Merge branch 'master' into ix_-preserve-type

1 files changed, 392 insertions, 273 deletions

diff --git a/numpy/core/fromnumeric.py b/numpy/core/fromnumeric.py
index 58f8696d2..b9cc98cae 100644
--- a/numpy/core/fromnumeric.py
+++ b/numpy/core/fromnumeric.py
@@ -14,7 +14,6 @@ from . import numerictypes as nt
 from .numeric import asarray, array, asanyarray, concatenate
 from . import _methods
 
-
 _dt_ = nt.sctype2char
 
 # functions that are methods
@@ -26,14 +25,9 @@ __all__ = [
     'rank', 'ravel', 'repeat', 'reshape', 'resize', 'round_',
     'searchsorted', 'shape', 'size', 'sometrue', 'sort', 'squeeze',
     'std', 'sum', 'swapaxes', 'take', 'trace', 'transpose', 'var',
-    ]
-
-
-try:
-    _gentype = types.GeneratorType
-except AttributeError:
-    _gentype = type(None)
+]
 
+_gentype = types.GeneratorType
 # save away Python sum
 _sum_ = sum
 
@@ -67,19 +61,54 @@ def _wrapfunc(obj, method, *args, **kwds):
         return _wrapit(obj, method, *args, **kwds)
 
 
+def _wrapreduction(obj, ufunc, method, axis, dtype, out, **kwargs):
+    passkwargs = {}
+    for k, v in kwargs.items():
+        if v is not np._NoValue:
+            passkwargs[k] = v
+
+    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(a, indices, axis=None, out=None, mode='raise'):
     """
     Take elements from an array along an axis.
 
-    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.
+    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
+    a : array_like (Ni..., M, Nk...)
         The source array.
-    indices : array_like
+    indices : array_like (Nj...)
         The indices of the values to extract.
 
         .. versionadded:: 1.8.0
@@ -88,7 +117,7 @@ def take(a, indices, axis=None, out=None, mode='raise'):
     axis : int, optional
         The axis over which to select values. By default, the flattened
         input array is used.
-    out : ndarray, optional
+    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.
     mode : {'raise', 'wrap', 'clip'}, optional
@@ -104,13 +133,31 @@ def take(a, indices, axis=None, out=None, mode='raise'):
 
     Returns
     -------
-    subarray : ndarray
+    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
     --------
@@ -176,11 +223,11 @@ def reshape(a, newshape, order='C'):
     Notes
     -----
     It is not always possible to change the shape of an array without
-    copying the data. If you want an error to be raise if the data is copied,
+    copying the data. If you want an error to be raised when the data is copied,
     you should assign the new shape to the shape attribute of the array::
 
      >>> a = np.zeros((10, 2))
-     # A transpose make the array non-contiguous
+     # A transpose makes the array non-contiguous
      >>> b = a.T
      # Taking a view makes it possible to modify the shape without modifying
      # the initial object.
@@ -432,6 +479,7 @@ def put(a, ind, v, mode='raise'):
     See Also
     --------
     putmask, place
+    put_along_axis : Put elements by matching the array and the index arrays
 
     Examples
     --------
@@ -571,7 +619,7 @@ def partition(a, kth, axis=-1, kind='introselect', order=None):
         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 all elements in the partitions is undefined. If
+        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.
     axis : int or None, optional
@@ -632,8 +680,9 @@ def partition(a, kth, axis=-1, kind='introselect', order=None):
 
     """
     if axis is None:
+        # flatten returns (1, N) for np.matrix, so always use the last axis
         a = asanyarray(a).flatten()
-        axis = 0
+        axis = -1
     else:
         a = asanyarray(a).copy(order="K")
     a.partition(kth, axis=axis, kind=kind, order=order)
@@ -676,7 +725,9 @@ def argpartition(a, kth, axis=-1, kind='introselect', order=None):
     -------
     index_array : ndarray, int
         Array of indices that partition `a` along the specified axis.
-        In other words, ``a[index_array]`` yields a partitioned `a`.
+        If `a` is one-dimensional, ``a[index_array]`` yields a partitioned `a`.
+        More generally, ``np.take_along_axis(a, index_array, axis=a)`` always
+        yields the partitioned `a`, irrespective of dimensionality.
 
     See Also
     --------
@@ -717,7 +768,7 @@ def sort(a, axis=-1, kind='quicksort', order=None):
     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'}, optional
+    kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
         Sorting algorithm. Default is 'quicksort'.
     order : str or list of str, optional
         When `a` is an array with fields defined, this argument specifies
@@ -747,13 +798,13 @@ def sort(a, axis=-1, kind='quicksort', order=None):
     order. The three available algorithms have the following
     properties:
 
-    =========== ======= ============= ============ =======
-       kind      speed   worst case    work space  stable
-    =========== ======= ============= ============ =======
+    =========== ======= ============= ============ ========
+       kind      speed   worst case    work space   stable
+    =========== ======= ============= ============ ========
     'quicksort'    1     O(n^2)            0          no
     'mergesort'    2     O(n*log(n))      ~n/2        yes
     'heapsort'     3     O(n*log(n))       0          no
-    =========== ======= ============= ============ =======
+    =========== ======= ============= ============ ========
 
     All the sort algorithms make temporary copies of the data when
     sorting along any but the last axis.  Consequently, sorting along
@@ -782,6 +833,10 @@ def sort(a, axis=-1, kind='quicksort', order=None):
     heapsort when it does not make enough progress. This makes its
     worst case O(n*log(n)).
 
+    'stable' automatically choses the best stable sorting algorithm
+    for the data type being sorted. It is currently mapped to
+    merge sort.
+
     Examples
     --------
     >>> a = np.array([[1,4],[3,1]])
@@ -815,8 +870,9 @@ def sort(a, axis=-1, kind='quicksort', order=None):
 
     """
     if axis is None:
+        # flatten returns (1, N) for np.matrix, so always use the last axis
         a = asanyarray(a).flatten()
-        axis = 0
+        axis = -1
     else:
         a = asanyarray(a).copy(order="K")
     a.sort(axis=axis, kind=kind, order=order)
@@ -838,7 +894,7 @@ def argsort(a, axis=-1, kind='quicksort', order=None):
     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'}, optional
+    kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
         Sorting algorithm.
     order : str or list of str, optional
         When `a` is an array with fields defined, this argument specifies
@@ -852,6 +908,8 @@ def argsort(a, axis=-1, kind='quicksort', order=None):
     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=a)`` always
+        yields the sorted `a`, irrespective of dimensionality.
 
     See Also
     --------
@@ -882,14 +940,22 @@ def argsort(a, axis=-1, kind='quicksort', order=None):
     array([[0, 3],
            [2, 2]])
 
-    >>> np.argsort(x, axis=0)
+    >>> np.argsort(x, axis=0)  # sorts along first axis (down)
     array([[0, 1],
            [1, 0]])
 
-    >>> np.argsort(x, axis=1)
+    >>> np.argsort(x, axis=1)  # sorts along last axis (across)
     array([[0, 1],
            [0, 1]])
 
+    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')])
@@ -952,11 +1018,19 @@ def argmax(a, axis=None, out=None):
     >>> 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]
+    5
+
     >>> b = np.arange(6)
     >>> b[1] = 5
     >>> b
     array([0, 5, 2, 3, 4, 5])
-    >>> np.argmax(b) # Only the first occurrence is returned.
+    >>> np.argmax(b)  # Only the first occurrence is returned.
     1
 
     """
@@ -1008,11 +1082,19 @@ def argmin(a, axis=None, out=None):
     >>> 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]
+    0
+
     >>> b = np.arange(6)
     >>> b[4] = 0
     >>> b
     array([0, 1, 2, 3, 0, 5])
-    >>> np.argmin(b) # Only the first occurrence is returned.
+    >>> np.argmin(b)  # Only the first occurrence is returned.
     0
 
     """
@@ -1027,6 +1109,15 @@ def searchsorted(a, v, side='left', sorter=None):
     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
@@ -1062,6 +1153,10 @@ def searchsorted(a, v, side='left', sorter=None):
     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 is a faster version of 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)
@@ -1103,6 +1198,16 @@ def resize(a, new_shape):
     --------
     ndarray.resize : resize an array in-place.
 
+    Notes
+    -----
+    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, taken
+    from `a` as they are laid out in memory, disregarding strides and axes.
+    (This is in case the new shape is smaller. For larger, see above.)
+    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]])
@@ -1120,20 +1225,18 @@ def resize(a, new_shape):
         new_shape = (new_shape,)
     a = ravel(a)
     Na = len(a)
-    if not Na:
-        return mu.zeros(new_shape, a.dtype)
     total_size = um.multiply.reduce(new_shape)
+    if Na == 0 or total_size == 0:
+        return mu.zeros(new_shape, a.dtype)
+
     n_copies = int(total_size / Na)
     extra = total_size % Na
 
-    if total_size == 0:
-        return a[:0]
-
     if extra != 0:
-        n_copies = n_copies+1
-        extra = Na-extra
+        n_copies = n_copies + 1
+        extra = Na - extra
 
-    a = concatenate((a,)*n_copies)
+    a = concatenate((a,) * n_copies)
     if extra > 0:
         a = a[:-extra]
 
@@ -1162,6 +1265,16 @@ def squeeze(a, axis=None):
         dimensions of length 1 removed. This is always `a` itself
         or a view into `a`.
 
+    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 singleton dimensions
+    reshape : Insert, remove, and combine dimensions, and resize existing ones
+
     Examples
     --------
     >>> x = np.array([[[0], [1], [2]]])
@@ -1169,7 +1282,13 @@ def squeeze(a, axis=None):
     (1, 3, 1)
     >>> np.squeeze(x).shape
     (3,)
-    >>> np.squeeze(x, axis=(2,)).shape
+    >>> 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)
 
     """
@@ -1177,13 +1296,10 @@ def squeeze(a, axis=None):
         squeeze = a.squeeze
     except AttributeError:
         return _wrapit(a, 'squeeze')
-    try:
-        # First try to use the new axis= parameter
-        return squeeze(axis=axis)
-    except TypeError:
-        # For backwards compatibility
+    if axis is None:
         return squeeze()
-
+    else:
+        return squeeze(axis=axis)
 
 def diagonal(a, offset=0, axis1=0, axis2=1):
     """
@@ -1236,13 +1352,14 @@ def diagonal(a, offset=0, axis1=0, axis2=1):
     Returns
     -------
     array_of_diagonals : ndarray
-        If `a` is 2-D and not a matrix, a 1-D array of the same type as `a`
-        containing the diagonal is returned. If `a` is a matrix, a 1-D
-        array containing the diagonal is returned in order to maintain
-        backward compatibility.  If the dimension of `a` is greater than
-        two, then an array of diagonals is returned, "packed" from
-        left-most dimension to right-most (e.g., if `a` is 3-D, then the
-        diagonals are "packed" along rows).
+        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
     ------
@@ -1396,10 +1513,9 @@ def ravel(a, order='C'):
     Returns
     -------
     y : array_like
-        If `a` is a matrix, y is a 1-D ndarray, otherwise y is an array of
-        the same subtype as `a`. The shape of the returned array is
-        ``(a.size,)``. Matrices are special cased for backward
-        compatibility.
+        y is an 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
     --------
@@ -1509,35 +1625,43 @@ def nonzero(a):
 
     Examples
     --------
-    >>> x = np.eye(3)
+    >>> x = np.array([[3, 0, 0], [0, 4, 0], [5, 6, 0]])
     >>> x
-    array([[ 1.,  0.,  0.],
-           [ 0.,  1.,  0.],
-           [ 0.,  0.,  1.]])
+    array([[3, 0, 0],
+           [0, 4, 0],
+           [5, 6, 0]])
     >>> np.nonzero(x)
-    (array([0, 1, 2]), array([0, 1, 2]))
+    (array([0, 1, 2, 2]), array([0, 1, 0, 1]))
 
     >>> x[np.nonzero(x)]
-    array([ 1.,  1.,  1.])
+    array([3, 4, 5, 6])
     >>> np.transpose(np.nonzero(x))
     array([[0, 0],
            [1, 1],
-           [2, 2]])
+           [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 = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
     >>> a > 3
     array([[False, False, False],
            [ True,  True,  True],
-           [ True,  True,  True]], dtype=bool)
+           [ True,  True,  True]])
     >>> np.nonzero(a > 3)
     (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))
 
-    The ``nonzero`` method of the boolean array can also be called.
+    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]))
@@ -1711,7 +1835,7 @@ def clip(a, a_min, a_max, out=None):
     return _wrapfunc(a, 'clip', a_min, a_max, out=out)
 
 
-def sum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
+def sum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue, initial=np._NoValue):
     """
     Sum of array elements over a given axis.
 
@@ -1748,8 +1872,12 @@ def sum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
         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-classes `sum` method does not implement `keepdims` any
+        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
 
     Returns
     -------
@@ -1797,74 +1925,26 @@ def sum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
     >>> 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
     """
-    kwargs = {}
-    if keepdims is not np._NoValue:
-        kwargs['keepdims'] = keepdims
     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.from_iter(generator)) or the python sum builtin instead.",
+            DeprecationWarning, stacklevel=2)
+
         res = _sum_(a)
         if out is not None:
             out[...] = res
             return out
         return res
-    if type(a) is not mu.ndarray:
-        try:
-            sum = a.sum
-        except AttributeError:
-            pass
-        else:
-            return sum(axis=axis, dtype=dtype, out=out, **kwargs)
-    return _methods._sum(a, axis=axis, dtype=dtype,
-                         out=out, **kwargs)
 
-
-def product(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
-    """
-    Return the product of array elements over a given axis.
-
-    See Also
-    --------
-    prod : equivalent function; see for details.
-
-    """
-    kwargs = {}
-    if keepdims is not np._NoValue:
-        kwargs['keepdims'] = keepdims
-    return um.multiply.reduce(a, axis=axis, dtype=dtype, out=out, **kwargs)
-
-
-def sometrue(a, axis=None, out=None, keepdims=np._NoValue):
-    """
-    Check whether some values are true.
-
-    Refer to `any` for full documentation.
-
-    See Also
-    --------
-    any : equivalent function
-
-    """
-    arr = asanyarray(a)
-    kwargs = {}
-    if keepdims is not np._NoValue:
-        kwargs['keepdims'] = keepdims
-    return arr.any(axis=axis, out=out, **kwargs)
-
-
-def alltrue(a, axis=None, out=None, keepdims=np._NoValue):
-    """
-    Check if all elements of input array are true.
-
-    See Also
-    --------
-    numpy.all : Equivalent function; see for details.
-
-    """
-    arr = asanyarray(a)
-    kwargs = {}
-    if keepdims is not np._NoValue:
-        kwargs['keepdims'] = keepdims
-    return arr.all(axis=axis, out=out, **kwargs)
+    return _wrapreduction(a, np.add, 'sum', axis, dtype, out, keepdims=keepdims,
+                          initial=initial)
 
 
 def any(a, axis=None, out=None, keepdims=np._NoValue):
@@ -1902,7 +1982,7 @@ def any(a, axis=None, out=None, keepdims=np._NoValue):
         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-classes `sum` method does not implement `keepdims` any
+        sub-class' method does not implement `keepdims` any
         exceptions will be raised.
 
     Returns
@@ -1928,7 +2008,7 @@ def any(a, axis=None, out=None, keepdims=np._NoValue):
     True
 
     >>> np.any([[True, False], [False, False]], axis=0)
-    array([ True, False], dtype=bool)
+    array([ True, False])
 
     >>> np.any([-1, 0, 5])
     True
@@ -1939,7 +2019,7 @@ def any(a, axis=None, out=None, keepdims=np._NoValue):
     >>> o=np.array([False])
     >>> z=np.any([-1, 4, 5], out=o)
     >>> z, o
-    (array([ True], dtype=bool), array([ True], dtype=bool))
+    (array([ True]), array([ True]))
     >>> # Check now that z is a reference to o
     >>> z is o
     True
@@ -1947,11 +2027,7 @@ def any(a, axis=None, out=None, keepdims=np._NoValue):
     (191614240, 191614240)
 
     """
-    arr = asanyarray(a)
-    kwargs = {}
-    if keepdims is not np._NoValue:
-        kwargs['keepdims'] = keepdims
-    return arr.any(axis=axis, out=out, **kwargs)
+    return _wrapreduction(a, np.logical_or, 'any', axis, None, out, keepdims=keepdims)
 
 
 def all(a, axis=None, out=None, keepdims=np._NoValue):
@@ -1987,7 +2063,7 @@ def all(a, axis=None, out=None, keepdims=np._NoValue):
         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-classes `sum` method does not implement `keepdims` any
+        sub-class' method does not implement `keepdims` any
         exceptions will be raised.
 
     Returns
@@ -2013,7 +2089,7 @@ def all(a, axis=None, out=None, keepdims=np._NoValue):
     False
 
     >>> np.all([[True,False],[True,True]], axis=0)
-    array([ True, False], dtype=bool)
+    array([ True, False])
 
     >>> np.all([-1, 4, 5])
     True
@@ -2024,14 +2100,10 @@ def all(a, axis=None, out=None, keepdims=np._NoValue):
     >>> o=np.array([False])
     >>> z=np.all([-1, 4, 5], out=o)
     >>> id(z), id(o), z                             # doctest: +SKIP
-    (28293632, 28293632, array([ True], dtype=bool))
+    (28293632, 28293632, array([ True]))
 
     """
-    arr = asanyarray(a)
-    kwargs = {}
-    if keepdims is not np._NoValue:
-        kwargs['keepdims'] = keepdims
-    return arr.all(axis=axis, out=out, **kwargs)
+    return _wrapreduction(a, np.logical_and, 'all', axis, None, out, keepdims=keepdims)
 
 
 def cumsum(a, axis=None, dtype=None, out=None):
@@ -2101,20 +2173,7 @@ def cumsum(a, axis=None, dtype=None, out=None):
     return _wrapfunc(a, 'cumsum', axis=axis, dtype=dtype, out=out)
 
 
-def cumproduct(a, axis=None, dtype=None, out=None):
-    """
-    Return the cumulative product over the given axis.
-
-
-    See Also
-    --------
-    cumprod : equivalent function; see for details.
-
-    """
-    return _wrapfunc(a, 'cumprod', axis=axis, dtype=dtype, out=out)
-
-
-def ptp(a, axis=None, out=None):
+def ptp(a, axis=None, out=None, keepdims=np._NoValue):
     """
     Range of values (maximum - minimum) along an axis.
 
@@ -2124,14 +2183,31 @@ def ptp(a, axis=None, out=None):
     ----------
     a : array_like
         Input values.
-    axis : int, optional
+    axis : None or int or tuple of ints, optional
         Axis along which to find the peaks.  By default, flatten the
-        array.
+        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
@@ -2152,10 +2228,20 @@ def ptp(a, axis=None, out=None):
     array([1, 1])
 
     """
-    return _wrapfunc(a, 'ptp', axis=axis, out=out)
+    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 amax(a, axis=None, out=None, keepdims=np._NoValue):
+def amax(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue):
     """
     Return the maximum of an array or maximum along an axis.
 
@@ -2184,9 +2270,16 @@ def amax(a, axis=None, out=None, keepdims=np._NoValue):
         If the default value is passed, then `keepdims` will not be
         passed through to the `amax` method of sub-classes of
         `ndarray`, however any non-default value will be.  If the
-        sub-classes `sum` method does not implement `keepdims` any
+        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
+
+
     Returns
     -------
     amax : ndarray or scalar
@@ -2232,31 +2325,33 @@ def amax(a, axis=None, out=None, keepdims=np._NoValue):
     >>> np.amax(a, axis=1)   # Maxima along the second axis
     array([1, 3])
 
-    >>> b = np.arange(5, dtype=np.float)
+    >>> b = np.arange(5, dtype=float)
     >>> b[2] = np.NaN
     >>> np.amax(b)
     nan
     >>> np.nanmax(b)
     4.0
 
-    """
-    kwargs = {}
-    if keepdims is not np._NoValue:
-        kwargs['keepdims'] = keepdims
+    You can use an initial value to compute the maximum of an empty slice, or
+    to initialize it to a different value:
 
-    if type(a) is not mu.ndarray:
-        try:
-            amax = a.max
-        except AttributeError:
-            pass
-        else:
-            return amax(axis=axis, out=out, **kwargs)
+    >>> np.max([[-50], [10]], axis=-1, initial=0)
+    array([ 0, 10])
 
-    return _methods._amax(a, axis=axis,
-                          out=out, **kwargs)
+    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)
 
 
-def amin(a, axis=None, out=None, keepdims=np._NoValue):
+def amin(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue):
     """
     Return the minimum of an array or minimum along an axis.
 
@@ -2285,9 +2380,15 @@ def amin(a, axis=None, out=None, keepdims=np._NoValue):
         If the default value is passed, then `keepdims` will not be
         passed through to the `amin` method of sub-classes of
         `ndarray`, however any non-default value will be.  If the
-        sub-classes `sum` method does not implement `keepdims` any
+        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
+
     Returns
     -------
     amin : ndarray or scalar
@@ -2333,27 +2434,29 @@ def amin(a, axis=None, out=None, keepdims=np._NoValue):
     >>> np.amin(a, axis=1)   # Minima along the second axis
     array([0, 2])
 
-    >>> b = np.arange(5, dtype=np.float)
+    >>> b = np.arange(5, dtype=float)
     >>> b[2] = np.NaN
     >>> np.amin(b)
     nan
     >>> np.nanmin(b)
     0.0
 
-    """
-    kwargs = {}
-    if keepdims is not np._NoValue:
-        kwargs['keepdims'] = keepdims
-    if type(a) is not mu.ndarray:
-        try:
-            amin = a.min
-        except AttributeError:
-            pass
-        else:
-            return amin(axis=axis, out=out, **kwargs)
+    >>> np.min([[-50], [10]], axis=-1, initial=0)
+    array([-50,   0])
 
-    return _methods._amin(a, axis=axis,
-                          out=out, **kwargs)
+    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)
 
 
 def alen(a):
@@ -2389,7 +2492,7 @@ def alen(a):
         return len(array(a, ndmin=1))
 
 
-def prod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
+def prod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue, initial=np._NoValue):
     """
     Return the product of array elements over a given axis.
 
@@ -2427,8 +2530,12 @@ def prod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
         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-classes `sum` method does not implement `keepdims` any
+        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
 
     Returns
     -------
@@ -2447,7 +2554,7 @@ def prod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
     raised on overflow.  That means that, on a 32-bit platform:
 
     >>> x = np.array([536870910, 536870910, 536870910, 536870910])
-    >>> np.prod(x) #random
+    >>> np.prod(x)  # random
     16
 
     The product of an empty array is the neutral element 1:
@@ -2483,23 +2590,16 @@ def prod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
     is the default platform integer:
 
     >>> x = np.array([1, 2, 3], dtype=np.int8)
-    >>> np.prod(x).dtype == np.int
+    >>> np.prod(x).dtype == int
     True
 
-    """
-    kwargs = {}
-    if keepdims is not np._NoValue:
-        kwargs['keepdims'] = keepdims
-    if type(a) is not mu.ndarray:
-        try:
-            prod = a.prod
-        except AttributeError:
-            pass
-        else:
-            return prod(axis=axis, dtype=dtype, out=out, **kwargs)
+    You can also start the product with a value other than one:
 
-    return _methods._prod(a, axis=axis, dtype=dtype,
-                          out=out, **kwargs)
+    >>> np.prod([1, 2], initial=5)
+    10
+    """
+    return _wrapreduction(a, np.multiply, 'prod', axis, dtype, out, keepdims=keepdims,
+                          initial=initial)
 
 
 def cumprod(a, axis=None, dtype=None, out=None):
@@ -2602,62 +2702,6 @@ def ndim(a):
         return asarray(a).ndim
 
 
-def rank(a):
-    """
-    Return the number of dimensions of an array.
-
-    If `a` is not already an array, a conversion is attempted.
-    Scalars are zero dimensional.
-
-    .. note::
-        This function is deprecated in NumPy 1.9 to avoid confusion with
-        `numpy.linalg.matrix_rank`. The ``ndim`` attribute or function
-        should be used instead.
-
-    Parameters
-    ----------
-    a : array_like
-        Array whose number of dimensions is desired. If `a` is not an array,
-        a conversion is attempted.
-
-    Returns
-    -------
-    number_of_dimensions : int
-        The number of dimensions in the array.
-
-    See Also
-    --------
-    ndim : equivalent function
-    ndarray.ndim : equivalent property
-    shape : dimensions of array
-    ndarray.shape : dimensions of array
-
-    Notes
-    -----
-    In the old Numeric package, `rank` was the term used for the number of
-    dimensions, but in NumPy `ndim` is used instead.
-
-    Examples
-    --------
-    >>> np.rank([1,2,3])
-    1
-    >>> np.rank(np.array([[1,2,3],[4,5,6]]))
-    2
-    >>> np.rank(1)
-    0
-
-    """
-    # 2014-04-12, 1.9
-    warnings.warn(
-        "`rank` is deprecated; use the `ndim` attribute or function instead. "
-        "To find the rank of a matrix see `numpy.linalg.matrix_rank`.",
-        VisibleDeprecationWarning, stacklevel=2)
-    try:
-        return a.ndim
-    except AttributeError:
-        return asarray(a).ndim
-
-
 def size(a, axis=None):
     """
     Return the number of elements along a given axis.
@@ -2750,11 +2794,11 @@ def around(a, decimals=0, out=None):
 
     References
     ----------
-    .. [1] "Lecture Notes on the Status of  IEEE 754", William Kahan,
-           http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF
+    .. [1] "Lecture Notes on the Status of IEEE 754", William Kahan,
+           https://people.eecs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF
     .. [2] "How Futile are Mindless Assessments of
            Roundoff in Floating-Point Computation?", William Kahan,
-           http://www.cs.berkeley.edu/~wkahan/Mindless.pdf
+           https://people.eecs.berkeley.edu/~wkahan/Mindless.pdf
 
     Examples
     --------
@@ -2826,7 +2870,7 @@ def mean(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
         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-classes `sum` method does not implement `keepdims` any
+        sub-class' method does not implement `keepdims` any
         exceptions will be raised.
 
     Returns
@@ -2933,7 +2977,7 @@ def std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue):
         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-classes `sum` method does not implement `keepdims` any
+        sub-class' method does not implement `keepdims` any
         exceptions will be raised.
 
     Returns
@@ -3052,7 +3096,7 @@ def var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue):
         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-classes `sum` method does not implement `keepdims` any
+        sub-class' method does not implement `keepdims` any
         exceptions will be raised.
 
     Returns
@@ -3128,3 +3172,78 @@ def var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue):
 
     return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
                          **kwargs)
+
+
+# Aliases of other functions. These have their own definitions only so that
+# they can have unique docstrings.
+
+def product(*args, **kwargs):
+    """
+    Return the product of array elements over a given axis.
+
+    See Also
+    --------
+    prod : equivalent function; see for details.
+    """
+    return prod(*args, **kwargs)
+
+
+def cumproduct(*args, **kwargs):
+    """
+    Return the cumulative product over the given axis.
+
+    See Also
+    --------
+    cumprod : equivalent function; see for details.
+    """
+    return cumprod(*args, **kwargs)
+
+
+def sometrue(*args, **kwargs):
+    """
+    Check whether some values are true.
+
+    Refer to `any` for full documentation.
+
+    See Also
+    --------
+    any : equivalent function; see for details.
+    """
+    return any(*args, **kwargs)
+
+
+def alltrue(*args, **kwargs):
+    """
+    Check if all elements of input array are true.
+
+    See Also
+    --------
+    numpy.all : Equivalent function; see for details.
+    """
+    return all(*args, **kwargs)
+
+
+def rank(a):
+    """
+    Return the number of dimensions of an array.
+
+    .. note::
+        This function is deprecated in NumPy 1.9 to avoid confusion with
+        `numpy.linalg.matrix_rank`. The ``ndim`` attribute or function
+        should be used instead.
+
+    See Also
+    --------
+    ndim : equivalent non-deprecated function
+
+    Notes
+    -----
+    In the old Numeric package, `rank` was the term used for the number of
+    dimensions, but in NumPy `ndim` is used instead.
+    """
+    # 2014-04-12, 1.9
+    warnings.warn(
+        "`rank` is deprecated; use the `ndim` attribute or function instead. "
+        "To find the rank of a matrix see `numpy.linalg.matrix_rank`.",
+        VisibleDeprecationWarning, stacklevel=2)
+    return ndim(a)