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ENH: Port single-copy np.block implementation to C #13186

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ENH: Port single-copy np.block implementation to C #13186

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4 changes: 4 additions & 0 deletions doc/release/1.17.0-notes.rst
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Expand Up @@ -176,6 +176,10 @@ thereby saving a level of indentation
In some cases where ``np.interp`` would previously return ``np.nan``, it now
returns an appropriate infinity.

``np.block`` is ported to C for performance and supports ``out`` argument
-------------------------------------------------------------------------
``np.block`` should have increased performance, particularly for inputs with
many small arrays. It also has a new ``out`` keyword argument.

Changes
=======
Expand Down
2 changes: 1 addition & 1 deletion numpy/core/numeric.py
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Expand Up @@ -26,7 +26,7 @@
inner, int_asbuffer, lexsort, matmul, may_share_memory,
min_scalar_type, ndarray, nditer, nested_iters, promote_types,
putmask, result_type, set_numeric_ops, shares_memory, vdot, where,
zeros, normalize_axis_index)
zeros, normalize_axis_index, block)
if sys.version_info[0] < 3:
from .multiarray import newbuffer, getbuffer

Expand Down
311 changes: 9 additions & 302 deletions numpy/core/shape_base.py
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Expand Up @@ -416,238 +416,8 @@ def stack(arrays, axis=0, out=None):
return _nx.concatenate(expanded_arrays, axis=axis, out=out)


def _block_format_index(index):
"""
Convert a list of indices ``[0, 1, 2]`` into ``"arrays[0][1][2]"``.
"""
idx_str = ''.join('[{}]'.format(i) for i in index if i is not None)
return 'arrays' + idx_str


def _block_check_depths_match(arrays, parent_index=[]):
"""
Recursive function checking that the depths of nested lists in `arrays`
all match. Mismatch raises a ValueError as described in the block
docstring below.

The entire index (rather than just the depth) needs to be calculated
for each innermost list, in case an error needs to be raised, so that
the index of the offending list can be printed as part of the error.

Parameters
----------
arrays : nested list of arrays
The arrays to check
parent_index : list of int
The full index of `arrays` within the nested lists passed to
`_block_check_depths_match` at the top of the recursion.

Returns
-------
first_index : list of int
The full index of an element from the bottom of the nesting in
`arrays`. If any element at the bottom is an empty list, this will
refer to it, and the last index along the empty axis will be `None`.
max_arr_ndim : int
The maximum of the ndims of the arrays nested in `arrays`.
final_size: int
The number of elements in the final array. This is used the motivate
the choice of algorithm used using benchmarking wisdom.

"""
if type(arrays) is tuple:
# not strictly necessary, but saves us from:
# - more than one way to do things - no point treating tuples like
# lists
# - horribly confusing behaviour that results when tuples are
# treated like ndarray
raise TypeError(
'{} is a tuple. '
'Only lists can be used to arrange blocks, and np.block does '
'not allow implicit conversion from tuple to ndarray.'.format(
_block_format_index(parent_index)
)
)
elif type(arrays) is list and len(arrays) > 0:
idxs_ndims = (_block_check_depths_match(arr, parent_index + [i])
for i, arr in enumerate(arrays))

first_index, max_arr_ndim, final_size = next(idxs_ndims)
for index, ndim, size in idxs_ndims:
final_size += size
if ndim > max_arr_ndim:
max_arr_ndim = ndim
if len(index) != len(first_index):
raise ValueError(
"List depths are mismatched. First element was at depth "
"{}, but there is an element at depth {} ({})".format(
len(first_index),
len(index),
_block_format_index(index)
)
)
# propagate our flag that indicates an empty list at the bottom
if index[-1] is None:
first_index = index

return first_index, max_arr_ndim, final_size
elif type(arrays) is list and len(arrays) == 0:
# We've 'bottomed out' on an empty list
return parent_index + [None], 0, 0
else:
# We've 'bottomed out' - arrays is either a scalar or an array
size = _nx.size(arrays)
return parent_index, _nx.ndim(arrays), size


def _atleast_nd(a, ndim):
# Ensures `a` has at least `ndim` dimensions by prepending
# ones to `a.shape` as necessary
return array(a, ndmin=ndim, copy=False, subok=True)


def _accumulate(values):
# Helper function because Python 2.7 doesn't have
# itertools.accumulate
value = 0
accumulated = []
for v in values:
value += v
accumulated.append(value)
return accumulated


def _concatenate_shapes(shapes, axis):
"""Given array shapes, return the resulting shape and slices prefixes.

These help in nested concatation.
Returns
-------
shape: tuple of int
This tuple satisfies:
```
shape, _ = _concatenate_shapes([arr.shape for shape in arrs], axis)
shape == concatenate(arrs, axis).shape
```

slice_prefixes: tuple of (slice(start, end), )
For a list of arrays being concatenated, this returns the slice
in the larger array at axis that needs to be sliced into.

For example, the following holds:
```
ret = concatenate([a, b, c], axis)
_, (sl_a, sl_b, sl_c) = concatenate_slices([a, b, c], axis)

ret[(slice(None),) * axis + sl_a] == a
ret[(slice(None),) * axis + sl_b] == b
ret[(slice(None),) * axis + sl_c] == c
```

Thses are called slice prefixes since they are used in the recursive
blocking algorithm to compute the left-most slices during the
recursion. Therefore, they must be prepended to rest of the slice
that was computed deeper in the recusion.

These are returned as tuples to ensure that they can quickly be added
to existing slice tuple without creating a new tuple everytime.

"""
# Cache a result that will be reused.
shape_at_axis = [shape[axis] for shape in shapes]

# Take a shape, any shape
first_shape = shapes[0]
first_shape_pre = first_shape[:axis]
first_shape_post = first_shape[axis+1:]

if any(shape[:axis] != first_shape_pre or
shape[axis+1:] != first_shape_post for shape in shapes):
raise ValueError(
'Mismatched array shapes in block along axis {}.'.format(axis))

shape = (first_shape_pre + (sum(shape_at_axis),) + first_shape[axis+1:])

offsets_at_axis = _accumulate(shape_at_axis)
slice_prefixes = [(slice(start, end),)
for start, end in zip([0] + offsets_at_axis,
offsets_at_axis)]
return shape, slice_prefixes


def _block_info_recursion(arrays, max_depth, result_ndim, depth=0):
"""
Returns the shape of the final array, along with a list
of slices and a list of arrays that can be used for assignment inside the
new array

Parameters
----------
arrays : nested list of arrays
The arrays to check
max_depth : list of int
The number of nested lists
result_ndim: int
The number of dimensions in thefinal array.

Returns
-------
shape : tuple of int
The shape that the final array will take on.
slices: list of tuple of slices
The slices into the full array required for assignment. These are
required to be prepended with ``(Ellipsis, )`` to obtain to correct
final index.
arrays: list of ndarray
The data to assign to each slice of the full array

"""
if depth < max_depth:
shapes, slices, arrays = zip(
*[_block_info_recursion(arr, max_depth, result_ndim, depth+1)
for arr in arrays])

axis = result_ndim - max_depth + depth
shape, slice_prefixes = _concatenate_shapes(shapes, axis)

# Prepend the slice prefix and flatten the slices
slices = [slice_prefix + the_slice
for slice_prefix, inner_slices in zip(slice_prefixes, slices)
for the_slice in inner_slices]

# Flatten the array list
arrays = functools.reduce(operator.add, arrays)

return shape, slices, arrays
else:
# We've 'bottomed out' - arrays is either a scalar or an array
# type(arrays) is not list
# Return the slice and the array inside a list to be consistent with
# the recursive case.
arr = _atleast_nd(arrays, result_ndim)
return arr.shape, [()], [arr]


def _block(arrays, max_depth, result_ndim, depth=0):
"""
Internal implementation of block based on repeated concatenation.
`arrays` is the argument passed to
block. `max_depth` is the depth of nested lists within `arrays` and
`result_ndim` is the greatest of the dimensions of the arrays in
`arrays` and the depth of the lists in `arrays` (see block docstring
for details).
"""
if depth < max_depth:
arrs = [_block(arr, max_depth, result_ndim, depth+1)
for arr in arrays]
return _nx.concatenate(arrs, axis=-(max_depth-depth))
else:
# We've 'bottomed out' - arrays is either a scalar or an array
# type(arrays) is not list
return _atleast_nd(arrays, result_ndim)


def _block_dispatcher(arrays):
def _block_dispatcher(arrays, out=None):
# Use type(...) is list to match the behavior of np.block(), which special
# cases list specifically rather than allowing for generic iterables or
# tuple. Also, we know that list.__array_function__ will never exist.
Expand All @@ -658,9 +428,12 @@ def _block_dispatcher(arrays):
else:
yield arrays

if out is not None:
yield out


@array_function_dispatch(_block_dispatcher)
def block(arrays):
def block(arrays, out=None):
"""
Assemble an nd-array from nested lists of blocks.

Expand Down Expand Up @@ -688,6 +461,8 @@ def block(arrays):
Elements shapes must match along the appropriate axes (without
broadcasting), but leading 1s will be prepended to the shape as
necessary to make the dimensions match.
out : ndarray
ndarray to which to copy the blocks.

Returns
-------
Expand Down Expand Up @@ -808,74 +583,6 @@ def block(arrays):


"""
arrays, list_ndim, result_ndim, final_size = _block_setup(arrays)

# It was found through benchmarking that making an array of final size
# around 256x256 was faster by straight concatenation on a
# i7-7700HQ processor and dual channel ram 2400MHz.
# It didn't seem to matter heavily on the dtype used.
#
# A 2D array using repeated concatenation requires 2 copies of the array.
#
# The fastest algorithm will depend on the ratio of CPU power to memory
# speed.
# One can monitor the results of the benchmark
# This function is benchmarked at
# https://pv.github.io/numpy-bench/#bench_shape_base.Block2D.time_block2d
# to tune this parameter until a C version of the `_block_info_recursion`
# algorithm is implemented which would likely be faster than the python
# version.
if list_ndim * final_size > (2 * 512 * 512):
return _block_slicing(arrays, list_ndim, result_ndim)
else:
return _block_concatenate(arrays, list_ndim, result_ndim)


# Theses helper functions are mostly used for testing.
# They allow us to write tests that directly call `_block_slicing`
# or `_block_concatenate` wtihout blocking large arrays to forse the wisdom
# to trigger the desired path.
def _block_setup(arrays):
"""
Returns
(`arrays`, list_ndim, result_ndim, final_size)
"""
bottom_index, arr_ndim, final_size = _block_check_depths_match(arrays)
list_ndim = len(bottom_index)
if bottom_index and bottom_index[-1] is None:
raise ValueError(
'List at {} cannot be empty'.format(
_block_format_index(bottom_index)
)
)
result_ndim = max(arr_ndim, list_ndim)
return arrays, list_ndim, result_ndim, final_size


def _block_slicing(arrays, list_ndim, result_ndim):
shape, slices, arrays = _block_info_recursion(
arrays, list_ndim, result_ndim)
dtype = _nx.result_type(*[arr.dtype for arr in arrays])

# Test preferring F only in the case that all input arrays are F
F_order = all(arr.flags['F_CONTIGUOUS'] for arr in arrays)
C_order = all(arr.flags['C_CONTIGUOUS'] for arr in arrays)
order = 'F' if F_order and not C_order else 'C'
result = _nx.empty(shape=shape, dtype=dtype, order=order)
# Note: In a c implementation, the function
# PyArray_CreateMultiSortedStridePerm could be used for more advanced
# guessing of the desired order.

for the_slice, arr in zip(slices, arrays):
result[(Ellipsis,) + the_slice] = arr
return result


def _block_concatenate(arrays, list_ndim, result_ndim):
result = _block(arrays, list_ndim, result_ndim)
if list_ndim == 0:
# Catch an edge case where _block returns a view because
# `arrays` is a single numpy array and not a list of numpy arrays.
# This might copy scalars or lists twice, but this isn't a likely
# usecase for those interested in performance
result = result.copy()
return result
return _nx.block(arrays, out=out)