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"""Module containing non-deprecated functions borrowed from Numeric.
"""
import functools
import math
import types
import numpy as np
from . import _methods, multiarray as mu, numerictypes as nt, overrides, umath as um
from ._multiarray_umath import _wrapfunc, _wrapit
from .multiarray import asanyarray, asarray, concatenate, normalize_axis_index
_dt_ = nt.sctype2char
# functions that are methods
__all__ = [
'all', 'amax', 'amin', 'any', 'argmax',
'argmin', 'argpartition', 'argsort', 'around', 'choose', 'clip',
'compress', 'cumprod', 'cumsum', 'cumulative_prod', 'cumulative_sum',
'diagonal', 'mean', 'max', 'min', 'minmax', 'matrix_transpose',
'ndim', 'nonzero', 'partition', 'prod', 'ptp', 'put',
'ravel', 'repeat', 'reshape', 'resize', 'round',
'searchsorted', 'shape', 'size', 'sort', 'squeeze',
'std', 'sum', 'swapaxes', 'take', 'top_k', 'trace',
'transpose', 'var',
]
_gentype = types.GeneratorType
# save away Python sum
_sum_ = sum
_NoValue = np._NoValue
array_function_dispatch = functools.partial(
overrides.array_function_dispatch, module='numpy')
# The positional-only signature and unrolled _NoValue checks (rather than
# **kwargs with a dict comprehension) are deliberate: these helpers are on
# the hot path of every reduction (sum, prod, min, max, any, all), and
# avoiding the creation and iteration of a temporary kwargs dict measurably
# reduces call overhead for small arrays. See gh-31845.
def _wrapreduction(obj, ufunc, method, axis, dtype, out,
keepdims=_NoValue, initial=_NoValue, where=_NoValue, /):
passkwargs = {}
if keepdims is not _NoValue:
passkwargs["keepdims"] = keepdims
if initial is not _NoValue:
passkwargs["initial"] = initial
if where is not _NoValue:
passkwargs["where"] = where
if type(obj) is not mu.ndarray:
try:
reduction = getattr(obj, method)
except AttributeError:
pass
else:
# This branch is needed for reductions like any which don't
# support a dtype.
if dtype is not None:
return reduction(axis=axis, dtype=dtype, out=out, **passkwargs)
else:
return reduction(axis=axis, out=out, **passkwargs)
return ufunc.reduce(obj, axis, dtype, out, **passkwargs)
def _wrapreduction_any_all(obj, ufunc, method, axis, out,
keepdims=_NoValue, where=_NoValue, /):
# Same as above function, but dtype is always bool (but never passed on)
passkwargs = {}
if keepdims is not _NoValue:
passkwargs["keepdims"] = keepdims
if where is not _NoValue:
passkwargs["where"] = where
if type(obj) is not mu.ndarray:
try:
reduction = getattr(obj, method)
except AttributeError:
pass
else:
return reduction(axis=axis, out=out, **passkwargs)
return ufunc.reduce(obj, axis, bool, out, **passkwargs)
def _take_dispatcher(a, indices, axis=None, out=None, mode=None):
return (a, out)
@array_function_dispatch(_take_dispatcher)
def take(a, indices, axis=None, out=None, mode='raise'):
"""
Take elements from an array along an axis.
When axis is not None, this function does the same thing as "fancy"
indexing (indexing arrays using arrays); however, it can be easier to use
if you need elements along a given axis. A call such as
``np.take(arr, indices, axis=3)`` is equivalent to
``arr[:,:,:,indices,...]``.
Explained without fancy indexing, this is equivalent to the following use
of `ndindex`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of
indices::
Ni, Nk = a.shape[:axis], a.shape[axis+1:]
Nj = indices.shape
for ii in ndindex(Ni):
for jj in ndindex(Nj):
for kk in ndindex(Nk):
out[ii + jj + kk] = a[ii + (indices[jj],) + kk]
Parameters
----------
a : array_like (Ni..., M, Nk...)
The source array.
indices : array_like (Nj...)
The indices of the values to extract.
Also allow scalars for indices.
axis : int, optional
The axis over which to select values. By default, the flattened
input array is used.
out : ndarray, optional (Ni..., Nj..., Nk...)
If provided, the result will be placed in this array. It should
be of the appropriate shape and dtype. Note that `out` is always
buffered if `mode='raise'`; use other modes for better performance.
mode : {'raise', 'wrap', 'clip'}, optional
Specifies how out-of-bounds indices will behave.
* 'raise' -- raise an error (default)
* 'wrap' -- wrap around
* 'clip' -- clip to the range
'clip' mode means that all indices that are too large are replaced
by the index that addresses the last element along that axis. Note
that this disables indexing with negative numbers.
Returns
-------
out : ndarray (Ni..., Nj..., Nk...)
The returned array has the same type as `a`.
See Also
--------
compress : Take elements using a boolean mask
ndarray.take : equivalent method
take_along_axis : Take elements by matching the array and the index arrays
Notes
-----
By eliminating the inner loop in the description above, and using `s_` to
build simple slice objects, `take` can be expressed in terms of applying
fancy indexing to each 1-d slice::
Ni, Nk = a.shape[:axis], a.shape[axis+1:]
for ii in ndindex(Ni):
for kk in ndindex(Nk):
out[ii + s_[...,] + kk] = a[ii + s_[:,] + kk][indices]
For this reason, it is equivalent to (but faster than) the following use
of `apply_along_axis`::
out = np.apply_along_axis(lambda a_1d: a_1d[indices], axis, a)
Examples
--------
>>> import numpy as np
>>> a = [4, 3, 5, 7, 6, 8]
>>> indices = [0, 1, 4]
>>> np.take(a, indices)
array([4, 3, 6])
In this example if `a` is an ndarray, "fancy" indexing can be used.
>>> a = np.array(a)
>>> a[indices]
array([4, 3, 6])
If `indices` is not one dimensional, the output also has these dimensions.
>>> np.take(a, [[0, 1], [2, 3]])
array([[4, 3],
[5, 7]])
"""
return _wrapfunc(a, 'take', indices, axis=axis, out=out, mode=mode)
def _top_k_dispatcher(a, k, /, *, axis=-1, mode="largest", sorted=True):
return (a,)
@array_function_dispatch(_top_k_dispatcher)
def top_k(a, k, /, *, axis=-1, mode="largest", sorted=True):
"""
Returns the ``k`` largest or smallest elements and their
indices along an axis.
A tuple of ``(values, indices)`` is returned, where ``values`` and
``indices`` are the values and indices, respectively, of the largest/smallest
elements of each row of the input array in the given ``axis``.
Parameters
----------
a: array_like
The source array
k: int
The number of largest/smallest elements to return. ``k`` must
be a non-negative integer and within indexable range specified by
``axis``.
axis: int, optional
Axis along which to find the largest/smallest elements.
The default is -1 (the last axis).
mode: {"largest", "smallest"}, optional
If "largest", the largest elements are returned. If "smallest",
the smallest elements are returned. The default is "largest".
Similarly to sorts, NaN values are pushed to the end and
therefore only present in the output if they are among the
top ``k`` values, regardless of the value of ``mode``.
sorted: bool, optional
If True, the top ``k`` elements are returned in sorted order.
If False, sorted order is not guaranteed. The default is True.
Returns
-------
tuple_of_array: tuple
The output tuple of ``(topk_values, topk_indices)``, where
``topk_values`` are the top ``k`` values and ``topk_indices``
are the corresponding indices. Both arrays are of the shape
of the input array with the dimension along ``axis`` replaced
by ``k``.
Notes
-----
The returned indices are not guaranteed to be stable, i.e., the order
of the returned indices for any duplicate values is not guaranteed to
be the same as their order in the input array. This is the case
regardless of the value of the ``sorted`` parameter.
See Also
--------
argpartition : Indirect partition.
sort : Full sorting.
Examples
--------
>>> a = np.array([[1,2,3,4], [4,3,2,1]])
>>> np.top_k(a, 2)
(array([[4, 3],
[4, 3]]),
array([[3, 2],
[0, 1]]))
>>> np.top_k(a, 2, axis=0)
(array([[4, 3, 3, 4],
[1, 2, 2, 1]]),
array([[1, 1, 0, 0],
[0, 0, 1, 1]]))
>>> np.top_k(a, 2, axis=1, mode="smallest")
(array([[1, 2],
[1, 2]]),
array([[0, 1],
[3, 2]]))
>>> np.top_k(np.array([1., 2., 3., np.nan]), 2)
(array([3., 2.]), array([2, 1]))
"""
if k < 0:
raise ValueError(f'k(={k}) provided must be a non-negative integer.')
if axis is None:
raise ValueError('axis=None is not supported. Please provide a valid axis.')
if mode not in ["largest", "smallest"]:
raise ValueError(f'mode(="{mode}") must be either "largest" or "smallest".')
largest = mode == "largest"
arr = np.asanyarray(a)
axis = normalize_axis_index(axis, arr.ndim)
kth = k - 1 if k > 0 else np.array([], dtype=np.intp)
indices = np.argpartition(arr, kth, axis=axis, descending=largest)
slice_ = (np.s_[:],) * axis + (np.s_[:k],)
indices = indices[slice_]
values = np.take_along_axis(arr, indices, axis=axis)
if sorted:
sort_indices = np.argsort(values, axis=axis, descending=largest, stable=False)
values = np.take_along_axis(values, sort_indices, axis=axis)
indices = np.take_along_axis(indices, sort_indices, axis=axis)
return (values, indices)
def _reshape_dispatcher(a, /, shape, order=None, *, copy=None):
return (a,)
@array_function_dispatch(_reshape_dispatcher)
def reshape(a, /, shape, order='C', *, copy=None):
"""
Returns a reshaped ndarray without changing data.
Parameters
----------
a : array_like
Array to be reshaped.
shape : int or tuple of ints
The new shape should be compatible with the original shape. If
an integer, then the result will be a 1-D array of that length.
One shape dimension can be -1. In this case, the value is
inferred from the length of the array and remaining dimensions.
order : {'C', 'F', 'A'}, optional
Read the elements of ``a`` using this index order, and place the
elements into the reshaped array using this index order. 'C'
means to read / write the elements using C-like index order,
with the last axis index changing fastest, back to the first
axis index changing slowest. 'F' means to read / write the
elements using Fortran-like index order, with the first index
changing fastest, and the last index changing slowest. Note that
the 'C' and 'F' options take no account of the memory layout of
the underlying array, and only refer to the order of indexing.
'A' means to read / write the elements in Fortran-like index
order if ``a`` is Fortran *contiguous* in memory, C-like order
otherwise.
copy : bool, optional
If ``True``, then the array data is copied. If ``None``, a copy will
only be made if it's required by ``order``. For ``False`` it raises
a ``ValueError`` if a copy cannot be avoided. Default: ``None``.
Returns
-------
reshaped_array : ndarray
This will be a new view object if possible; otherwise, it will
be a copy. Note there is no guarantee of the *memory layout* (C- or
Fortran- contiguous) of the returned array.
See Also
--------
ndarray.reshape : Equivalent method.
Notes
-----
It is not always possible to change the shape of an array without copying
the data.
The ``order`` keyword gives the index ordering both for *fetching*
the values from ``a``, and then *placing* the values into the output
array. For example, let's say you have an array:
>>> a = np.arange(6).reshape((3, 2))
>>> a
array([[0, 1],
[2, 3],
[4, 5]])
You can think of reshaping as first raveling the array (using the given
index order), then inserting the elements from the raveled array into the
new array using the same kind of index ordering as was used for the
raveling.
>>> np.reshape(a, (2, 3)) # C-like index ordering
array([[0, 1, 2],
[3, 4, 5]])
>>> np.reshape(np.ravel(a), (2, 3)) # equivalent to C ravel then C reshape
array([[0, 1, 2],
[3, 4, 5]])
>>> np.reshape(a, (2, 3), order='F') # Fortran-like index ordering
array([[0, 4, 3],
[2, 1, 5]])
>>> np.reshape(np.ravel(a, order='F'), (2, 3), order='F')
array([[0, 4, 3],
[2, 1, 5]])
Examples
--------
>>> import numpy as np
>>> a = np.array([[1,2,3], [4,5,6]])
>>> np.reshape(a, 6)
array([1, 2, 3, 4, 5, 6])
>>> np.reshape(a, 6, order='F')
array([1, 4, 2, 5, 3, 6])
>>> np.reshape(a, (3,-1)) # the unspecified value is inferred to be 2
array([[1, 2],
[3, 4],
[5, 6]])
"""
if copy is not None:
return _wrapfunc(a, 'reshape', shape, order=order, copy=copy)
return _wrapfunc(a, 'reshape', shape, order=order)
def _choose_dispatcher(a, choices, out=None, mode=None):
yield a
yield from choices
yield out
@array_function_dispatch(_choose_dispatcher)
def choose(a, choices, out=None, mode='raise'):
"""
Construct an array from an index array and a list of arrays to choose from.
First of all, if confused or uncertain, definitely look at the Examples -
in its full generality, this function is less simple than it might
seem from the following code description::
np.choose(a,c) == np.array([c[a[I]][I] for I in np.ndindex(a.shape)])
But this omits some subtleties. Here is a fully general summary:
Given an "index" array (`a`) of integers and a sequence of ``n`` arrays
(`choices`), `a` and each choice array are first broadcast, as necessary,
to arrays of a common shape; calling these *Ba* and *Bchoices[i], i =
0,...,n-1* we have that, necessarily, ``Ba.shape == Bchoices[i].shape``
for each ``i``. Then, a new array with shape ``Ba.shape`` is created as
follows:
* if ``mode='raise'`` (the default), then, first of all, each element of
``a`` (and thus ``Ba``) must be in the range ``[0, n-1]``; now, suppose
that ``i`` (in that range) is the value at the ``(j0, j1, ..., jm)``
position in ``Ba`` - then the value at the same position in the new array
is the value in ``Bchoices[i]`` at that same position;
* if ``mode='wrap'``, values in `a` (and thus `Ba`) may be any (signed)
integer; modular arithmetic is used to map integers outside the range
`[0, n-1]` back into that range; and then the new array is constructed
as above;
* if ``mode='clip'``, values in `a` (and thus ``Ba``) may be any (signed)
integer; negative integers are mapped to 0; values greater than ``n-1``
are mapped to ``n-1``; and then the new array is constructed as above.
Parameters
----------
a : int array
This array must contain integers in ``[0, n-1]``, where ``n`` is the
number of choices, unless ``mode=wrap`` or ``mode=clip``, in which
cases any integers are permissible.
choices : sequence of arrays
Choice arrays. `a` and all of the choices must be broadcastable to the
same shape. If `choices` is itself an array (not recommended), then
its outermost dimension (i.e., the one corresponding to
``choices.shape[0]``) is taken as defining the "sequence".
out : array, optional
If provided, the result will be inserted into this array. It should
be of the appropriate shape and dtype. Note that `out` is always
buffered if ``mode='raise'``; use other modes for better performance.
mode : {'raise' (default), 'wrap', 'clip'}, optional
Specifies how indices outside ``[0, n-1]`` will be treated:
* 'raise' : an exception is raised
* 'wrap' : value becomes value mod ``n``
* 'clip' : values < 0 are mapped to 0, values > n-1 are mapped to n-1
Returns
-------
merged_array : array
The merged result.
Raises
------
ValueError: shape mismatch
If `a` and each choice array are not all broadcastable to the same
shape.
See Also
--------
ndarray.choose : equivalent method
numpy.take_along_axis : Preferable if `choices` is an array
Notes
-----
To reduce the chance of misinterpretation, even though the following
"abuse" is nominally supported, `choices` should neither be, nor be
thought of as, a single array, i.e., the outermost sequence-like container
should be either a list or a tuple.
Examples
--------
>>> import numpy as np
>>> choices = [[0, 1, 2, 3], [10, 11, 12, 13],
... [20, 21, 22, 23], [30, 31, 32, 33]]
>>> np.choose([2, 3, 1, 0], choices
... # the first element of the result will be the first element of the
... # third (2+1) "array" in choices, namely, 20; the second element
... # will be the second element of the fourth (3+1) choice array, i.e.,
... # 31, etc.
... )
array([20, 31, 12, 3])
>>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (4-1)
array([20, 31, 12, 3])
>>> # because there are 4 choice arrays
>>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4)
array([20, 1, 12, 3])
>>> # i.e., 0
A couple examples illustrating how choose broadcasts:
>>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]]
>>> choices = [-10, 10]
>>> np.choose(a, choices)
array([[ 10, -10, 10],
[-10, 10, -10],
[ 10, -10, 10]])
>>> # With thanks to Anne Archibald
>>> a = np.array([0, 1]).reshape((2,1,1))
>>> c1 = np.array([1, 2, 3]).reshape((1,3,1))
>>> c2 = np.array([-1, -2, -3, -4, -5]).reshape((1,1,5))
>>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2
array([[[ 1, 1, 1, 1, 1],
[ 2, 2, 2, 2, 2],
[ 3, 3, 3, 3, 3]],
[[-1, -2, -3, -4, -5],
[-1, -2, -3, -4, -5],
[-1, -2, -3, -4, -5]]])
"""
return _wrapfunc(a, 'choose', choices, out=out, mode=mode)
def _repeat_dispatcher(a, repeats, axis=None):
return (a,)
@array_function_dispatch(_repeat_dispatcher)
def repeat(a, repeats, axis=None):
"""
Repeat each element of an array after themselves
Parameters
----------
a : array_like
Input array.
repeats : int or array of ints
The number of repetitions for each element. `repeats` is broadcasted
to fit the shape of the given axis.
axis : int, optional
The axis along which to repeat values. By default, use the
flattened input array, and return a flat output array.
Returns
-------
repeated_array : ndarray
Output array which has the same shape as `a`, except along
the given axis.
See Also
--------
tile : Tile an array.
unique : Find the unique elements of an array.
Examples
--------
>>> import numpy as np
>>> np.repeat(3, 4)
array([3, 3, 3, 3])
>>> np.repeat([4, 5, 6], [1, 2, 3])
array([4, 5, 5, 6, 6, 6])
>>> x = np.array([[1,2],[3,4]])
>>> np.repeat(x, 2)
array([1, 1, 2, 2, 3, 3, 4, 4])
>>> np.repeat(x, 3, axis=1)
array([[1, 1, 1, 2, 2, 2],
[3, 3, 3, 4, 4, 4]])
>>> np.repeat(x, [1, 2], axis=0)
array([[1, 2],
[3, 4],
[3, 4]])
"""
return _wrapfunc(a, 'repeat', repeats, axis=axis)
def _put_dispatcher(a, ind, v, mode=None):
return (a, ind, v)
@array_function_dispatch(_put_dispatcher)
def put(a, ind, v, mode='raise'):
"""
Replaces specified elements of an array with given values.
The indexing works on the flattened target array. `put` is roughly
equivalent to:
::
a.flat[ind] = v
Parameters
----------
a : ndarray
Target array.
ind : array_like
Target indices, interpreted as integers.
v : array_like
Values to place in `a` at target indices. If `v` is shorter than
`ind` it will be repeated as necessary.
mode : {'raise', 'wrap', 'clip'}, optional
Specifies how out-of-bounds indices will behave.
* 'raise' -- raise an error (default)
* 'wrap' -- wrap around
* 'clip' -- clip to the range
'clip' mode means that all indices that are too large are replaced
by the index that addresses the last element along that axis. Note
that this disables indexing with negative numbers. In 'raise' mode,
if an exception occurs the target array may still be modified.
See Also
--------
putmask, place
put_along_axis : Put elements by matching the array and the index arrays
Examples
--------
>>> import numpy as np
>>> a = np.arange(5)
>>> np.put(a, [0, 2], [-44, -55])
>>> a
array([-44, 1, -55, 3, 4])
>>> a = np.arange(5)
>>> np.put(a, 22, -5, mode='clip')
>>> a
array([ 0, 1, 2, 3, -5])
"""
try:
put = a.put
except AttributeError as e:
raise TypeError(f"argument 1 must be numpy.ndarray, not {type(a)}") from e
return put(ind, v, mode=mode)
def _swapaxes_dispatcher(a, axis1, axis2):
return (a,)
@array_function_dispatch(_swapaxes_dispatcher)
def swapaxes(a, axis1, axis2):
"""
Interchange two axes of an array.
Parameters
----------
a : array_like
Input array.
axis1 : int
First axis.
axis2 : int
Second axis.
Returns
-------
a_swapped : ndarray
For NumPy >= 1.10.0, if `a` is an ndarray, then a view of `a` is
returned; otherwise a new array is created. For earlier NumPy
versions a view of `a` is returned only if the order of the
axes is changed, otherwise the input array is returned.
Examples
--------
>>> import numpy as np
>>> x = np.array([[1,2,3]])
>>> np.swapaxes(x,0,1)
array([[1],
[2],
[3]])
>>> x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]])
>>> x
array([[[0, 1],
[2, 3]],
[[4, 5],
[6, 7]]])
>>> np.swapaxes(x,0,2)
array([[[0, 4],
[2, 6]],
[[1, 5],
[3, 7]]])
"""
return _wrapfunc(a, 'swapaxes', axis1, axis2)
def _transpose_dispatcher(a, axes=None):
return (a,)
@array_function_dispatch(_transpose_dispatcher)
def transpose(a, axes=None):
"""
Returns an array with axes transposed.
For a 1-D array, this returns an unchanged view of the original array, as a
transposed vector is simply the same vector.
To convert a 1-D array into a 2-D column vector, an additional dimension
must be added, e.g., ``np.atleast_2d(a).T`` achieves this, as does
``a[:, np.newaxis]``.
For a 2-D array, this is the standard matrix transpose.
For an n-D array, if axes are given, their order indicates how the
axes are permuted (see Examples). If axes are not provided, then
``transpose(a).shape == a.shape[::-1]``.
Parameters
----------
a : array_like
Input array.
axes : tuple or list of ints, optional
If specified, it must be a tuple or list which contains a permutation
of [0, 1, ..., N-1] where N is the number of axes of `a`. Negative
indices can also be used to specify axes. The i-th axis of the returned
array will correspond to the axis numbered ``axes[i]`` of the input.
If not specified, defaults to ``range(a.ndim)[::-1]``, which reverses
the order of the axes.
Returns
-------
p : ndarray
`a` with its axes permuted. A view is returned whenever possible.
See Also
--------
ndarray.transpose : Equivalent method.
moveaxis : Move axes of an array to new positions.
argsort : Return the indices that would sort an array.
Notes
-----
Use ``transpose(a, argsort(axes))`` to invert the transposition of tensors
when using the `axes` keyword argument.
Examples
--------
>>> import numpy as np
>>> a = np.array([[1, 2], [3, 4]])
>>> a
array([[1, 2],
[3, 4]])
>>> np.transpose(a)
array([[1, 3],
[2, 4]])
>>> a = np.array([1, 2, 3, 4])
>>> a
array([1, 2, 3, 4])
>>> np.transpose(a)
array([1, 2, 3, 4])
>>> a = np.ones((1, 2, 3))
>>> np.transpose(a, (1, 0, 2)).shape
(2, 1, 3)
>>> a = np.ones((2, 3, 4, 5))
>>> np.transpose(a).shape
(5, 4, 3, 2)
>>> a = np.arange(3*4*5).reshape((3, 4, 5))
>>> np.transpose(a, (-1, 0, -2)).shape
(5, 3, 4)
"""
return _wrapfunc(a, 'transpose', axes)
def _matrix_transpose_dispatcher(x):
return (x,)
@array_function_dispatch(_matrix_transpose_dispatcher)
def matrix_transpose(x, /):
"""
Transposes a matrix (or a stack of matrices) ``x``.
This function is Array API compatible.
Parameters
----------
x : array_like
Input array having shape (..., M, N) and whose two innermost
dimensions form ``MxN`` matrices.
Returns
-------
out : ndarray
An array containing the transpose for each matrix and having shape
(..., N, M).
See Also
--------
transpose : Generic transpose method.
Examples
--------
>>> import numpy as np
>>> np.matrix_transpose([[1, 2], [3, 4]])
array([[1, 3],
[2, 4]])
>>> np.matrix_transpose([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
array([[[1, 3],
[2, 4]],
[[5, 7],
[6, 8]]])
"""
x = asanyarray(x)
if x.ndim < 2:
raise ValueError(
f"Input array must be at least 2-dimensional, but it is {x.ndim}"
)
return swapaxes(x, -1, -2)
def _partition_dispatcher(a, kth, axis=None, kind=None, order=None, descending=None):
return (a,)
@array_function_dispatch(_partition_dispatcher)
def partition(a, kth, axis=-1, kind=np._NoValue, order=None, descending=np._NoValue):
"""
Return a partitioned copy of an array.
Creates a copy of the array and partially sorts it in such a way that
the value of the element in the k-th position is in the position it would be
in a sorted array. In the output array, all elements that would be to the left
of the k-th element in a sorted array are located to the left of this element and
all that would be to the right are located to its right. The ordering of the
elements in the two partitions on the either side of the k-th element in the
output array is undefined.
Parameters
----------
a : array_like
Array to be sorted.
kth : int or sequence of ints
Element index to partition by. In the returned array, the k-th
value of the array will be in the position it would be in a
sorted array, all elements that are less than this element (or
greater if `descending` is True) will be moved before it, and
all elements that are greater than or equal to this element
(or less than or equal if `descending` is True) will be moved after it.
The order of all elements within each partition is undefined. If
provided with a sequence of k-th it will partition all elements
indexed by k-th of them into their sorted position at once.
axis : int or None, optional
Axis along which to sort. If None, the array is flattened before
sorting. The default is -1, which sorts along the last axis.
kind : {'introselect'}, optional
NumPy currently offers only one selection algorithm, 'introselect',
and this parameter provides no additional functionality. Default
is ``None``.
order : str or list of str, optional
When `a` is an array with fields defined, this argument
specifies which fields to compare first, second, etc. A single
field can be specified as a string. Not all fields need be
specified, but unspecified fields will still be used, in the
order in which they come up in the dtype, to break ties.
descending : bool, optional
Sort order. If ``True``, the array will be partitioned in
descending order. If ``False`` or ``None``, the array will be
partitioned in ascending order. Values that are NaN are partitioned
towards the end of the array regardless of order. Default: ``None``.
.. versionadded:: 2.6.0
Returns
-------
partitioned_array : ndarray
Array of the same type and shape as `a`.
See Also
--------
ndarray.partition : Method to sort an array in-place.
argpartition : Indirect partition.
sort : Full sorting
Notes
-----
The various selection algorithms are characterized by their average
speed, worst case performance, work space size, and whether they are
stable. A stable sort keeps items with the same key in the same
relative order. The available algorithms have the following
properties:
================= ======= ============= ============ =======
kind speed worst case work space stable
================= ======= ============= ============ =======
'introselect' 1 O(n) 0 no
================= ======= ============= ============ =======
All the partition algorithms make temporary copies of the data when
partitioning along any but the last axis. Consequently,
partitioning along the last axis is faster and uses less space than
partitioning along any other axis.
The sort order for complex numbers is lexicographic. If both the
real and imaginary parts are non-nan then the order is determined by
the real parts except when they are equal, in which case the order
is determined by the imaginary parts.
Regardless of sort order, `np.nan` is partitioned to the right of
any other value.
Examples
--------
>>> import numpy as np
>>> a = np.array([7, 1, 7, 7, 1, 5, 7, 2, 3, 2, 6, 2, 3, 0])
>>> p = np.partition(a, 4)
>>> p
array([0, 1, 2, 1, 2, 5, 2, 3, 3, 6, 7, 7, 7, 7]) # may vary
``p[4]`` is 2; all elements in ``p[:4]`` are less than or equal
to ``p[4]``, and all elements in ``p[5:]`` are greater than or
equal to ``p[4]``. The partition is::
[0, 1, 2, 1], [2], [5, 2, 3, 3, 6, 7, 7, 7, 7]
The next example shows the use of multiple values passed to `kth`.
>>> p2 = np.partition(a, (4, 8))
>>> p2
array([0, 1, 2, 1, 2, 3, 3, 2, 5, 6, 7, 7, 7, 7])
``p2[4]`` is 2 and ``p2[8]`` is 5. All elements in ``p2[:4]``
are less than or equal to ``p2[4]``, all elements in ``p2[5:8]``
are greater than or equal to ``p2[4]`` and less than or equal to
``p2[8]``, and all elements in ``p2[9:]`` are greater than or
equal to ``p2[8]``. The partition is::
[0, 1, 2, 1], [2], [3, 3, 2], [5], [6, 7, 7, 7, 7]
"""
if axis is None:
# flatten returns (1, N) for np.matrix, so always use the last axis
a = asanyarray(a).flatten()
axis = -1
else:
a = asanyarray(a).copy(order="K")
# Sanitize for backward compatibility
kwargs = {}
if descending is not np._NoValue:
kwargs['descending'] = descending
if kind is not np._NoValue:
kwargs['kind'] = kind
a.partition(kth, axis=axis, order=order, **kwargs)
return a
def _argpartition_dispatcher(a, kth, axis=None, kind=None, order=None, descending=None):
return (a,)
@array_function_dispatch(_argpartition_dispatcher)
def argpartition(a, kth, axis=-1, kind=np._NoValue, order=None, descending=np._NoValue):
"""
Perform an indirect partition along the given axis using the
algorithm specified by the `kind` keyword. It returns an array of
indices of the same shape as `a` that index data along the given
axis in partitioned order.
Parameters
----------
a : array_like
Array to sort.
kth : int or sequence of ints
Element index to partition by. In the returned array, the k-th
value of the array will be in the position it would be in a
sorted array, all elements that are less than this element (or
greater if `descending` is True) will be moved before it, and
all elements that are greater than or equal to this element
(or less than or equal if `descending` is True) will be moved after it.
The order of all elements within each partition is undefined. If
provided with a sequence of k-th it will partition all elements
indexed by k-th of them into their sorted position at once.
axis : int or None, optional
Axis along which to sort. The default is -1 (the last axis). If
None, the flattened array is used.
kind : {'introselect'}, optional
NumPy currently offers only one selection algorithm, 'introselect',
and this parameter provides no additional functionality. Default
is ``None``.
order : str or list of str, optional
When `a` is an array with fields defined, this argument
specifies which fields to compare first, second, etc. A single
field can be specified as a string, and not all fields need be
specified, but unspecified fields will still be used, in the
order in which they come up in the dtype, to break ties.
descending : bool, optional