two version of R2R are here HEAD master

1 files changed, 3920 insertions, 0 deletions

diff --git a/.venv/lib/python3.12/site-packages/numpy/core/fromnumeric.py b/.venv/lib/python3.12/site-packages/numpy/core/fromnumeric.py
new file mode 100644
index 00000000..69cabb33
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/core/fromnumeric.py
@@ -0,0 +1,3920 @@
+"""Module containing non-deprecated functions borrowed from Numeric.
+
+"""
+import functools
+import types
+import warnings
+
+import numpy as np
+from .._utils import set_module
+from . import multiarray as mu
+from . import overrides
+from . import umath as um
+from . import numerictypes as nt
+from .multiarray import asarray, array, asanyarray, concatenate
+from . import _methods
+
+_dt_ = nt.sctype2char
+
+# functions that are methods
+__all__ = [
+    'all', 'alltrue', 'amax', 'amin', 'any', 'argmax',
+    'argmin', 'argpartition', 'argsort', 'around', 'choose', 'clip',
+    'compress', 'cumprod', 'cumproduct', 'cumsum', 'diagonal', 'mean',
+    'max', 'min',
+    'ndim', 'nonzero', 'partition', 'prod', 'product', 'ptp', 'put',
+    'ravel', 'repeat', 'reshape', 'resize', 'round', 'round_',
+    'searchsorted', 'shape', 'size', 'sometrue', 'sort', 'squeeze',
+    'std', 'sum', 'swapaxes', 'take', 'trace', 'transpose', 'var',
+]
+
+_gentype = types.GeneratorType
+# save away Python sum
+_sum_ = sum
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+# functions that are now methods
+def _wrapit(obj, method, *args, **kwds):
+    try:
+        wrap = obj.__array_wrap__
+    except AttributeError:
+        wrap = None
+    result = getattr(asarray(obj), method)(*args, **kwds)
+    if wrap:
+        if not isinstance(result, mu.ndarray):
+            result = asarray(result)
+        result = wrap(result)
+    return result
+
+
+def _wrapfunc(obj, method, *args, **kwds):
+    bound = getattr(obj, method, None)
+    if bound is None:
+        return _wrapit(obj, method, *args, **kwds)
+
+    try:
+        return bound(*args, **kwds)
+    except TypeError:
+        # A TypeError occurs if the object does have such a method in its
+        # class, but its signature is not identical to that of NumPy's. This
+        # situation has occurred in the case of a downstream library like
+        # 'pandas'.
+        #
+        # Call _wrapit from within the except clause to ensure a potential
+        # exception has a traceback chain.
+        return _wrapit(obj, method, *args, **kwds)
+
+
+def _wrapreduction(obj, ufunc, method, axis, dtype, out, **kwargs):
+    passkwargs = {k: v for k, v in kwargs.items()
+                  if v is not np._NoValue}
+
+    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 _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.
+
+        .. versionadded:: 1.8.0
+
+        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(Nj):
+                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
+    --------
+    >>> 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 _reshape_dispatcher(a, newshape, order=None):
+    return (a,)
+
+
+# not deprecated --- copy if necessary, view otherwise
+@array_function_dispatch(_reshape_dispatcher)
+def reshape(a, newshape, order='C'):
+    """
+    Gives a new shape to an array without changing its data.
+
+    Parameters
+    ----------
+    a : array_like
+        Array to be reshaped.
+    newshape : 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.
+
+    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
+    --------
+    >>> 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]])
+    """
+    return _wrapfunc(a, 'reshape', newshape, 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 (below ndi =
+    `numpy.lib.index_tricks`):
+
+    ``np.choose(a,c) == np.array([c[a[I]][I] for I in ndi.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
+    --------
+
+    >>> 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
+    --------
+    >>> np.repeat(3, 4)
+    array([3, 3, 3, 3])
+    >>> 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
+    --------
+    >>> 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("argument 1 must be numpy.ndarray, "
+                        "not {name}".format(name=type(a).__name__)) 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
+    --------
+    >>> 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.atleast2d(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`. 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
+    --------
+    >>> 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)
+
+    """
+    return _wrapfunc(a, 'transpose', axes)
+
+
+def _partition_dispatcher(a, kth, axis=None, kind=None, order=None):
+    return (a,)
+
+
+@array_function_dispatch(_partition_dispatcher)
+def partition(a, kth, axis=-1, kind='introselect', order=None):
+    """
+    Return a partitioned copy of an array.
+
+    Creates a copy of the array with its elements rearranged in such a
+    way that the value of the element in k-th position is in the position
+    the value would be in a sorted array.  In the partitioned array, all
+    elements before the k-th element are less than or equal to that
+    element, and all the elements after the k-th element are greater than
+    or equal to that element.  The ordering of the elements in the two
+    partitions is undefined.
+
+    .. versionadded:: 1.8.0
+
+    Parameters
+    ----------
+    a : array_like
+        Array to be sorted.
+    kth : int or sequence of ints
+        Element index to partition by. The k-th value of the element
+        will be in its final sorted position and all smaller elements
+        will be moved before it and all equal or greater elements behind
+        it. The order of all elements in the partitions 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.
+
+        .. deprecated:: 1.22.0
+            Passing booleans as index is deprecated.
+    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
+        Selection algorithm. Default is 'introselect'.
+    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.
+
+    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.
+
+    Examples
+    --------
+    >>> 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])
+
+    ``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")
+    a.partition(kth, axis=axis, kind=kind, order=order)
+    return a
+
+
+def _argpartition_dispatcher(a, kth, axis=None, kind=None, order=None):
+    return (a,)
+
+
+@array_function_dispatch(_argpartition_dispatcher)
+def argpartition(a, kth, axis=-1, kind='introselect', order=None):
+    """
+    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.
+
+    .. versionadded:: 1.8.0
+
+    Parameters
+    ----------
+    a : array_like
+        Array to sort.
+    kth : int or sequence of ints
+        Element index to partition by. The k-th element will be in its
+        final sorted position and all smaller elements will be moved
+        before it and all larger elements behind it. The order of all
+        elements in the partitions is undefined. If provided with a
+        sequence of k-th it will partition all of them into their sorted
+        position at once.
+
+        .. deprecated:: 1.22.0
+            Passing booleans as index is deprecated.
+    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
+        Selection algorithm. Default is 'introselect'
+    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.
+
+    Returns
+    -------
+    index_array : ndarray, int
+        Array of indices that partition `a` along the specified axis.
+        If `a` is one-dimensional, ``a[index_array]`` yields a partitioned `a`.
+        More generally, ``np.take_along_axis(a, index_array, axis=axis)``
+        always yields the partitioned `a`, irrespective of dimensionality.
+
+    See Also
+    --------
+    partition : Describes partition algorithms used.
+    ndarray.partition : Inplace partition.
+    argsort : Full indirect sort.
+    take_along_axis : Apply ``index_array`` from argpartition
+                      to an array as if by calling partition.
+
+    Notes
+    -----
+    See `partition` for notes on the different selection algorithms.
+
+    Examples
+    --------
+    One dimensional array:
+
+    >>> x = np.array([3, 4, 2, 1])
+    >>> x[np.argpartition(x, 3)]
+    array([2, 1, 3, 4])
+    >>> x[np.argpartition(x, (1, 3))]
+    array([1, 2, 3, 4])
+
+    >>> x = [3, 4, 2, 1]
+    >>> np.array(x)[np.argpartition(x, 3)]
+    array([2, 1, 3, 4])
+
+    Multi-dimensional array:
+
+    >>> x = np.array([[3, 4, 2], [1, 3, 1]])
+    >>> index_array = np.argpartition(x, kth=1, axis=-1)
+    >>> np.take_along_axis(x, index_array, axis=-1)  # same as np.partition(x, kth=1)
+    array([[2, 3, 4],
+           [1, 1, 3]])
+
+    """
+    return _wrapfunc(a, 'argpartition', kth, axis=axis, kind=kind, order=order)
+
+
+def _sort_dispatcher(a, axis=None, kind=None, order=None):
+    return (a,)
+
+
+@array_function_dispatch(_sort_dispatcher)
+def sort(a, axis=-1, kind=None, order=None):
+    """
+    Return a sorted copy of an array.
+
+    Parameters
+    ----------
+    a : array_like
+        Array to be sorted.
+    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 : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
+        Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
+        and 'mergesort' use timsort or radix sort under the covers and, in general,
+        the actual implementation will vary with data type. The 'mergesort' option
+        is retained for backwards compatibility.
+
+        .. versionchanged:: 1.15.0.
+           The 'stable' option was added.
+
+    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.
+
+    Returns
+    -------
+    sorted_array : ndarray
+        Array of the same type and shape as `a`.
+
+    See Also
+    --------
+    ndarray.sort : Method to sort an array in-place.
+    argsort : Indirect sort.
+    lexsort : Indirect stable sort on multiple keys.
+    searchsorted : Find elements in a sorted array.
+    partition : Partial sort.
+
+    Notes
+    -----
+    The various sorting 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 four algorithms implemented in NumPy have the following
+    properties:
+
+    =========== ======= ============= ============ ========
+       kind      speed   worst case    work space   stable
+    =========== ======= ============= ============ ========
+    'quicksort'    1     O(n^2)            0          no
+    'heapsort'     3     O(n*log(n))       0          no
+    'mergesort'    2     O(n*log(n))      ~n/2        yes
+    'timsort'      2     O(n*log(n))      ~n/2        yes
+    =========== ======= ============= ============ ========
+
+    .. note:: The datatype determines which of 'mergesort' or 'timsort'
+       is actually used, even if 'mergesort' is specified. User selection
+       at a finer scale is not currently available.
+
+    All the sort algorithms make temporary copies of the data when
+    sorting along any but the last axis.  Consequently, sorting along
+    the last axis is faster and uses less space than sorting 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.
+
+    Previous to numpy 1.4.0 sorting real and complex arrays containing nan
+    values led to undefined behaviour. In numpy versions >= 1.4.0 nan
+    values are sorted to the end. The extended sort order is:
+
+      * Real: [R, nan]
+      * Complex: [R + Rj, R + nanj, nan + Rj, nan + nanj]
+
+    where R is a non-nan real value. Complex values with the same nan
+    placements are sorted according to the non-nan part if it exists.
+    Non-nan values are sorted as before.
+
+    .. versionadded:: 1.12.0
+
+    quicksort has been changed to `introsort <https://en.wikipedia.org/wiki/Introsort>`_.
+    When sorting does not make enough progress it switches to
+    `heapsort <https://en.wikipedia.org/wiki/Heapsort>`_.
+    This implementation makes quicksort O(n*log(n)) in the worst case.
+
+    'stable' automatically chooses the best stable sorting algorithm
+    for the data type being sorted.
+    It, along with 'mergesort' is currently mapped to
+    `timsort <https://en.wikipedia.org/wiki/Timsort>`_
+    or `radix sort <https://en.wikipedia.org/wiki/Radix_sort>`_
+    depending on the data type.
+    API forward compatibility currently limits the
+    ability to select the implementation and it is hardwired for the different
+    data types.
+
+    .. versionadded:: 1.17.0
+
+    Timsort is added for better performance on already or nearly
+    sorted data. On random data timsort is almost identical to
+    mergesort. It is now used for stable sort while quicksort is still the
+    default sort if none is chosen. For timsort details, refer to
+    `CPython listsort.txt <https://github.com/python/cpython/blob/3.7/Objects/listsort.txt>`_.
+    'mergesort' and 'stable' are mapped to radix sort for integer data types. Radix sort is an
+    O(n) sort instead of O(n log n).
+
+    .. versionchanged:: 1.18.0
+
+    NaT now sorts to the end of arrays for consistency with NaN.
+
+    Examples
+    --------
+    >>> a = np.array([[1,4],[3,1]])
+    >>> np.sort(a)                # sort along the last axis
+    array([[1, 4],
+           [1, 3]])
+    >>> np.sort(a, axis=None)     # sort the flattened array
+    array([1, 1, 3, 4])
+    >>> np.sort(a, axis=0)        # sort along the first axis
+    array([[1, 1],
+           [3, 4]])
+
+    Use the `order` keyword to specify a field to use when sorting a
+    structured array:
+
+    >>> dtype = [('name', 'S10'), ('height', float), ('age', int)]
+    >>> values = [('Arthur', 1.8, 41), ('Lancelot', 1.9, 38),
+    ...           ('Galahad', 1.7, 38)]
+    >>> a = np.array(values, dtype=dtype)       # create a structured array
+    >>> np.sort(a, order='height')                        # doctest: +SKIP
+    array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41),
+           ('Lancelot', 1.8999999999999999, 38)],
+          dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])
+
+    Sort by age, then height if ages are equal:
+
+    >>> np.sort(a, order=['age', 'height'])               # doctest: +SKIP
+    array([('Galahad', 1.7, 38), ('Lancelot', 1.8999999999999999, 38),
+           ('Arthur', 1.8, 41)],
+          dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])
+
+    """
+    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")
+    a.sort(axis=axis, kind=kind, order=order)
+    return a
+
+
+def _argsort_dispatcher(a, axis=None, kind=None, order=None):
+    return (a,)
+
+
+@array_function_dispatch(_argsort_dispatcher)
+def argsort(a, axis=-1, kind=None, order=None):
+    """
+    Returns the indices that would sort an array.
+
+    Perform an indirect sort 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 sorted order.
+
+    Parameters
+    ----------
+    a : array_like
+        Array to sort.
+    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 : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
+        Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
+        and 'mergesort' use timsort under the covers and, in general, the
+        actual implementation will vary with data type. The 'mergesort' option
+        is retained for backwards compatibility.
+
+        .. versionchanged:: 1.15.0.
+           The 'stable' option was added.
+    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.
+
+    Returns
+    -------
+    index_array : ndarray, int
+        Array of indices that sort `a` along the specified `axis`.
+        If `a` is one-dimensional, ``a[index_array]`` yields a sorted `a`.
+        More generally, ``np.take_along_axis(a, index_array, axis=axis)``
+        always yields the sorted `a`, irrespective of dimensionality.
+
+    See Also
+    --------
+    sort : Describes sorting algorithms used.
+    lexsort : Indirect stable sort with multiple keys.
+    ndarray.sort : Inplace sort.
+    argpartition : Indirect partial sort.
+    take_along_axis : Apply ``index_array`` from argsort
+                      to an array as if by calling sort.
+
+    Notes
+    -----
+    See `sort` for notes on the different sorting algorithms.
+
+    As of NumPy 1.4.0 `argsort` works with real/complex arrays containing
+    nan values. The enhanced sort order is documented in `sort`.
+
+    Examples
+    --------
+    One dimensional array:
+
+    >>> x = np.array([3, 1, 2])
+    >>> np.argsort(x)
+    array([1, 2, 0])
+
+    Two-dimensional array:
+
+    >>> x = np.array([[0, 3], [2, 2]])
+    >>> x
+    array([[0, 3],
+           [2, 2]])
+
+    >>> ind = np.argsort(x, axis=0)  # sorts along first axis (down)
+    >>> ind
+    array([[0, 1],
+           [1, 0]])
+    >>> np.take_along_axis(x, ind, axis=0)  # same as np.sort(x, axis=0)
+    array([[0, 2],
+           [2, 3]])
+
+    >>> ind = np.argsort(x, axis=1)  # sorts along last axis (across)
+    >>> ind
+    array([[0, 1],
+           [0, 1]])
+    >>> np.take_along_axis(x, ind, axis=1)  # same as np.sort(x, axis=1)
+    array([[0, 3],
+           [2, 2]])
+
+    Indices of the sorted elements of a N-dimensional array:
+
+    >>> ind = np.unravel_index(np.argsort(x, axis=None), x.shape)
+    >>> ind
+    (array([0, 1, 1, 0]), array([0, 0, 1, 1]))
+    >>> x[ind]  # same as np.sort(x, axis=None)
+    array([0, 2, 2, 3])
+
+    Sorting with keys:
+
+    >>> x = np.array([(1, 0), (0, 1)], dtype=[('x', '<i4'), ('y', '<i4')])
+    >>> x
+    array([(1, 0), (0, 1)],
+          dtype=[('x', '<i4'), ('y', '<i4')])
+
+    >>> np.argsort(x, order=('x','y'))
+    array([1, 0])
+
+    >>> np.argsort(x, order=('y','x'))
+    array([0, 1])
+
+    """
+    return _wrapfunc(a, 'argsort', axis=axis, kind=kind, order=order)
+
+
+def _argmax_dispatcher(a, axis=None, out=None, *, keepdims=np._NoValue):
+    return (a, out)
+
+
+@array_function_dispatch(_argmax_dispatcher)
+def argmax(a, axis=None, out=None, *, keepdims=np._NoValue):
+    """
+    Returns the indices of the maximum values along an axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int, optional
+        By default, the index is into the flattened array, otherwise
+        along the specified axis.
+    out : array, optional
+        If provided, the result will be inserted into this array. It should
+        be of the appropriate shape and dtype.
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the array.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    index_array : ndarray of ints
+        Array of indices into the array. It has the same shape as `a.shape`
+        with the dimension along `axis` removed. If `keepdims` is set to True,
+        then the size of `axis` will be 1 with the resulting array having same
+        shape as `a.shape`.
+
+    See Also
+    --------
+    ndarray.argmax, argmin
+    amax : The maximum value along a given axis.
+    unravel_index : Convert a flat index into an index tuple.
+    take_along_axis : Apply ``np.expand_dims(index_array, axis)``
+                      from argmax to an array as if by calling max.
+
+    Notes
+    -----
+    In case of multiple occurrences of the maximum values, the indices
+    corresponding to the first occurrence are returned.
+
+    Examples
+    --------
+    >>> a = np.arange(6).reshape(2,3) + 10
+    >>> a
+    array([[10, 11, 12],
+           [13, 14, 15]])
+    >>> np.argmax(a)
+    5
+    >>> np.argmax(a, axis=0)
+    array([1, 1, 1])
+    >>> np.argmax(a, axis=1)
+    array([2, 2])
+
+    Indexes of the maximal elements of a N-dimensional array:
+
+    >>> ind = np.unravel_index(np.argmax(a, axis=None), a.shape)
+    >>> ind
+    (1, 2)
+    >>> a[ind]
+    15
+
+    >>> b = np.arange(6)
+    >>> b[1] = 5
+    >>> b
+    array([0, 5, 2, 3, 4, 5])
+    >>> np.argmax(b)  # Only the first occurrence is returned.
+    1
+
+    >>> x = np.array([[4,2,3], [1,0,3]])
+    >>> index_array = np.argmax(x, axis=-1)
+    >>> # Same as np.amax(x, axis=-1, keepdims=True)
+    >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1)
+    array([[4],
+           [3]])
+    >>> # Same as np.amax(x, axis=-1)
+    >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1).squeeze(axis=-1)
+    array([4, 3])
+
+    Setting `keepdims` to `True`,
+
+    >>> x = np.arange(24).reshape((2, 3, 4))
+    >>> res = np.argmax(x, axis=1, keepdims=True)
+    >>> res.shape
+    (2, 1, 4)
+    """
+    kwds = {'keepdims': keepdims} if keepdims is not np._NoValue else {}
+    return _wrapfunc(a, 'argmax', axis=axis, out=out, **kwds)
+
+
+def _argmin_dispatcher(a, axis=None, out=None, *, keepdims=np._NoValue):
+    return (a, out)
+
+
+@array_function_dispatch(_argmin_dispatcher)
+def argmin(a, axis=None, out=None, *, keepdims=np._NoValue):
+    """
+    Returns the indices of the minimum values along an axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int, optional
+        By default, the index is into the flattened array, otherwise
+        along the specified axis.
+    out : array, optional
+        If provided, the result will be inserted into this array. It should
+        be of the appropriate shape and dtype.
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the array.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    index_array : ndarray of ints
+        Array of indices into the array. It has the same shape as `a.shape`
+        with the dimension along `axis` removed. If `keepdims` is set to True,
+        then the size of `axis` will be 1 with the resulting array having same
+        shape as `a.shape`.
+
+    See Also
+    --------
+    ndarray.argmin, argmax
+    amin : The minimum value along a given axis.
+    unravel_index : Convert a flat index into an index tuple.
+    take_along_axis : Apply ``np.expand_dims(index_array, axis)``
+                      from argmin to an array as if by calling min.
+
+    Notes
+    -----
+    In case of multiple occurrences of the minimum values, the indices
+    corresponding to the first occurrence are returned.
+
+    Examples
+    --------
+    >>> a = np.arange(6).reshape(2,3) + 10
+    >>> a
+    array([[10, 11, 12],
+           [13, 14, 15]])
+    >>> np.argmin(a)
+    0
+    >>> np.argmin(a, axis=0)
+    array([0, 0, 0])
+    >>> np.argmin(a, axis=1)
+    array([0, 0])
+
+    Indices of the minimum elements of a N-dimensional array:
+
+    >>> ind = np.unravel_index(np.argmin(a, axis=None), a.shape)
+    >>> ind
+    (0, 0)
+    >>> a[ind]
+    10
+
+    >>> b = np.arange(6) + 10
+    >>> b[4] = 10
+    >>> b
+    array([10, 11, 12, 13, 10, 15])
+    >>> np.argmin(b)  # Only the first occurrence is returned.
+    0
+
+    >>> x = np.array([[4,2,3], [1,0,3]])
+    >>> index_array = np.argmin(x, axis=-1)
+    >>> # Same as np.amin(x, axis=-1, keepdims=True)
+    >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1)
+    array([[2],
+           [0]])
+    >>> # Same as np.amax(x, axis=-1)
+    >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1).squeeze(axis=-1)
+    array([2, 0])
+
+    Setting `keepdims` to `True`,
+
+    >>> x = np.arange(24).reshape((2, 3, 4))
+    >>> res = np.argmin(x, axis=1, keepdims=True)
+    >>> res.shape
+    (2, 1, 4)
+    """
+    kwds = {'keepdims': keepdims} if keepdims is not np._NoValue else {}
+    return _wrapfunc(a, 'argmin', axis=axis, out=out, **kwds)
+
+
+def _searchsorted_dispatcher(a, v, side=None, sorter=None):
+    return (a, v, sorter)
+
+
+@array_function_dispatch(_searchsorted_dispatcher)
+def searchsorted(a, v, side='left', sorter=None):
+    """
+    Find indices where elements should be inserted to maintain order.
+
+    Find the indices into a sorted array `a` such that, if the
+    corresponding elements in `v` were inserted before the indices, the
+    order of `a` would be preserved.
+
+    Assuming that `a` is sorted:
+
+    ======  ============================
+    `side`  returned index `i` satisfies
+    ======  ============================
+    left    ``a[i-1] < v <= a[i]``
+    right   ``a[i-1] <= v < a[i]``
+    ======  ============================
+
+    Parameters
+    ----------
+    a : 1-D array_like
+        Input array. If `sorter` is None, then it must be sorted in
+        ascending order, otherwise `sorter` must be an array of indices
+        that sort it.
+    v : array_like
+        Values to insert into `a`.
+    side : {'left', 'right'}, optional
+        If 'left', the index of the first suitable location found is given.
+        If 'right', return the last such index.  If there is no suitable
+        index, return either 0 or N (where N is the length of `a`).
+    sorter : 1-D array_like, optional
+        Optional array of integer indices that sort array a into ascending
+        order. They are typically the result of argsort.
+
+        .. versionadded:: 1.7.0
+
+    Returns
+    -------
+    indices : int or array of ints
+        Array of insertion points with the same shape as `v`,
+        or an integer if `v` is a scalar.
+
+    See Also
+    --------
+    sort : Return a sorted copy of an array.
+    histogram : Produce histogram from 1-D data.
+
+    Notes
+    -----
+    Binary search is used to find the required insertion points.
+
+    As of NumPy 1.4.0 `searchsorted` works with real/complex arrays containing
+    `nan` values. The enhanced sort order is documented in `sort`.
+
+    This function uses the same algorithm as the builtin python `bisect.bisect_left`
+    (``side='left'``) and `bisect.bisect_right` (``side='right'``) functions,
+    which is also vectorized in the `v` argument.
+
+    Examples
+    --------
+    >>> np.searchsorted([1,2,3,4,5], 3)
+    2
+    >>> np.searchsorted([1,2,3,4,5], 3, side='right')
+    3
+    >>> np.searchsorted([1,2,3,4,5], [-10, 10, 2, 3])
+    array([0, 5, 1, 2])
+
+    """
+    return _wrapfunc(a, 'searchsorted', v, side=side, sorter=sorter)
+
+
+def _resize_dispatcher(a, new_shape):
+    return (a,)
+
+
+@array_function_dispatch(_resize_dispatcher)
+def resize(a, new_shape):
+    """
+    Return a new array with the specified shape.
+
+    If the new array is larger than the original array, then the new
+    array is filled with repeated copies of `a`.  Note that this behavior
+    is different from a.resize(new_shape) which fills with zeros instead
+    of repeated copies of `a`.
+
+    Parameters
+    ----------
+    a : array_like
+        Array to be resized.
+
+    new_shape : int or tuple of int
+        Shape of resized array.
+
+    Returns
+    -------
+    reshaped_array : ndarray
+        The new array is formed from the data in the old array, repeated
+        if necessary to fill out the required number of elements.  The
+        data are repeated iterating over the array in C-order.
+
+    See Also
+    --------
+    numpy.reshape : Reshape an array without changing the total size.
+    numpy.pad : Enlarge and pad an array.
+    numpy.repeat : Repeat elements of an array.
+    ndarray.resize : resize an array in-place.
+
+    Notes
+    -----
+    When the total size of the array does not change `~numpy.reshape` should
+    be used.  In most other cases either indexing (to reduce the size)
+    or padding (to increase the size) may be a more appropriate solution.
+
+    Warning: This functionality does **not** consider axes separately,
+    i.e. it does not apply interpolation/extrapolation.
+    It fills the return array with the required number of elements, iterating
+    over `a` in C-order, disregarding axes (and cycling back from the start if
+    the new shape is larger).  This functionality is therefore not suitable to
+    resize images, or data where each axis represents a separate and distinct
+    entity.
+
+    Examples
+    --------
+    >>> a=np.array([[0,1],[2,3]])
+    >>> np.resize(a,(2,3))
+    array([[0, 1, 2],
+           [3, 0, 1]])
+    >>> np.resize(a,(1,4))
+    array([[0, 1, 2, 3]])
+    >>> np.resize(a,(2,4))
+    array([[0, 1, 2, 3],
+           [0, 1, 2, 3]])
+
+    """
+    if isinstance(new_shape, (int, nt.integer)):
+        new_shape = (new_shape,)
+
+    a = ravel(a)
+
+    new_size = 1
+    for dim_length in new_shape:
+        new_size *= dim_length
+        if dim_length < 0:
+            raise ValueError('all elements of `new_shape` must be non-negative')
+
+    if a.size == 0 or new_size == 0:
+        # First case must zero fill. The second would have repeats == 0.
+        return np.zeros_like(a, shape=new_shape)
+
+    repeats = -(-new_size // a.size)  # ceil division
+    a = concatenate((a,) * repeats)[:new_size]
+
+    return reshape(a, new_shape)
+
+
+def _squeeze_dispatcher(a, axis=None):
+    return (a,)
+
+
+@array_function_dispatch(_squeeze_dispatcher)
+def squeeze(a, axis=None):
+    """
+    Remove axes of length one from `a`.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : None or int or tuple of ints, optional
+        .. versionadded:: 1.7.0
+
+        Selects a subset of the entries of length one in the
+        shape. If an axis is selected with shape entry greater than
+        one, an error is raised.
+
+    Returns
+    -------
+    squeezed : ndarray
+        The input array, but with all or a subset of the
+        dimensions of length 1 removed. This is always `a` itself
+        or a view into `a`. Note that if all axes are squeezed,
+        the result is a 0d array and not a scalar.
+
+    Raises
+    ------
+    ValueError
+        If `axis` is not None, and an axis being squeezed is not of length 1
+
+    See Also
+    --------
+    expand_dims : The inverse operation, adding entries of length one
+    reshape : Insert, remove, and combine dimensions, and resize existing ones
+
+    Examples
+    --------
+    >>> x = np.array([[[0], [1], [2]]])
+    >>> x.shape
+    (1, 3, 1)
+    >>> np.squeeze(x).shape
+    (3,)
+    >>> np.squeeze(x, axis=0).shape
+    (3, 1)
+    >>> np.squeeze(x, axis=1).shape
+    Traceback (most recent call last):
+    ...
+    ValueError: cannot select an axis to squeeze out which has size not equal to one
+    >>> np.squeeze(x, axis=2).shape
+    (1, 3)
+    >>> x = np.array([[1234]])
+    >>> x.shape
+    (1, 1)
+    >>> np.squeeze(x)
+    array(1234)  # 0d array
+    >>> np.squeeze(x).shape
+    ()
+    >>> np.squeeze(x)[()]
+    1234
+
+    """
+    try:
+        squeeze = a.squeeze
+    except AttributeError:
+        return _wrapit(a, 'squeeze', axis=axis)
+    if axis is None:
+        return squeeze()
+    else:
+        return squeeze(axis=axis)
+
+
+def _diagonal_dispatcher(a, offset=None, axis1=None, axis2=None):
+    return (a,)
+
+
+@array_function_dispatch(_diagonal_dispatcher)
+def diagonal(a, offset=0, axis1=0, axis2=1):
+    """
+    Return specified diagonals.
+
+    If `a` is 2-D, returns the diagonal of `a` with the given offset,
+    i.e., the collection of elements of the form ``a[i, i+offset]``.  If
+    `a` has more than two dimensions, then the axes specified by `axis1`
+    and `axis2` are used to determine the 2-D sub-array whose diagonal is
+    returned.  The shape of the resulting array can be determined by
+    removing `axis1` and `axis2` and appending an index to the right equal
+    to the size of the resulting diagonals.
+
+    In versions of NumPy prior to 1.7, this function always returned a new,
+    independent array containing a copy of the values in the diagonal.
+
+    In NumPy 1.7 and 1.8, it continues to return a copy of the diagonal,
+    but depending on this fact is deprecated. Writing to the resulting
+    array continues to work as it used to, but a FutureWarning is issued.
+
+    Starting in NumPy 1.9 it returns a read-only view on the original array.
+    Attempting to write to the resulting array will produce an error.
+
+    In some future release, it will return a read/write view and writing to
+    the returned array will alter your original array.  The returned array
+    will have the same type as the input array.
+
+    If you don't write to the array returned by this function, then you can
+    just ignore all of the above.
+
+    If you depend on the current behavior, then we suggest copying the
+    returned array explicitly, i.e., use ``np.diagonal(a).copy()`` instead
+    of just ``np.diagonal(a)``. This will work with both past and future
+    versions of NumPy.
+
+    Parameters
+    ----------
+    a : array_like
+        Array from which the diagonals are taken.
+    offset : int, optional
+        Offset of the diagonal from the main diagonal.  Can be positive or
+        negative.  Defaults to main diagonal (0).
+    axis1 : int, optional
+        Axis to be used as the first axis of the 2-D sub-arrays from which
+        the diagonals should be taken.  Defaults to first axis (0).
+    axis2 : int, optional
+        Axis to be used as the second axis of the 2-D sub-arrays from
+        which the diagonals should be taken. Defaults to second axis (1).
+
+    Returns
+    -------
+    array_of_diagonals : ndarray
+        If `a` is 2-D, then a 1-D array containing the diagonal and of the
+        same type as `a` is returned unless `a` is a `matrix`, in which case
+        a 1-D array rather than a (2-D) `matrix` is returned in order to
+        maintain backward compatibility.
+
+        If ``a.ndim > 2``, then the dimensions specified by `axis1` and `axis2`
+        are removed, and a new axis inserted at the end corresponding to the
+        diagonal.
+
+    Raises
+    ------
+    ValueError
+        If the dimension of `a` is less than 2.
+
+    See Also
+    --------
+    diag : MATLAB work-a-like for 1-D and 2-D arrays.
+    diagflat : Create diagonal arrays.
+    trace : Sum along diagonals.
+
+    Examples
+    --------
+    >>> a = np.arange(4).reshape(2,2)
+    >>> a
+    array([[0, 1],
+           [2, 3]])
+    >>> a.diagonal()
+    array([0, 3])
+    >>> a.diagonal(1)
+    array([1])
+
+    A 3-D example:
+
+    >>> a = np.arange(8).reshape(2,2,2); a
+    array([[[0, 1],
+            [2, 3]],
+           [[4, 5],
+            [6, 7]]])
+    >>> a.diagonal(0,  # Main diagonals of two arrays created by skipping
+    ...            0,  # across the outer(left)-most axis last and
+    ...            1)  # the "middle" (row) axis first.
+    array([[0, 6],
+           [1, 7]])
+
+    The sub-arrays whose main diagonals we just obtained; note that each
+    corresponds to fixing the right-most (column) axis, and that the
+    diagonals are "packed" in rows.
+
+    >>> a[:,:,0]  # main diagonal is [0 6]
+    array([[0, 2],
+           [4, 6]])
+    >>> a[:,:,1]  # main diagonal is [1 7]
+    array([[1, 3],
+           [5, 7]])
+
+    The anti-diagonal can be obtained by reversing the order of elements
+    using either `numpy.flipud` or `numpy.fliplr`.
+
+    >>> a = np.arange(9).reshape(3, 3)
+    >>> a
+    array([[0, 1, 2],
+           [3, 4, 5],
+           [6, 7, 8]])
+    >>> np.fliplr(a).diagonal()  # Horizontal flip
+    array([2, 4, 6])
+    >>> np.flipud(a).diagonal()  # Vertical flip
+    array([6, 4, 2])
+
+    Note that the order in which the diagonal is retrieved varies depending
+    on the flip function.
+    """
+    if isinstance(a, np.matrix):
+        # Make diagonal of matrix 1-D to preserve backward compatibility.
+        return asarray(a).diagonal(offset=offset, axis1=axis1, axis2=axis2)
+    else:
+        return asanyarray(a).diagonal(offset=offset, axis1=axis1, axis2=axis2)
+
+
+def _trace_dispatcher(
+        a, offset=None, axis1=None, axis2=None, dtype=None, out=None):
+    return (a, out)
+
+
+@array_function_dispatch(_trace_dispatcher)
+def trace(a, offset=0, axis1=0, axis2=1, dtype=None, out=None):
+    """
+    Return the sum along diagonals of the array.
+
+    If `a` is 2-D, the sum along its diagonal with the given offset
+    is returned, i.e., the sum of elements ``a[i,i+offset]`` for all i.
+
+    If `a` has more than two dimensions, then the axes specified by axis1 and
+    axis2 are used to determine the 2-D sub-arrays whose traces are returned.
+    The shape of the resulting array is the same as that of `a` with `axis1`
+    and `axis2` removed.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array, from which the diagonals are taken.
+    offset : int, optional
+        Offset of the diagonal from the main diagonal. Can be both positive
+        and negative. Defaults to 0.
+    axis1, axis2 : int, optional
+        Axes to be used as the first and second axis of the 2-D sub-arrays
+        from which the diagonals should be taken. Defaults are the first two
+        axes of `a`.
+    dtype : dtype, optional
+        Determines the data-type of the returned array and of the accumulator
+        where the elements are summed. If dtype has the value None and `a` is
+        of integer type of precision less than the default integer
+        precision, then the default integer precision is used. Otherwise,
+        the precision is the same as that of `a`.
+    out : ndarray, optional
+        Array into which the output is placed. Its type is preserved and
+        it must be of the right shape to hold the output.
+
+    Returns
+    -------
+    sum_along_diagonals : ndarray
+        If `a` is 2-D, the sum along the diagonal is returned.  If `a` has
+        larger dimensions, then an array of sums along diagonals is returned.
+
+    See Also
+    --------
+    diag, diagonal, diagflat
+
+    Examples
+    --------
+    >>> np.trace(np.eye(3))
+    3.0
+    >>> a = np.arange(8).reshape((2,2,2))
+    >>> np.trace(a)
+    array([6, 8])
+
+    >>> a = np.arange(24).reshape((2,2,2,3))
+    >>> np.trace(a).shape
+    (2, 3)
+
+    """
+    if isinstance(a, np.matrix):
+        # Get trace of matrix via an array to preserve backward compatibility.
+        return asarray(a).trace(offset=offset, axis1=axis1, axis2=axis2, dtype=dtype, out=out)
+    else:
+        return asanyarray(a).trace(offset=offset, axis1=axis1, axis2=axis2, dtype=dtype, out=out)
+
+
+def _ravel_dispatcher(a, order=None):
+    return (a,)
+
+
+@array_function_dispatch(_ravel_dispatcher)
+def ravel(a, order='C'):
+    """Return a contiguous flattened array.
+
+    A 1-D array, containing the elements of the input, is returned.  A copy is
+    made only if needed.
+
+    As of NumPy 1.10, the returned array will have the same type as the input
+    array. (for example, a masked array will be returned for a masked array
+    input)
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.  The elements in `a` are read in the order specified by
+        `order`, and packed as a 1-D array.
+    order : {'C','F', 'A', 'K'}, optional
+
+        The elements of `a` are read using this index order. 'C' means
+        to index the elements in row-major, C-style order,
+        with the last axis index changing fastest, back to the first
+        axis index changing slowest.  'F' means to index the elements
+        in column-major, Fortran-style 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 axis indexing.  'A' means to read the elements in
+        Fortran-like index order if `a` is Fortran *contiguous* in
+        memory, C-like order otherwise.  'K' means to read the
+        elements in the order they occur in memory, except for
+        reversing the data when strides are negative.  By default, 'C'
+        index order is used.
+
+    Returns
+    -------
+    y : array_like
+        y is a contiguous 1-D array of the same subtype as `a`,
+        with shape ``(a.size,)``.
+        Note that matrices are special cased for backward compatibility,
+        if `a` is a matrix, then y is a 1-D ndarray.
+
+    See Also
+    --------
+    ndarray.flat : 1-D iterator over an array.
+    ndarray.flatten : 1-D array copy of the elements of an array
+                      in row-major order.
+    ndarray.reshape : Change the shape of an array without changing its data.
+
+    Notes
+    -----
+    In row-major, C-style order, in two dimensions, the row index
+    varies the slowest, and the column index the quickest.  This can
+    be generalized to multiple dimensions, where row-major order
+    implies that the index along the first axis varies slowest, and
+    the index along the last quickest.  The opposite holds for
+    column-major, Fortran-style index ordering.
+
+    When a view is desired in as many cases as possible, ``arr.reshape(-1)``
+    may be preferable. However, ``ravel`` supports ``K`` in the optional
+    ``order`` argument while ``reshape`` does not.
+
+    Examples
+    --------
+    It is equivalent to ``reshape(-1, order=order)``.
+
+    >>> x = np.array([[1, 2, 3], [4, 5, 6]])
+    >>> np.ravel(x)
+    array([1, 2, 3, 4, 5, 6])
+
+    >>> x.reshape(-1)
+    array([1, 2, 3, 4, 5, 6])
+
+    >>> np.ravel(x, order='F')
+    array([1, 4, 2, 5, 3, 6])
+
+    When ``order`` is 'A', it will preserve the array's 'C' or 'F' ordering:
+
+    >>> np.ravel(x.T)
+    array([1, 4, 2, 5, 3, 6])
+    >>> np.ravel(x.T, order='A')
+    array([1, 2, 3, 4, 5, 6])
+
+    When ``order`` is 'K', it will preserve orderings that are neither 'C'
+    nor 'F', but won't reverse axes:
+
+    >>> a = np.arange(3)[::-1]; a
+    array([2, 1, 0])
+    >>> a.ravel(order='C')
+    array([2, 1, 0])
+    >>> a.ravel(order='K')
+    array([2, 1, 0])
+
+    >>> a = np.arange(12).reshape(2,3,2).swapaxes(1,2); a
+    array([[[ 0,  2,  4],
+            [ 1,  3,  5]],
+           [[ 6,  8, 10],
+            [ 7,  9, 11]]])
+    >>> a.ravel(order='C')
+    array([ 0,  2,  4,  1,  3,  5,  6,  8, 10,  7,  9, 11])
+    >>> a.ravel(order='K')
+    array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])
+
+    """
+    if isinstance(a, np.matrix):
+        return asarray(a).ravel(order=order)
+    else:
+        return asanyarray(a).ravel(order=order)
+
+
+def _nonzero_dispatcher(a):
+    return (a,)
+
+
+@array_function_dispatch(_nonzero_dispatcher)
+def nonzero(a):
+    """
+    Return the indices of the elements that are non-zero.
+
+    Returns a tuple of arrays, one for each dimension of `a`,
+    containing the indices of the non-zero elements in that
+    dimension. The values in `a` are always tested and returned in
+    row-major, C-style order.
+
+    To group the indices by element, rather than dimension, use `argwhere`,
+    which returns a row for each non-zero element.
+
+    .. note::
+
+       When called on a zero-d array or scalar, ``nonzero(a)`` is treated
+       as ``nonzero(atleast_1d(a))``.
+
+       .. deprecated:: 1.17.0
+
+          Use `atleast_1d` explicitly if this behavior is deliberate.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+
+    Returns
+    -------
+    tuple_of_arrays : tuple
+        Indices of elements that are non-zero.
+
+    See Also
+    --------
+    flatnonzero :
+        Return indices that are non-zero in the flattened version of the input
+        array.
+    ndarray.nonzero :
+        Equivalent ndarray method.
+    count_nonzero :
+        Counts the number of non-zero elements in the input array.
+
+    Notes
+    -----
+    While the nonzero values can be obtained with ``a[nonzero(a)]``, it is
+    recommended to use ``x[x.astype(bool)]`` or ``x[x != 0]`` instead, which
+    will correctly handle 0-d arrays.
+
+    Examples
+    --------
+    >>> x = np.array([[3, 0, 0], [0, 4, 0], [5, 6, 0]])
+    >>> x
+    array([[3, 0, 0],
+           [0, 4, 0],
+           [5, 6, 0]])
+    >>> np.nonzero(x)
+    (array([0, 1, 2, 2]), array([0, 1, 0, 1]))
+
+    >>> x[np.nonzero(x)]
+    array([3, 4, 5, 6])
+    >>> np.transpose(np.nonzero(x))
+    array([[0, 0],
+           [1, 1],
+           [2, 0],
+           [2, 1]])
+
+    A common use for ``nonzero`` is to find the indices of an array, where
+    a condition is True.  Given an array `a`, the condition `a` > 3 is a
+    boolean array and since False is interpreted as 0, np.nonzero(a > 3)
+    yields the indices of the `a` where the condition is true.
+
+    >>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    >>> a > 3
+    array([[False, False, False],
+           [ True,  True,  True],
+           [ True,  True,  True]])
+    >>> np.nonzero(a > 3)
+    (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))
+
+    Using this result to index `a` is equivalent to using the mask directly:
+
+    >>> a[np.nonzero(a > 3)]
+    array([4, 5, 6, 7, 8, 9])
+    >>> a[a > 3]  # prefer this spelling
+    array([4, 5, 6, 7, 8, 9])
+
+    ``nonzero`` can also be called as a method of the array.
+
+    >>> (a > 3).nonzero()
+    (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))
+
+    """
+    return _wrapfunc(a, 'nonzero')
+
+
+def _shape_dispatcher(a):
+    return (a,)
+
+
+@array_function_dispatch(_shape_dispatcher)
+def shape(a):
+    """
+    Return the shape of an array.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+
+    Returns
+    -------
+    shape : tuple of ints
+        The elements of the shape tuple give the lengths of the
+        corresponding array dimensions.
+
+    See Also
+    --------
+    len : ``len(a)`` is equivalent to ``np.shape(a)[0]`` for N-D arrays with
+          ``N>=1``.
+    ndarray.shape : Equivalent array method.
+
+    Examples
+    --------
+    >>> np.shape(np.eye(3))
+    (3, 3)
+    >>> np.shape([[1, 3]])
+    (1, 2)
+    >>> np.shape([0])
+    (1,)
+    >>> np.shape(0)
+    ()
+
+    >>> a = np.array([(1, 2), (3, 4), (5, 6)],
+    ...              dtype=[('x', 'i4'), ('y', 'i4')])
+    >>> np.shape(a)
+    (3,)
+    >>> a.shape
+    (3,)
+
+    """
+    try:
+        result = a.shape
+    except AttributeError:
+        result = asarray(a).shape
+    return result
+
+
+def _compress_dispatcher(condition, a, axis=None, out=None):
+    return (condition, a, out)
+
+
+@array_function_dispatch(_compress_dispatcher)
+def compress(condition, a, axis=None, out=None):
+    """
+    Return selected slices of an array along given axis.
+
+    When working along a given axis, a slice along that axis is returned in
+    `output` for each index where `condition` evaluates to True. When
+    working on a 1-D array, `compress` is equivalent to `extract`.
+
+    Parameters
+    ----------
+    condition : 1-D array of bools
+        Array that selects which entries to return. If len(condition)
+        is less than the size of `a` along the given axis, then output is
+        truncated to the length of the condition array.
+    a : array_like
+        Array from which to extract a part.
+    axis : int, optional
+        Axis along which to take slices. If None (default), work on the
+        flattened array.
+    out : ndarray, optional
+        Output array.  Its type is preserved and it must be of the right
+        shape to hold the output.
+
+    Returns
+    -------
+    compressed_array : ndarray
+        A copy of `a` without the slices along axis for which `condition`
+        is false.
+
+    See Also
+    --------
+    take, choose, diag, diagonal, select
+    ndarray.compress : Equivalent method in ndarray
+    extract : Equivalent method when working on 1-D arrays
+    :ref:`ufuncs-output-type`
+
+    Examples
+    --------
+    >>> a = np.array([[1, 2], [3, 4], [5, 6]])
+    >>> a
+    array([[1, 2],
+           [3, 4],
+           [5, 6]])
+    >>> np.compress([0, 1], a, axis=0)
+    array([[3, 4]])
+    >>> np.compress([False, True, True], a, axis=0)
+    array([[3, 4],
+           [5, 6]])
+    >>> np.compress([False, True], a, axis=1)
+    array([[2],
+           [4],
+           [6]])
+
+    Working on the flattened array does not return slices along an axis but
+    selects elements.
+
+    >>> np.compress([False, True], a)
+    array([2])
+
+    """
+    return _wrapfunc(a, 'compress', condition, axis=axis, out=out)
+
+
+def _clip_dispatcher(a, a_min, a_max, out=None, **kwargs):
+    return (a, a_min, a_max)
+
+
+@array_function_dispatch(_clip_dispatcher)
+def clip(a, a_min, a_max, out=None, **kwargs):
+    """
+    Clip (limit) the values in an array.
+
+    Given an interval, values outside the interval are clipped to
+    the interval edges.  For example, if an interval of ``[0, 1]``
+    is specified, values smaller than 0 become 0, and values larger
+    than 1 become 1.
+
+    Equivalent to but faster than ``np.minimum(a_max, np.maximum(a, a_min))``.
+
+    No check is performed to ensure ``a_min < a_max``.
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing elements to clip.
+    a_min, a_max : array_like or None
+        Minimum and maximum value. If ``None``, clipping is not performed on
+        the corresponding edge. Only one of `a_min` and `a_max` may be
+        ``None``. Both are broadcast against `a`.
+    out : ndarray, optional
+        The results will be placed in this array. It may be the input
+        array for in-place clipping.  `out` must be of the right shape
+        to hold the output.  Its type is preserved.
+    **kwargs
+        For other keyword-only arguments, see the
+        :ref:`ufunc docs <ufuncs.kwargs>`.
+
+        .. versionadded:: 1.17.0
+
+    Returns
+    -------
+    clipped_array : ndarray
+        An array with the elements of `a`, but where values
+        < `a_min` are replaced with `a_min`, and those > `a_max`
+        with `a_max`.
+
+    See Also
+    --------
+    :ref:`ufuncs-output-type`
+
+    Notes
+    -----
+    When `a_min` is greater than `a_max`, `clip` returns an
+    array in which all values are equal to `a_max`,
+    as shown in the second example.
+
+    Examples
+    --------
+    >>> a = np.arange(10)
+    >>> a
+    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
+    >>> np.clip(a, 1, 8)
+    array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8])
+    >>> np.clip(a, 8, 1)
+    array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])
+    >>> np.clip(a, 3, 6, out=a)
+    array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])
+    >>> a
+    array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])
+    >>> a = np.arange(10)
+    >>> a
+    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
+    >>> np.clip(a, [3, 4, 1, 1, 1, 4, 4, 4, 4, 4], 8)
+    array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8])
+
+    """
+    return _wrapfunc(a, 'clip', a_min, a_max, out=out, **kwargs)
+
+
+def _sum_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
+                    initial=None, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_sum_dispatcher)
+def sum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
+        initial=np._NoValue, where=np._NoValue):
+    """
+    Sum of array elements over a given axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Elements to sum.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which a sum is performed.  The default,
+        axis=None, will sum all of the elements of the input array.  If
+        axis is negative it counts from the last to the first axis.
+
+        .. versionadded:: 1.7.0
+
+        If axis is a tuple of ints, a sum is performed on all of the axes
+        specified in the tuple instead of a single axis or all the axes as
+        before.
+    dtype : dtype, optional
+        The type of the returned array and of the accumulator in which the
+        elements are summed.  The dtype of `a` is used by default unless `a`
+        has an integer dtype of less precision than the default platform
+        integer.  In that case, if `a` is signed then the platform integer
+        is used while if `a` is unsigned then an unsigned integer of the
+        same precision as the platform integer is used.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must have
+        the same shape as the expected output, but the type of the output
+        values will be cast if necessary.
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `sum` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+    initial : scalar, optional
+        Starting value for the sum. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.15.0
+
+    where : array_like of bool, optional
+        Elements to include in the sum. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.17.0
+
+    Returns
+    -------
+    sum_along_axis : ndarray
+        An array with the same shape as `a`, with the specified
+        axis removed.   If `a` is a 0-d array, or if `axis` is None, a scalar
+        is returned.  If an output array is specified, a reference to
+        `out` is returned.
+
+    See Also
+    --------
+    ndarray.sum : Equivalent method.
+
+    add.reduce : Equivalent functionality of `add`.
+
+    cumsum : Cumulative sum of array elements.
+
+    trapz : Integration of array values using the composite trapezoidal rule.
+
+    mean, average
+
+    Notes
+    -----
+    Arithmetic is modular when using integer types, and no error is
+    raised on overflow.
+
+    The sum of an empty array is the neutral element 0:
+
+    >>> np.sum([])
+    0.0
+
+    For floating point numbers the numerical precision of sum (and
+    ``np.add.reduce``) is in general limited by directly adding each number
+    individually to the result causing rounding errors in every step.
+    However, often numpy will use a  numerically better approach (partial
+    pairwise summation) leading to improved precision in many use-cases.
+    This improved precision is always provided when no ``axis`` is given.
+    When ``axis`` is given, it will depend on which axis is summed.
+    Technically, to provide the best speed possible, the improved precision
+    is only used when the summation is along the fast axis in memory.
+    Note that the exact precision may vary depending on other parameters.
+    In contrast to NumPy, Python's ``math.fsum`` function uses a slower but
+    more precise approach to summation.
+    Especially when summing a large number of lower precision floating point
+    numbers, such as ``float32``, numerical errors can become significant.
+    In such cases it can be advisable to use `dtype="float64"` to use a higher
+    precision for the output.
+
+    Examples
+    --------
+    >>> np.sum([0.5, 1.5])
+    2.0
+    >>> np.sum([0.5, 0.7, 0.2, 1.5], dtype=np.int32)
+    1
+    >>> np.sum([[0, 1], [0, 5]])
+    6
+    >>> np.sum([[0, 1], [0, 5]], axis=0)
+    array([0, 6])
+    >>> np.sum([[0, 1], [0, 5]], axis=1)
+    array([1, 5])
+    >>> np.sum([[0, 1], [np.nan, 5]], where=[False, True], axis=1)
+    array([1., 5.])
+
+    If the accumulator is too small, overflow occurs:
+
+    >>> np.ones(128, dtype=np.int8).sum(dtype=np.int8)
+    -128
+
+    You can also start the sum with a value other than zero:
+
+    >>> np.sum([10], initial=5)
+    15
+    """
+    if isinstance(a, _gentype):
+        # 2018-02-25, 1.15.0
+        warnings.warn(
+            "Calling np.sum(generator) is deprecated, and in the future will give a different result. "
+            "Use np.sum(np.fromiter(generator)) or the python sum builtin instead.",
+            DeprecationWarning, stacklevel=2)
+
+        res = _sum_(a)
+        if out is not None:
+            out[...] = res
+            return out
+        return res
+
+    return _wrapreduction(a, np.add, 'sum', axis, dtype, out, keepdims=keepdims,
+                          initial=initial, where=where)
+
+
+def _any_dispatcher(a, axis=None, out=None, keepdims=None, *,
+                    where=np._NoValue):
+    return (a, where, out)
+
+
+@array_function_dispatch(_any_dispatcher)
+def any(a, axis=None, out=None, keepdims=np._NoValue, *, where=np._NoValue):
+    """
+    Test whether any array element along a given axis evaluates to True.
+
+    Returns single boolean if `axis` is ``None``
+
+    Parameters
+    ----------
+    a : array_like
+        Input array or object that can be converted to an array.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which a logical OR reduction is performed.
+        The default (``axis=None``) is to perform a logical OR over all
+        the dimensions of the input array. `axis` may be negative, in
+        which case it counts from the last to the first axis.
+
+        .. versionadded:: 1.7.0
+
+        If this is a tuple of ints, a reduction is performed on multiple
+        axes, instead of a single axis or all the axes as before.
+    out : ndarray, optional
+        Alternate output array in which to place the result.  It must have
+        the same shape as the expected output and its type is preserved
+        (e.g., if it is of type float, then it will remain so, returning
+        1.0 for True and 0.0 for False, regardless of the type of `a`).
+        See :ref:`ufuncs-output-type` for more details.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `any` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    where : array_like of bool, optional
+        Elements to include in checking for any `True` values.
+        See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    any : bool or ndarray
+        A new boolean or `ndarray` is returned unless `out` is specified,
+        in which case a reference to `out` is returned.
+
+    See Also
+    --------
+    ndarray.any : equivalent method
+
+    all : Test whether all elements along a given axis evaluate to True.
+
+    Notes
+    -----
+    Not a Number (NaN), positive infinity and negative infinity evaluate
+    to `True` because these are not equal to zero.
+
+    Examples
+    --------
+    >>> np.any([[True, False], [True, True]])
+    True
+
+    >>> np.any([[True, False], [False, False]], axis=0)
+    array([ True, False])
+
+    >>> np.any([-1, 0, 5])
+    True
+
+    >>> np.any(np.nan)
+    True
+
+    >>> np.any([[True, False], [False, False]], where=[[False], [True]])
+    False
+
+    >>> o=np.array(False)
+    >>> z=np.any([-1, 4, 5], out=o)
+    >>> z, o
+    (array(True), array(True))
+    >>> # Check now that z is a reference to o
+    >>> z is o
+    True
+    >>> id(z), id(o) # identity of z and o              # doctest: +SKIP
+    (191614240, 191614240)
+
+    """
+    return _wrapreduction(a, np.logical_or, 'any', axis, None, out,
+                          keepdims=keepdims, where=where)
+
+
+def _all_dispatcher(a, axis=None, out=None, keepdims=None, *,
+                    where=None):
+    return (a, where, out)
+
+
+@array_function_dispatch(_all_dispatcher)
+def all(a, axis=None, out=None, keepdims=np._NoValue, *, where=np._NoValue):
+    """
+    Test whether all array elements along a given axis evaluate to True.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array or object that can be converted to an array.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which a logical AND reduction is performed.
+        The default (``axis=None``) is to perform a logical AND over all
+        the dimensions of the input array. `axis` may be negative, in
+        which case it counts from the last to the first axis.
+
+        .. versionadded:: 1.7.0
+
+        If this is a tuple of ints, a reduction is performed on multiple
+        axes, instead of a single axis or all the axes as before.
+    out : ndarray, optional
+        Alternate output array in which to place the result.
+        It must have the same shape as the expected output and its
+        type is preserved (e.g., if ``dtype(out)`` is float, the result
+        will consist of 0.0's and 1.0's). See :ref:`ufuncs-output-type` for more
+        details.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `all` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    where : array_like of bool, optional
+        Elements to include in checking for all `True` values.
+        See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    all : ndarray, bool
+        A new boolean or array is returned unless `out` is specified,
+        in which case a reference to `out` is returned.
+
+    See Also
+    --------
+    ndarray.all : equivalent method
+
+    any : Test whether any element along a given axis evaluates to True.
+
+    Notes
+    -----
+    Not a Number (NaN), positive infinity and negative infinity
+    evaluate to `True` because these are not equal to zero.
+
+    Examples
+    --------
+    >>> np.all([[True,False],[True,True]])
+    False
+
+    >>> np.all([[True,False],[True,True]], axis=0)
+    array([ True, False])
+
+    >>> np.all([-1, 4, 5])
+    True
+
+    >>> np.all([1.0, np.nan])
+    True
+
+    >>> np.all([[True, True], [False, True]], where=[[True], [False]])
+    True
+
+    >>> o=np.array(False)
+    >>> z=np.all([-1, 4, 5], out=o)
+    >>> id(z), id(o), z
+    (28293632, 28293632, array(True)) # may vary
+
+    """
+    return _wrapreduction(a, np.logical_and, 'all', axis, None, out,
+                          keepdims=keepdims, where=where)
+
+
+def _cumsum_dispatcher(a, axis=None, dtype=None, out=None):
+    return (a, out)
+
+
+@array_function_dispatch(_cumsum_dispatcher)
+def cumsum(a, axis=None, dtype=None, out=None):
+    """
+    Return the cumulative sum of the elements along a given axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int, optional
+        Axis along which the cumulative sum is computed. The default
+        (None) is to compute the cumsum over the flattened array.
+    dtype : dtype, optional
+        Type of the returned array and of the accumulator in which the
+        elements are summed.  If `dtype` is not specified, it defaults
+        to the dtype of `a`, unless `a` has an integer dtype with a
+        precision less than that of the default platform integer.  In
+        that case, the default platform integer is used.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must
+        have the same shape and buffer length as the expected output
+        but the type will be cast if necessary. See :ref:`ufuncs-output-type` for
+        more details.
+
+    Returns
+    -------
+    cumsum_along_axis : ndarray.
+        A new array holding the result is returned unless `out` is
+        specified, in which case a reference to `out` is returned. The
+        result has the same size as `a`, and the same shape as `a` if
+        `axis` is not None or `a` is a 1-d array.
+
+    See Also
+    --------
+    sum : Sum array elements.
+    trapz : Integration of array values using the composite trapezoidal rule.
+    diff : Calculate the n-th discrete difference along given axis.
+
+    Notes
+    -----
+    Arithmetic is modular when using integer types, and no error is
+    raised on overflow.
+
+    ``cumsum(a)[-1]`` may not be equal to ``sum(a)`` for floating-point
+    values since ``sum`` may use a pairwise summation routine, reducing
+    the roundoff-error. See `sum` for more information.
+
+    Examples
+    --------
+    >>> a = np.array([[1,2,3], [4,5,6]])
+    >>> a
+    array([[1, 2, 3],
+           [4, 5, 6]])
+    >>> np.cumsum(a)
+    array([ 1,  3,  6, 10, 15, 21])
+    >>> np.cumsum(a, dtype=float)     # specifies type of output value(s)
+    array([  1.,   3.,   6.,  10.,  15.,  21.])
+
+    >>> np.cumsum(a,axis=0)      # sum over rows for each of the 3 columns
+    array([[1, 2, 3],
+           [5, 7, 9]])
+    >>> np.cumsum(a,axis=1)      # sum over columns for each of the 2 rows
+    array([[ 1,  3,  6],
+           [ 4,  9, 15]])
+
+    ``cumsum(b)[-1]`` may not be equal to ``sum(b)``
+
+    >>> b = np.array([1, 2e-9, 3e-9] * 1000000)
+    >>> b.cumsum()[-1]
+    1000000.0050045159
+    >>> b.sum()
+    1000000.0050000029
+
+    """
+    return _wrapfunc(a, 'cumsum', axis=axis, dtype=dtype, out=out)
+
+
+def _ptp_dispatcher(a, axis=None, out=None, keepdims=None):
+    return (a, out)
+
+
+@array_function_dispatch(_ptp_dispatcher)
+def ptp(a, axis=None, out=None, keepdims=np._NoValue):
+    """
+    Range of values (maximum - minimum) along an axis.
+
+    The name of the function comes from the acronym for 'peak to peak'.
+
+    .. warning::
+        `ptp` preserves the data type of the array. This means the
+        return value for an input of signed integers with n bits
+        (e.g. `np.int8`, `np.int16`, etc) is also a signed integer
+        with n bits.  In that case, peak-to-peak values greater than
+        ``2**(n-1)-1`` will be returned as negative values. An example
+        with a work-around is shown below.
+
+    Parameters
+    ----------
+    a : array_like
+        Input values.
+    axis : None or int or tuple of ints, optional
+        Axis along which to find the peaks.  By default, flatten the
+        array.  `axis` may be negative, in
+        which case it counts from the last to the first axis.
+
+        .. versionadded:: 1.15.0
+
+        If this is a tuple of ints, a reduction is performed on multiple
+        axes, instead of a single axis or all the axes as before.
+    out : array_like
+        Alternative output array in which to place the result. It must
+        have the same shape and buffer length as the expected output,
+        but the type of the output values will be cast if necessary.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `ptp` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    Returns
+    -------
+    ptp : ndarray or scalar
+        The range of a given array - `scalar` if array is one-dimensional
+        or a new array holding the result along the given axis
+
+    Examples
+    --------
+    >>> x = np.array([[4, 9, 2, 10],
+    ...               [6, 9, 7, 12]])
+
+    >>> np.ptp(x, axis=1)
+    array([8, 6])
+
+    >>> np.ptp(x, axis=0)
+    array([2, 0, 5, 2])
+
+    >>> np.ptp(x)
+    10
+
+    This example shows that a negative value can be returned when
+    the input is an array of signed integers.
+
+    >>> y = np.array([[1, 127],
+    ...               [0, 127],
+    ...               [-1, 127],
+    ...               [-2, 127]], dtype=np.int8)
+    >>> np.ptp(y, axis=1)
+    array([ 126,  127, -128, -127], dtype=int8)
+
+    A work-around is to use the `view()` method to view the result as
+    unsigned integers with the same bit width:
+
+    >>> np.ptp(y, axis=1).view(np.uint8)
+    array([126, 127, 128, 129], dtype=uint8)
+
+    """
+    kwargs = {}
+    if keepdims is not np._NoValue:
+        kwargs['keepdims'] = keepdims
+    if type(a) is not mu.ndarray:
+        try:
+            ptp = a.ptp
+        except AttributeError:
+            pass
+        else:
+            return ptp(axis=axis, out=out, **kwargs)
+    return _methods._ptp(a, axis=axis, out=out, **kwargs)
+
+
+def _max_dispatcher(a, axis=None, out=None, keepdims=None, initial=None,
+                    where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_max_dispatcher)
+@set_module('numpy')
+def max(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
+         where=np._NoValue):
+    """
+    Return the maximum of an array or maximum along an axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which to operate.  By default, flattened input is
+        used.
+
+        .. versionadded:: 1.7.0
+
+        If this is a tuple of ints, the maximum is selected over multiple axes,
+        instead of a single axis or all the axes as before.
+    out : ndarray, optional
+        Alternative output array in which to place the result.  Must
+        be of the same shape and buffer length as the expected output.
+        See :ref:`ufuncs-output-type` for more details.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the ``max`` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    initial : scalar, optional
+        The minimum value of an output element. Must be present to allow
+        computation on empty slice. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.15.0
+
+    where : array_like of bool, optional
+        Elements to compare for the maximum. See `~numpy.ufunc.reduce`
+        for details.
+
+        .. versionadded:: 1.17.0
+
+    Returns
+    -------
+    max : ndarray or scalar
+        Maximum of `a`. If `axis` is None, the result is a scalar value.
+        If `axis` is an int, the result is an array of dimension
+        ``a.ndim - 1``. If `axis` is a tuple, the result is an array of 
+        dimension ``a.ndim - len(axis)``.
+
+    See Also
+    --------
+    amin :
+        The minimum value of an array along a given axis, propagating any NaNs.
+    nanmax :
+        The maximum value of an array along a given axis, ignoring any NaNs.
+    maximum :
+        Element-wise maximum of two arrays, propagating any NaNs.
+    fmax :
+        Element-wise maximum of two arrays, ignoring any NaNs.
+    argmax :
+        Return the indices of the maximum values.
+
+    nanmin, minimum, fmin
+
+    Notes
+    -----
+    NaN values are propagated, that is if at least one item is NaN, the
+    corresponding max value will be NaN as well. To ignore NaN values
+    (MATLAB behavior), please use nanmax.
+
+    Don't use `~numpy.max` for element-wise comparison of 2 arrays; when
+    ``a.shape[0]`` is 2, ``maximum(a[0], a[1])`` is faster than
+    ``max(a, axis=0)``.
+
+    Examples
+    --------
+    >>> a = np.arange(4).reshape((2,2))
+    >>> a
+    array([[0, 1],
+           [2, 3]])
+    >>> np.max(a)           # Maximum of the flattened array
+    3
+    >>> np.max(a, axis=0)   # Maxima along the first axis
+    array([2, 3])
+    >>> np.max(a, axis=1)   # Maxima along the second axis
+    array([1, 3])
+    >>> np.max(a, where=[False, True], initial=-1, axis=0)
+    array([-1,  3])
+    >>> b = np.arange(5, dtype=float)
+    >>> b[2] = np.NaN
+    >>> np.max(b)
+    nan
+    >>> np.max(b, where=~np.isnan(b), initial=-1)
+    4.0
+    >>> np.nanmax(b)
+    4.0
+
+    You can use an initial value to compute the maximum of an empty slice, or
+    to initialize it to a different value:
+
+    >>> np.max([[-50], [10]], axis=-1, initial=0)
+    array([ 0, 10])
+
+    Notice that the initial value is used as one of the elements for which the
+    maximum is determined, unlike for the default argument Python's max
+    function, which is only used for empty iterables.
+
+    >>> np.max([5], initial=6)
+    6
+    >>> max([5], default=6)
+    5
+    """
+    return _wrapreduction(a, np.maximum, 'max', axis, None, out,
+                          keepdims=keepdims, initial=initial, where=where)
+
+
+@array_function_dispatch(_max_dispatcher)
+def amax(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
+         where=np._NoValue):
+    """
+    Return the maximum of an array or maximum along an axis.
+
+    `amax` is an alias of `~numpy.max`.
+
+    See Also
+    --------
+    max : alias of this function
+    ndarray.max : equivalent method
+    """
+    return _wrapreduction(a, np.maximum, 'max', axis, None, out,
+                          keepdims=keepdims, initial=initial, where=where)
+
+
+def _min_dispatcher(a, axis=None, out=None, keepdims=None, initial=None,
+                    where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_min_dispatcher)
+def min(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
+        where=np._NoValue):
+    """
+    Return the minimum of an array or minimum along an axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which to operate.  By default, flattened input is
+        used.
+
+        .. versionadded:: 1.7.0
+
+        If this is a tuple of ints, the minimum is selected over multiple axes,
+        instead of a single axis or all the axes as before.
+    out : ndarray, optional
+        Alternative output array in which to place the result.  Must
+        be of the same shape and buffer length as the expected output.
+        See :ref:`ufuncs-output-type` for more details.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the ``min`` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    initial : scalar, optional
+        The maximum value of an output element. Must be present to allow
+        computation on empty slice. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.15.0
+
+    where : array_like of bool, optional
+        Elements to compare for the minimum. See `~numpy.ufunc.reduce`
+        for details.
+
+        .. versionadded:: 1.17.0
+
+    Returns
+    -------
+    min : ndarray or scalar
+        Minimum of `a`. If `axis` is None, the result is a scalar value.
+        If `axis` is an int, the result is an array of dimension
+        ``a.ndim - 1``.  If `axis` is a tuple, the result is an array of 
+        dimension ``a.ndim - len(axis)``.
+
+    See Also
+    --------
+    amax :
+        The maximum value of an array along a given axis, propagating any NaNs.
+    nanmin :
+        The minimum value of an array along a given axis, ignoring any NaNs.
+    minimum :
+        Element-wise minimum of two arrays, propagating any NaNs.
+    fmin :
+        Element-wise minimum of two arrays, ignoring any NaNs.
+    argmin :
+        Return the indices of the minimum values.
+
+    nanmax, maximum, fmax
+
+    Notes
+    -----
+    NaN values are propagated, that is if at least one item is NaN, the
+    corresponding min value will be NaN as well. To ignore NaN values
+    (MATLAB behavior), please use nanmin.
+
+    Don't use `~numpy.min` for element-wise comparison of 2 arrays; when
+    ``a.shape[0]`` is 2, ``minimum(a[0], a[1])`` is faster than
+    ``min(a, axis=0)``.
+
+    Examples
+    --------
+    >>> a = np.arange(4).reshape((2,2))
+    >>> a
+    array([[0, 1],
+           [2, 3]])
+    >>> np.min(a)           # Minimum of the flattened array
+    0
+    >>> np.min(a, axis=0)   # Minima along the first axis
+    array([0, 1])
+    >>> np.min(a, axis=1)   # Minima along the second axis
+    array([0, 2])
+    >>> np.min(a, where=[False, True], initial=10, axis=0)
+    array([10,  1])
+
+    >>> b = np.arange(5, dtype=float)
+    >>> b[2] = np.NaN
+    >>> np.min(b)
+    nan
+    >>> np.min(b, where=~np.isnan(b), initial=10)
+    0.0
+    >>> np.nanmin(b)
+    0.0
+
+    >>> np.min([[-50], [10]], axis=-1, initial=0)
+    array([-50,   0])
+
+    Notice that the initial value is used as one of the elements for which the
+    minimum is determined, unlike for the default argument Python's max
+    function, which is only used for empty iterables.
+
+    Notice that this isn't the same as Python's ``default`` argument.
+
+    >>> np.min([6], initial=5)
+    5
+    >>> min([6], default=5)
+    6
+    """
+    return _wrapreduction(a, np.minimum, 'min', axis, None, out,
+                          keepdims=keepdims, initial=initial, where=where)
+
+
+@array_function_dispatch(_min_dispatcher)
+def amin(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
+         where=np._NoValue):
+    """
+    Return the minimum of an array or minimum along an axis.
+
+    `amin` is an alias of `~numpy.min`.
+
+    See Also
+    --------
+    min : alias of this function
+    ndarray.min : equivalent method
+    """
+    return _wrapreduction(a, np.minimum, 'min', axis, None, out,
+                          keepdims=keepdims, initial=initial, where=where)
+
+
+def _prod_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
+                     initial=None, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_prod_dispatcher)
+def prod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
+         initial=np._NoValue, where=np._NoValue):
+    """
+    Return the product of array elements over a given axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which a product is performed.  The default,
+        axis=None, will calculate the product of all the elements in the
+        input array. If axis is negative it counts from the last to the
+        first axis.
+
+        .. versionadded:: 1.7.0
+
+        If axis is a tuple of ints, a product is performed on all of the
+        axes specified in the tuple instead of a single axis or all the
+        axes as before.
+    dtype : dtype, optional
+        The type of the returned array, as well as of the accumulator in
+        which the elements are multiplied.  The dtype of `a` is used by
+        default unless `a` has an integer dtype of less precision than the
+        default platform integer.  In that case, if `a` is signed then the
+        platform integer is used while if `a` is unsigned then an unsigned
+        integer of the same precision as the platform integer is used.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must have
+        the same shape as the expected output, but the type of the output
+        values will be cast if necessary.
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left in the
+        result as dimensions with size one. With this option, the result
+        will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `prod` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+    initial : scalar, optional
+        The starting value for this product. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.15.0
+
+    where : array_like of bool, optional
+        Elements to include in the product. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.17.0
+
+    Returns
+    -------
+    product_along_axis : ndarray, see `dtype` parameter above.
+        An array shaped as `a` but with the specified axis removed.
+        Returns a reference to `out` if specified.
+
+    See Also
+    --------
+    ndarray.prod : equivalent method
+    :ref:`ufuncs-output-type`
+
+    Notes
+    -----
+    Arithmetic is modular when using integer types, and no error is
+    raised on overflow.  That means that, on a 32-bit platform:
+
+    >>> x = np.array([536870910, 536870910, 536870910, 536870910])
+    >>> np.prod(x)
+    16 # may vary
+
+    The product of an empty array is the neutral element 1:
+
+    >>> np.prod([])
+    1.0
+
+    Examples
+    --------
+    By default, calculate the product of all elements:
+
+    >>> np.prod([1.,2.])
+    2.0
+
+    Even when the input array is two-dimensional:
+
+    >>> a = np.array([[1., 2.], [3., 4.]])
+    >>> np.prod(a)
+    24.0
+
+    But we can also specify the axis over which to multiply:
+
+    >>> np.prod(a, axis=1)
+    array([  2.,  12.])
+    >>> np.prod(a, axis=0)
+    array([3., 8.])
+    
+    Or select specific elements to include:
+
+    >>> np.prod([1., np.nan, 3.], where=[True, False, True])
+    3.0
+
+    If the type of `x` is unsigned, then the output type is
+    the unsigned platform integer:
+
+    >>> x = np.array([1, 2, 3], dtype=np.uint8)
+    >>> np.prod(x).dtype == np.uint
+    True
+
+    If `x` is of a signed integer type, then the output type
+    is the default platform integer:
+
+    >>> x = np.array([1, 2, 3], dtype=np.int8)
+    >>> np.prod(x).dtype == int
+    True
+
+    You can also start the product with a value other than one:
+
+    >>> np.prod([1, 2], initial=5)
+    10
+    """
+    return _wrapreduction(a, np.multiply, 'prod', axis, dtype, out,
+                          keepdims=keepdims, initial=initial, where=where)
+
+
+def _cumprod_dispatcher(a, axis=None, dtype=None, out=None):
+    return (a, out)
+
+
+@array_function_dispatch(_cumprod_dispatcher)
+def cumprod(a, axis=None, dtype=None, out=None):
+    """
+    Return the cumulative product of elements along a given axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int, optional
+        Axis along which the cumulative product is computed.  By default
+        the input is flattened.
+    dtype : dtype, optional
+        Type of the returned array, as well as of the accumulator in which
+        the elements are multiplied.  If *dtype* is not specified, it
+        defaults to the dtype of `a`, unless `a` has an integer dtype with
+        a precision less than that of the default platform integer.  In
+        that case, the default platform integer is used instead.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must
+        have the same shape and buffer length as the expected output
+        but the type of the resulting values will be cast if necessary.
+
+    Returns
+    -------
+    cumprod : ndarray
+        A new array holding the result is returned unless `out` is
+        specified, in which case a reference to out is returned.
+
+    See Also
+    --------
+    :ref:`ufuncs-output-type`
+
+    Notes
+    -----
+    Arithmetic is modular when using integer types, and no error is
+    raised on overflow.
+
+    Examples
+    --------
+    >>> a = np.array([1,2,3])
+    >>> np.cumprod(a) # intermediate results 1, 1*2
+    ...               # total product 1*2*3 = 6
+    array([1, 2, 6])
+    >>> a = np.array([[1, 2, 3], [4, 5, 6]])
+    >>> np.cumprod(a, dtype=float) # specify type of output
+    array([   1.,    2.,    6.,   24.,  120.,  720.])
+
+    The cumulative product for each column (i.e., over the rows) of `a`:
+
+    >>> np.cumprod(a, axis=0)
+    array([[ 1,  2,  3],
+           [ 4, 10, 18]])
+
+    The cumulative product for each row (i.e. over the columns) of `a`:
+
+    >>> np.cumprod(a,axis=1)
+    array([[  1,   2,   6],
+           [  4,  20, 120]])
+
+    """
+    return _wrapfunc(a, 'cumprod', axis=axis, dtype=dtype, out=out)
+
+
+def _ndim_dispatcher(a):
+    return (a,)
+
+
+@array_function_dispatch(_ndim_dispatcher)
+def ndim(a):
+    """
+    Return the number of dimensions of an array.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.  If it is not already an ndarray, a conversion is
+        attempted.
+
+    Returns
+    -------
+    number_of_dimensions : int
+        The number of dimensions in `a`.  Scalars are zero-dimensional.
+
+    See Also
+    --------
+    ndarray.ndim : equivalent method
+    shape : dimensions of array
+    ndarray.shape : dimensions of array
+
+    Examples
+    --------
+    >>> np.ndim([[1,2,3],[4,5,6]])
+    2
+    >>> np.ndim(np.array([[1,2,3],[4,5,6]]))
+    2
+    >>> np.ndim(1)
+    0
+
+    """
+    try:
+        return a.ndim
+    except AttributeError:
+        return asarray(a).ndim
+
+
+def _size_dispatcher(a, axis=None):
+    return (a,)
+
+
+@array_function_dispatch(_size_dispatcher)
+def size(a, axis=None):
+    """
+    Return the number of elements along a given axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : int, optional
+        Axis along which the elements are counted.  By default, give
+        the total number of elements.
+
+    Returns
+    -------
+    element_count : int
+        Number of elements along the specified axis.
+
+    See Also
+    --------
+    shape : dimensions of array
+    ndarray.shape : dimensions of array
+    ndarray.size : number of elements in array
+
+    Examples
+    --------
+    >>> a = np.array([[1,2,3],[4,5,6]])
+    >>> np.size(a)
+    6
+    >>> np.size(a,1)
+    3
+    >>> np.size(a,0)
+    2
+
+    """
+    if axis is None:
+        try:
+            return a.size
+        except AttributeError:
+            return asarray(a).size
+    else:
+        try:
+            return a.shape[axis]
+        except AttributeError:
+            return asarray(a).shape[axis]
+
+
+def _round_dispatcher(a, decimals=None, out=None):
+    return (a, out)
+
+
+@array_function_dispatch(_round_dispatcher)
+def round(a, decimals=0, out=None):
+    """
+    Evenly round to the given number of decimals.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    decimals : int, optional
+        Number of decimal places to round to (default: 0).  If
+        decimals is negative, it specifies the number of positions to
+        the left of the decimal point.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must have
+        the same shape as the expected output, but the type of the output
+        values will be cast if necessary. See :ref:`ufuncs-output-type` for more
+        details.
+
+    Returns
+    -------
+    rounded_array : ndarray
+        An array of the same type as `a`, containing the rounded values.
+        Unless `out` was specified, a new array is created.  A reference to
+        the result is returned.
+
+        The real and imaginary parts of complex numbers are rounded
+        separately.  The result of rounding a float is a float.
+
+    See Also
+    --------
+    ndarray.round : equivalent method
+    around : an alias for this function
+    ceil, fix, floor, rint, trunc
+
+
+    Notes
+    -----
+    For values exactly halfway between rounded decimal values, NumPy
+    rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0,
+    -0.5 and 0.5 round to 0.0, etc.
+
+    ``np.round`` uses a fast but sometimes inexact algorithm to round
+    floating-point datatypes. For positive `decimals` it is equivalent to
+    ``np.true_divide(np.rint(a * 10**decimals), 10**decimals)``, which has
+    error due to the inexact representation of decimal fractions in the IEEE
+    floating point standard [1]_ and errors introduced when scaling by powers
+    of ten. For instance, note the extra "1" in the following:
+
+        >>> np.round(56294995342131.5, 3)
+        56294995342131.51
+
+    If your goal is to print such values with a fixed number of decimals, it is
+    preferable to use numpy's float printing routines to limit the number of
+    printed decimals:
+
+        >>> np.format_float_positional(56294995342131.5, precision=3)
+        '56294995342131.5'
+
+    The float printing routines use an accurate but much more computationally
+    demanding algorithm to compute the number of digits after the decimal
+    point.
+
+    Alternatively, Python's builtin `round` function uses a more accurate
+    but slower algorithm for 64-bit floating point values:
+
+        >>> round(56294995342131.5, 3)
+        56294995342131.5
+        >>> np.round(16.055, 2), round(16.055, 2)  # equals 16.0549999999999997
+        (16.06, 16.05)
+
+
+    References
+    ----------
+    .. [1] "Lecture Notes on the Status of IEEE 754", William Kahan,
+           https://people.eecs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF
+
+    Examples
+    --------
+    >>> np.round([0.37, 1.64])
+    array([0., 2.])
+    >>> np.round([0.37, 1.64], decimals=1)
+    array([0.4, 1.6])
+    >>> np.round([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value
+    array([0., 2., 2., 4., 4.])
+    >>> np.round([1,2,3,11], decimals=1) # ndarray of ints is returned
+    array([ 1,  2,  3, 11])
+    >>> np.round([1,2,3,11], decimals=-1)
+    array([ 0,  0,  0, 10])
+
+    """
+    return _wrapfunc(a, 'round', decimals=decimals, out=out)
+
+
+@array_function_dispatch(_round_dispatcher)
+def around(a, decimals=0, out=None):
+    """
+    Round an array to the given number of decimals.
+
+    `around` is an alias of `~numpy.round`.
+
+    See Also
+    --------
+    ndarray.round : equivalent method
+    round : alias for this function
+    ceil, fix, floor, rint, trunc
+
+    """
+    return _wrapfunc(a, 'round', decimals=decimals, out=out)
+
+
+def _mean_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None, *,
+                     where=None):
+    return (a, where, out)
+
+
+@array_function_dispatch(_mean_dispatcher)
+def mean(a, axis=None, dtype=None, out=None, keepdims=np._NoValue, *,
+         where=np._NoValue):
+    """
+    Compute the arithmetic mean along the specified axis.
+
+    Returns the average of the array elements.  The average is taken over
+    the flattened array by default, otherwise over the specified axis.
+    `float64` intermediate and return values are used for integer inputs.
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose mean is desired. If `a` is not an
+        array, a conversion is attempted.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which the means are computed. The default is to
+        compute the mean of the flattened array.
+
+        .. versionadded:: 1.7.0
+
+        If this is a tuple of ints, a mean is performed over multiple axes,
+        instead of a single axis or all the axes as before.
+    dtype : data-type, optional
+        Type to use in computing the mean.  For integer inputs, the default
+        is `float64`; for floating point inputs, it is the same as the
+        input dtype.
+    out : ndarray, optional
+        Alternate output array in which to place the result.  The default
+        is ``None``; if provided, it must have the same shape as the
+        expected output, but the type will be cast if necessary.
+        See :ref:`ufuncs-output-type` for more details.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `mean` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    where : array_like of bool, optional
+        Elements to include in the mean. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    m : ndarray, see dtype parameter above
+        If `out=None`, returns a new array containing the mean values,
+        otherwise a reference to the output array is returned.
+
+    See Also
+    --------
+    average : Weighted average
+    std, var, nanmean, nanstd, nanvar
+
+    Notes
+    -----
+    The arithmetic mean is the sum of the elements along the axis divided
+    by the number of elements.
+
+    Note that for floating-point input, the mean is computed using the
+    same precision the input has.  Depending on the input data, this can
+    cause the results to be inaccurate, especially for `float32` (see
+    example below).  Specifying a higher-precision accumulator using the
+    `dtype` keyword can alleviate this issue.
+
+    By default, `float16` results are computed using `float32` intermediates
+    for extra precision.
+
+    Examples
+    --------
+    >>> a = np.array([[1, 2], [3, 4]])
+    >>> np.mean(a)
+    2.5
+    >>> np.mean(a, axis=0)
+    array([2., 3.])
+    >>> np.mean(a, axis=1)
+    array([1.5, 3.5])
+
+    In single precision, `mean` can be inaccurate:
+
+    >>> a = np.zeros((2, 512*512), dtype=np.float32)
+    >>> a[0, :] = 1.0
+    >>> a[1, :] = 0.1
+    >>> np.mean(a)
+    0.54999924
+
+    Computing the mean in float64 is more accurate:
+
+    >>> np.mean(a, dtype=np.float64)
+    0.55000000074505806 # may vary
+
+    Specifying a where argument:
+
+    >>> a = np.array([[5, 9, 13], [14, 10, 12], [11, 15, 19]])
+    >>> np.mean(a)
+    12.0
+    >>> np.mean(a, where=[[True], [False], [False]])
+    9.0
+
+    """
+    kwargs = {}
+    if keepdims is not np._NoValue:
+        kwargs['keepdims'] = keepdims
+    if where is not np._NoValue:
+        kwargs['where'] = where
+    if type(a) is not mu.ndarray:
+        try:
+            mean = a.mean
+        except AttributeError:
+            pass
+        else:
+            return mean(axis=axis, dtype=dtype, out=out, **kwargs)
+
+    return _methods._mean(a, axis=axis, dtype=dtype,
+                          out=out, **kwargs)
+
+
+def _std_dispatcher(a, axis=None, dtype=None, out=None, ddof=None,
+                    keepdims=None, *, where=None):
+    return (a, where, out)
+
+
+@array_function_dispatch(_std_dispatcher)
+def std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue, *,
+        where=np._NoValue):
+    """
+    Compute the standard deviation along the specified axis.
+
+    Returns the standard deviation, a measure of the spread of a distribution,
+    of the array elements. The standard deviation is computed for the
+    flattened array by default, otherwise over the specified axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Calculate the standard deviation of these values.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which the standard deviation is computed. The
+        default is to compute the standard deviation of the flattened array.
+
+        .. versionadded:: 1.7.0
+
+        If this is a tuple of ints, a standard deviation is performed over
+        multiple axes, instead of a single axis or all the axes as before.
+    dtype : dtype, optional
+        Type to use in computing the standard deviation. For arrays of
+        integer type the default is float64, for arrays of float types it is
+        the same as the array type.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must have
+        the same shape as the expected output but the type (of the calculated
+        values) will be cast if necessary.
+    ddof : int, optional
+        Means Delta Degrees of Freedom.  The divisor used in calculations
+        is ``N - ddof``, where ``N`` represents the number of elements.
+        By default `ddof` is zero.
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `std` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    where : array_like of bool, optional
+        Elements to include in the standard deviation.
+        See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    standard_deviation : ndarray, see dtype parameter above.
+        If `out` is None, return a new array containing the standard deviation,
+        otherwise return a reference to the output array.
+
+    See Also
+    --------
+    var, mean, nanmean, nanstd, nanvar
+    :ref:`ufuncs-output-type`
+
+    Notes
+    -----
+    The standard deviation is the square root of the average of the squared
+    deviations from the mean, i.e., ``std = sqrt(mean(x))``, where
+    ``x = abs(a - a.mean())**2``.
+
+    The average squared deviation is typically calculated as ``x.sum() / N``,
+    where ``N = len(x)``. If, however, `ddof` is specified, the divisor
+    ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1``
+    provides an unbiased estimator of the variance of the infinite population.
+    ``ddof=0`` provides a maximum likelihood estimate of the variance for
+    normally distributed variables. The standard deviation computed in this
+    function is the square root of the estimated variance, so even with
+    ``ddof=1``, it will not be an unbiased estimate of the standard deviation
+    per se.
+
+    Note that, for complex numbers, `std` takes the absolute
+    value before squaring, so that the result is always real and nonnegative.
+
+    For floating-point input, the *std* is computed using the same
+    precision the input has. Depending on the input data, this can cause
+    the results to be inaccurate, especially for float32 (see example below).
+    Specifying a higher-accuracy accumulator using the `dtype` keyword can
+    alleviate this issue.
+
+    Examples
+    --------
+    >>> a = np.array([[1, 2], [3, 4]])
+    >>> np.std(a)
+    1.1180339887498949 # may vary
+    >>> np.std(a, axis=0)
+    array([1.,  1.])
+    >>> np.std(a, axis=1)
+    array([0.5,  0.5])
+
+    In single precision, std() can be inaccurate:
+
+    >>> a = np.zeros((2, 512*512), dtype=np.float32)
+    >>> a[0, :] = 1.0
+    >>> a[1, :] = 0.1
+    >>> np.std(a)
+    0.45000005
+
+    Computing the standard deviation in float64 is more accurate:
+
+    >>> np.std(a, dtype=np.float64)
+    0.44999999925494177 # may vary
+
+    Specifying a where argument:
+
+    >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])
+    >>> np.std(a)
+    2.614064523559687 # may vary
+    >>> np.std(a, where=[[True], [True], [False]])
+    2.0
+
+    """
+    kwargs = {}
+    if keepdims is not np._NoValue:
+        kwargs['keepdims'] = keepdims
+    if where is not np._NoValue:
+        kwargs['where'] = where
+    if type(a) is not mu.ndarray:
+        try:
+            std = a.std
+        except AttributeError:
+            pass
+        else:
+            return std(axis=axis, dtype=dtype, out=out, ddof=ddof, **kwargs)
+
+    return _methods._std(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
+                         **kwargs)
+
+
+def _var_dispatcher(a, axis=None, dtype=None, out=None, ddof=None,
+                    keepdims=None, *, where=None):
+    return (a, where, out)
+
+
+@array_function_dispatch(_var_dispatcher)
+def var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue, *,
+        where=np._NoValue):
+    """
+    Compute the variance along the specified axis.
+
+    Returns the variance of the array elements, a measure of the spread of a
+    distribution.  The variance is computed for the flattened array by
+    default, otherwise over the specified axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose variance is desired.  If `a` is not an
+        array, a conversion is attempted.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which the variance is computed.  The default is to
+        compute the variance of the flattened array.
+
+        .. versionadded:: 1.7.0
+
+        If this is a tuple of ints, a variance is performed over multiple axes,
+        instead of a single axis or all the axes as before.
+    dtype : data-type, optional
+        Type to use in computing the variance.  For arrays of integer type
+        the default is `float64`; for arrays of float types it is the same as
+        the array type.
+    out : ndarray, optional
+        Alternate output array in which to place the result.  It must have
+        the same shape as the expected output, but the type is cast if
+        necessary.
+    ddof : int, optional
+        "Delta Degrees of Freedom": the divisor used in the calculation is
+        ``N - ddof``, where ``N`` represents the number of elements. By
+        default `ddof` is zero.
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `var` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    where : array_like of bool, optional
+        Elements to include in the variance. See `~numpy.ufunc.reduce` for
+        details.
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    variance : ndarray, see dtype parameter above
+        If ``out=None``, returns a new array containing the variance;
+        otherwise, a reference to the output array is returned.
+
+    See Also
+    --------
+    std, mean, nanmean, nanstd, nanvar
+    :ref:`ufuncs-output-type`
+
+    Notes
+    -----
+    The variance is the average of the squared deviations from the mean,
+    i.e.,  ``var = mean(x)``, where ``x = abs(a - a.mean())**2``.
+
+    The mean is typically calculated as ``x.sum() / N``, where ``N = len(x)``.
+    If, however, `ddof` is specified, the divisor ``N - ddof`` is used
+    instead.  In standard statistical practice, ``ddof=1`` provides an
+    unbiased estimator of the variance of a hypothetical infinite population.
+    ``ddof=0`` provides a maximum likelihood estimate of the variance for
+    normally distributed variables.
+
+    Note that for complex numbers, the absolute value is taken before
+    squaring, so that the result is always real and nonnegative.
+
+    For floating-point input, the variance is computed using the same
+    precision the input has.  Depending on the input data, this can cause
+    the results to be inaccurate, especially for `float32` (see example
+    below).  Specifying a higher-accuracy accumulator using the ``dtype``
+    keyword can alleviate this issue.
+
+    Examples
+    --------
+    >>> a = np.array([[1, 2], [3, 4]])
+    >>> np.var(a)
+    1.25
+    >>> np.var(a, axis=0)
+    array([1.,  1.])
+    >>> np.var(a, axis=1)
+    array([0.25,  0.25])
+
+    In single precision, var() can be inaccurate:
+
+    >>> a = np.zeros((2, 512*512), dtype=np.float32)
+    >>> a[0, :] = 1.0
+    >>> a[1, :] = 0.1
+    >>> np.var(a)
+    0.20250003
+
+    Computing the variance in float64 is more accurate:
+
+    >>> np.var(a, dtype=np.float64)
+    0.20249999932944759 # may vary
+    >>> ((1-0.55)**2 + (0.1-0.55)**2)/2
+    0.2025
+
+    Specifying a where argument:
+
+    >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])
+    >>> np.var(a)
+    6.833333333333333 # may vary
+    >>> np.var(a, where=[[True], [True], [False]])
+    4.0
+
+    """
+    kwargs = {}
+    if keepdims is not np._NoValue:
+        kwargs['keepdims'] = keepdims
+    if where is not np._NoValue:
+        kwargs['where'] = where
+
+    if type(a) is not mu.ndarray:
+        try:
+            var = a.var
+
+        except AttributeError:
+            pass
+        else:
+            return var(axis=axis, dtype=dtype, out=out, ddof=ddof, **kwargs)
+
+    return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
+                         **kwargs)
+
+
+# Aliases of other functions. Provided unique docstrings 
+# are for reference purposes only. Wherever possible,
+# avoid using them.
+
+
+def _round__dispatcher(a, decimals=None, out=None):
+    # 2023-02-28, 1.25.0
+    warnings.warn("`round_` is deprecated as of NumPy 1.25.0, and will be "
+                  "removed in NumPy 2.0. Please use `round` instead.",
+                  DeprecationWarning, stacklevel=3)
+    return (a, out)
+
+
+@array_function_dispatch(_round__dispatcher)
+def round_(a, decimals=0, out=None):
+    """
+    Round an array to the given number of decimals.
+
+    `~numpy.round_` is a disrecommended backwards-compatibility
+    alias of `~numpy.around` and `~numpy.round`.
+
+    .. deprecated:: 1.25.0
+        ``round_`` is deprecated as of NumPy 1.25.0, and will be
+        removed in NumPy 2.0. Please use `round` instead.
+
+    See Also
+    --------
+    around : equivalent function; see for details.
+    """
+    return around(a, decimals=decimals, out=out)
+
+
+def _product_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
+                        initial=None, where=None):
+    # 2023-03-02, 1.25.0
+    warnings.warn("`product` is deprecated as of NumPy 1.25.0, and will be "
+                  "removed in NumPy 2.0. Please use `prod` instead.",
+                  DeprecationWarning, stacklevel=3)
+    return (a, out)
+
+
+@array_function_dispatch(_product_dispatcher, verify=False)
+def product(*args, **kwargs):
+    """
+    Return the product of array elements over a given axis.
+
+    .. deprecated:: 1.25.0
+        ``product`` is deprecated as of NumPy 1.25.0, and will be
+        removed in NumPy 2.0. Please use `prod` instead.
+
+    See Also
+    --------
+    prod : equivalent function; see for details.
+    """
+    return prod(*args, **kwargs)
+
+
+def _cumproduct_dispatcher(a, axis=None, dtype=None, out=None):
+    # 2023-03-02, 1.25.0
+    warnings.warn("`cumproduct` is deprecated as of NumPy 1.25.0, and will be "
+                  "removed in NumPy 2.0. Please use `cumprod` instead.",
+                  DeprecationWarning, stacklevel=3)
+    return (a, out)
+
+
+@array_function_dispatch(_cumproduct_dispatcher, verify=False)
+def cumproduct(*args, **kwargs):
+    """
+    Return the cumulative product over the given axis.
+
+    .. deprecated:: 1.25.0
+        ``cumproduct`` is deprecated as of NumPy 1.25.0, and will be
+        removed in NumPy 2.0. Please use `cumprod` instead.
+
+    See Also
+    --------
+    cumprod : equivalent function; see for details.
+    """
+    return cumprod(*args, **kwargs)
+
+
+def _sometrue_dispatcher(a, axis=None, out=None, keepdims=None, *,
+                         where=np._NoValue):
+    # 2023-03-02, 1.25.0
+    warnings.warn("`sometrue` is deprecated as of NumPy 1.25.0, and will be "
+                  "removed in NumPy 2.0. Please use `any` instead.",
+                  DeprecationWarning, stacklevel=3)
+    return (a, where, out)
+
+
+@array_function_dispatch(_sometrue_dispatcher, verify=False)
+def sometrue(*args, **kwargs):
+    """
+    Check whether some values are true.
+
+    Refer to `any` for full documentation.
+
+    .. deprecated:: 1.25.0
+        ``sometrue`` is deprecated as of NumPy 1.25.0, and will be
+        removed in NumPy 2.0. Please use `any` instead.
+
+    See Also
+    --------
+    any : equivalent function; see for details.
+    """
+    return any(*args, **kwargs)
+
+
+def _alltrue_dispatcher(a, axis=None, out=None, keepdims=None, *, where=None):
+    # 2023-03-02, 1.25.0
+    warnings.warn("`alltrue` is deprecated as of NumPy 1.25.0, and will be "
+                  "removed in NumPy 2.0. Please use `all` instead.",
+                  DeprecationWarning, stacklevel=3)
+    return (a, where, out)
+
+
+@array_function_dispatch(_alltrue_dispatcher, verify=False)
+def alltrue(*args, **kwargs):
+    """
+    Check if all elements of input array are true.
+
+    .. deprecated:: 1.25.0
+        ``alltrue`` is deprecated as of NumPy 1.25.0, and will be
+        removed in NumPy 2.0. Please use `all` instead.
+
+    See Also
+    --------
+    numpy.all : Equivalent function; see for details.
+    """
+    return all(*args, **kwargs)