Enumerations
enum class	xt::quantile_method { xt::quantile_method::interpolated_inverted_cdf = 4 , xt::quantile_method::hazen , xt::quantile_method::weibull , xt::quantile_method::linear , xt::quantile_method::median_unbiased , xt::quantile_method::normal_unbiased }
	Quantile interpolation method. More...

Functions
template<class E >
auto	xt::sort (const xexpression< E > &e, std::ptrdiff_t axis=-1)
	Sort xexpression (optionally along axis) The sort is performed using the `std::sort` functions.

template<class E >
auto	xt::argsort (const xexpression< E > &e, std::ptrdiff_t axis=-1, sorting_method method=sorting_method::quick)
	Argsort xexpression (optionally along axis) Performs an indirect sort along the given axis.

template<class E , class C , class R = detail::flatten_sort_result_type_t<E>, class = std::enable_if_t<!xtl::is_integral<C>::value, int>>
R	xt::partition (const xexpression< E > &e, C kth_container, placeholders::xtuph)
	Partially sort xexpression.

template<class E , class C , class R = typename detail::linear_argsort_result_type<typename detail::sort_eval_type<E>::type>::type, class = std::enable_if_t<!xtl::is_integral<C>::value, int>>
R	xt::argpartition (const xexpression< E > &e, C kth_container, placeholders::xtuph)
	Partially sort arguments.

template<class T = double, class E , class P >
auto	xt::quantile (E &&e, const P &probas, std::ptrdiff_t axis, T alpha, T beta)
	Compute quantiles over the given axis.

template<class T = double, class E , class P >
auto	xt::quantile (E &&e, const P &probas, T alpha, T beta)
	Compute quantiles of the whole expression.

template<class T = double, class E , class P >
auto	xt::quantile (E &&e, const P &probas, std::ptrdiff_t axis, quantile_method method=quantile_method::linear)
	Compute quantiles over the given axis.

template<class T = double, class E , class P >
auto	xt::quantile (E &&e, const P &probas, quantile_method method=quantile_method::linear)
	Compute quantiles of the whole expression.

template<class E >
auto	xt::median (E &&e, std::ptrdiff_t axis)
	Find the median along the specified axis.

template<layout_type L = ::xt::layout_type::row_major, class E >
auto	xt::argmax (const xexpression< E > &e, std::ptrdiff_t axis)
	Find position of maximal value in xexpression By default, the returned index is into the flattened array.

template<class E >
auto	xt::unique (const xexpression< E > &e)
	Find unique elements of a xexpression.

template<class E1 , class E2 >
auto	xt::setdiff1d (const xexpression< E1 > &ar1, const xexpression< E2 > &ar2)
	Find the set difference of two xexpressions.

Detailed Description

Because sorting functions need to access the tensor data repeatedly, they evaluate their input and may allocate temporaries.

Enumeration Type Documentation

◆ quantile_method

enum class xt::quantile_method

strong

Quantile interpolation method.

Predefined methods for interpolating quantiles, as defined in (Hyndman and Fan, 1996).

See also: (Hyndman and Fan, 1996) R. J. Hyndman and Y. Fan, "Sample quantiles in statistical packages", The American Statistician, 50(4), pp. 361-365, 1996; xt::quantile(E&& e, P const& probas, std::ptrdiff_t axis, xt::quantile_method method)

Enumerator
interpolated_inverted_cdf	Method 4 of (Hyndman and Fan, 1996) with `alpha=0` and `beta=1`.
hazen	Method 5 of (Hyndman and Fan, 1996) with `alpha=1/2` and `beta=1/2`.
weibull	Method 6 of (Hyndman and Fan, 1996) with `alpha=0` and `beta=0`.
linear	Method 7 of (Hyndman and Fan, 1996) with `alpha=1` and `beta=1`.
median_unbiased	Method 8 of (Hyndman and Fan, 1996) with `alpha=1/3` and `beta=1/3`.
normal_unbiased	Method 9 of (Hyndman and Fan, 1996) with `alpha=3/8` and `beta=3/8`.

Definition at line 983 of file xsort.hpp.

Function Documentation

◆ argmax()

template<layout_type L = ::xt::layout_type::row_major, class E >

auto xt::argmax	(	const xexpression< E > &	e,
		std::ptrdiff_t	axis )

inline

Find position of maximal value in xexpression By default, the returned index is into the flattened array.

If axis is specified, the indices are along the specified axis.

Parameters

e	input xexpression
axis	select axis (optional)

Returns: returns xarray with positions of maximal value

Definition at line 1295 of file xsort.hpp.

◆ argpartition()

template<class E , class C , class R = typename detail::linear_argsort_result_type<typename detail::sort_eval_type<E>::type>::type, class = std::enable_if_t<!xtl::is_integral<C>::value, int>>

R xt::argpartition	(	const xexpression< E > &	e,
		C	kth_container,
		placeholders::xtuph	)

inline

Partially sort arguments.

Argpartition shuffles the indices to a xexpression in a way so that the index for the kth element in the returned xexpression is in the place it would appear in a sorted array and all elements smaller than this entry are placed (unsorted) before.

The optional third parameter can either be an axis or xnone() in which case the xexpression will be flattened.

This function uses std::nth_element internally.

xt::xarray<float> a = {1, 10, -10, 123};
std::cout << xt::argpartition(a, 0) << std::endl; // {2, 0, 3, 1} the correct entry at index 0
std::cout << xt::argpartition(a, 3) << std::endl; // {0, 1, 2, 3} the correct entry at index 3
std::cout << xt::argpartition(a, {0, 3}) << std::endl; // {2, 0, 1, 3} the correct entries at index 0
and 3 

Parameters

e	input xexpression
kth_container	a container of `indices` that should contain the correctly sorted value
axis	either integer (default = -1) to sort along last axis or `xnone()` to flatten before sorting

Returns: xcontainer with indices of partial sort of input

Definition at line 664 of file xsort.hpp.

◆ argsort()

template<class E >

auto xt::argsort	(	const xexpression< E > &	e,
		std::ptrdiff_t	axis = -1,
		sorting_method	method = sorting_method::quick )

inline

Argsort xexpression (optionally along axis) Performs an indirect sort along the given axis.

Returns an xarray of indices of the same shape as e that index data along the given axis in sorted order.

Parameters

e	xexpression to argsort
axis	axis along which argsort is performed
method	sorting algorithm to use

Returns: argsorted index array

See also: xt::sorting_method

Definition at line 452 of file xsort.hpp.

◆ median()

template<class E >

auto xt::median	(	E &&	e,
		std::ptrdiff_t	axis )

inline

Find the median along the specified axis.

Given a vector V of length N, the median of V is the middle value of a sorted copy of V, V_sorted - i e., V_sorted[(N-1)/2], when N is odd, and the average of the two middle values of V_sorted when N is even.

Parameters

axis	axis along which the medians are computed. If not set, computes the median along a flattened version of the input.
e	input xexpression

Returns: median value

Definition at line 1126 of file xsort.hpp.

◆ partition()

template<class E , class C , class R = detail::flatten_sort_result_type_t<E>, class = std::enable_if_t<!xtl::is_integral<C>::value, int>>

R xt::partition	(	const xexpression< E > &	e,
		C	kth_container,
		placeholders::xtuph	)

inline

Partially sort xexpression.

Partition shuffles the xexpression in a way so that the kth element in the returned xexpression is in the place it would appear in a sorted array and all elements smaller than this entry are placed (unsorted) before.

The optional third parameter can either be an axis or xnone() in which case the xexpression will be flattened.

This function uses std::nth_element internally.

xt::xarray<float> a = {1, 10, -10, 123};
std::cout << xt::partition(a, 0) << std::endl; // {-10, 1, 123, 10} the correct entry at index 0
std::cout << xt::partition(a, 3) << std::endl; // {1, 10, -10, 123} the correct entry at index 3
std::cout << xt::partition(a, {0, 3}) << std::endl; // {-10, 1, 10, 123} the correct entries at index 0
and 3 

Parameters

e	input xexpression
kth_container	a container of `indices` that should contain the correctly sorted value
axis	either integer (default = -1) to sort along last axis or `xnone()` to flatten before sorting

Returns: partially sorted xcontainer

Definition at line 569 of file xsort.hpp.

◆ quantile() [1/4]

template<class T = double, class E , class P >

auto xt::quantile	(	E &&	e,
		const P &	probas,
		quantile_method	method = quantile_method::linear )

inline

Compute quantiles of the whole expression.

The quantiles are computed over the whole expression, as if flatten in a one-dimensional expression. The function takes the name of a predefined method to compute to interpolate between values.

See also: xt::quantile_method; xt::quantile(E&& e, P const& probas, std::ptrdiff_t axis, xt::quantile_method method)

Definition at line 1076 of file xsort.hpp.

◆ quantile() [2/4]

template<class T = double, class E , class P >

auto xt::quantile	(	E &&	e,
		const P &	probas,
		std::ptrdiff_t	axis,
		quantile_method	method = quantile_method::linear )

inline

Compute quantiles over the given axis.

The function takes the name of a predefined method to compute to interpolate between values.

See also: xt::quantile_method; xt::quantile(E&& e, P const& probas, std::ptrdiff_t axis, T alpha, T beta)

Definition at line 1010 of file xsort.hpp.

◆ quantile() [3/4]

template<class T = double, class E , class P >

auto xt::quantile	(	E &&	e,
		const P &	probas,
		std::ptrdiff_t	axis,
		T	alpha,
		T	beta )

inline

Compute quantiles over the given axis.

In a sorted array represneting a distribution of numbers, the quantile of a probability p is the the cut value q such that a fraction p of the distribution is lesser or equal to q. When the cutpoint falls between two elemnts of the sample distribution, a interpolation is computed using the alpha and beta coefficients, as descripted in (Hyndman and Fan, 1996).

The algorithm partially sorts entries in a copy along the axis axis.

Parameters

e	Expression containing the distribution over which the quantiles are computed.
probas	An list of probability associated with each desired quantiles. All elements must be in the range `[0, 1]`.
axis	The dimension in which to compute the quantiles, i.e the axis representing the distribution.
alpha	Interpolation parameter. Must be in the range `[0, 1]]`.
beta	Interpolation parameter. Must be in the range `[0, 1]]`.

Template Parameters

T	The type in which the quantile are computed.

Returns: An expression with as many dimensions as the input e. The first axis correspond to the quantiles. The other axes are the axes that remain after the reduction of e.

See also: (Hyndman and Fan, 1996) R. J. Hyndman and Y. Fan, "Sample quantiles in statistical packages", The American Statistician, 50(4), pp. 361-365, 1996; https://en.wikipedia.org/wiki/Quantile

Definition at line 906 of file xsort.hpp.

◆ quantile() [4/4]

template<class T = double, class E , class P >

auto xt::quantile	(	E &&	e,
		const P &	probas,
		T	alpha,
		T	beta )

inline

Compute quantiles of the whole expression.

The quantiles are computed over the whole expression, as if flatten in a one-dimensional expression.

See also: xt::quantile(E&& e, P const& probas, std::ptrdiff_t axis, T alpha, T beta)

Definition at line 960 of file xsort.hpp.

◆ setdiff1d()

template<class E1 , class E2 >

auto xt::setdiff1d	(	const xexpression< E1 > &	ar1,
		const xexpression< E2 > &	ar2 )

inline

Find the set difference of two xexpressions.

This returns a flattened xtensor with the sorted, unique values in ar1 that are not in ar2.

Parameters

ar1	input xexpression (will be flattened)
ar2	input xexpression

Definition at line 1332 of file xsort.hpp.

◆ sort()

template<class E >

auto xt::sort	(	const xexpression< E > &	e,
		std::ptrdiff_t	axis = -1 )

inline

Sort xexpression (optionally along axis) The sort is performed using the std::sort functions.

A copy of the xexpression is created and returned.

Parameters

e	xexpression to sort
axis	axis along which sort is performed

Returns: sorted array (copy)

Definition at line 255 of file xsort.hpp.

◆ unique()

template<class E >

auto xt::unique ( const xexpression< E > & e )

inline

Find unique elements of a xexpression.

This returns a flattened xtensor with sorted, unique elements from the original expression.

Parameters

e	input xexpression (will be flattened)

Definition at line 1311 of file xsort.hpp.

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ quantile_method

Function Documentation

◆ argmax()

◆ argpartition()

◆ argsort()

◆ median()

◆ partition()

◆ quantile() [1/4]

◆ quantile() [2/4]

◆ quantile() [3/4]

◆ quantile() [4/4]

◆ setdiff1d()

◆ sort()

◆ unique()