparse.CUSPARSE_MV_ALG_DEFAULT
v = cupy.empty((n, ), dtype=A.dtype)
uu = cupy.empty((ncv, ), dtype=A.dtype)
one = numpy.array(1.0, dtype=A.dtype)
zero = numpy.array(0.0, dtype=A.dtype)
mone = numpy.array(-1.0, dtype=A.dtype)
outer_A = A
def aux(A, V, u, alpha, beta, i_start, i_end):
assert A is outer_A
beta_eps = inversion_eps(A.dtype)
# Get ready for spmv if enabled
if cusparse_handle is not None:
# Note: I would like to reuse descriptors and working buffer
# on the next update, but I gave it up because it sometimes
# caused illegal memory access error.
spmv_desc_A = cusparse.SpMatDescriptor.create(A)
spmv_desc_v = cusparse.DnVecDescriptor.create(v)
spmv_desc_u = cusparse.DnVecDescriptor.create(u)
buff_size = _cusparse.spMV_bufferSize(
cusparse_handle, spmv_op_a, spmv_alpha.ctypes.data,
spmv_desc_A.desc, spmv_desc_v.desc, spmv_beta.ctypes.data,
spmv_desc_u.desc, spmv_cuda_dtype, spmv_alg)
spmv_buff = cupy.empty(buff_size, cupy.int8)
v[...] = V[i_start]
for i in range(i_start, i_end):
# Matrix-vector multiplication
if cusparse_handle is None:
u[...] = A @ v
else:
_cusparse.spMV(cusparse_handle, spmv_op_a,
spmv_alpha.ctypes.data, spmv_desc_A.desc,
spmv_desc_v.desc, spmv_beta.ctypes.data,
spmv_desc_u.desc, spmv_cuda_dtype, spmv_alg,
spmv_buff.data.ptr)
# Call dotc
_cublas.setPointerMode(cublas_handle,
_cublas.CUBLAS_POINTER_MODE_DEVICE)
try:
dotc(cublas_handle, n, v.data.ptr, 1, u.data.ptr, 1,
alpha.data.ptr + i * alpha.itemsize)
finally:
_cublas.setPointerMode(cublas_handle, cublas_pointer_mode)
# Orthogonalize
gemm(cublas_handle, _cublas.CUBLAS_OP_C, _cublas.CUBLAS_OP_N, 1,
i + 1, n, one.ctypes.data, u.data.ptr, n, V.data.ptr, n,
zero.ctypes.data, uu.data.ptr, 1)
gemm(cublas_handle, _cublas.CUBLAS_OP_N, _cublas.CUBLAS_OP_C, n, 1,
i + 1, mone.ctypes.data, V.data.ptr, n, uu.data.ptr, 1,
one.ctypes.data, u.data.ptr, n)
# Call nrm2
_cublas.setPointerMode(cublas_handle,
_cublas.CUBLAS_POINTER_MODE_DEVICE)
try:
nrm2(cublas_handle, n, u.data.ptr, 1,
beta.data.ptr + i * beta.itemsize)
finally:
_cublas.setPointerMode(cublas_handle, cublas_pointer_mode)
# Break here as the normalization below touches V[i+1]
if i >= i_end - 1:
break
if beta[i] < beta_eps:
V[i + 1:i_end, :] = 0
u[...] = 0
v[...] = 0
break
if i == i_start:
beta_eps *= beta[i] # scale eps to largest beta
# Normalize
_kernel_normalize(u, beta, i, n, v, V)
return aux