numpy.core.fromnumeric

module documentation

Module containing non-deprecated functions borrowed from Numeric.

Variable	`array_function_dispatch`	Undocumented
Function	`_alen_dispathcer`	Undocumented
Function	`_all_dispatcher`	Undocumented
Function	`_amax_dispatcher`	Undocumented
Function	`_amin_dispatcher`	Undocumented
Function	`_any_dispatcher`	Undocumented
Function	`_argmax_dispatcher`	Undocumented
Function	`_argmin_dispatcher`	Undocumented
Function	`_argpartition_dispatcher`	Undocumented
Function	`_argsort_dispatcher`	Undocumented
Function	`_around_dispatcher`	Undocumented
Function	`_choose_dispatcher`	Undocumented
Function	`_clip_dispatcher`	Undocumented
Function	`_compress_dispatcher`	Undocumented
Function	`_cumprod_dispatcher`	Undocumented
Function	`_cumsum_dispatcher`	Undocumented
Function	`_diagonal_dispatcher`	Undocumented
Function	`_mean_dispatcher`	Undocumented
Function	`_ndim_dispatcher`	Undocumented
Function	`_nonzero_dispatcher`	Undocumented
Function	`_partition_dispatcher`	Undocumented
Function	`_prod_dispatcher`	Undocumented
Function	`_ptp_dispatcher`	Undocumented
Function	`_put_dispatcher`	Undocumented
Function	`_ravel_dispatcher`	Undocumented
Function	`_repeat_dispatcher`	Undocumented
Function	`_reshape_dispatcher`	Undocumented
Function	`_resize_dispatcher`	Undocumented
Function	`_searchsorted_dispatcher`	Undocumented
Function	`_shape_dispatcher`	Undocumented
Function	`_size_dispatcher`	Undocumented
Function	`_sort_dispatcher`	Undocumented
Function	`_squeeze_dispatcher`	Undocumented
Function	`_std_dispatcher`	Undocumented
Function	`_sum_dispatcher`	Undocumented
Function	`_swapaxes_dispatcher`	Undocumented
Function	`_take_dispatcher`	Undocumented
Function	`_trace_dispatcher`	Undocumented
Function	`_transpose_dispatcher`	Undocumented
Function	`_var_dispatcher`	Undocumented
Function	`_wrapfunc`	Undocumented
Function	`_wrapit`	Undocumented
Function	`_wrapreduction`	Undocumented
Function	`alen`	Return the length of the first dimension of the input array.
Function	`all`	Test whether all array elements along a given axis evaluate to True.
Function	`alltrue`	Check if all elements of input array are true.
Function	`amax`	Return the maximum of an array or maximum along an axis.
Function	`amin`	Return the minimum of an array or minimum along an axis.
Function	`any`	Test whether any array element along a given axis evaluates to True.
Function	`argmax`	Returns the indices of the maximum values along an axis.
Function	`argmin`	Returns the indices of the minimum values along an axis.
Function	`argpartition`	No summary
Function	`argsort`	Returns the indices that would sort an array.
Function	`around`	Evenly round to the given number of decimals.
Function	`choose`	Construct an array from an index array and a list of arrays to choose from.
Function	`clip`	Clip (limit) the values in an array.
Function	`compress`	Return selected slices of an array along given axis.
Function	`cumprod`	Return the cumulative product of elements along a given axis.
Function	`cumproduct`	Return the cumulative product over the given axis.
Function	`cumsum`	Return the cumulative sum of the elements along a given axis.
Function	`diagonal`	Return specified diagonals.
Function	`mean`	Compute the arithmetic mean along the specified axis.
Function	`ndim`	Return the number of dimensions of an array.
Function	`nonzero`	Return the indices of the elements that are non-zero.
Function	`partition`	Return a partitioned copy of an array.
Function	`prod`	Return the product of array elements over a given axis.
Function	`product`	Return the product of array elements over a given axis.
Function	`ptp`	Range of values (maximum - minimum) along an axis.
Function	`put`	Replaces specified elements of an array with given values.
Function	`ravel`	Return a contiguous flattened array.
Function	`repeat`	Repeat elements of an array.
Function	`reshape`	Gives a new shape to an array without changing its data.
Function	`resize`	Return a new array with the specified shape.
Function	`round_`	Round an array to the given number of decimals.
Function	`searchsorted`	Find indices where elements should be inserted to maintain order.
Function	`shape`	Return the shape of an array.
Function	`size`	Return the number of elements along a given axis.
Function	`sometrue`	Check whether some values are true.
Function	`sort`	Return a sorted copy of an array.
Function	`squeeze`	Remove axes of length one from `a`.
Function	`std`	Compute the standard deviation along the specified axis.
Function	`sum`	Sum of array elements over a given axis.
Function	`swapaxes`	Interchange two axes of an array.
Function	`take`	Take elements from an array along an axis.
Function	`trace`	Return the sum along diagonals of the array.
Function	`transpose`	Reverse or permute the axes of an array; returns the modified array.
Function	`var`	Compute the variance along the specified axis.

array_function_dispatch =

Undocumented

def _alen_dispathcer(a):

Undocumented

def _all_dispatcher(a, axis=None, out=None, keepdims=None, *, where=None):

Undocumented

def _amax_dispatcher(a, axis=None, out=None, keepdims=None, initial=None, where=None):

Undocumented

def _amin_dispatcher(a, axis=None, out=None, keepdims=None, initial=None, where=None):

Undocumented

def _any_dispatcher(a, axis=None, out=None, keepdims=None, *, where=np._NoValue):

Undocumented

def _argmax_dispatcher(a, axis=None, out=None, *, keepdims=np._NoValue):

Undocumented

def _argmin_dispatcher(a, axis=None, out=None, *, keepdims=np._NoValue):

Undocumented

def _argpartition_dispatcher(a, kth, axis=None, kind=None, order=None):

Undocumented

def _argsort_dispatcher(a, axis=None, kind=None, order=None):

Undocumented

def _around_dispatcher(a, decimals=None, out=None):

Undocumented

def _choose_dispatcher(a, choices, out=None, mode=None):

Undocumented

def _clip_dispatcher(a, a_min, a_max, out=None, **kwargs):

Undocumented

def _compress_dispatcher(condition, a, axis=None, out=None):

Undocumented

def _cumprod_dispatcher(a, axis=None, dtype=None, out=None):

Undocumented

def _cumsum_dispatcher(a, axis=None, dtype=None, out=None):

Undocumented

def _diagonal_dispatcher(a, offset=None, axis1=None, axis2=None):

Undocumented

def _mean_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None, *, where=None):

Undocumented

def _ndim_dispatcher(a):

Undocumented

def _nonzero_dispatcher(a):

Undocumented

def _partition_dispatcher(a, kth, axis=None, kind=None, order=None):

Undocumented

def _prod_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None, initial=None, where=None):

Undocumented

def _ptp_dispatcher(a, axis=None, out=None, keepdims=None):

Undocumented

def _put_dispatcher(a, ind, v, mode=None):

Undocumented

def _ravel_dispatcher(a, order=None):

Undocumented

def _repeat_dispatcher(a, repeats, axis=None):

Undocumented

def _reshape_dispatcher(a, newshape, order=None):

Undocumented

def _resize_dispatcher(a, new_shape):

Undocumented

def _searchsorted_dispatcher(a, v, side=None, sorter=None):

Undocumented

def _shape_dispatcher(a):

Undocumented

def _size_dispatcher(a, axis=None):

Undocumented

def _sort_dispatcher(a, axis=None, kind=None, order=None):

Undocumented

def _squeeze_dispatcher(a, axis=None):

Undocumented

def _std_dispatcher(a, axis=None, dtype=None, out=None, ddof=None, keepdims=None, *, where=None):

Undocumented

def _sum_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None, initial=None, where=None):

Undocumented

def _swapaxes_dispatcher(a, axis1, axis2):

Undocumented

def _take_dispatcher(a, indices, axis=None, out=None, mode=None):

Undocumented

def _trace_dispatcher(a, offset=None, axis1=None, axis2=None, dtype=None, out=None):

Undocumented

def _transpose_dispatcher(a, axes=None):

Undocumented

def _var_dispatcher(a, axis=None, dtype=None, out=None, ddof=None, keepdims=None, *, where=None):

Undocumented

def _wrapfunc(obj, method, *args, **kwds):

Undocumented

def _wrapit(obj, method, *args, **kwds):

Undocumented

def _wrapreduction(obj, ufunc, method, axis, dtype, out, **kwargs):

Undocumented

@array_function_dispatch(_alen_dispathcer)
def alen(a):

Return the length of the first dimension of the input array.

Deprecated since version 1.18: numpy.alen is deprecated, use len instead.

Parameters

a : array_like: Input array.

Returns

alen : int: Length of the first dimension of a.

Examples

>>> a = np.zeros((7,4,5))
>>> a.shape[0]
7
>>> np.alen(a)
7

@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.

New in version 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.

New in version 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.

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

@array_function_dispatch(_all_dispatcher, verify=False)
def alltrue(*args, **kwargs):

Check if all elements of input array are true.

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.

New in version 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 amax 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.

New in version 1.15.0.

where : array_like of bool, optional

Elements to compare for the maximum. See ~numpy.ufunc.reduce for details.

New in version 1.17.0.

Returns

amax : ndarray or scalar: Maximum of a. If axis is None, the result is a scalar value. If axis is given, the result is an array of dimension a.ndim - 1.

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 amax for element-wise comparison of 2 arrays; when a.shape[0] is 2, maximum(a[0], a[1]) is faster than amax(a, axis=0).

Examples

>>> a = np.arange(4).reshape((2,2))
>>> a
array([[0, 1],
       [2, 3]])
>>> np.amax(a)           # Maximum of the flattened array
3
>>> np.amax(a, axis=0)   # Maxima along the first axis
array([2, 3])
>>> np.amax(a, axis=1)   # Maxima along the second axis
array([1, 3])
>>> np.amax(a, where=[False, True], initial=-1, axis=0)
array([-1,  3])
>>> b = np.arange(5, dtype=float)
>>> b[2] = np.NaN
>>> np.amax(b)
nan
>>> np.amax(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.amax([[-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.amax([5], initial=6)
6
>>> max([5], default=6)
5

@array_function_dispatch(_amin_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.

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.

New in version 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 amin 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.

New in version 1.15.0.

where : array_like of bool, optional

Elements to compare for the minimum. See ~numpy.ufunc.reduce for details.

New in version 1.17.0.

Returns

amin : ndarray or scalar: Minimum of a. If axis is None, the result is a scalar value. If axis is given, the result is an array of dimension a.ndim - 1.

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 amin for element-wise comparison of 2 arrays; when a.shape[0] is 2, minimum(a[0], a[1]) is faster than amin(a, axis=0).

Examples

>>> a = np.arange(4).reshape((2,2))
>>> a
array([[0, 1],
       [2, 3]])
>>> np.amin(a)           # Minimum of the flattened array
0
>>> np.amin(a, axis=0)   # Minima along the first axis
array([0, 1])
>>> np.amin(a, axis=1)   # Minima along the second axis
array([0, 2])
>>> np.amin(a, where=[False, True], initial=10, axis=0)
array([10,  1])

>>> b = np.arange(5, dtype=float)
>>> b[2] = np.NaN
>>> np.amin(b)
nan
>>> np.amin(b, where=~np.isnan(b), initial=10)
0.0
>>> np.nanmin(b)
0.0

>>> np.amin([[-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.amin([6], initial=5)
5
>>> min([6], default=5)
6

@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 unless axis is not 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.

New in version 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.

New in version 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.

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)

@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.

New in version 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.

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)

@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.

New in version 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.

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)

@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.

New in version 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 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 since version 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=a) always yields the partitioned a, irrespective of dimensionality.

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]])

@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.

Changed in version 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.

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])

@array_function_dispatch(_around_dispatcher)
def around(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.

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.around 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.around([0.37, 1.64])
array([0., 2.])
>>> np.around([0.37, 1.64], decimals=1)
array([0.4, 1.6])
>>> np.around([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value
array([0., 2., 2., 4., 4.])
>>> np.around([1,2,3,11], decimals=1) # ndarray of ints is returned
array([ 1,  2,  3, 11])
>>> np.around([1,2,3,11], decimals=-1)
array([ 0,  0,  0, 10])

@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.

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]]])

@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>`.

New in version 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.

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])

@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.

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])

@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.

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]])

@array_function_dispatch(_cumprod_dispatcher, verify=False)
def cumproduct(*args, **kwargs):

Return the cumulative product over the 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.

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

@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.

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.

@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.

New in version 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.

New in version 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.

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

@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.

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

@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 since version 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.

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]))

@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 it would be in a sorted array. All elements smaller than the k-th element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined.

New in version 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 since version 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.

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([3, 4, 2, 1])
>>> np.partition(a, 3)
array([2, 1, 3, 4])

>>> np.partition(a, (1, 3))
array([1, 2, 3, 4])

@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.

New in version 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.

New in version 1.15.0.

where : array_like of bool, optional

Elements to include in the product. See ~numpy.ufunc.reduce for details.

New in version 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.

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:

>>> np.prod([[1.,2.],[3.,4.]])
24.0

But we can also specify the axis over which to multiply:

>>> np.prod([[1.,2.],[3.,4.]], axis=1)
array([  2.,  12.])

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

@array_function_dispatch(_prod_dispatcher, verify=False)
def product(*args, **kwargs):

Return the product of array elements over a given axis.

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.

New in version 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: A new array holding the result, unless out was specified, in which case a reference to out is returned.

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)

@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.

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])

@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 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.

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.

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])

@array_function_dispatch(_repeat_dispatcher)
def repeat(a, repeats, axis=None):

Repeat elements of an array.

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.

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]])

@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.

Notes

It is not always possible to change the shape of an array without 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 makes the array non-contiguous
>>> b = a.T

# Taking a view makes it possible to modify the shape without modifying
# the initial object.
>>> c = b.view()
>>> c.shape = (20)
Traceback (most recent call last):
   ...
AttributeError: Incompatible shape for in-place modification. Use
`.reshape()` to make a copy with the desired shape.

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]])

@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.

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]])

@array_function_dispatch(_around_dispatcher)
def round_(a, decimals=0, out=None):

Round an array to the given number of decimals.

`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.

New in version 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.

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])

@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.

Examples

>>> np.shape(np.eye(3))
(3, 3)
>>> np.shape([[1, 2]])
(1, 2)
>>> np.shape([0])
(1,)
>>> np.shape(0)
()

>>> a = np.array([(1, 2), (3, 4)], dtype=[('x', 'i4'), ('y', 'i4')])
>>> np.shape(a)
(2,)
>>> a.shape
(2,)

@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.

Examples

>>> a = np.array([[1,2,3],[4,5,6]])
>>> np.size(a)
6
>>> np.size(a,1)
3
>>> np.size(a,0)
2

@array_function_dispatch(_any_dispatcher, verify=False)
def sometrue(*args, **kwargs):

Check whether some values are true.

Refer to any for full documentation.

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.

Changed in version 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.

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.

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.

New in version 1.12.0.

quicksort has been changed to introsort. When sorting does not make enough progress it switches to 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 or 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.

New in version 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. '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).

Changed in version 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')])

@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: New in version 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

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

@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.

New in version 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.

New in version 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.

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

@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.

New in version 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.

New in version 1.15.0.

where : array_like of bool, optional

Elements to include in the sum. See ~numpy.ufunc.reduce for details.

New in version 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.

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

@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]]])

@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.

New in version 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.

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]])

@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.

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)

@array_function_dispatch(_transpose_dispatcher)
def transpose(a, axes=None):

Reverse or permute the axes of an array; returns the modified array.

For an array a with two axes, transpose(a) gives the matrix transpose.

Refer to numpy.ndarray.transpose for full documentation.

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.

Notes

Use transpose(a, argsort(axes)) to invert the transposition of tensors when using the axes keyword argument.

Transposing a 1-D array returns an unchanged view of the original array.

Examples

>>> x = np.arange(4).reshape((2,2))
>>> x
array([[0, 1],
       [2, 3]])

>>> np.transpose(x)
array([[0, 2],
       [1, 3]])

>>> x = np.ones((1, 2, 3))
>>> np.transpose(x, (1, 0, 2)).shape
(2, 1, 3)

>>> x = np.ones((2, 3, 4, 5))
>>> np.transpose(x).shape
(5, 4, 3, 2)

@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.

New in version 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.

New in version 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.

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

numpy.core.fromnumeric

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`numpy.core.fromnumeric`