def qr(a, mode='reduced'):
"""QR decomposition.
Decompose a given two-dimensional matrix into ``Q * R``, where ``Q``
is an orthonormal and ``R`` is an upper-triangular matrix.
Args:
a (cupy.ndarray): The input matrix.
mode (str): The mode of decomposition. Currently 'reduced',
'complete', 'r', and 'raw' modes are supported. The default mode
is 'reduced', in which matrix ``A = (M, N)`` is decomposed into
``Q``, ``R`` with dimensions ``(M, K)``, ``(K, N)``, where
``K = min(M, N)``.
Returns:
cupy.ndarray, or tuple of ndarray:
Although the type of returned object depends on the mode,
it returns a tuple of ``(Q, R)`` by default.
For details, please see the document of :func:`numpy.linalg.qr`.
.. warning::
This function calls one or more cuSOLVER routine(s) which may yield
invalid results if input conditions are not met.
To detect these invalid results, you can set the `linalg`
configuration to a value that is not `ignore` in
:func:`cupyx.errstate` or :func:`cupyx.seterr`.
.. seealso:: :func:`numpy.linalg.qr`
"""
# TODO(Saito): Current implementation only accepts two-dimensional arrays
_util._assert_cupy_array(a)
_util._assert_rank2(a)
if mode not in ('reduced', 'complete', 'r', 'raw'):
if mode in ('f', 'full', 'e', 'economic'):
msg = 'The deprecated mode \'{}\' is not supported'.format(mode)
raise ValueError(msg)
else:
raise ValueError('Unrecognized mode \'{}\''.format(mode))
# support float32, float64, complex64, and complex128
if a.dtype.char in 'fdFD':
dtype = a.dtype.char
else:
dtype = numpy.promote_types(a.dtype.char, 'f').char
m, n = a.shape
mn = min(m, n)
if mn == 0:
if mode == 'reduced':
return cupy.empty((m, 0), dtype), cupy.empty((0, n), dtype)
elif mode == 'complete':
return cupy.identity(m, dtype), cupy.empty((m, n), dtype)
elif mode == 'r':
return cupy.empty((0, n), dtype)
else: # mode == 'raw'
# compatibility with numpy.linalg.qr
dtype = numpy.promote_types(dtype, 'd')
return cupy.empty((n, m), dtype), cupy.empty((0, ), dtype)
x = a.transpose().astype(dtype, order='C', copy=True)
handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
if dtype == 'f':
geqrf_bufferSize = cusolver.sgeqrf_bufferSize
geqrf = cusolver.sgeqrf
elif dtype == 'd':
geqrf_bufferSize = cusolver.dgeqrf_bufferSize
geqrf = cusolver.dgeqrf
elif dtype == 'F':
geqrf_bufferSize = cusolver.cgeqrf_bufferSize
geqrf = cusolver.cgeqrf
elif dtype == 'D':
geqrf_bufferSize = cusolver.zgeqrf_bufferSize
geqrf = cusolver.zgeqrf
else:
msg = ('dtype must be float32, float64, complex64 or complex128'
' (actual: {})'.format(a.dtype))
raise ValueError(msg)
# compute working space of geqrf and solve R
buffersize = geqrf_bufferSize(handle, m, n, x.data.ptr, n)
workspace = cupy.empty(buffersize, dtype=dtype)
tau = cupy.empty(mn, dtype=dtype)
geqrf(handle, m, n, x.data.ptr, m, tau.data.ptr, workspace.data.ptr,
buffersize, dev_info.data.ptr)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
geqrf, dev_info)
if mode == 'r':
r = x[:, :mn].transpose()
return _util._triu(r)
if mode == 'raw':
if a.dtype.char == 'f':
# The original numpy.linalg.qr returns float64 in raw mode,
# whereas the cusolver returns float32. We agree that the
# following code would be inappropriate, however, in this time
# we explicitly convert them to float64 for compatibility.
return x.astype(numpy.float64), tau.astype(numpy.float64)
elif a.dtype.char == 'F':
# The same applies to complex64
return x.astype(numpy.complex128), tau.astype(numpy.complex128)
return x, tau
if mode == 'complete' and m > n:
mc = m
q = cupy.empty((m, m), dtype)
else:
mc = mn
q = cupy.empty((n, m), dtype)
q[:n] = x
# compute working space of orgqr and solve Q
if dtype == 'f':
orgqr_bufferSize = cusolver.sorgqr_bufferSize
orgqr = cusolver.sorgqr
elif dtype == 'd':
orgqr_bufferSize = cusolver.dorgqr_bufferSize
orgqr = cusolver.dorgqr
elif dtype == 'F':
orgqr_bufferSize = cusolver.cungqr_bufferSize
orgqr = cusolver.cungqr
elif dtype == 'D':
orgqr_bufferSize = cusolver.zungqr_bufferSize
orgqr = cusolver.zungqr
buffersize = orgqr_bufferSize(handle, m, mc, mn, q.data.ptr, m,
tau.data.ptr)
workspace = cupy.empty(buffersize, dtype=dtype)
orgqr(handle, m, mc, mn, q.data.ptr, m, tau.data.ptr, workspace.data.ptr,
buffersize, dev_info.data.ptr)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
orgqr, dev_info)
q = q[:mc].transpose()
r = x[:, :mc].transpose()
return q, _util._triu(r)
def qr(a, mode='reduced'):
"""QR decomposition.
Decompose a given two-dimensional matrix into ``Q * R``, where ``Q``
is an orthonormal and ``R`` is an upper-triangular matrix.
Args:
a (cupy.ndarray): The input matrix.
mode (str): The mode of decomposition. Currently 'reduced',
'complete', 'r', and 'raw' modes are supported. The default mode
is 'reduced', in which matrix ``A = (..., M, N)`` is decomposed
into ``Q``, ``R`` with dimensions ``(..., M, K)``, ``(..., K, N)``,
where ``K = min(M, N)``.
Returns:
cupy.ndarray, or tuple of ndarray:
Although the type of returned object depends on the mode,
it returns a tuple of ``(Q, R)`` by default.
For details, please see the document of :func:`numpy.linalg.qr`.
.. warning::
This function calls one or more cuSOLVER routine(s) which may yield
invalid results if input conditions are not met.
To detect these invalid results, you can set the `linalg`
configuration to a value that is not `ignore` in
:func:`cupyx.errstate` or :func:`cupyx.seterr`.
.. seealso:: :func:`numpy.linalg.qr`
"""
_util._assert_cupy_array(a)
if mode not in ('reduced', 'complete', 'r', 'raw'):
if mode in ('f', 'full', 'e', 'economic'):
msg = 'The deprecated mode \'{}\' is not supported'.format(mode)
else:
msg = 'Unrecognized mode \'{}\''.format(mode)
raise ValueError(msg)
if a.ndim > 2:
return _qr_batched(a, mode)
# support float32, float64, complex64, and complex128
dtype, out_dtype = _util.linalg_common_type(a)
m, n = a.shape
k = min(m, n)
if k == 0:
if mode == 'reduced':
return cupy.empty((m, 0), out_dtype), cupy.empty((0, n), out_dtype)
elif mode == 'complete':
return cupy.identity(m, out_dtype), cupy.empty((m, n), out_dtype)
elif mode == 'r':
return cupy.empty((0, n), out_dtype)
else: # mode == 'raw'
return cupy.empty((n, m), out_dtype), cupy.empty((0,), out_dtype)
x = a.transpose().astype(dtype, order='C', copy=True)
handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
if dtype == 'f':
geqrf_bufferSize = cusolver.sgeqrf_bufferSize
geqrf = cusolver.sgeqrf
elif dtype == 'd':
geqrf_bufferSize = cusolver.dgeqrf_bufferSize
geqrf = cusolver.dgeqrf
elif dtype == 'F':
geqrf_bufferSize = cusolver.cgeqrf_bufferSize
geqrf = cusolver.cgeqrf
elif dtype == 'D':
geqrf_bufferSize = cusolver.zgeqrf_bufferSize
geqrf = cusolver.zgeqrf
else:
msg = ('dtype must be float32, float64, complex64 or complex128'
' (actual: {})'.format(a.dtype))
raise ValueError(msg)
# compute working space of geqrf and solve R
buffersize = geqrf_bufferSize(handle, m, n, x.data.ptr, n)
workspace = cupy.empty(buffersize, dtype=dtype)
tau = cupy.empty(k, dtype=dtype)
geqrf(handle, m, n, x.data.ptr, m,
tau.data.ptr, workspace.data.ptr, buffersize, dev_info.data.ptr)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
geqrf, dev_info)
if mode == 'r':
r = x[:, :k].transpose()
return _util._triu(r).astype(out_dtype, copy=False)
if mode == 'raw':
return (
x.astype(out_dtype, copy=False),
tau.astype(out_dtype, copy=False))
if mode == 'complete' and m > n:
mc = m
q = cupy.empty((m, m), dtype)
else:
mc = k
q = cupy.empty((n, m), dtype)
q[:n] = x
# compute working space of orgqr and solve Q
if dtype == 'f':
orgqr_bufferSize = cusolver.sorgqr_bufferSize
orgqr = cusolver.sorgqr
elif dtype == 'd':
orgqr_bufferSize = cusolver.dorgqr_bufferSize
orgqr = cusolver.dorgqr
elif dtype == 'F':
orgqr_bufferSize = cusolver.cungqr_bufferSize
orgqr = cusolver.cungqr
elif dtype == 'D':
orgqr_bufferSize = cusolver.zungqr_bufferSize
orgqr = cusolver.zungqr
buffersize = orgqr_bufferSize(
handle, m, mc, k, q.data.ptr, m, tau.data.ptr)
workspace = cupy.empty(buffersize, dtype=dtype)
orgqr(
handle, m, mc, k, q.data.ptr, m, tau.data.ptr, workspace.data.ptr,
buffersize, dev_info.data.ptr)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
orgqr, dev_info)
q = q[:mc].transpose()
r = x[:, :mc].transpose()
return (
q.astype(out_dtype, copy=False),
_util._triu(r).astype(out_dtype, copy=False))