math_utils.h File Reference

Some useful math functions. More...

#include <functional>
#include <complex>
#include <limits>
#include <cmath>
#include "refobj.h"

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Classes
class	accomp_pred< T >
	Compare predicate based on accomp to use in STL. More...
class	comp_function< arg_t, result_t, comp_t >
	used to construct max_function and min_function More...
class	max_function< arg_t, result_t >
	maximal value of given functions More...
class	min_function< arg_t, result_t >
	minimal value of given functions More...
class	ptr_stor_t< T >
	Pointer storage class for a vector followinfg storage_prototype. More...
class	base_iterator< value_t >
	base class for virtual iterators More...
class	virtual_iterator< iterator_t, value_t >
	virtualizator for iterators More...
class	comb_range_t< iT >
	Iterates over all combinations of numbers from 0 to count[i] in each direction. More...

Functions
template<class T >
int	test_NaN (T x)
	tests if x is NaN
template<class T >
T	ceil2 (const T val)
	round given value up to the near number of the type 2^N
template<class T >
bool	accomp (const T x, const T y, const T val=T(1), int mult_epsilon=1024)
	compare x and y within some accuracy which depends on parameter val.
template<class T >
T	acfloor (const T x, T val=T(1), int mult_epsilon=1024)
	return floor(x) or ceil(x) [if x is equal to ceil(x) within some accuracy which depends on parameter val]
template<class T >
T	acdiv (T x, T y, int mult_epsilon=1024)
	calculates ratio between x and y.
template<class T >
T	log_reduce (const T &x)
	Logarithmically reduces the argument: log_reduce(x) = log(x), x>e log_reduce(x) -> -log(-x), x<e linear between [-e,e], first derivative continuous.
template<class T >
T	align_to_grid (const T &x, const T &x0, const T &dx)
	Alignes x to the neares node of dx, starting from x0.
template<class T >
int	step_fun (const T &t1, const T &t2)
	returns -1 if t1<t2; 1 if t2>t1; 0 if t1==t2 can be used in implementation of operators < or > for some classes
template<int N, class arr_t >
std::size_t	find_diagonal (const arr_t &sizes, int sum, std::vector< arr_t > &inds)
	Finds all possible integer tuples of dimension N>0, where the sum of integer elements in a tuple equals sum and the elements are between [0, sizes[i]) in each dimension i.

Detailed Description

Some useful math functions.

Function Documentation

acdiv()

template<class T >

T acdiv	(	T	x,
		T	y,
		int	mult_epsilon = 1024
	)

calculates ratio between x and y.

if this ratio is close to some integer number with some accuracy, then returns this integer number.

align_to_grid()

template<class T >

T align_to_grid	(	const T &	x,
		const T &	x0,
		const T &	dx
	)

Alignes x to the neares node of dx, starting from x0.

Returns

the aligned value

find_diagonal()

template<int N, class arr_t >

std::size_t find_diagonal	(	const arr_t &	sizes,
		int	sum,
		std::vector< arr_t > &	inds
	)

Finds all possible integer tuples of dimension N>0, where the sum of integer elements in a tuple equals sum and the elements are between [0, sizes[i]) in each dimension i.

The tuples are constructed as instances of arr_t and pushed back to vector inds.

Returns

the number of tuples found.