toolbox::math Namespace Reference

Functions
template<typename TContainer >
void	check_empty (const TContainer &data, const char *func_name)
	检查容器是否为空并抛出异常/Check if the container is empty and throw an exception
template<typename TContainer >
double	mean (const TContainer &data)
	计算容器中元素的平均值/Compute the mean (average) of elements in a container
template<typename TContainer >
double	median (const TContainer &data)
	计算容器中元素的中位数/Compute the median of elements in a container
template<typename TContainer >
std::vector< typename TContainer::value_type >	mode (const TContainer &data)
	计算容器中元素的众数（可能有多个）/Compute the mode(s) of elements in a container (may be multiple)
template<typename TContainer >
double	variance (const TContainer &data, bool sample_variance=true)
	计算方差（默认样本方差 N-1）/Compute the variance (default is sample variance N-1)
template<typename TContainer >
double	stdev (const TContainer &data, bool sample_stdev=true)
	计算标准差（默认样本标准差）/Compute the standard deviation (default is sample standard deviation)
template<typename TContainer >
TContainer::value_type	sum (const TContainer &data)
	计算容器中元素的总和（返回容器元素类型）/Compute the sum of elements in the container (returns container element type)
template<typename TContainer >
double	sum_d (const TContainer &data)
	计算容器中元素的总和（返回 double 类型以保证精度和范围）/Compute the sum of elements in the container (returns double for precision and range)
template<typename TContainer >
TContainer::value_type	min (const TContainer &data)
	查找容器中的最小值/Find the minimum value in the container
template<typename TContainer >
TContainer::value_type	max (const TContainer &data)
	查找容器中的最大值/Find the maximum value in the container
template<typename TContainer >
TContainer::value_type	range (const TContainer &data)
	计算容器中元素的全距（最大值-最小值）/Compute the range (max - min) of elements in the container
template<typename TContainer >
double	percentile (const TContainer &data, double p)
	计算百分位数（使用最近邻等级法和线性插值）/Compute the percentile (using nearest-rank and linear interpolation)
template<typename TContainer >
std::vector< typename TContainer::value_type >	min_k (const TContainer &data, size_t k)
	返回容器中k个最小的元素，升序排列/Return the k smallest elements in the container, sorted ascending
template<typename TContainer >
std::vector< typename TContainer::value_type >	max_k (const TContainer &data, size_t k)
	返回容器中k个最大的元素，降序排列/Return the k largest elements in the container, sorted descending

Detailed Description

< 用于排序和查找最值/For sorting and finding min/max 用于数学运算/For mathematical operations 用于函数对象/For function objects 用于迭代器操作/For iterator operations 用于映射统计/For map statistics 用于累加/For accumulation 用于异常处理/For exception handling 用于字符串处理/For string handling 用于类型特性/For type traits 用于通用工具/For general utilities 用于动态数组/For dynamic arrays

Function Documentation

check_empty()

template<typename TContainer >

void toolbox::math::check_empty	(	const TContainer &	data,
		const char *	func_name
	)

检查容器是否为空并抛出异常/Check if the container is empty and throw an exception

Template Parameters

TContainer

容器类型/Container type

Parameters

data	输入容器/Input container
func_name	函数名（用于错误信息）/Function name (for error message)

Note

若容器为空则抛出 std::invalid_argument 异常/Throws std::invalid_argument if container is empty

std::vector<int> v;
check_empty(v, "mean"); // 抛出异常/Throws exception

max()

template<typename TContainer >

TContainer::value_type toolbox::math::max

(

const TContainer &

data

)

查找容器中的最大值/Find the maximum value in the container

Template Parameters

TContainer

容器类型，元素需可比较/Container type, elements must be comparable

Parameters

data	输入容器/Input container

Returns

ValueType 最大值/Maximum value

Exceptions

std::invalid_argument

如果容器为空/If the container is empty

std::vector<int> v{3, 1, 2};
int mx = toolbox::math::max(v); // mx == 3

max_k()

template<typename TContainer >

std::vector< typename TContainer::value_type > toolbox::math::max_k	(	const TContainer &	data,
		size_t	k
	)

返回容器中k个最大的元素，降序排列/Return the k largest elements in the container, sorted descending

Template Parameters

TContainer

容器类型，元素需可比较/Container type, elements must be comparable

Parameters

data	输入容器/Input container
k	需要返回的最大元素个数/Number of largest elements to return

Returns

std::vector<ValueType> k个最大元素/k largest elements

Exceptions

std::invalid_argument

如果k>0且容器为空/If k>0 and container is empty

Note

若k为0返回空集合，若k>=容器大小则返回所有元素降序排序/Returns empty if k==0, returns all sorted descending if k>=container size

std::vector<int> v{5, 1, 3, 2, 4};
auto maxs = toolbox::math::max_k(v, 2); // maxs == {5, 4}

mean()

template<typename TContainer >

double toolbox::math::mean

(

const TContainer &

data

)

计算容器中元素的平均值/Compute the mean (average) of elements in a container

Template Parameters

TContainer

容器类型，元素需为算术类型/Container type, elements must be arithmetic

Parameters

data	输入容器/Input container

Returns

double 平均值/Mean value

Exceptions

std::invalid_argument

如果容器为空/If the container is empty

std::vector<int> v{1, 2, 3, 4};
double m = toolbox::math::mean(v); // m == 2.5

median()

template<typename TContainer >

double toolbox::math::median

(

const TContainer &

data

)

计算容器中元素的中位数/Compute the median of elements in a container

Template Parameters

TContainer

容器类型，元素需为算术类型且可比较/Container type, elements must be arithmetic and comparable

Parameters

data	输入容器/Input container

Returns

double 中位数/Median value

Exceptions

std::invalid_argument

如果容器为空/If the container is empty

std::vector<int> v{1, 3, 2};
double med = toolbox::math::median(v); // med == 2

min()

template<typename TContainer >

TContainer::value_type toolbox::math::min

(

const TContainer &

data

)

查找容器中的最小值/Find the minimum value in the container

Template Parameters

TContainer

容器类型，元素需可比较/Container type, elements must be comparable

Parameters

data	输入容器/Input container

Returns

ValueType 最小值/Minimum value

Exceptions

std::invalid_argument

如果容器为空/If the container is empty

std::vector<int> v{3, 1, 2};
int mn = toolbox::math::min(v); // mn == 1

min_k()

template<typename TContainer >

std::vector< typename TContainer::value_type > toolbox::math::min_k	(	const TContainer &	data,
		size_t	k
	)

返回容器中k个最小的元素，升序排列/Return the k smallest elements in the container, sorted ascending

Template Parameters

TContainer

容器类型，元素需可比较/Container type, elements must be comparable

Parameters

data	输入容器/Input container
k	需要返回的最小元素个数/Number of smallest elements to return

Returns

std::vector<ValueType> k个最小元素/k smallest elements

Exceptions

std::invalid_argument

如果k>0且容器为空/If k>0 and container is empty

Note

若k为0返回空集合，若k>=容器大小则返回所有元素排序/Returns empty if k==0, returns all sorted if k>=container size

std::vector<int> v{5, 1, 3, 2, 4};
auto mins = toolbox::math::min_k(v, 3); // mins == {1, 2, 3}

mode()

template<typename TContainer >

std::vector< typename TContainer::value_type > toolbox::math::mode

(

const TContainer &

data

)

计算容器中元素的众数（可能有多个）/Compute the mode(s) of elements in a container (may be multiple)

Template Parameters

TContainer

容器类型，元素需可比较/Container type, elements must be comparable

Parameters

data	输入容器/Input container

Returns

std::vector<typename TContainer::value_type> 众数集合/Vector of mode(s)

Note

若容器为空，返回空集合/Returns empty vector if container is empty

std::vector<int> v{1, 2, 2, 3, 3};
auto modes = toolbox::math::mode(v); // modes == {2, 3}

percentile()

template<typename TContainer >

double toolbox::math::percentile	(	const TContainer &	data,
		double	p
	)

计算百分位数（使用最近邻等级法和线性插值）/Compute the percentile (using nearest-rank and linear interpolation)

Template Parameters

TContainer

容器类型，元素需为算术类型且可比较/Container type, elements must be arithmetic and comparable

Parameters

data	输入容器/Input container
p	百分位，范围[0.0, 1.0]/Percentile, in [0.0, 1.0]

Returns

double 百分位数/Percentile value

Exceptions

std::invalid_argument	如果容器为空/If the container is empty
std::out_of_range	如果p不在[0.0, 1.0]范围/If p is not in [0.0, 1.0]

std::vector<int> v{1, 2, 3, 4, 5};
double p50 = toolbox::math::percentile(v, 0.5); // p50 == 3
double p90 = toolbox::math::percentile(v, 0.9); // p90 == 4.6

range()

template<typename TContainer >

TContainer::value_type toolbox::math::range

(

const TContainer &

data

)

计算容器中元素的全距（最大值-最小值）/Compute the range (max - min) of elements in the container

Template Parameters

TContainer

容器类型，元素需为算术类型且可比较/Container type, elements must be arithmetic and comparable

Parameters

data	输入容器/Input container

Returns

ValueType 全距/Range

Exceptions

std::invalid_argument

如果容器为空/If the container is empty

std::vector<int> v{3, 1, 2};
int r = toolbox::math::range(v); // r == 2

stdev()

template<typename TContainer >

double toolbox::math::stdev	(	const TContainer &	data,
		bool	sample_stdev = true
	)

计算标准差（默认样本标准差）/Compute the standard deviation (default is sample standard deviation)

Template Parameters

TContainer

容器类型，元素需为算术类型/Container type, elements must be arithmetic

Parameters

data	输入容器/Input container
sample_stdev	是否计算样本标准差（true）或总体标准差（false）/Whether to compute sample stdev (true) or population stdev (false)

Returns

double 标准差/Standard deviation

Exceptions

std::invalid_argument	如果样本标准差且元素少于2/If sample stdev and less than 2 elements
std::invalid_argument	如果总体标准差且容器为空/If population stdev and container is empty

std::vector<double> v{1.0, 2.0, 3.0};
double sd = toolbox::math::stdev(v); // 样本标准差/sample stdev
double sd_pop = toolbox::math::stdev(v, false); // 总体标准差/population
stdev

sum()

template<typename TContainer >

TContainer::value_type toolbox::math::sum

(

const TContainer &

data

)

计算容器中元素的总和（返回容器元素类型）/Compute the sum of elements in the container (returns container element type)

Template Parameters

TContainer

容器类型，元素需为算术类型/Container type, elements must be arithmetic

Parameters

data	输入容器/Input container

Returns

ValueType 总和/Sum

Note

空容器返回0/Returns 0 for empty container

std::vector<int> v{1, 2, 3};
int s = toolbox::math::sum(v); // s == 6

sum_d()

template<typename TContainer >

double toolbox::math::sum_d

(

const TContainer &

data

)

计算容器中元素的总和（返回 double 类型以保证精度和范围）/Compute the sum of elements in the container (returns double for precision and range)

Template Parameters

TContainer

容器类型，元素需为算术类型/Container type, elements must be arithmetic

Parameters

data	输入容器/Input container

Returns

double 总和/Sum

Note

空容器返回0.0/Returns 0.0 for empty container

std::vector<int> v{1, 2, 3};
double s = toolbox::math::sum_d(v); // s == 6.0

variance()

template<typename TContainer >

double toolbox::math::variance	(	const TContainer &	data,
		bool	sample_variance = true
	)

计算方差（默认样本方差 N-1）/Compute the variance (default is sample variance N-1)

Template Parameters

TContainer

容器类型，元素需为算术类型/Container type, elements must be arithmetic

Parameters

data	输入容器/Input container
sample_variance	是否计算样本方差（true）或总体方差（false）/Whether to compute sample variance (true) or population variance (false)

Returns

double 方差/Variance

Exceptions

std::invalid_argument	如果样本方差且元素少于2/If sample variance and less than 2 elements
std::invalid_argument	如果总体方差且容器为空/If population variance and container is empty

std::vector<double> v{1.0, 2.0, 3.0};
double var = toolbox::math::variance(v); // 样本方差/sample variance
double var_pop = toolbox::math::variance(v, false); // 总体方差/population
variance