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'stack', 'vstack']
overrides.array_function_dispatch, module='numpy')
return arys
def atleast_1d(*arys): """ Convert inputs to arrays with at least one dimension.
Scalar inputs are converted to 1-dimensional arrays, whilst higher-dimensional inputs are preserved.
Parameters ---------- arys1, arys2, ... : array_like One or more input arrays.
Returns ------- ret : ndarray An array, or list of arrays, each with ``a.ndim >= 1``. Copies are made only if necessary.
See Also -------- atleast_2d, atleast_3d
Examples -------- >>> np.atleast_1d(1.0) array([ 1.])
>>> x = np.arange(9.0).reshape(3,3) >>> np.atleast_1d(x) array([[ 0., 1., 2.], [ 3., 4., 5.], [ 6., 7., 8.]]) >>> np.atleast_1d(x) is x True
>>> np.atleast_1d(1, [3, 4]) [array([1]), array([3, 4])]
""" else: else:
return arys
def atleast_2d(*arys): """ View inputs as arrays with at least two dimensions.
Parameters ---------- arys1, arys2, ... : array_like One or more array-like sequences. Non-array inputs are converted to arrays. Arrays that already have two or more dimensions are preserved.
Returns ------- res, res2, ... : ndarray An array, or list of arrays, each with ``a.ndim >= 2``. Copies are avoided where possible, and views with two or more dimensions are returned.
See Also -------- atleast_1d, atleast_3d
Examples -------- >>> np.atleast_2d(3.0) array([[ 3.]])
>>> x = np.arange(3.0) >>> np.atleast_2d(x) array([[ 0., 1., 2.]]) >>> np.atleast_2d(x).base is x True
>>> np.atleast_2d(1, [1, 2], [[1, 2]]) [array([[1]]), array([[1, 2]]), array([[1, 2]])]
""" else: else: return res
return arys
def atleast_3d(*arys): """ View inputs as arrays with at least three dimensions.
Parameters ---------- arys1, arys2, ... : array_like One or more array-like sequences. Non-array inputs are converted to arrays. Arrays that already have three or more dimensions are preserved.
Returns ------- res1, res2, ... : ndarray An array, or list of arrays, each with ``a.ndim >= 3``. Copies are avoided where possible, and views with three or more dimensions are returned. For example, a 1-D array of shape ``(N,)`` becomes a view of shape ``(1, N, 1)``, and a 2-D array of shape ``(M, N)`` becomes a view of shape ``(M, N, 1)``.
See Also -------- atleast_1d, atleast_2d
Examples -------- >>> np.atleast_3d(3.0) array([[[ 3.]]])
>>> x = np.arange(3.0) >>> np.atleast_3d(x).shape (1, 3, 1)
>>> x = np.arange(12.0).reshape(4,3) >>> np.atleast_3d(x).shape (4, 3, 1) >>> np.atleast_3d(x).base is x.base # x is a reshape, so not base itself True
>>> for arr in np.atleast_3d([1, 2], [[1, 2]], [[[1, 2]]]): ... print(arr, arr.shape) ... [[[1] [2]]] (1, 2, 1) [[[1] [2]]] (1, 2, 1) [[[1 2]]] (1, 1, 2)
""" result = ary.reshape(1, 1, 1) result = ary[newaxis,:, newaxis] result = ary[:,:, newaxis] else: else: return res
warnings.warn('arrays to stack must be passed as a "sequence" type ' 'such as list or tuple. Support for non-sequence ' 'iterables such as generators is deprecated as of ' 'NumPy 1.16 and will raise an error in the future.', FutureWarning, stacklevel=stacklevel) return ()
return _arrays_for_stack_dispatcher(tup)
def vstack(tup): """ Stack arrays in sequence vertically (row wise).
This is equivalent to concatenation along the first axis after 1-D arrays of shape `(N,)` have been reshaped to `(1,N)`. Rebuilds arrays divided by `vsplit`.
This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions `concatenate`, `stack` and `block` provide more general stacking and concatenation operations.
Parameters ---------- tup : sequence of ndarrays The arrays must have the same shape along all but the first axis. 1-D arrays must have the same length.
Returns ------- stacked : ndarray The array formed by stacking the given arrays, will be at least 2-D.
See Also -------- stack : Join a sequence of arrays along a new axis. hstack : Stack arrays in sequence horizontally (column wise). dstack : Stack arrays in sequence depth wise (along third dimension). concatenate : Join a sequence of arrays along an existing axis. vsplit : Split array into a list of multiple sub-arrays vertically. block : Assemble arrays from blocks.
Examples -------- >>> a = np.array([1, 2, 3]) >>> b = np.array([2, 3, 4]) >>> np.vstack((a,b)) array([[1, 2, 3], [2, 3, 4]])
>>> a = np.array([[1], [2], [3]]) >>> b = np.array([[2], [3], [4]]) >>> np.vstack((a,b)) array([[1], [2], [3], [2], [3], [4]])
"""
def hstack(tup): """ Stack arrays in sequence horizontally (column wise).
This is equivalent to concatenation along the second axis, except for 1-D arrays where it concatenates along the first axis. Rebuilds arrays divided by `hsplit`.
This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions `concatenate`, `stack` and `block` provide more general stacking and concatenation operations.
Parameters ---------- tup : sequence of ndarrays The arrays must have the same shape along all but the second axis, except 1-D arrays which can be any length.
Returns ------- stacked : ndarray The array formed by stacking the given arrays.
See Also -------- stack : Join a sequence of arrays along a new axis. vstack : Stack arrays in sequence vertically (row wise). dstack : Stack arrays in sequence depth wise (along third axis). concatenate : Join a sequence of arrays along an existing axis. hsplit : Split array along second axis. block : Assemble arrays from blocks.
Examples -------- >>> a = np.array((1,2,3)) >>> b = np.array((2,3,4)) >>> np.hstack((a,b)) array([1, 2, 3, 2, 3, 4]) >>> a = np.array([[1],[2],[3]]) >>> b = np.array([[2],[3],[4]]) >>> np.hstack((a,b)) array([[1, 2], [2, 3], [3, 4]])
""" # As a special case, dimension 0 of 1-dimensional arrays is "horizontal" else:
arrays = _arrays_for_stack_dispatcher(arrays, stacklevel=6) if out is not None: # optimize for the typical case where only arrays is provided arrays = list(arrays) arrays.append(out) return arrays
""" Join a sequence of arrays along a new axis.
The `axis` parameter specifies the index of the new axis in the dimensions of the result. For example, if ``axis=0`` it will be the first dimension and if ``axis=-1`` it will be the last dimension.
.. versionadded:: 1.10.0
Parameters ---------- arrays : sequence of array_like Each array must have the same shape. axis : int, optional The axis in the result array along which the input arrays are stacked. out : ndarray, optional If provided, the destination to place the result. The shape must be correct, matching that of what stack would have returned if no out argument were specified.
Returns ------- stacked : ndarray The stacked array has one more dimension than the input arrays.
See Also -------- concatenate : Join a sequence of arrays along an existing axis. split : Split array into a list of multiple sub-arrays of equal size. block : Assemble arrays from blocks.
Examples -------- >>> arrays = [np.random.randn(3, 4) for _ in range(10)] >>> np.stack(arrays, axis=0).shape (10, 3, 4)
>>> np.stack(arrays, axis=1).shape (3, 10, 4)
>>> np.stack(arrays, axis=2).shape (3, 4, 10)
>>> a = np.array([1, 2, 3]) >>> b = np.array([2, 3, 4]) >>> np.stack((a, b)) array([[1, 2, 3], [2, 3, 4]])
>>> np.stack((a, b), axis=-1) array([[1, 2], [2, 3], [3, 4]])
""" _warn_for_nonsequence(arrays) arrays = [asanyarray(arr) for arr in arrays] if not arrays: raise ValueError('need at least one array to stack')
shapes = {arr.shape for arr in arrays} if len(shapes) != 1: raise ValueError('all input arrays must have the same shape')
result_ndim = arrays[0].ndim + 1 axis = normalize_axis_index(axis, result_ndim)
sl = (slice(None),) * axis + (_nx.newaxis,) expanded_arrays = [arr[sl] for arr in arrays] return _nx.concatenate(expanded_arrays, axis=axis, out=out)
""" 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
""" 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
# Ensures `a` has at least `ndim` dimensions by prepending # ones to `a.shape` as necessary return array(a, ndmin=ndim, copy=False, subok=True)
# 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
"""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
""" 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]
""" 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)
# 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. if type(arrays) is list: for subarrays in arrays: for subarray in _block_dispatcher(subarrays): yield subarray else: yield arrays
def block(arrays): """ Assemble an nd-array from nested lists of blocks.
Blocks in the innermost lists are concatenated (see `concatenate`) along the last dimension (-1), then these are concatenated along the second-last dimension (-2), and so on until the outermost list is reached.
Blocks can be of any dimension, but will not be broadcasted using the normal rules. Instead, leading axes of size 1 are inserted, to make ``block.ndim`` the same for all blocks. This is primarily useful for working with scalars, and means that code like ``np.block([v, 1])`` is valid, where ``v.ndim == 1``.
When the nested list is two levels deep, this allows block matrices to be constructed from their components.
.. versionadded:: 1.13.0
Parameters ---------- arrays : nested list of array_like or scalars (but not tuples) If passed a single ndarray or scalar (a nested list of depth 0), this is returned unmodified (and not copied).
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.
Returns ------- block_array : ndarray The array assembled from the given blocks.
The dimensionality of the output is equal to the greatest of: * the dimensionality of all the inputs * the depth to which the input list is nested
Raises ------ ValueError * If list depths are mismatched - for instance, ``[[a, b], c]`` is illegal, and should be spelt ``[[a, b], [c]]`` * If lists are empty - for instance, ``[[a, b], []]``
See Also -------- concatenate : Join a sequence of arrays together. stack : Stack arrays in sequence along a new dimension. hstack : Stack arrays in sequence horizontally (column wise). vstack : Stack arrays in sequence vertically (row wise). dstack : Stack arrays in sequence depth wise (along third dimension). vsplit : Split array into a list of multiple sub-arrays vertically.
Notes -----
When called with only scalars, ``np.block`` is equivalent to an ndarray call. So ``np.block([[1, 2], [3, 4]])`` is equivalent to ``np.array([[1, 2], [3, 4]])``.
This function does not enforce that the blocks lie on a fixed grid. ``np.block([[a, b], [c, d]])`` is not restricted to arrays of the form::
AAAbb AAAbb cccDD
But is also allowed to produce, for some ``a, b, c, d``::
AAAbb AAAbb cDDDD
Since concatenation happens along the last axis first, `block` is _not_ capable of producing the following directly::
AAAbb cccbb cccDD
Matlab's "square bracket stacking", ``[A, B, ...; p, q, ...]``, is equivalent to ``np.block([[A, B, ...], [p, q, ...]])``.
Examples -------- The most common use of this function is to build a block matrix
>>> A = np.eye(2) * 2 >>> B = np.eye(3) * 3 >>> np.block([ ... [A, np.zeros((2, 3))], ... [np.ones((3, 2)), B ] ... ]) array([[ 2., 0., 0., 0., 0.], [ 0., 2., 0., 0., 0.], [ 1., 1., 3., 0., 0.], [ 1., 1., 0., 3., 0.], [ 1., 1., 0., 0., 3.]])
With a list of depth 1, `block` can be used as `hstack`
>>> np.block([1, 2, 3]) # hstack([1, 2, 3]) array([1, 2, 3])
>>> a = np.array([1, 2, 3]) >>> b = np.array([2, 3, 4]) >>> np.block([a, b, 10]) # hstack([a, b, 10]) array([1, 2, 3, 2, 3, 4, 10])
>>> A = np.ones((2, 2), int) >>> B = 2 * A >>> np.block([A, B]) # hstack([A, B]) array([[1, 1, 2, 2], [1, 1, 2, 2]])
With a list of depth 2, `block` can be used in place of `vstack`:
>>> a = np.array([1, 2, 3]) >>> b = np.array([2, 3, 4]) >>> np.block([[a], [b]]) # vstack([a, b]) array([[1, 2, 3], [2, 3, 4]])
>>> A = np.ones((2, 2), int) >>> B = 2 * A >>> np.block([[A], [B]]) # vstack([A, B]) array([[1, 1], [1, 1], [2, 2], [2, 2]])
It can also be used in places of `atleast_1d` and `atleast_2d`
>>> a = np.array(0) >>> b = np.array([1]) >>> np.block([a]) # atleast_1d(a) array([0]) >>> np.block([b]) # atleast_1d(b) array([1])
>>> np.block([[a]]) # atleast_2d(a) array([[0]]) >>> np.block([[b]]) # atleast_2d(b) array([[1]])
""" 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 # 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. """ 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
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
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 |