def _promote(type1, type2):
if type2 is None:
return type1
if type1.shape is not None:
if not type1.shape == type2.shape:
raise Exception("We do not handle changes to dtypes that have shape")
return np.promote_types(type1.base, type2.base), type1.shape
return np.promote_types(type1, type2)
def axpy(self, alpha, x, ind=None, x_ind=None):
assert self.check_ind_unique(ind)
assert x.check_ind(x_ind)
assert self.dim == x.dim
assert self.len_ind(ind) == x.len_ind(x_ind) or x.len_ind(x_ind) == 1
assert isinstance(alpha, _INDEXTYPES) \
or isinstance(alpha, np.ndarray) and alpha.shape == (self.len_ind(ind),)
if self._refcount[0] > 1:
self._deep_copy()
if NUMPY_INDEX_QUIRK:
if self._len == 0 and hasattr(ind, '__len__'):
ind = None
if x._len == 0 and hasattr(x_ind, '__len__'):
x_ind = None
if np.all(alpha == 0):
return
B = x._array[:x._len] if x_ind is None else x._array[x_ind]
alpha_type = type(alpha)
alpha_dtype = alpha.dtype if alpha_type is np.ndarray else alpha_type
if self._array.dtype != alpha_dtype or self._array.dtype != B.dtype:
dtype = np.promote_types(self._array.dtype, alpha_dtype)
dtype = np.promote_types(dtype, B.dtype)
self._array = self._array.astype(dtype)
if np.all(alpha == 1):
if ind is None:
self._array[:self._len] += B
elif isinstance(ind, Number) and B.ndim == 2:
self._array[ind] += B.reshape((B.shape[1],))
else:
self._array[ind] += B
elif np.all(alpha == -1):
if ind is None:
self._array[:self._len] -= B
elif isinstance(ind, Number) and B.ndim == 2:
self._array[ind] -= B.reshape((B.shape[1],))
else:
self._array[ind] -= B
else:
if isinstance(alpha, np.ndarray):
alpha = alpha[:, np.newaxis]
if ind is None:
self._array[:self._len] += (B * alpha)
elif isinstance(ind, Number):
self._array[ind] += (B * alpha).reshape((-1,))
else:
self._array[ind] += (B * alpha)
def multiply_dm_dm(matrix1, matrix2):
"""Multiply a block diagonal matrix by another diagonal matrix.
Parameters
----------
matrix1 : (nblocks, n, m) np.ndarray
An array containing `nblocks` diagonal blocks of size (`n`, `m`).
matrix2 : (nblocks, m, k) np.ndarray
An array containing `nblocks` diagonal blocks of size (`m`, `k`).
Returns
-------
nmatrix : (nblocks, n, k) np.ndarray
An array containing `nblocks` diagonal blocks of size (`n`, `k`).
"""
nblocks, n, m = matrix1.shape
k = matrix2.shape[2]
if matrix2.shape[:2] != (nblocks, m):
raise Exception("Shapes not compatible.")
# Check dtype
dt = np.promote_types(matrix1.dtype, matrix2.dtype)
nmatrix = np.empty((nblocks, n, k), dtype=dt)
for i in range(nblocks):
nmatrix[i] = np.dot(matrix1[i], matrix2[i])
return nmatrix
def generic(self, args, kws):
assert not kws
if len(args) == 1:
# 0-dim arrays return one result array
ary = args[0]
ndim = max(ary.ndim, 1)
retty = types.UniTuple(types.Array(types.intp, 1, 'C'), ndim)
return signature(retty, ary)
elif len(args) == 3:
cond, x, y = args
retdty = from_dtype(np.promote_types(
as_dtype(getattr(args[1], 'dtype', args[1])),
as_dtype(getattr(args[2], 'dtype', args[2]))))
if isinstance(cond, types.Array):
# array where()
if isinstance(x, types.Array) and isinstance(y, types.Array):
if (cond.ndim == x.ndim == y.ndim):
if x.layout == y.layout == cond.layout:
retty = types.Array(retdty, x.ndim, x.layout)
else:
retty = types.Array(retdty, x.ndim, 'C')
return signature(retty, *args)
else:
# x and y both scalar
retty = types.Array(retdty, cond.ndim, cond.layout)
return signature(retty, *args)
else:
# scalar where()
if not isinstance(x, types.Array):
retty = types.Array(retdty, 0, 'C')
return signature(retty, *args)
def test_basic(self):
a, b = self.a, self.b
x = eval("a @ b")
assert_equal(x.dtype,
np.promote_types(a.dtype, b.dtype))
assert_allclose(x.todense(),
np.dot(a.todense(), b.todense()), atol=1e-15)
def tensordot(lhs, rhs, axes=2):
if isinstance(axes, Iterable):
left_axes, right_axes = axes
else:
left_axes = tuple(range(lhs.ndim - 1, lhs.ndim - axes - 1, -1))
right_axes = tuple(range(0, axes))
if isinstance(left_axes, int):
left_axes = (left_axes,)
if isinstance(right_axes, int):
right_axes = (right_axes,)
if isinstance(left_axes, list):
left_axes = tuple(left_axes)
if isinstance(right_axes, list):
right_axes = tuple(right_axes)
dt = np.promote_types(lhs.dtype, rhs.dtype)
left_index = list(alphabet[:lhs.ndim])
right_index = list(ALPHABET[:rhs.ndim])
out_index = left_index + right_index
for l, r in zip(left_axes, right_axes):
out_index.remove(right_index[r])
right_index[r] = left_index[l]
intermediate = atop(_tensordot, out_index,
lhs, left_index,
rhs, right_index, dtype=dt,
axes=(left_axes, right_axes))
result = intermediate.sum(axis=left_axes)
return result
def get_volume_pixeldata(sorted_slices):
"""
the slice and intercept calculation can cause the slices to have different dtypes
we should get the correct dtype that can cover all of them
:type sorted_slices: list of slices
:param sorted_slices: sliced sored in the correct order to create volume
"""
slices = []
combined_dtype = None
for slice_ in sorted_slices:
slice_data = _get_slice_pixeldata(slice_)
slice_data = slice_data[numpy.newaxis, :, :]
slices.append(slice_data)
if combined_dtype is None:
combined_dtype = slice_data.dtype
else:
combined_dtype = numpy.promote_types(combined_dtype, slice_data.dtype)
# create the new volume with with the correct data
vol = numpy.concatenate(slices, axis=0)
# Done
vol = numpy.transpose(vol, (2, 1, 0))
return vol
def unify_pairs(self, first, second):
"""
Choose PyObject type as the abstract if we fail to determine a concrete
type.
"""
# TODO: should add an option to reject unsafe type conversion
d = self.type_compatibility(fromty=first, toty=second)
if d is None:
return types.pyobject
elif d == 'exact':
# Same type
return first
elif d == 'promote':
return second
elif d in ('safe', 'unsafe'):
assert first in types.number_domain
assert second in types.number_domain
a = numpy.dtype(str(first))
b = numpy.dtype(str(second))
# Just use NumPy coercion rules
sel = numpy.promote_types(a, b)
# Convert NumPy dtype back to Numba types
return getattr(types, str(sel))
else:
raise Exception("type_compatibility returned %s" % d)
def append(self, other, remove_from_other=False):
assert self.dim == other.dim
assert not remove_from_other or (other is not self and getattr(other, 'base', None) is not self)
if self._refcount[0] > 1:
self._deep_copy()
other_array = other.to_numpy()
len_other = len(other_array)
if len_other == 0:
return
if len_other <= self._array.shape[0] - self._len:
if self._array.dtype != other_array.dtype:
self._array = self._array.astype(np.promote_types(self._array.dtype, other_array.dtype))
self._array[self._len:self._len + len_other] = other_array
else:
self._array = np.append(self._array[:self._len], other_array, axis=0)
self._len += len_other
if remove_from_other:
if other.is_view:
del other.base[other.ind]
else:
del other[:]
def dtype(self):
"""Return dtype of image data in file."""
# subblock data can be of different pixel type
dtype = self.filtered_subblock_directory[0].dtype[-2:]
for directory_entry in self.filtered_subblock_directory:
dtype = numpy.promote_types(dtype, directory_entry.dtype[-2:])
return dtype
def unify_pairs(self, first, second):
"""
Choose PyObject type as the abstract if we fail to determine a concrete
type.
"""
# TODO: should add an option to reject unsafe type conversion
d = self.type_compatibility(fromty=first, toty=second)
if d is None:
# Complex is not allowed to downcast implicitly.
# Need to try the other direction of implicit cast to find the
# most general type of the two.
first, second = second, first # swap operand order
d = self.type_compatibility(fromty=first, toty=second)
if d is None:
return types.pyobject
elif d == 'exact':
# Same type
return first
elif d == 'promote':
return second
elif d in ('safe', 'unsafe'):
assert first in types.number_domain
assert second in types.number_domain
a = numpy.dtype(str(first))
b = numpy.dtype(str(second))
# Just use NumPy coercion rules
sel = numpy.promote_types(a, b)
# Convert NumPy dtype back to Numba types
return getattr(types, str(sel))
elif d in 'int-tuple-coerce':
return types.UniTuple(dtype=types.intp, count=len(first))
else:
raise Exception("type_compatibility returned %s" % d)
def full_cumsum(data, axis=None, dtype=None):
"""
A version of `numpy.cumsum` that includes the sum of the empty slice (zero). This
makes it satisfy the invariant::
cumsum(a)[i] == sum(a[:i])
which is a useful property to simplify the formula for the moving average. The result
will be one entry longer than *data* along *axis*.
"""
# All we need to do is construct a result array with the appropriate type and
# dimensions, and then feed a slice of it to cumsum, setting the rest to zero.
shape = list(data.shape)
if axis is None:
shape[0] += 1
else:
shape[axis] += 1
# Mimic cumsum's behavior with the dtype argument: use the original data type or
# the system's native word, whichever has the greater width. (This prevents us from
# attempting a cumulative sum using an 8-bit integer, for instance.)
if dtype is None:
dtype = np.promote_types(data.dtype, np.min_scalar_type(-sys.maxint))
out = np.zeros(shape, dtype)
s = axis_slice(axis)
np.cumsum(data, axis, dtype, out[s[1:]])
return out
def _resample_coord(coord, src_coord, direction, target_points, interpolate):
if coord.ndim != 1:
raise iris.exceptions.NotYetImplementedError(
'Linear interpolation of multi-dimensional coordinates.')
coord_points = coord.points
if coord is src_coord:
dtype = coord_points.dtype
if dtype.kind == 'i':
dtype = np.promote_types(dtype, np.float16)
new_points = np.array(target_points, dtype=dtype)
else:
if getattr(src_coord, 'circular', False):
coord_points = np.append(coord_points, coord_points[0])
# If the source coordinate was monotonic decreasing, we need to
# flip this coordinate's values.
if direction == -1:
coord_points = iris.util.reverse(coord_points, axes=0)
new_points = interpolate(coord_points, target_points)
# Watch out for DimCoord instances that are no longer monotonic
# after the resampling.
try:
new_coord = coord.copy(new_points)
except ValueError:
new_coord = iris.coords.AuxCoord.from_coord(coord).copy(new_points)
return new_coord
def _set_or_promote_dtype(self, column_dtypes, c, dtype):
existing_dtype = column_dtypes.get(c)
if existing_dtype is None or existing_dtype != dtype:
# Promote ints to floats - as we can't easily represent NaNs
if np.issubdtype(dtype, int):
dtype = np.dtype('f8')
column_dtypes[c] = np.promote_types(column_dtypes.get(c, dtype), dtype)
def normalize_compare_value(self, other):
other_dtype = np.min_scalar_type(other)
if other_dtype.kind in 'biuf':
other_dtype = np.promote_types(self.dtype, other_dtype)
ary = utils.scalar_broadcast_to(other, shape=len(self),
dtype=other_dtype)
return self.replace(data=Buffer(ary), dtype=ary.dtype)
else:
raise TypeError('cannot broadcast {}'.format(type(other)))
def _update_edges(self, weights, copy=False):
weights = np.asarray(weights)
res_dtype = np.promote_types(weights.dtype, self._adj.dtype)
adj = self._adj.astype(res_dtype, copy=copy)
adj[adj != 0] = weights
if copy:
return DenseAdjacencyMatrixGraph(adj)
self._adj = adj
return self
def _weightable_adj(self, weight, copy):
weight = np.atleast_1d(weight)
adj = self._adj
res_dtype = np.promote_types(weight.dtype, adj.dtype)
if copy:
adj = adj.copy()
if res_dtype is not adj.dtype:
adj.data = adj.data.astype(res_dtype)
return adj
def test_dense_sparse(self):
# dense @ sparse -> dense
a, b = self.a.todense(), self.b
x = eval("a @ b")
assert_(isinstance(x, np.ndarray))
assert_equal(x.dtype,
np.promote_types(a.dtype, b.dtype))
assert_allclose(x,
np.dot(a, b.todense()), atol=1e-15)
def _promote_types(self, dtype, dtype_str):
if dtype_str == str(dtype):
return dtype
prev_dtype = self._dtype(dtype_str)
if dtype.names is None:
rtn = np.promote_types(dtype, prev_dtype)
else:
rtn = _promote_struct_dtypes(dtype, prev_dtype)
rtn = np.dtype(rtn, metadata=dict(dtype.metadata or {}))
return rtn
def __isub__(self, other):
assert self.dim == other.dim
if self._refcount[0] > 1:
self._deep_copy()
other_dtype = other.base._array.dtype if other.is_view else other._array.dtype
common_dtype = np.promote_types(self._array.dtype, other_dtype)
if self._array.dtype != common_dtype:
self._array = self._array.astype(common_dtype)
self._array[:self._len] -= other.base._array[other.ind] if other.is_view else other._array[:other._len]
return self
def func(d1, d2):
a1 = None if d1 is None else np.array(1, dtype=d1)
a2 = None if d2 is None else np.array(1, dtype=d2)
if d1 is None and d2 is None:
assert_raises(ValueError, cast, [a1, a2])
return
expected = d1 if d2 is None else d2 if d1 is None else np.promote_types(d1, d2)
a1_, a2_ = cast([a1, a2])
assert_dtype(a1_, expected)
assert_dtype(a2_, expected)
def __imul__(self, other):
assert isinstance(other, Number) \
or isinstance(other, np.ndarray) and other.shape == (len(self),)
if self._refcount[0] > 1:
self._deep_copy()
other_dtype = other.dtype if isinstance(other, np.ndarray) else type(other)
common_dtype = np.promote_types(self._array.dtype, other_dtype)
if self._array.dtype != common_dtype:
self._array = self._array.astype(common_dtype)
self._array[:self._len] *= other
return self
def combine(self, other):
if hasattr(other, "dtype"):
combined_dtype = np.promote_types(self.dtype, other.dtype)
if combined_dtype == self.dtype:
return self
elif combined_dtype == other.dtype:
return other
else:
return from_dtype(combined_dtype)
else:
raise IncompatibleTypes(self, other)
def vander(x,N):
x = np.asarray(x)
if x.ndim != 1:
raise ValueError("x must be a 1-D array or sequence")
v = np.empty((len(x), N), dtype=np.promote_types(x.dtype, int))
if N > 0:
v[:,0] = 1
if N > 1:
v[:, 1:] = x[:, None]
np.multiply.accumulate(v[:, 1:], out=v[:, 1:], axis=1)
return v
def __iadd__(self, other):
assert self.dim == other.dim
assert self.base.check_ind_unique(self.ind)
if self.base._refcount[0] > 1:
self._deep_copy()
other_dtype = other.base._array.dtype if other.is_view else other._array.dtype
common_dtype = np.promote_types(self.base._array.dtype, other_dtype)
if self.base._array.dtype != common_dtype:
self.base._array = self.base._array.astype(common_dtype)
self.base.array[self.ind] += other.base._array[other.ind] if other.is_view else other._array[:other._len]
return self
def add_edges(self, from_idx, to_idx, weight=1, symmetric=False, copy=False):
weight = np.atleast_1d(1 if weight is None else weight)
res_dtype = np.promote_types(weight.dtype, self._adj.dtype)
adj = self._adj.astype(res_dtype, copy=copy)
adj[from_idx, to_idx] = weight
if symmetric:
adj[to_idx, from_idx] = weight
if copy:
return DenseAdjacencyMatrixGraph(adj)
self._adj = adj
return self
def combine(self, other):
if isinstance(other, ScalarT):
combined_dtype = np.promote_types(self.dtype, other.dtype)
if combined_dtype == self.dtype:
return self
elif combined_dtype == other.dtype:
return other
else:
return from_dtype(combined_dtype)
else:
raise IncompatibleTypes(self, other)
def assemble_lincomb(self, operators, coefficients, solver_options=None, name=None):
if not all(isinstance(op, (NumpyMatrixOperator, ZeroOperator, IdentityOperator)) for op in operators):
return None
common_mat_dtype = reduce(np.promote_types,
(op._matrix.dtype for op in operators if hasattr(op, '_matrix')))
common_coef_dtype = reduce(np.promote_types, (type(c.real if c.imag == 0 else c) for c in coefficients))
common_dtype = np.promote_types(common_mat_dtype, common_coef_dtype)
if coefficients[0] == 1:
matrix = operators[0]._matrix.astype(common_dtype)
else:
if coefficients[0].imag == 0:
matrix = operators[0]._matrix * coefficients[0].real
else:
matrix = operators[0]._matrix * coefficients[0]
if matrix.dtype != common_dtype:
matrix = matrix.astype(common_dtype)
for op, c in zip(operators[1:], coefficients[1:]):
if type(op) is ZeroOperator:
continue
elif type(op) is IdentityOperator:
if operators[0].sparse:
try:
matrix += (scipy.sparse.eye(matrix.shape[0]) * c)
except NotImplementedError:
matrix = matrix + (scipy.sparse.eye(matrix.shape[0]) * c)
else:
matrix += (np.eye(matrix.shape[0]) * c)
elif c == 1:
try:
matrix += op._matrix
except NotImplementedError:
matrix = matrix + op._matrix
elif c == -1:
try:
matrix -= op._matrix
except NotImplementedError:
matrix = matrix - op._matrix
elif c.imag == 0:
try:
matrix += (op._matrix * c.real)
except NotImplementedError:
matrix = matrix + (op._matrix * c.real)
else:
try:
matrix += (op._matrix * c)
except NotImplementedError:
matrix = matrix + (op._matrix * c)
return NumpyMatrixOperator(matrix,
source_id=self.source.id,
range_id=self.range.id,
solver_options=solver_options)
def unify(self, typingctx, other):
"""
Unify the two number types using Numpy's rules.
"""
from .. import numpy_support
if isinstance(other, Number):
# XXX: this can produce unsafe conversions,
# e.g. would unify {int64, uint64} to float64
a = numpy_support.as_dtype(self)
b = numpy_support.as_dtype(other)
sel = numpy.promote_types(a, b)
return numpy_support.from_dtype(sel)
def approx_fprime(x, f, epsilon=None, args=(), kwargs={}, centered=False):
'''
Gradient of function, or Jacobian if function f returns 1d array
Parameters
----------
x : array
parameters at which the derivative is evaluated
f : function
`f(*((x,)+args), **kwargs)` returning either one value or 1d array
epsilon : float, optional
Stepsize, if None, optimal stepsize is used. This is EPS**(1/2)*x for
`centered` == False and EPS**(1/3)*x for `centered` == True.
args : tuple
Tuple of additional arguments for function `f`.
kwargs : dict
Dictionary of additional keyword arguments for function `f`.
centered : bool
Whether central difference should be returned. If not, does forward
differencing.
Returns
-------
grad : array
gradient or Jacobian
Notes
-----
If f returns a 1d array, it returns a Jacobian. If a 2d array is returned
by f (e.g., with a value for each observation), it returns a 3d array
with the Jacobian of each observation with shape xk x nobs x xk. I.e.,
the Jacobian of the first observation would be [:, 0, :]
'''
n = len(x)
# TODO: add scaled stepsize
f0 = f(*((x,)+args), **kwargs)
dim = np.atleast_1d(f0).shape # it could be a scalar
grad = np.zeros((n,) + dim, np.promote_types(float, x.dtype))
ei = np.zeros((n,), float)
if not centered:
epsilon = _get_epsilon(x, 2, epsilon, n)
for k in range(n):
ei[k] = epsilon[k]
grad[k, :] = (f(*((x+ei,) + args), **kwargs) - f0)/epsilon[k]
ei[k] = 0.0
else:
epsilon = _get_epsilon(x, 3, epsilon, n) / 2.
for k in range(len(x)):
ei[k] = epsilon[k]
grad[k, :] = (f(*((x+ei,)+args), **kwargs) -
f(*((x-ei,)+args), **kwargs))/(2 * epsilon[k])
ei[k] = 0.0
return grad.squeeze().T
def coefficients_from_grid_functions_list(grid_funs):
"""
Return a vector of coefficients of a list of grid functions.
Given a list [f0, f1, f2, ...] this function returns a
single Numpy vector containing [f1.coefficients, f2.coefficients, ...].
Parameters
----------
grid_funs : list of GridFunction objects
A list containing the grid functions
"""
vec_len = 0
input_type = _np.dtype("float32")
for item in grid_funs:
input_type = _np.promote_types(input_type, item.coefficients.dtype)
vec_len += item.space.global_dof_count
res = _np.zeros(vec_len, dtype=input_type)
pos = 0
for item in grid_funs:
dof_count = item.space.global_dof_count
res[pos:pos + dof_count] = item.coefficients
pos += dof_count
return res
def reindexer(X, fill_value=fill_value):
if not np.can_cast(fill_value, X.dtype):
out_dtype = np.promote_types(np.array(fill_value).dtype, X.dtype)
else:
out_dtype = X.dtype
idxmtx = sparse.coo_matrix(
(np.ones(len(new_pts), dtype=int), (cur_pts, new_pts)),
shape=(old_size, new_size),
dtype=out_dtype,
)
out = X @ idxmtx
if fill_value != 0:
to_fill = new_var.get_indexer(new_var.difference(cur_var))
if len(to_fill) > 0:
# More efficient to set columns on csc
if sparse.issparse(out):
out = sparse.csc_matrix(out)
with warnings.catch_warnings():
warnings.simplefilter("ignore", sparse.SparseEfficiencyWarning)
out[:, to_fill] = fill_value
return out
def scal(self, alpha, ind=None):
assert self.check_ind_unique(ind)
assert isinstance(alpha, _INDEXTYPES) \
or isinstance(alpha, np.ndarray) and alpha.shape == (self.len_ind(ind),)
if self._refcount[0] > 1:
self._deep_copy()
if NUMPY_INDEX_QUIRK and self._len == 0:
return
if isinstance(alpha, np.ndarray) and not isinstance(ind, Number):
alpha = alpha[:, np.newaxis]
alpha_type = type(alpha)
alpha_dtype = alpha.dtype if alpha_type is np.ndarray else alpha_type
if self._array.dtype != alpha_dtype:
self._array = self._array.astype(
np.promote_types(self._array.dtype, alpha_dtype))
if ind is None:
self._array[:self._len] *= alpha
else:
self._array[ind] *= alpha
def _init_attrs_from_file(self, filename):
with rasterio.drivers():
with rasterio.open(filename, 'r') as src:
#: dict: rasterio metadata of first file
self.md = src.meta.copy()
self.crs = src.crs
self.affine = src.affine
self.res = src.res
self.ul = src.ul(0, 0)
self.height = src.height
self.width = src.width
self.count = src.count
self.length = len(self.df)
self.block_windows = list(src.block_windows())
self.nodatavals = src.nodatavals
# We only use one datatype for reading -- promote to largest
# if hetereogeneous
self.dtype = src.dtypes[0]
if not all([dt == self.dtype for dt in src.dtypes[1:]]):
logger.warning('GDAL reader cannot read multiple data '
'types. Promoting memory allocation to '
'largest datatype of source bands')
for dtype in src.dtypes[1:]:
self.dtype = np.promote_types(self.dtype, dtype)
def test_butterworth_2D_realfft(high_pass, dtype, squared_butterworth):
"""Filtering a real-valued array is equivalent to filtering a
complex-valued array where the imaginary part is zero.
"""
im = np.random.randn(32, 64).astype(dtype)
kwargs = dict(
cutoff_frequency_ratio=0.20,
high_pass=high_pass,
squared_butterworth=squared_butterworth,
)
expected_dtype = _supported_float_type(im.dtype)
filtered_real = butterworth(im, **kwargs)
assert filtered_real.dtype == expected_dtype
cplx_dtype = np.promote_types(im.dtype, np.complex64)
filtered_cplx = butterworth(im.astype(cplx_dtype), **kwargs)
assert filtered_cplx.real.dtype == expected_dtype
if expected_dtype == np.float64:
rtol = atol = 1e-13
else:
rtol = atol = 1e-5
assert_allclose(filtered_real, filtered_cplx.real, rtol=rtol, atol=atol)
def _get_output(output, input, shape=None, complex_output=False):
if shape is None:
shape = input.shape
if output is None:
if not complex_output:
output = numpy.zeros(shape, dtype=input.dtype.name)
else:
complex_type = numpy.promote_types(input.dtype, numpy.complex64)
output = numpy.zeros(shape, dtype=complex_type)
elif isinstance(output, (type, numpy.dtype)):
# Classes (like `np.float32`) and dtypes are interpreted as dtype
if complex_output and numpy.dtype(output).kind != 'c':
raise RuntimeError("output must have complex dtype")
output = numpy.zeros(shape, dtype=output)
elif isinstance(output, str):
output = numpy.typeDict[output]
if complex_output and numpy.dtype(output).kind != 'c':
raise RuntimeError("output must have complex dtype")
output = numpy.zeros(shape, dtype=output)
elif output.shape != shape:
raise RuntimeError("output shape not correct")
elif complex_output and output.dtype.kind != 'c':
raise RuntimeError("output must have complex dtype")
return output
def get_minimal_dtype(arrays, increase_itemsize_factor=1):
assert isinstance(arrays, list), (
"Expected a list of arrays or dtypes, got type %s." % (type(arrays),))
assert len(arrays) > 0, (
"Cannot estimate minimal dtype of an empty iterable.")
input_dts = normalize_dtypes(arrays)
# This loop construct handles (1) list of a single dtype, (2) list of two
# dtypes and (3) list of 3+ dtypes. Note that promote_dtypes() always
# expects exactly two dtypes.
promoted_dt = input_dts[0]
input_dts = input_dts[1:]
while len(input_dts) >= 1:
promoted_dt = np.promote_types(promoted_dt, input_dts[0])
input_dts = input_dts[1:]
if increase_itemsize_factor > 1:
assert isinstance(promoted_dt, np.dtype), (
"Expected numpy.dtype output from numpy.promote_dtypes, got type "
"%s." % (type(promoted_dt),))
return increase_itemsize_of_dtype(promoted_dt,
increase_itemsize_factor)
return promoted_dt
def multiply_by_dense(sp, dn):
check_shape_for_pointwise_op(sp.shape, dn.shape)
sp_m, sp_n = sp.shape
dn_m, dn_n = dn.shape
m, n = max(sp_m, dn_m), max(sp_n, dn_n)
nnz = sp.nnz * (m // sp_m) * (n // sp_n)
dtype = numpy.promote_types(sp.dtype, dn.dtype)
data = cupy.empty(nnz, dtype=dtype)
indices = cupy.empty(nnz, dtype=sp.indices.dtype)
if m > sp_m:
if n > sp_n:
indptr = cupy.arange(0, nnz + 1, n, dtype=sp.indptr.dtype)
else:
indptr = cupy.arange(0, nnz + 1, sp.nnz, dtype=sp.indptr.dtype)
else:
indptr = sp.indptr.copy()
if n > sp_n:
indptr *= n
# out = sp * dn
cupy_multiply_by_dense()(sp.data, sp.indptr, sp.indices, sp_m, sp_n, dn,
dn_m, dn_n, indptr, m, n, data, indices)
return csr_matrix((data, indices, indptr), shape=(m, n))
def min_column_type(x, expected_type):
"""
Return the smallest dtype which can represent all
elements of the `NumericalColumn` `x`
If the column is not a subtype of `np.signedinteger` or `np.floating`
returns the same dtype as the dtype of `x` without modification
"""
if not isinstance(x, cudf.core.column.NumericalColumn):
raise TypeError("Argument x must be of type column.NumericalColumn")
if x.valid_count == 0:
return x.dtype
if np.issubdtype(x.dtype, np.floating):
return get_min_float_dtype(x)
elif np.issubdtype(expected_type, np.integer):
max_bound_dtype = np.min_scalar_type(x.max())
min_bound_dtype = np.min_scalar_type(x.min())
result_type = np.promote_types(max_bound_dtype, min_bound_dtype)
else:
result_type = x.dtype
return cudf.dtype(result_type)
def testLargestSV(test):
query = {TEST.TYPE_EXPECTED: np.float64}
instance = test[TEST.INSTANCE]
# account for "extra computation stage" (gram) in largestSV
query[TEST.TOL_POWER] = test.get(TEST.TOL_POWER, 1.) * 2
query[TEST.TOL_MINEPS] = _getTypeEps(safeTypeExpansion(instance.dtype))
# determine reference result
largestSV = np.linalg.svd(test[TEST.REFERENCE], compute_uv=False)[0]
query[TEST.RESULT_REF] = np.array(largestSV,
dtype=np.promote_types(
largestSV.dtype, np.float64))
# largestSV may not converge fast enough for a bad random starting point
# so retry some times before throwing up
for tries in range(9):
maxSteps = 100. * 10.**(tries / 2.)
query[TEST.RESULT_OUTPUT] = np.array(
instance.getLargestSV(maxSteps=maxSteps, alwaysReturn=True))
result = compareResults(test, query)
if result[TEST.RESULT]:
break
return result
def normalize_binop_value(
self, other: ScalarLike) -> Union[ColumnBase, ScalarLike]:
if other is None:
return other
if isinstance(other, cudf.Scalar):
if self.dtype == other.dtype:
return other
# expensive device-host transfer just to
# adjust the dtype
other = other.value
elif isinstance(other, np.ndarray) and other.ndim == 0:
other = other.item()
other_dtype = np.min_scalar_type(other)
if other_dtype.kind in {"b", "i", "u", "f"}:
if isinstance(other, cudf.Scalar):
return other
other_dtype = np.promote_types(self.dtype, other_dtype)
if other_dtype == np.dtype("float16"):
other_dtype = np.dtype("float32")
other = other_dtype.type(other)
if self.dtype.kind == "b":
other_dtype = min_signed_type(other)
if np.isscalar(other):
other = np.dtype(other_dtype).type(other)
return other
else:
ary = utils.scalar_broadcast_to(other,
size=len(self),
dtype=other_dtype)
return column.build_column(
data=Buffer(ary),
dtype=ary.dtype,
mask=self.mask,
)
else:
raise TypeError(f"cannot broadcast {type(other)}")
def np_promote_all_types(*dtypes):
""" Return the largest NumPy datatype required to hold all types
Parameters
----------
dtypes : iterable
NumPy datatypes to promote
Returns
-------
np.dtype
Smallest NumPy datatype required to store all input datatypes
See Also
--------
np.promote_types
"""
dtype = dtypes[0]
if not all([dt == dtype for dt in dtypes[1:]]):
logger.debug('Promoting memory allocation to largest datatype of '
'source bands')
for _dtype in dtypes[1:]:
dtype = np.promote_types(dtype, _dtype)
return dtype
def _qr_batched(a, mode):
batch_shape = a.shape[:-2]
batch_size = internal.prod(batch_shape)
m, n = a.shape[-2:]
# first handle any 0-size inputs
if batch_size == 0 or m == 0 or n == 0:
# support float32, float64, complex64, and complex128
dtype, out_dtype = _util.linalg_common_type(a)
if mode == 'raw':
# compatibility with numpy.linalg.qr
out_dtype = numpy.promote_types(out_dtype, 'd')
if mode == 'reduced':
return (cupy.empty(batch_shape + (m, 0), out_dtype),
cupy.empty(batch_shape + (0, n), out_dtype))
elif mode == 'complete':
q = _util.stacked_identity(batch_shape, m, out_dtype)
return (q, cupy.empty(batch_shape + (m, n), out_dtype))
elif mode == 'r':
return cupy.empty(batch_shape + (0, n), out_dtype)
elif mode == 'raw':
return (cupy.empty(batch_shape + (n, m), out_dtype),
cupy.empty(batch_shape + (0, ), out_dtype))
# ...then delegate real computation to cuSOLVER/rocSOLVER
a = a.reshape(-1, *(a.shape[-2:]))
out = _geqrf_orgqr_batched(a, mode)
if mode == 'r':
return out.reshape(batch_shape + out.shape[-2:])
q, r = out
q = q.reshape(batch_shape + q.shape[-2:])
idx = -1 if mode == 'raw' else -2
r.reshape(batch_shape + r.shape[idx:])
return (q, r)
def get_volume_pixeldata(sorted_slices):
"""
the slice and intercept calculation can cause the slices to have different dtypes
we should get the correct dtype that can cover all of them
:type sorted_slices: list of slices
:param sorted_slices: sliced sored in the correct order to create volume
"""
slices = []
combined_dtype = None
for slice_ in sorted_slices:
slice_data = _get_slice_pixeldata(slice_)
slice_data = slice_data[numpy.newaxis, :, :]
slices.append(slice_data)
if combined_dtype is None:
combined_dtype = slice_data.dtype
else:
combined_dtype = numpy.promote_types(combined_dtype, slice_data.dtype)
# create the new volume with with the correct data
vol = numpy.concatenate(slices, axis=0)
# Done
vol = numpy.transpose(vol, (2, 1, 0))
return vol
def FISTA(fmatA, arrB, numLambda=0.1, numMaxSteps=100):
'''
Wrapper around the FISTA algrithm to allow processing of arrays of signals
fmatA - input system matrix
arrB - input data vector (measurements)
numLambda - balancing parameter in optimization problem
between data fidelity and sparsity
numMaxSteps - maximum number of steps to run
numL - step size during the conjugate gradient step
'''
if len(arrB.shape) > 2:
raise ValueError("Only n x m arrays are supported for FISTA")
# calculate the largest singular value to get the right step size
numL = 1.0 / (fmatA.largestSV**2)
t = 1
arrX = np.zeros((fmatA.numM, arrB.shape[1]),
dtype=np.promote_types(np.float32, arrB.dtype))
# initial arrY
arrY = np.copy(arrX)
# start iterating
for numStep in range(numMaxSteps):
arrXold = np.copy(arrX)
# do the gradient step and threshold
arrStep = arrY - numL * fmatA.backward(fmatA.forward(arrY) - arrB)
arrX = _softThreshold(arrStep, numL * numLambda * 0.5)
# update t
tOld = t
t = (1 + np.sqrt(1 + 4 * t**2)) / 2
# update arrY
arrY = arrX + ((tOld - 1) / t) * (arrX - arrXold)
# return the unthresholded values for all non-zero support elements
return np.where(arrX != 0, arrStep, arrX)
def spsolve(A, b, permc_spec=None, use_umfpack=True):
"""Solve the sparse linear system Ax=b, where b may be a vector or a matrix.
Parameters
----------
A : ndarray or sparse matrix
The square matrix A will be converted into CSC or CSR form
b : ndarray or sparse matrix
The matrix or vector representing the right hand side of the equation.
If a vector, b.shape must be (n,) or (n, 1).
permc_spec : str, optional
How to permute the columns of the matrix for sparsity preservation.
(default: 'COLAMD')
- ``NATURAL``: natural ordering.
- ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
- ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
- ``COLAMD``: approximate minimum degree column ordering
use_umfpack : bool, optional
if True (default) then use umfpack for the solution. This is
only referenced if b is a vector and ``scikit-umfpack`` is installed.
Returns
-------
x : ndarray or sparse matrix
the solution of the sparse linear equation.
If b is a vector, then x is a vector of size A.shape[1]
If b is a matrix, then x is a matrix of size (A.shape[1], b.shape[1])
Notes
-----
For solving the matrix expression AX = B, this solver assumes the resulting
matrix X is sparse, as is often the case for very sparse inputs. If the
resulting X is dense, the construction of this sparse result will be
relatively expensive. In that case, consider converting A to a dense
matrix and using scipy.linalg.solve or its variants.
Examples
--------
>>> from scipy.sparse import csc_matrix
>>> from scipy.sparse.linalg import spsolve
>>> A = csc_matrix([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
>>> B = csc_matrix([[2, 0], [-1, 0], [2, 0]], dtype=float)
>>> x = spsolve(A, B)
>>> np.allclose(A.dot(x).todense(), B.todense())
True
"""
if not (isspmatrix_csc(A) or isspmatrix_csr(A)):
A = csc_matrix(A)
warn('spsolve requires A be CSC or CSR matrix format',
SparseEfficiencyWarning)
# b is a vector only if b have shape (n,) or (n, 1)
b_is_sparse = isspmatrix(b)
if not b_is_sparse:
b = asarray(b)
b_is_vector = ((b.ndim == 1) or (b.ndim == 2 and b.shape[1] == 1))
A.sort_indices()
A = A.asfptype() # upcast to a floating point format
result_dtype = np.promote_types(A.dtype, b.dtype)
if A.dtype != result_dtype:
A = A.astype(result_dtype)
if b.dtype != result_dtype:
b = b.astype(result_dtype)
# validate input shapes
M, N = A.shape
if (M != N):
raise ValueError("matrix must be square (has shape %s)" % ((M, N), ))
if M != b.shape[0]:
raise ValueError("matrix - rhs dimension mismatch (%s - %s)" %
(A.shape, b.shape[0]))
use_umfpack = use_umfpack and useUmfpack
if b_is_vector and use_umfpack:
if b_is_sparse:
b_vec = b.toarray()
else:
b_vec = b
b_vec = asarray(b_vec, dtype=A.dtype).ravel()
if noScikit:
raise RuntimeError('Scikits.umfpack not installed.')
if A.dtype.char not in 'dD':
raise ValueError("convert matrix data to double, please, using"
" .astype(), or set linsolve.useUmfpack = False")
umf = umfpack.UmfpackContext(_get_umf_family(A))
x = umf.linsolve(umfpack.UMFPACK_A, A, b_vec, autoTranspose=True)
else:
if b_is_vector and b_is_sparse:
b = b.toarray()
b_is_sparse = False
if not b_is_sparse:
if isspmatrix_csc(A):
flag = 1 # CSC format
else:
flag = 0 # CSR format
options = dict(ColPerm=permc_spec)
x, info = _superlu.gssv(N,
A.nnz,
A.data,
A.indices,
A.indptr,
b,
flag,
options=options)
if info != 0:
warn("Matrix is exactly singular", MatrixRankWarning)
x.fill(np.nan)
if b_is_vector:
x = x.ravel()
else:
# b is sparse
Afactsolve = factorized(A)
if not isspmatrix_csc(b):
warn(
'spsolve is more efficient when sparse b '
'is in the CSC matrix format', SparseEfficiencyWarning)
b = csc_matrix(b)
# Create a sparse output matrix by repeatedly applying
# the sparse factorization to solve columns of b.
data_segs = []
row_segs = []
col_segs = []
for j in range(b.shape[1]):
bj = b[:, j].A.ravel()
xj = Afactsolve(bj)
w = np.flatnonzero(xj)
segment_length = w.shape[0]
row_segs.append(w)
col_segs.append(np.ones(segment_length, dtype=int) * j)
data_segs.append(np.asarray(xj[w], dtype=A.dtype))
sparse_data = np.concatenate(data_segs)
sparse_row = np.concatenate(row_segs)
sparse_col = np.concatenate(col_segs)
x = A.__class__((sparse_data, (sparse_row, sparse_col)),
shape=b.shape,
dtype=A.dtype)
return x
def resample(data_in, x_in, x_out, y, data_out=None, kind='linear'):
"""Resample the data of one spectrum using interpolation.
Dependent variables y1, y2, ... in the input data are resampled in the
independent variable x using interpolation models y1(x), y2(x), ...
evaluated on a new grid of x values. The independent variable will
typically be a wavelength or frequency and the independent variables can
be fluxes, inverse variances, etc.
Interpolation is intended for cases where the input and output grids have
comparable densities. When neighboring samples are correlated, the
resampling process should be essentially lossless. When the output
grid is sparser than the input grid, it may be more appropriate to
"downsample", i.e., average dependent variables over consecutive ranges
of input samples.
The basic usage of this function is:
>>> data = np.ones((5,),
... [('wlen', float), ('flux', float), ('ivar', float)])
>>> data['wlen'] = np.arange(4000, 5000, 200)
>>> wlen_out = np.arange(4100, 4700, 200)
>>> out = resample(data, 'wlen', wlen_out, ('flux', 'ivar'))
>>> np.all(out ==
... np.array([(4100, 1.0, 1.0), (4300, 1.0, 1.0), (4500, 1.0, 1.0)],
... dtype=[('wlen', '<i8'), ('flux', '<f8'), ('ivar', '<f8')]))
True
The input grid can also be external to the structured array of spectral
data, for example:
>>> data = np.ones((5,), [('flux', float), ('ivar', float)])
>>> wlen_in = np.arange(4000, 5000, 200)
>>> wlen_out = np.arange(4100, 4900, 200)
>>> out = resample(data, wlen_in, wlen_out, ('flux', 'ivar'))
>>> np.all(out ==
... np.array([(1.0, 1.0), (1.0, 1.0), (1.0, 1.0), (1.0, 1.0)],
... dtype=[('flux', '<f8'), ('ivar', '<f8')]))
True
If the output grid extends beyond the input grid, a `masked array
<http://docs.scipy.org/doc/numpy/reference/maskedarray.html>`__ will be
returned with any values requiring extrapolation masked:
>>> wlen_out = np.arange(3500, 5500, 500)
>>> out = resample(data, wlen_in, wlen_out, 'flux')
>>> np.all(out.mask ==
... np.array([(True,), (False,), (False,), (True,)],
... dtype=[('flux', 'bool')]))
True
If the input data is masked, any output interpolated values that depend on
an input masked value will be masked in the output:
>>> data = ma.ones((5,), [('flux', float), ('ivar', float)])
>>> data['flux'][2] = ma.masked
>>> wlen_out = np.arange(4100, 4900, 200)
>>> out = resample(data, wlen_in, wlen_out, 'flux')
>>> np.all(out.mask ==
... np.array([(False,), (True,), (True,), (False,)],
... dtype=[('flux', 'bool')]))
True
Interpolation is performed using :class:`scipy.interpolate.inter1pd`.
Parameters
----------
data_in : numpy.ndarray or numpy.ma.MaskedArray
Structured numpy array of input spectral data to resample. The input
array must be one-dimensional.
x_in : string or numpy.ndarray
A field name in data_in containing the independent variable to use
for interpolation, or else an array of values with the same shape
as the input data.
x_out : numpy.ndarray
An array of values for the independent variable where interpolation
models should be evaluated to calculate the output values.
y : string or iterable of strings.
A field name or a list of field names present in the input data that
should be resampled by interpolation and included in the output.
data_out : numpy.ndarray or None
Structured numpy array where the output result should be written. If
None is specified, then an appropriately sized array will be allocated
and returned. Use this method to take control of the memory allocation
and, for example, re-use the same array when resampling many spectra.
kind : string or integer
Specify the kind of interpolation models to build using any of the
forms allowed by :class:`scipy.interpolate.inter1pd`. If any input
dependent values are masked, only the ``nearest` and ``linear``
values are allowed.
Returns
-------
numpy.ndarray or numpy.ma.MaskedArray
Structured numpy array of the resampled result containing all ``y``
fields and (if ``x_in`` is specified as a string) the output ``x``
field. The output will be a :class:`numpy.ma.MaskedArray` if ``x_out``
extends beyond ``x_in`` or if ``data_in`` is masked.
"""
if not isinstance(data_in, np.ndarray):
raise ValueError('Invalid data_in type: {0}.'.format(type(data_in)))
if data_in.dtype.fields is None:
raise ValueError('Input data_in is not a structured array.')
if len(data_in.shape) > 1:
raise ValueError('Input data_in is multidimensional.')
if isinstance(x_in, str):
if x_in not in data_in.dtype.names:
raise ValueError('No such x_in field: {0}.'.format(x_in))
x_out_name = x_in
x_in = data_in[x_in]
else:
if not isinstance(x_in, np.ndarray):
raise ValueError('Invalid x_in type: {0}.'.format(type(x_in)))
if x_in.shape != data_in.shape:
raise ValueError('Incompatible shapes for x_in and data_in.')
x_out_name = None
if not isinstance(x_out, np.ndarray):
raise ValueError('Invalid x_out type: {0}.'.format(type(data_out)))
if ma.isMA(x_in) and np.any(x_in.mask):
raise ValueError('Cannot resample masked x_in.')
x_type = np.promote_types(x_in.dtype, x_out.dtype)
dtype_out = []
if x_out_name is not None:
dtype_out.append((x_out_name, x_out.dtype))
if isinstance(y, str):
# Use a list instead of a tuple here so y_names can be used
# to index data_in below.
y_names = [y,]
else:
try:
y_names = [name for name in y]
except TypeError:
raise ValueError('Invalid y type: {0}.'.format(type(y)))
for not_first, y in enumerate(y_names):
if y not in data_in.dtype.names:
raise ValueError('No such y field: {0}.'.format(y))
if not_first:
if data_in[y].dtype != y_type:
raise ValueError('All y fields must have the same type.')
else:
y_type = data_in[y].dtype
dtype_out.append((y, y_type))
y_shape = (len(y_names),)
if ma.isMA(data_in):
# Copy the structured 1D array into a 2D unstructured array
# and set masked values to NaN.
y_in = np.zeros(data_in.shape + y_shape, y_type)
for i,y in enumerate(y_names):
y_in[:,i] = data_in[y].filled(np.nan)
else:
if pkgr.parse_version(np.__version__) >= pkgr.parse_version('1.16'):
# The slicing does not work in numpy 1.16 and above
# we use structured_to_unstructured to get the slice that we care about
y_in = rfn.structured_to_unstructured(
data_in[y_names]).reshape(data_in.shape + y_shape)
else:
y_in = data_in[y_names]
# View the structured 1D array as a 2D unstructured array (without
# copying any memory).
y_in = y_in.view(y_type).reshape(data_in.shape + y_shape)
# interp1d will only propagate NaNs correctly for certain values of `kind`.
# With numpy = 1.6 or 1.7, only 'nearest' and 'linear' work.
# With numpy = 1.8 or 1.9, 'slinear' and kind = 0 or 1 also work.
if np.any(np.isnan(y_in)):
if kind not in ('nearest', 'linear'):
raise ValueError(
'Interpolation kind not supported for masked data: {0}.'
.format(kind))
try:
interpolator = scipy.interpolate.interp1d(
x_in, y_in, kind=kind, axis=0, copy=False,
bounds_error=False, fill_value=np.nan)
except NotImplementedError:
raise ValueError('Interpolation kind not supported: {0}.'.format(kind))
shape_out = (len(x_out),)
if data_out is None:
data_out = np.empty(shape_out, dtype_out)
else:
if data_out.shape != shape_out:
raise ValueError(
'data_out has wrong shape: {0}. Expected: {1}.'
.format(data_out.shape, shape_out))
if data_out.dtype != dtype_out:
raise ValueError(
'data_out has wrong dtype: {0}. Expected: {1}.'
.format(data_out.dtype, dtype_out))
if x_out_name is not None:
data_out[x_out_name][:] = x_out
y_out = interpolator(x_out)
for i,y in enumerate(y_names):
data_out[y][:] = y_out[:,i]
if ma.isMA(data_in) or np.any(np.isnan(y_out)):
data_out = ma.MaskedArray(data_out)
data_out.mask = False
for y in y_names:
data_out[y].mask = np.isnan(data_out[y].data)
return data_out
def _concrete_matmul_(self, other: "LocalOperator") -> "LocalOperator":
if not isinstance(other, LocalOperator):
return NotImplemented
op = self.copy(dtype=np.promote_types(self.dtype, _dtype(other)))
op @= other
return op
def spsolve(A, b, permc_spec=None, use_umfpack=True):
"""Solve the sparse linear system Ax=b, where b may be a vector or a matrix.
Parameters
----------
A : ndarray or sparse matrix
The square matrix A will be converted into CSC or CSR form
b : ndarray or sparse matrix
The matrix or vector representing the right hand side of the equation.
If a vector, b.shape must be (n,) or (n, 1).
permc_spec : str, optional
How to permute the columns of the matrix for sparsity preservation.
(default: 'COLAMD')
- ``NATURAL``: natural ordering.
- ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
- ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
- ``COLAMD``: approximate minimum degree column ordering [1]_, [2]_.
use_umfpack : bool, optional
if True (default) then use UMFPACK for the solution [3]_, [4]_, [5]_,
[6]_ . This is only referenced if b is a vector and
``scikits.umfpack`` is installed.
Returns
-------
x : ndarray or sparse matrix
the solution of the sparse linear equation.
If b is a vector, then x is a vector of size A.shape[1]
If b is a matrix, then x is a matrix of size (A.shape[1], b.shape[1])
Notes
-----
For solving the matrix expression AX = B, this solver assumes the resulting
matrix X is sparse, as is often the case for very sparse inputs. If the
resulting X is dense, the construction of this sparse result will be
relatively expensive. In that case, consider converting A to a dense
matrix and using scipy.linalg.solve or its variants.
References
----------
.. [1] T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836:
COLAMD, an approximate column minimum degree ordering algorithm,
ACM Trans. on Mathematical Software, 30(3), 2004, pp. 377--380.
:doi:`10.1145/1024074.1024080`
.. [2] T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, A column approximate
minimum degree ordering algorithm, ACM Trans. on Mathematical
Software, 30(3), 2004, pp. 353--376. :doi:`10.1145/1024074.1024079`
.. [3] T. A. Davis, Algorithm 832: UMFPACK - an unsymmetric-pattern
multifrontal method with a column pre-ordering strategy, ACM
Trans. on Mathematical Software, 30(2), 2004, pp. 196--199.
https://dl.acm.org/doi/abs/10.1145/992200.992206
.. [4] T. A. Davis, A column pre-ordering strategy for the
unsymmetric-pattern multifrontal method, ACM Trans.
on Mathematical Software, 30(2), 2004, pp. 165--195.
https://dl.acm.org/doi/abs/10.1145/992200.992205
.. [5] T. A. Davis and I. S. Duff, A combined unifrontal/multifrontal
method for unsymmetric sparse matrices, ACM Trans. on
Mathematical Software, 25(1), 1999, pp. 1--19.
https://doi.org/10.1145/305658.287640
.. [6] T. A. Davis and I. S. Duff, An unsymmetric-pattern multifrontal
method for sparse LU factorization, SIAM J. Matrix Analysis and
Computations, 18(1), 1997, pp. 140--158.
https://doi.org/10.1137/S0895479894246905T.
Examples
--------
>>> from scipy.sparse import csc_matrix
>>> from scipy.sparse.linalg import spsolve
>>> A = csc_matrix([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
>>> B = csc_matrix([[2, 0], [-1, 0], [2, 0]], dtype=float)
>>> x = spsolve(A, B)
>>> np.allclose(A.dot(x).toarray(), B.toarray())
True
"""
if is_pydata_spmatrix(A):
A = A.to_scipy_sparse().tocsc()
if not (isspmatrix_csc(A) or isspmatrix_csr(A)):
A = csc_matrix(A)
warn('spsolve requires A be CSC or CSR matrix format',
SparseEfficiencyWarning)
# b is a vector only if b have shape (n,) or (n, 1)
b_is_sparse = isspmatrix(b) or is_pydata_spmatrix(b)
if not b_is_sparse:
b = asarray(b)
b_is_vector = ((b.ndim == 1) or (b.ndim == 2 and b.shape[1] == 1))
# sum duplicates for non-canonical format
A.sum_duplicates()
A = A.asfptype() # upcast to a floating point format
result_dtype = np.promote_types(A.dtype, b.dtype)
if A.dtype != result_dtype:
A = A.astype(result_dtype)
if b.dtype != result_dtype:
b = b.astype(result_dtype)
# validate input shapes
M, N = A.shape
if (M != N):
raise ValueError("matrix must be square (has shape %s)" % ((M, N), ))
if M != b.shape[0]:
raise ValueError("matrix - rhs dimension mismatch (%s - %s)" %
(A.shape, b.shape[0]))
use_umfpack = use_umfpack and useUmfpack
if b_is_vector and use_umfpack:
if b_is_sparse:
b_vec = b.toarray()
else:
b_vec = b
b_vec = asarray(b_vec, dtype=A.dtype).ravel()
if noScikit:
raise RuntimeError('Scikits.umfpack not installed.')
if A.dtype.char not in 'dD':
raise ValueError("convert matrix data to double, please, using"
" .astype(), or set linsolve.useUmfpack = False")
umf_family, A = _get_umf_family(A)
umf = umfpack.UmfpackContext(umf_family)
x = umf.linsolve(umfpack.UMFPACK_A, A, b_vec, autoTranspose=True)
else:
if b_is_vector and b_is_sparse:
b = b.toarray()
b_is_sparse = False
if not b_is_sparse:
if isspmatrix_csc(A):
flag = 1 # CSC format
else:
flag = 0 # CSR format
options = dict(ColPerm=permc_spec)
x, info = _superlu.gssv(N,
A.nnz,
A.data,
A.indices,
A.indptr,
b,
flag,
options=options)
if info != 0:
warn("Matrix is exactly singular", MatrixRankWarning)
x.fill(np.nan)
if b_is_vector:
x = x.ravel()
else:
# b is sparse
Afactsolve = factorized(A)
if not (isspmatrix_csc(b) or is_pydata_spmatrix(b)):
warn(
'spsolve is more efficient when sparse b '
'is in the CSC matrix format', SparseEfficiencyWarning)
b = csc_matrix(b)
# Create a sparse output matrix by repeatedly applying
# the sparse factorization to solve columns of b.
data_segs = []
row_segs = []
col_segs = []
for j in range(b.shape[1]):
# TODO: replace this with
# bj = b[:, j].toarray().ravel()
# once 1D sparse arrays are supported.
# That is a slightly faster code path.
bj = b[:, [j]].toarray().ravel()
xj = Afactsolve(bj)
w = np.flatnonzero(xj)
segment_length = w.shape[0]
row_segs.append(w)
col_segs.append(np.full(segment_length, j, dtype=int))
data_segs.append(np.asarray(xj[w], dtype=A.dtype))
sparse_data = np.concatenate(data_segs)
sparse_row = np.concatenate(row_segs)
sparse_col = np.concatenate(col_segs)
x = A.__class__((sparse_data, (sparse_row, sparse_col)),
shape=b.shape,
dtype=A.dtype)
if is_pydata_spmatrix(b):
x = b.__class__(x)
return x
def cholesky(a):
"""Cholesky decomposition.
Decompose a given two-dimensional square matrix into ``L * L.T``,
where ``L`` is a lower-triangular matrix and ``.T`` is a conjugate
transpose operator.
Args:
a (cupy.ndarray): The input matrix with dimension ``(N, N)``
Returns:
cupy.ndarray: The lower-triangular matrix.
.. 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.cholesky`
"""
_util._assert_cupy_array(a)
_util._assert_nd_squareness(a)
if a.ndim > 2:
return _potrf_batched(a)
if a.dtype.char == 'f' or a.dtype.char == 'd':
dtype = a.dtype.char
else:
dtype = numpy.promote_types(a.dtype.char, 'f').char
x = a.astype(dtype, order='C', copy=True)
n = len(a)
handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
if dtype == 'f':
potrf = cusolver.spotrf
potrf_bufferSize = cusolver.spotrf_bufferSize
elif dtype == 'd':
potrf = cusolver.dpotrf
potrf_bufferSize = cusolver.dpotrf_bufferSize
elif dtype == 'F':
potrf = cusolver.cpotrf
potrf_bufferSize = cusolver.cpotrf_bufferSize
else: # dtype == 'D':
potrf = cusolver.zpotrf
potrf_bufferSize = cusolver.zpotrf_bufferSize
buffersize = potrf_bufferSize(handle, cublas.CUBLAS_FILL_MODE_UPPER, n,
x.data.ptr, n)
workspace = cupy.empty(buffersize, dtype=dtype)
potrf(handle, cublas.CUBLAS_FILL_MODE_UPPER, n, x.data.ptr, n,
workspace.data.ptr, buffersize, dev_info.data.ptr)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
potrf, dev_info)
_util._tril(x, k=0)
return x
def cov(a, y=None, rowvar=True, bias=False, ddof=None):
"""Returns the covariance matrix of an array.
This function currently does not support ``fweights`` and ``aweights``
options.
Args:
a (cupy.ndarray): Array to compute covariance matrix.
y (cupy.ndarray): An additional set of variables and observations.
rowvar (bool): If ``True``, then each row represents a variable, with
observations in the columns. Otherwise, the relationship is
transposed.
bias (bool): If ``False``, normalization is by ``(N - 1)``, where N is
the number of observations given (unbiased estimate). If ``True``,
then normalization is by ``N``.
ddof (int): If not ``None`` the default value implied by bias is
overridden. Note that ``ddof=1`` will return the unbiased estimate
and ``ddof=0`` will return the simple average.
Returns:
cupy.ndarray: The covariance matrix of the input array.
.. seealso:: :func:`numpy.cov`
"""
if ddof is not None and ddof != int(ddof):
raise ValueError('ddof must be integer')
if a.ndim > 2:
raise ValueError('Input must be <= 2-d')
if y is None:
dtype = numpy.promote_types(a.dtype, numpy.float64)
else:
if y.ndim > 2:
raise ValueError('y must be <= 2-d')
dtype = functools.reduce(numpy.promote_types,
(a.dtype, y.dtype, numpy.float64))
X = cupy.array(a, ndmin=2, dtype=dtype)
if not rowvar and X.shape[0] != 1:
X = X.T
if X.shape[0] == 0:
return cupy.array([]).reshape(0, 0)
if y is not None:
y = cupy.array(y, copy=False, ndmin=2, dtype=dtype)
if not rowvar and y.shape[0] != 1:
y = y.T
X = core.concatenate_method((X, y), axis=0)
if ddof is None:
ddof = 0 if bias else 1
fact = X.shape[1] - ddof
if fact <= 0:
warnings.warn('Degrees of freedom <= 0 for slice',
RuntimeWarning,
stacklevel=2)
fact = 0.0
X -= X.mean(axis=1)[:, None]
out = X.dot(X.T.conj()) * (1 / cupy.float64(fact))
return out.squeeze()
def predict_conditional(self, params):
"""
In-sample prediction, conditional on the current and previous regime
Parameters
----------
params : array_like
Array of parameters at which to create predictions.
Returns
-------
predict : array_like
Array of predictions conditional on current, and possibly past,
regimes
"""
params = np.array(params, ndmin=1)
# Prediction is based on:
# y_t = x_t beta^{(S_t)} +
# \phi_1^{(S_t)} (y_{t-1} - x_{t-1} beta^{(S_t-1)}) + ...
# \phi_p^{(S_t)} (y_{t-p} - x_{t-p} beta^{(S_t-p)}) + eps_t
if self._k_exog > 0:
xb = []
for i in range(self.k_regimes):
coeffs = params[self.parameters[i, 'exog']]
xb.append(np.dot(self.orig_exog, coeffs))
predict = np.zeros(
(self.k_regimes,) * (self.order + 1) + (self.nobs,),
dtype=np.promote_types(np.float64, params.dtype))
# Iterate over S_{t} = i
for i in range(self.k_regimes):
ar_coeffs = params[self.parameters[i, 'autoregressive']]
# y_t - x_t beta^{(S_t)}
ix = self._predict_slices[:]
ix[0] = i
ix = tuple(ix)
if self._k_exog > 0:
predict[ix] += xb[i][self.order:]
# Iterate over j = 2, .., p
for j in range(1, self.order + 1):
for k in range(self.k_regimes):
# This gets a specific time-period / regime slice:
# S_{t} = i, S_{t-j} = k, across all other time-period /
# regime slices.
ix = self._predict_slices[:]
ix[0] = i
ix[j] = k
ix = tuple(ix)
start = self.order - j
end = -j
if self._k_exog > 0:
predict[ix] += ar_coeffs[j-1] * (
self.orig_endog[start:end] - xb[k][start:end])
else:
predict[ix] += ar_coeffs[j-1] * (
self.orig_endog[start:end])
return predict
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 promote_types(type1, type2): # pylint: disable=missing-function-docstring
type1 = _to_numpy_type(type1)
type2 = _to_numpy_type(type2)
return np_dtypes.canonicalize_dtype(np.promote_types(type1, type2))
def _declare_partials(self, of, wrt, dependent=True, rows=None, cols=None, val=None):
"""
Store subjacobian metadata for later use.
Parameters
----------
of : str or list of str
The name of the residual(s) that derivatives are being computed for.
May also contain a glob pattern.
wrt : str or list of str
The name of the variables that derivatives are taken with respect to.
This can contain the name of any input or output variable.
May also contain a glob pattern.
dependent : bool(True)
If False, specifies no dependence between the output(s) and the
input(s). This is only necessary in the case of a sparse global
jacobian, because if 'dependent=False' is not specified and
declare_partials is not called for a given pair, then a dense
matrix of zeros will be allocated in the sparse global jacobian
for that pair. In the case of a dense global jacobian it doesn't
matter because the space for a dense subjac will always be
allocated for every pair.
rows : ndarray of int or None
Row indices for each nonzero entry. For sparse subjacobians only.
cols : ndarray of int or None
Column indices for each nonzero entry. For sparse subjacobians only.
val : float or ndarray of float or scipy.sparse
Value of subjacobian. If rows and cols are not None, this will
contain the values found at each (row, col) location in the subjac.
"""
if dependent and val is not None and not issparse(val):
val = np.atleast_1d(val)
# np.promote_types will choose the smallest dtype that can contain both arguments
safe_dtype = np.promote_types(val.dtype, float)
val = val.astype(safe_dtype, copy=False)
if dependent and rows is not None:
rows = np.array(rows, dtype=int, copy=False)
cols = np.array(cols, dtype=int, copy=False)
if rows.shape != cols.shape:
raise ValueError('rows and cols must have the same shape,'
' rows: {}, cols: {}'.format(rows.shape, cols.shape))
if val is not None and val.shape != (1,) and rows.shape != val.shape:
raise ValueError('If rows and cols are specified, val must be a scalar or have the '
'same shape, val: {}, rows/cols: {}'.format(val.shape, rows.shape))
if val is None:
val = np.zeros_like(rows, dtype=float)
pattern_matches = self._find_partial_matches(of, wrt)
multiple_items = False
for of_bundle, wrt_bundle in product(*pattern_matches):
of_pattern, of_matches = of_bundle
wrt_pattern, wrt_matches = wrt_bundle
if not of_matches:
raise ValueError('No matches were found for of="{}"'.format(of_pattern))
if not wrt_matches:
raise ValueError('No matches were found for wrt="{}"'.format(wrt_pattern))
make_copies = (multiple_items
or len(of_matches) > 1
or len(wrt_matches) > 1)
# Setting this to true means that future loop iterations (i.e. if there are multiple
# items in either of or wrt) will make copies.
multiple_items = True
for rel_key in product(of_matches, wrt_matches):
abs_key = rel_key2abs_key(self, rel_key)
if not dependent:
if abs_key in self._subjacs_info:
del self._subjacs_info[abs_key]
continue
if abs_key in self._subjacs_info:
meta = self._subjacs_info[abs_key]
else:
meta = SUBJAC_META_DEFAULTS.copy()
meta['rows'] = rows
meta['cols'] = cols
meta['value'] = deepcopy(val) if make_copies else val
meta['dependent'] = dependent
self._check_partials_meta(abs_key, meta)
self._subjacs_info[abs_key] = meta
def inv(a):
"""Computes the inverse of a matrix.
This function computes matrix ``a_inv`` from n-dimensional regular matrix
``a`` such that ``dot(a, a_inv) == eye(n)``.
Args:
a (cupy.ndarray): The regular matrix
Returns:
cupy.ndarray: The inverse of a matrix.
.. 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.inv`
"""
if a.ndim >= 3:
return _batched_inv(a)
# to prevent `a` to be overwritten
a = a.copy()
util._assert_cupy_array(a)
util._assert_rank2(a)
util._assert_nd_squareness(a)
# 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')
cusolver_handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
ipiv = cupy.empty((a.shape[0], 1), dtype=numpy.intc)
if dtype == 'f':
getrf = cusolver.sgetrf
getrf_bufferSize = cusolver.sgetrf_bufferSize
getrs = cusolver.sgetrs
elif dtype == 'd':
getrf = cusolver.dgetrf
getrf_bufferSize = cusolver.dgetrf_bufferSize
getrs = cusolver.dgetrs
elif dtype == 'F':
getrf = cusolver.cgetrf
getrf_bufferSize = cusolver.cgetrf_bufferSize
getrs = cusolver.cgetrs
elif dtype == 'D':
getrf = cusolver.zgetrf
getrf_bufferSize = cusolver.zgetrf_bufferSize
getrs = cusolver.zgetrs
else:
msg = ('dtype must be float32, float64, complex64 or complex128'
' (actual: {})'.format(a.dtype))
raise ValueError(msg)
m = a.shape[0]
buffersize = getrf_bufferSize(cusolver_handle, m, m, a.data.ptr, m)
workspace = cupy.empty(buffersize, dtype=dtype)
# LU factorization
getrf(cusolver_handle, m, m, a.data.ptr, m, workspace.data.ptr,
ipiv.data.ptr, dev_info.data.ptr)
cupy.linalg.util._check_cusolver_dev_info_if_synchronization_allowed(
getrf, dev_info)
b = cupy.eye(m, dtype=dtype)
# solve for the inverse
getrs(cusolver_handle, 0, m, m, a.data.ptr, m, ipiv.data.ptr, b.data.ptr,
m, dev_info.data.ptr)
cupy.linalg.util._check_cusolver_dev_info_if_synchronization_allowed(
getrs, dev_info)
return b
def __init__(
self,
mean: Union[float, np.floating, np.ndarray, linops.LinearOperator],
cov: Union[float, np.floating, np.ndarray, linops.LinearOperator],
cov_cholesky: Optional[Union[float, np.floating, np.ndarray,
linops.LinearOperator]] = None,
random_state: RandomStateArgType = None,
):
# Type normalization
if np.isscalar(mean):
mean = _utils.as_numpy_scalar(mean)
if np.isscalar(cov):
cov = _utils.as_numpy_scalar(cov)
if np.isscalar(cov_cholesky):
cov_cholesky = _utils.as_numpy_scalar(cov_cholesky)
# Data type normalization
dtype = np.promote_types(mean.dtype, cov.dtype)
if not np.issubdtype(dtype, np.floating):
dtype = np.dtype(np.double)
mean = mean.astype(dtype, order="C", casting="safe", copy=False)
cov = cov.astype(dtype, order="C", casting="safe", copy=False)
# Shape checking
if not 0 <= mean.ndim <= 2:
raise ValueError(
f"Gaussian random variables must either be scalars, vectors, or "
f"matrices (or linear operators), but the given mean is a {mean.ndim}-"
f"dimensional tensor.")
expected_cov_shape = (np.prod(mean.shape), ) * 2 if len(
mean.shape) > 0 else ()
if cov.shape != expected_cov_shape:
raise ValueError(
f"The covariance matrix must be of shape {expected_cov_shape}, but "
f"shape {cov.shape} was given.")
self._mean = mean
self._cov = cov
self._compute_cov_cholesky: Callable[[], _ValueType] = None
self._cov_cholesky = cov_cholesky # recall: None if not provided
# Method selection
univariate = mean.ndim == 0
dense = isinstance(mean, np.ndarray) and isinstance(cov, np.ndarray)
cov_operator = isinstance(cov, linops.LinearOperator)
if univariate:
# Univariate Gaussian
sample = self._univariate_sample
in_support = Normal._univariate_in_support
pdf = self._univariate_pdf
logpdf = self._univariate_logpdf
cdf = self._univariate_cdf
logcdf = self._univariate_logcdf
quantile = self._univariate_quantile
median = lambda: self._mean
var = lambda: self._cov
entropy = self._univariate_entropy
self._compute_cov_cholesky = self._univariate_cov_cholesky
elif dense or cov_operator:
# Multi- and matrixvariate Gaussians
sample = self._dense_sample
in_support = Normal._dense_in_support
pdf = self._dense_pdf
logpdf = self._dense_logpdf
cdf = self._dense_cdf
logcdf = self._dense_logcdf
quantile = None
median = None
var = self._dense_var
entropy = self._dense_entropy
self._compute_cov_cholesky = self.dense_cov_cholesky
# Ensure that the Cholesky factor has the same type as the covariance,
# and, if necessary, promote data types. Check for (in this order): type, shape, dtype.
if self._cov_cholesky is not None:
if not isinstance(self._cov_cholesky, type(self._cov)):
raise TypeError(
f"The covariance matrix is of type `{type(self._cov)}`, so its "
f"Cholesky decomposition must be of the same type, but an "
f"object of type `{type(self._cov_cholesky)}` was given."
)
if self._cov_cholesky.shape != self._cov.shape:
raise ValueError(
f"The cholesky decomposition of the covariance matrix must "
f"have the same shape as the covariance matrix, i.e. "
f"{self._cov.shape}, but shape {self._cov_cholesky.shape} was given"
)
if self._cov_cholesky.dtype != self._cov.dtype:
self._cov_cholesky = self._cov_cholesky.astype(
self._cov.dtype, casting="safe", copy=False)
if isinstance(cov, linops.SymmetricKronecker):
m, n = mean.shape
if m != n or n != cov.A.shape[0] or n != cov.B.shape[1]:
raise ValueError(
"Normal distributions with symmetric Kronecker structured "
"kernels must have square mean and square kernels factors with "
"matching dimensions.")
if cov.identical_factors:
sample = self._symmetric_kronecker_identical_factors_sample
# pylint: disable=redefined-variable-type
self._compute_cov_cholesky = (
self.
_symmetric_kronecker_identical_factors_cov_cholesky)
elif isinstance(cov, linops.Kronecker):
m, n = mean.shape
if (m != cov.A.shape[0] or m != cov.A.shape[1]
or n != cov.B.shape[0] or n != cov.B.shape[1]):
raise ValueError(
"Kronecker structured kernels must have factors with the same "
"shape as the mean.")
self._compute_cov_cholesky = self._kronecker_cov_cholesky
else:
raise ValueError(
f"Cannot instantiate normal distribution with mean of type "
f"{mean.__class__.__name__} and kernels of type "
f"{cov.__class__.__name__}.")
super().__init__(
shape=mean.shape,
dtype=mean.dtype,
random_state=random_state,
parameters={
"mean": self._mean,
"cov": self._cov
},
sample=sample,
in_support=in_support,
pdf=pdf,
logpdf=logpdf,
cdf=cdf,
logcdf=logcdf,
quantile=quantile,
mode=lambda: self._mean,
median=median,
mean=lambda: self._mean,
cov=lambda: self._cov,
var=var,
entropy=entropy,
)
def _gibbs_removal_1d(x, axis=0, n_points=3):
"""Suppresses Gibbs ringing along a given axis using fourier sub-shifts.
Parameters
----------
x : 2D ndarray
Matrix x.
axis : int (0 or 1)
Axis in which Gibbs oscillations will be suppressed.
Default is set to 0.
n_points : int, optional
Number of neighbours to access local TV (see note).
Default is set to 3.
Returns
-------
xc : 2D ndarray
Matrix with suppressed Gibbs oscillations along the given axis.
Notes
-----
This function suppresses the effects of Gibbs oscillations based on the
analysis of local total variation (TV). Although artefact correction is
done based on two adjacent points for each voxel, total variation should be
accessed in a larger range of neighbours. The number of neighbours to be
considered in TV calculation can be adjusted using the parameter n_points.
"""
dtype_float = np.promote_types(x.real.dtype, np.float32)
ssamp = np.linspace(0.02, 0.9, num=45, dtype=dtype_float)
xs = x.copy() if axis else x.T.copy()
# TV for shift zero (baseline)
tvr, tvl = _image_tv(xs, axis=1, n_points=n_points)
tvp = np.minimum(tvr, tvl)
tvn = tvp.copy()
# Find optimal shift for gibbs removal
isp = xs.copy()
isn = xs.copy()
sp = np.zeros(xs.shape, dtype=dtype_float)
sn = np.zeros(xs.shape, dtype=dtype_float)
N = xs.shape[1]
c = _fft.fft(xs, axis=1)
k = _fft.fftfreq(N, 1 / (2.0j * np.pi))
k = k.astype(c.dtype, copy=False)
for s in ssamp:
ks = k * s
# Access positive shift for given s
img_p = abs(_fft.ifft(c * np.exp(ks), axis=1))
tvsr, tvsl = _image_tv(img_p, axis=1, n_points=n_points)
tvs_p = np.minimum(tvsr, tvsl)
# Access negative shift for given s
img_n = abs(_fft.ifft(c * np.exp(-ks), axis=1))
tvsr, tvsl = _image_tv(img_n, axis=1, n_points=n_points)
tvs_n = np.minimum(tvsr, tvsl)
# Update positive shift params
isp[tvp > tvs_p] = img_p[tvp > tvs_p]
sp[tvp > tvs_p] = s
tvp[tvp > tvs_p] = tvs_p[tvp > tvs_p]
# Update negative shift params
isn[tvn > tvs_n] = img_n[tvn > tvs_n]
sn[tvn > tvs_n] = s
tvn[tvn > tvs_n] = tvs_n[tvn > tvs_n]
# check non-zero sub-voxel shifts
idx = np.nonzero(sp + sn)
# use positive and negative optimal sub-voxel shifts to interpolate to
# original grid points
xs[idx] = (isp[idx] - isn[idx])/(sp[idx] + sn[idx])*sn[idx] + isn[idx]
return xs if axis else xs.T
def histogram(image, nbins=256):
"""Return histogram of image.
Unlike `numpy.histogram`, this function returns the centers of bins and
does not rebin integer arrays. For integer arrays, each integer value has
its own bin, which improves speed and intensity-resolution.
The histogram is computed on the flattened image: for color images, the
function should be used separately on each channel to obtain a histogram
for each color channel.
Parameters
----------
image : array
Input image.
nbins : int
Number of bins used to calculate histogram. This value is ignored for
integer arrays.
Returns
-------
hist : array
The values of the histogram.
bin_centers : array
The values at the center of the bins.
Examples
--------
>>> from skimage import data, exposure, util
>>> image = util.img_as_float(data.camera())
>>> np.histogram(image, bins=2)
(array([107432, 154712]), array([ 0. , 0.5, 1. ]))
>>> exposure.histogram(image, nbins=2)
(array([107432, 154712]), array([ 0.25, 0.75]))
"""
sh = image.shape
if len(sh) == 3 and sh[-1] < 4:
warnings.warn("This might be a color image. The histogram will be "
"computed on the flattened image. You can instead "
"apply this function to each color channel.")
# For integer types, histogramming with bincount is more efficient.
if np.issubdtype(image.dtype, np.integer):
offset = 0
image_min = np.min(image)
if image_min < 0:
offset = image_min
image_range = np.max(image).astype(np.int64) - image_min
# get smallest dtype that can hold both minimum and offset maximum
offset_dtype = np.promote_types(np.min_scalar_type(image_range),
np.min_scalar_type(image_min))
if image.dtype != offset_dtype:
# prevent overflow errors when offsetting
image = image.astype(offset_dtype)
image = image - offset
hist = np.bincount(image.ravel())
bin_centers = np.arange(len(hist)) + offset
# clip histogram to start with a non-zero bin
idx = np.nonzero(hist)[0][0]
return hist[idx:], bin_centers[idx:]
else:
hist, bin_edges = np.histogram(image.flat, nbins)
bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2.
return hist, bin_centers
def svd(a, full_matrices=True, compute_uv=True):
"""Singular Value Decomposition.
Factorizes the matrix ``a`` as ``u * np.diag(s) * v``, where ``u`` and
``v`` are unitary and ``s`` is an one-dimensional array of ``a``'s
singular values.
Args:
a (cupy.ndarray): The input matrix with dimension ``(..., M, N)``.
full_matrices (bool): If True, it returns u and v with dimensions
``(..., M, M)`` and ``(..., N, N)``. Otherwise, the dimensions
of u and v are ``(..., M, K)`` and ``(..., K, N)``, respectively,
where ``K = min(M, N)``.
compute_uv (bool): If ``False``, it only returns singular values.
Returns:
tuple of :class:`cupy.ndarray`:
A tuple of ``(u, s, v)`` such that ``a = u * np.diag(s) * v``.
.. 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`.
.. note::
On CUDA, when ``a.ndim > 2`` and the matrix dimensions <= 32, a fast
code path based on Jacobian method (``gesvdj``) is taken. Otherwise,
a QR method (``gesvd``) is used.
On ROCm, there is no such a fast code path that switches the underlying
algorithm.
.. seealso:: :func:`numpy.linalg.svd`
"""
_util._assert_cupy_array(a)
# Cast to float32 or float64
a_dtype = numpy.promote_types(a.dtype.char, 'f').char
if a_dtype == 'f':
s_dtype = 'f'
elif a_dtype == 'd':
s_dtype = 'd'
elif a_dtype == 'F':
s_dtype = 'f'
else: # a_dtype == 'D':
a_dtype = 'D'
s_dtype = 'd'
if a.ndim > 2:
return _svd_batched(a, a_dtype, full_matrices, compute_uv)
# Remark 1: gesvd only supports m >= n (WHAT?)
# Remark 2: gesvd returns matrix U and V^H
n, m = a.shape
if m == 0 or n == 0:
s = cupy.empty((0, ), s_dtype)
if compute_uv:
if full_matrices:
u = cupy.eye(n, dtype=a_dtype)
vt = cupy.eye(m, dtype=a_dtype)
else:
u = cupy.empty((n, 0), dtype=a_dtype)
vt = cupy.empty((0, m), dtype=a_dtype)
return u, s, vt
else:
return s
# `a` must be copied because xgesvd destroys the matrix
if m >= n:
x = a.astype(a_dtype, order='C', copy=True)
trans_flag = False
else:
m, n = a.shape
x = a.transpose().astype(a_dtype, order='C', copy=True)
trans_flag = True
k = n # = min(m, n) where m >= n is ensured above
if compute_uv:
if full_matrices:
u = cupy.empty((m, m), dtype=a_dtype)
vt = x[:, :n]
job_u = ord('A')
job_vt = ord('O')
else:
u = x
vt = cupy.empty((k, n), dtype=a_dtype)
job_u = ord('O')
job_vt = ord('S')
u_ptr, vt_ptr = u.data.ptr, vt.data.ptr
else:
u_ptr, vt_ptr = 0, 0 # Use nullptr
job_u = ord('N')
job_vt = ord('N')
s = cupy.empty(k, dtype=s_dtype)
handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
if a_dtype == 'f':
gesvd = cusolver.sgesvd
gesvd_bufferSize = cusolver.sgesvd_bufferSize
elif a_dtype == 'd':
gesvd = cusolver.dgesvd
gesvd_bufferSize = cusolver.dgesvd_bufferSize
elif a_dtype == 'F':
gesvd = cusolver.cgesvd
gesvd_bufferSize = cusolver.cgesvd_bufferSize
else: # a_dtype == 'D':
gesvd = cusolver.zgesvd
gesvd_bufferSize = cusolver.zgesvd_bufferSize
buffersize = gesvd_bufferSize(handle, m, n)
workspace = cupy.empty(buffersize, dtype=a_dtype)
if not runtime.is_hip:
# rwork can be NULL if the information from supperdiagonal isn't needed
# https://docs.nvidia.com/cuda/cusolver/index.html#cuSolverDN-lt-t-gt-gesvd # noqa
rwork_ptr = 0
else:
rwork = cupy.empty(min(m, n) - 1, dtype=s_dtype)
rwork_ptr = rwork.data.ptr
gesvd(handle, job_u, job_vt, m, n, x.data.ptr, m, s.data.ptr, u_ptr, m,
vt_ptr, n, workspace.data.ptr, buffersize, rwork_ptr,
dev_info.data.ptr)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
gesvd, dev_info)
# Note that the returned array may need to be transposed
# depending on the structure of an input
if compute_uv:
if trans_flag:
return u.transpose(), s, vt.transpose()
else:
return vt, s, u
else:
return s