def _(a, value):
a = asanyarray(a)
value = asanyarray(value)
ainds = tuple(range(a.ndim))[::-1]
vinds = tuple(range(value.ndim))[::-1]
oinds = max(ainds, vinds, key=len)
return blockwise(f, oinds, a, ainds, value, vinds, dtype=a.dtype)
def compute_jhr(time_bin_indices, time_bin_counts, antenna1, antenna2, jones,
residual, model, flag):
mode = check_type(jones, residual)
if mode != DIAG_DIAG:
raise NotImplementedError("Only DIAG-DIAG case has been implemented")
jones_shape = ('row', 'ant', 'chan', 'dir', 'corr')
vis_shape = ('row', 'chan', 'corr')
model_shape = ('row', 'chan', 'dir', 'corr')
return blockwise(
np_compute_jhr,
jones_shape,
time_bin_indices,
('row', ),
time_bin_counts,
('row', ),
antenna1,
('row', ),
antenna2,
('row', ),
jones,
jones_shape,
residual,
vis_shape,
model,
model_shape,
flag,
vis_shape,
adjust_chunks={"row": antenna1.chunks[0]},
new_axes={"corr2": 2}, # why?
dtype=model.dtype,
align_arrays=False)
def masked_array(data, mask=np.ma.nomask, fill_value=None, **kwargs):
data = asanyarray(data)
inds = tuple(range(data.ndim))
arginds = [inds, data, inds]
if getattr(fill_value, "shape", ()):
raise ValueError("non-scalar fill_value not supported")
kwargs["fill_value"] = fill_value
if mask is not np.ma.nomask:
mask = asanyarray(mask)
if mask.size == 1:
mask = mask.reshape((1, ) * data.ndim)
elif data.shape != mask.shape:
raise np.ma.MaskError("Mask and data not compatible: data shape "
"is %s, and mask shape is "
"%s." % (repr(data.shape), repr(mask.shape)))
arginds.extend([mask, inds])
if "dtype" in kwargs:
kwargs["masked_dtype"] = kwargs["dtype"]
else:
kwargs["dtype"] = data.dtype
return blockwise(_masked_array, *arginds, **kwargs)
def fit_spi_components(data,
weights,
freqs,
freq0,
alphai=None,
I0i=None,
beam=None,
tol=1e-5,
maxiter=100):
""" Dask wrapper fit_spi_components function """
return blockwise(_fit_spi_components_wrapper, ("vars", "comps"),
data, ("comps", "chan"),
weights, ("chan", ),
freqs, ("chan", ),
freq0,
None,
alphai, ("comps", ) if alphai is not None else None,
I0i, ("comps", ) if I0i is not None else None,
beam, ("comps", "chan") if beam is not None else None,
tol,
None,
maxiter,
None,
new_axes={"vars": 4},
dtype=data.dtype)
def masked_equal(a, value):
a = asanyarray(a)
if getattr(value, "shape", ()):
raise ValueError("da.ma.masked_equal doesn't support array `value`s")
inds = tuple(range(a.ndim))
return blockwise(np.ma.masked_equal,
inds,
a,
inds,
value, (),
dtype=a.dtype)
def compute_and_corrupt_vis(time_bin_indices, time_bin_counts, antenna1,
antenna2, jones, model, uvw, freq, lm):
if jones.chunks[1][0] != jones.shape[1]:
raise ValueError("Cannot chunk jones over antenna")
if jones.chunks[3][0] != jones.shape[3]:
raise ValueError("Cannot chunk jones over direction")
if model.chunks[2][0] != model.shape[2]:
raise ValueError("Cannot chunk model over direction")
if uvw.chunks[1][0] != uvw.shape[1]:
raise ValueError("Cannot chunk uvw over last axis")
if lm.chunks[1][0] != lm.shape[1]:
raise ValueError("Cannot chunks lm over direction")
if lm.chunks[2][0] != lm.shape[2]:
raise ValueError("Cannot chunks lm over last axis")
mode = check_type(jones, model, vis_type='model')
if mode == DIAG_DIAG:
out_shape = ("row", "chan", "corr1")
model_shape = ("row", "chan", "dir", "corr1")
jones_shape = ("row", "ant", "chan", "dir", "corr1")
elif mode == DIAG:
out_shape = ("row", "chan", "corr1", "corr2")
model_shape = ("row", "chan", "dir", "corr1", "corr2")
jones_shape = ("row", "ant", "chan", "dir", "corr1")
elif mode == FULL:
out_shape = ("row", "chan", "corr1", "corr2")
model_shape = ("row", "chan", "dir", "corr1", "corr2")
jones_shape = ("row", "ant", "chan", "dir", "corr1", "corr2")
else:
raise ValueError("Unknown mode argument of %s" % mode)
# the new_axes={"corr2": 2} is required because of a dask bug
# see https://github.com/dask/dask/issues/5550
return blockwise(_compute_and_corrupt_vis_wrapper,
out_shape,
time_bin_indices, ("row", ),
time_bin_counts, ("row", ),
antenna1, ("row", ),
antenna2, ("row", ),
jones,
jones_shape,
model,
model_shape,
uvw, ("row", "three"),
freq, ("chan", ),
lm, ("row", "dir", "two"),
adjust_chunks={"row": antenna1.chunks[0]},
new_axes={"corr2": 2},
dtype=model.dtype,
align_arrays=False)
def fromfunction(func, chunks="auto", shape=None, dtype=None, **kwargs):
dtype = dtype or float
chunks = normalize_chunks(chunks, shape, dtype=dtype)
inds = tuple(range(len(shape)))
arrs = [arange(s, dtype=dtype, chunks=c) for s, c in zip(shape, chunks)]
arrs = meshgrid(*arrs, indexing="ij")
args = sum(zip(arrs, itertools.repeat(inds)), ())
res = blockwise(func, inds, *args, token="fromfunction", **kwargs)
return res
def masked_where(condition, a):
cshape = getattr(condition, "shape", ())
if cshape and cshape != a.shape:
raise IndexError("Inconsistant shape between the condition and the "
"input (got %s and %s)" % (cshape, a.shape))
condition = asanyarray(condition)
a = asanyarray(a)
ainds = tuple(range(a.ndim))
cinds = tuple(range(condition.ndim))
return blockwise(np.ma.masked_where,
ainds,
condition,
cinds,
a,
ainds,
dtype=a.dtype)
def residual_vis(time_bin_indices, time_bin_counts, antenna1, antenna2, jones,
vis, flag, model):
if jones.chunks[1][0] != jones.shape[1]:
raise ValueError("Cannot chunk jones over antenna")
if jones.chunks[3][0] != jones.shape[3]:
raise ValueError("Cannot chunk jones over direction")
if model.chunks[2][0] != model.shape[2]:
raise ValueError("Cannot chunk model over direction")
mode = check_type(jones, vis)
if mode == DIAG_DIAG:
out_shape = ("row", "chan", "corr1")
model_shape = ("row", "chan", "dir", "corr1")
jones_shape = ("row", "ant", "chan", "dir", "corr1")
elif mode == DIAG:
out_shape = ("row", "chan", "corr1", "corr2")
model_shape = ("row", "chan", "dir", "corr1", "corr2")
jones_shape = ("row", "ant", "chan", "dir", "corr1")
elif mode == FULL:
out_shape = ("row", "chan", "corr1", "corr2")
model_shape = ("row", "chan", "dir", "corr1", "corr2")
jones_shape = ("row", "ant", "chan", "dir", "corr1", "corr2")
else:
raise ValueError("Unknown mode argument of %s" % mode)
# the new_axes={"corr2": 2} is required because of a dask bug
# see https://github.com/dask/dask/issues/5550
return blockwise(_residual_vis_wrapper,
out_shape,
time_bin_indices, ("row", ),
time_bin_counts, ("row", ),
antenna1, ("row", ),
antenna2, ("row", ),
jones,
jones_shape,
vis,
out_shape,
flag,
out_shape,
model,
model_shape,
adjust_chunks={"row": antenna1.chunks[0]},
new_axes={"corr2": 2},
dtype=vis.dtype,
align_arrays=False)
def outer(self, A, B, **kwargs):
if self.nin != 2:
raise ValueError(
"outer product only supported for binary functions")
if "out" in kwargs:
raise ValueError("`out` kwarg not supported")
A_is_dask = is_dask_collection(A)
B_is_dask = is_dask_collection(B)
if not A_is_dask and not B_is_dask:
return self._ufunc.outer(A, B, **kwargs)
elif (A_is_dask and not isinstance(A, Array)
or B_is_dask and not isinstance(B, Array)):
raise NotImplementedError(
"Dask objects besides `dask.array.Array` "
"are not supported at this time.")
A = asarray(A)
B = asarray(B)
ndim = A.ndim + B.ndim
out_inds = tuple(range(ndim))
A_inds = out_inds[:A.ndim]
B_inds = out_inds[A.ndim:]
dtype = apply_infer_dtype(self._ufunc.outer, [A, B],
kwargs,
"ufunc.outer",
suggest_dtype=False)
if "dtype" in kwargs:
func = partial(self._ufunc.outer, dtype=kwargs.pop("dtype"))
else:
func = self._ufunc.outer
return blockwise(
func,
out_inds,
A,
A_inds,
B,
B_inds,
dtype=dtype,
token=self.__name__ + ".outer",
**kwargs,
)
def apply_gufunc(
func,
signature,
*args,
axes=None,
axis=None,
keepdims=False,
output_dtypes=None,
output_sizes=None,
vectorize=None,
allow_rechunk=False,
meta=None,
**kwargs,
):
"""
Apply a generalized ufunc or similar python function to arrays.
``signature`` determines if the function consumes or produces core
dimensions. The remaining dimensions in given input arrays (``*args``)
are considered loop dimensions and are required to broadcast
naturally against each other.
In other terms, this function is like ``np.vectorize``, but for
the blocks of dask arrays. If the function itself shall also
be vectorized use ``vectorize=True`` for convenience.
Parameters
----------
func : callable
Function to call like ``func(*args, **kwargs)`` on input arrays
(``*args``) that returns an array or tuple of arrays. If multiple
arguments with non-matching dimensions are supplied, this function is
expected to vectorize (broadcast) over axes of positional arguments in
the style of NumPy universal functions [1]_ (if this is not the case,
set ``vectorize=True``). If this function returns multiple outputs,
``output_core_dims`` has to be set as well.
signature: string
Specifies what core dimensions are consumed and produced by ``func``.
According to the specification of numpy.gufunc signature [2]_
*args : numeric
Input arrays or scalars to the callable function.
axes: List of tuples, optional, keyword only
A list of tuples with indices of axes a generalized ufunc should operate on.
For instance, for a signature of ``"(i,j),(j,k)->(i,k)"`` appropriate for
matrix multiplication, the base elements are two-dimensional matrices
and these are taken to be stored in the two last axes of each argument. The
corresponding axes keyword would be ``[(-2, -1), (-2, -1), (-2, -1)]``.
For simplicity, for generalized ufuncs that operate on 1-dimensional arrays
(vectors), a single integer is accepted instead of a single-element tuple,
and for generalized ufuncs for which all outputs are scalars, the output
tuples can be omitted.
axis: int, optional, keyword only
A single axis over which a generalized ufunc should operate. This is a short-cut
for ufuncs that operate over a single, shared core dimension, equivalent to passing
in axes with entries of (axis,) for each single-core-dimension argument and ``()`` for
all others. For instance, for a signature ``"(i),(i)->()"``, it is equivalent to passing
in ``axes=[(axis,), (axis,), ()]``.
keepdims: bool, optional, keyword only
If this is set to True, axes which are reduced over will be left in the result as
a dimension with size one, so that the result will broadcast correctly against the
inputs. This option can only be used for generalized ufuncs that operate on inputs
that all have the same number of core dimensions and with outputs that have no core
dimensions , i.e., with signatures like ``"(i),(i)->()"`` or ``"(m,m)->()"``.
If used, the location of the dimensions in the output can be controlled with axes
and axis.
output_dtypes : Optional, dtype or list of dtypes, keyword only
Valid numpy dtype specification or list thereof.
If not given, a call of ``func`` with a small set of data
is performed in order to try to automatically determine the
output dtypes.
output_sizes : dict, optional, keyword only
Optional mapping from dimension names to sizes for outputs. Only used if
new core dimensions (not found on inputs) appear on outputs.
vectorize: bool, keyword only
If set to ``True``, ``np.vectorize`` is applied to ``func`` for
convenience. Defaults to ``False``.
allow_rechunk: Optional, bool, keyword only
Allows rechunking, otherwise chunk sizes need to match and core
dimensions are to consist only of one chunk.
Warning: enabling this can increase memory usage significantly.
Defaults to ``False``.
meta: Optional, tuple, keyword only
tuple of empty ndarrays describing the shape and dtype of the output of the gufunc.
Defaults to ``None``.
**kwargs : dict
Extra keyword arguments to pass to `func`
Returns
-------
Single dask.array.Array or tuple of dask.array.Array
Examples
--------
>>> import dask.array as da
>>> import numpy as np
>>> def stats(x):
... return np.mean(x, axis=-1), np.std(x, axis=-1)
>>> a = da.random.normal(size=(10,20,30), chunks=(5, 10, 30))
>>> mean, std = da.apply_gufunc(stats, "(i)->(),()", a)
>>> mean.compute().shape
(10, 20)
>>> def outer_product(x, y):
... return np.einsum("i,j->ij", x, y)
>>> a = da.random.normal(size=( 20,30), chunks=(10, 30))
>>> b = da.random.normal(size=(10, 1,40), chunks=(5, 1, 40))
>>> c = da.apply_gufunc(outer_product, "(i),(j)->(i,j)", a, b, vectorize=True)
>>> c.compute().shape
(10, 20, 30, 40)
References
----------
.. [1] https://docs.scipy.org/doc/numpy/reference/ufuncs.html
.. [2] https://docs.scipy.org/doc/numpy/reference/c-api/generalized-ufuncs.html
"""
# Input processing:
## Signature
if not isinstance(signature, str):
raise TypeError("`signature` has to be of type string")
# NumPy versions before https://github.com/numpy/numpy/pull/19627
# would not ignore whitespace characters in `signature` like they
# are supposed to. We remove the whitespace here as a workaround.
signature = re.sub(r"\s+", "", signature)
input_coredimss, output_coredimss = _parse_gufunc_signature(signature)
## Determine nout: nout = None for functions of one direct return; nout = int for return tuples
nout = None if not isinstance(output_coredimss,
list) else len(output_coredimss)
## Consolidate onto `meta`
if meta is not None and output_dtypes is not None:
raise ValueError(
"Only one of `meta` and `output_dtypes` should be given (`meta` is preferred)."
)
if meta is None:
if output_dtypes is None:
## Infer `output_dtypes`
if vectorize:
tempfunc = np.vectorize(func, signature=signature)
else:
tempfunc = func
output_dtypes = apply_infer_dtype(tempfunc, args, kwargs,
"apply_gufunc", "output_dtypes",
nout)
## Turn `output_dtypes` into `meta`
if (nout is None and isinstance(output_dtypes, (tuple, list))
and len(output_dtypes) == 1):
output_dtypes = output_dtypes[0]
sample = args[0] if args else None
if nout is None:
meta = meta_from_array(sample, dtype=output_dtypes)
else:
meta = tuple(
meta_from_array(sample, dtype=odt) for odt in output_dtypes)
## Normalize `meta` format
meta = meta_from_array(meta)
if isinstance(meta, list):
meta = tuple(meta)
## Validate `meta`
if nout is None:
if isinstance(meta, tuple):
if len(meta) == 1:
meta = meta[0]
else:
raise ValueError(
"For a function with one output, must give a single item for `output_dtypes`/`meta`, "
"not a tuple or list.")
else:
if not isinstance(meta, tuple):
raise ValueError(
f"For a function with {nout} outputs, must give a tuple or list for `output_dtypes`/`meta`, "
"not a single item.")
if len(meta) != nout:
raise ValueError(
f"For a function with {nout} outputs, must give a tuple or list of {nout} items for "
f"`output_dtypes`/`meta`, not {len(meta)}.")
## Vectorize function, if required
if vectorize:
otypes = [x.dtype
for x in meta] if isinstance(meta, tuple) else [meta.dtype]
func = np.vectorize(func, signature=signature, otypes=otypes)
## Miscellaneous
if output_sizes is None:
output_sizes = {}
## Axes
input_axes, output_axes = _validate_normalize_axes(axes, axis, keepdims,
input_coredimss,
output_coredimss)
# Main code:
## Cast all input arrays to dask
args = [asarray(a) for a in args]
if len(input_coredimss) != len(args):
raise ValueError(
"According to `signature`, `func` requires %d arguments, but %s given"
% (len(input_coredimss), len(args)))
## Axes: transpose input arguments
transposed_args = []
for arg, iax, input_coredims in zip(args, input_axes, input_coredimss):
shape = arg.shape
iax = tuple(a if a < 0 else a - len(shape) for a in iax)
tidc = tuple(i
for i in range(-len(shape) + 0, 0) if i not in iax) + iax
transposed_arg = arg.transpose(tidc)
transposed_args.append(transposed_arg)
args = transposed_args
## Assess input args for loop dims
input_shapes = [a.shape for a in args]
input_chunkss = [a.chunks for a in args]
num_loopdims = [
len(s) - len(cd) for s, cd in zip(input_shapes, input_coredimss)
]
max_loopdims = max(num_loopdims) if num_loopdims else None
core_input_shapes = [
dict(zip(icd, s[n:]))
for s, n, icd in zip(input_shapes, num_loopdims, input_coredimss)
]
core_shapes = merge(*core_input_shapes)
core_shapes.update(output_sizes)
loop_input_dimss = [
tuple("__loopdim%d__" % d
for d in range(max_loopdims - n, max_loopdims))
for n in num_loopdims
]
input_dimss = [l + c for l, c in zip(loop_input_dimss, input_coredimss)]
loop_output_dims = max(loop_input_dimss,
key=len) if loop_input_dimss else tuple()
## Assess input args for same size and chunk sizes
### Collect sizes and chunksizes of all dims in all arrays
dimsizess = {}
chunksizess = {}
for dims, shape, chunksizes in zip(input_dimss, input_shapes,
input_chunkss):
for dim, size, chunksize in zip(dims, shape, chunksizes):
dimsizes = dimsizess.get(dim, [])
dimsizes.append(size)
dimsizess[dim] = dimsizes
chunksizes_ = chunksizess.get(dim, [])
chunksizes_.append(chunksize)
chunksizess[dim] = chunksizes_
### Assert correct partitioning, for case:
for dim, sizes in dimsizess.items():
#### Check that the arrays have same length for same dimensions or dimension `1`
if set(sizes) | {1} != {1, max(sizes)}:
raise ValueError(
f"Dimension `'{dim}'` with different lengths in arrays")
if not allow_rechunk:
chunksizes = chunksizess[dim]
#### Check if core dimensions consist of only one chunk
if (dim in core_shapes) and (chunksizes[0][0] < core_shapes[dim]):
raise ValueError(
"Core dimension `'{}'` consists of multiple chunks. To fix, rechunk into a single \
chunk along this dimension or set `allow_rechunk=True`, but beware that this may increase memory usage \
significantly.".format(dim))
#### Check if loop dimensions consist of same chunksizes, when they have sizes > 1
relevant_chunksizes = list(
unique(c for s, c in zip(sizes, chunksizes) if s > 1))
if len(relevant_chunksizes) > 1:
raise ValueError(
f"Dimension `'{dim}'` with different chunksize present")
## Apply function - use blockwise here
arginds = list(concat(zip(args, input_dimss)))
### Use existing `blockwise` but only with loopdims to enforce
### concatenation for coredims that appear also at the output
### Modifying `blockwise` could improve things here.
tmp = blockwise(func,
loop_output_dims,
*arginds,
concatenate=True,
meta=meta,
**kwargs)
# NOTE: we likely could just use `meta` instead of `tmp._meta`,
# but we use it and validate it anyway just to be sure nothing odd has happened.
metas = tmp._meta
if nout is None:
assert not isinstance(
metas, (list, tuple)
), f"meta changed from single output to multiple output during blockwise: {meta} -> {metas}"
metas = (metas, )
else:
assert isinstance(
metas, (list, tuple)
), f"meta changed from multiple output to single output during blockwise: {meta} -> {metas}"
assert (
len(metas) == nout
), f"Number of outputs changed from {nout} to {len(metas)} during blockwise"
## Prepare output shapes
loop_output_shape = tmp.shape
loop_output_chunks = tmp.chunks
keys = list(flatten(tmp.__dask_keys__()))
name, token = keys[0][0].split("-")
### *) Treat direct output
if nout is None:
output_coredimss = [output_coredimss]
## Split output
leaf_arrs = []
for i, (ocd, oax,
meta) in enumerate(zip(output_coredimss, output_axes, metas)):
core_output_shape = tuple(core_shapes[d] for d in ocd)
core_chunkinds = len(ocd) * (0, )
output_shape = loop_output_shape + core_output_shape
output_chunks = loop_output_chunks + core_output_shape
leaf_name = "%s_%d-%s" % (name, i, token)
leaf_dsk = {(leaf_name, ) + key[1:] + core_chunkinds:
((getitem, key, i) if nout else key)
for key in keys}
graph = HighLevelGraph.from_collections(leaf_name,
leaf_dsk,
dependencies=[tmp])
meta = meta_from_array(meta, len(output_shape))
leaf_arr = Array(graph,
leaf_name,
chunks=output_chunks,
shape=output_shape,
meta=meta)
### Axes:
if keepdims:
slices = len(
leaf_arr.shape) * (slice(None), ) + len(oax) * (np.newaxis, )
leaf_arr = leaf_arr[slices]
tidcs = [None] * len(leaf_arr.shape)
for ii, oa in zip(range(-len(oax), 0), oax):
tidcs[oa] = ii
j = 0
for ii in range(len(tidcs)):
if tidcs[ii] is None:
tidcs[ii] = j
j += 1
leaf_arr = leaf_arr.transpose(tidcs)
leaf_arrs.append(leaf_arr)
return (*leaf_arrs, ) if nout else leaf_arrs[0] # Undo *) from above
def einsum(*operands, dtype=None, optimize=False, split_every=None, **kwargs):
"""Dask added an additional keyword-only argument ``split_every``.
split_every: int >= 2 or dict(axis: int), optional
Determines the depth of the recursive aggregation.
Deafults to ``None`` which would let dask heuristically
decide a good default.
"""
einsum_dtype = dtype
inputs, outputs, ops = parse_einsum_input(operands)
subscripts = "->".join((inputs, outputs))
# Infer the output dtype from operands
if dtype is None:
dtype = np.result_type(*[o.dtype for o in ops])
if optimize is not False:
# Avoid computation of dask arrays within np.einsum_path
# by passing in small numpy arrays broadcasted
# up to the right shape
fake_ops = [
np.broadcast_to(o.dtype.type(0), shape=o.shape) for o in ops
]
optimize, _ = np.einsum_path(subscripts, *fake_ops, optimize=optimize)
inputs = [tuple(i) for i in inputs.split(",")]
# Set of all indices
all_inds = {a for i in inputs for a in i}
# Which indices are contracted?
contract_inds = all_inds - set(outputs)
ncontract_inds = len(contract_inds)
# Introduce the contracted indices into the blockwise product
# so that we get numpy arrays, not lists
result = blockwise(
chunk_einsum,
tuple(outputs) + tuple(contract_inds),
*(a for ap in zip(ops, inputs) for a in ap),
# blockwise parameters
adjust_chunks={ind: 1
for ind in contract_inds},
dtype=dtype,
# np.einsum parameters
subscripts=subscripts,
kernel_dtype=einsum_dtype,
ncontract_inds=ncontract_inds,
optimize=optimize,
**kwargs,
)
# Now reduce over any extra contraction dimensions
if ncontract_inds > 0:
size = len(outputs)
return result.sum(axis=list(range(size, size + ncontract_inds)),
split_every=split_every)
return result