#include <Alg.h>

Collaboration diagram for Nice::Alg:

Static Public Member Functions
template<class T >
static void	SWAP (T &a, T &b)
	exchange (swap) two values. More...

template<class T >
static const T	SQR (const T a)
	compute the square of a value More...

static void	linearFit (boost::numeric::ublas::vector< double > &_x, boost::numeric::ublas::vector< double > &_y, boost::numeric::ublas::vector< double > &_sig, boost::numeric::ublas::vector< double > &_a, boost::numeric::ublas::vector< bool > &_ia, boost::numeric::ublas::matrix< double > &_covar, double &_chisq, void _funcs(const double, boost::numeric::ublas::vector< double > &))
	linear least-square solver using normal equations More...

static void	gaussj (boost::numeric::ublas::matrix< double > &a, boost::numeric::ublas::matrix< double > &b)
	Gauss-Jordan elimination. More...

static void	covsrt (boost::numeric::ublas::matrix< double > &_covar, boost::numeric::ublas::vector< bool > &_ia, const int _mfit)
	Sorts covariance matrix. More...

template<typename T >
static std::vector< std::vector< int > >	subSets (T N, T m)
	construct subsets of size m out of n elements More...

static Nice::SeqPoint	generateSpiral (const Nice::Circle &c, int type, double latConst)
	construct a chain of points on a c.c.w. spiral. More...

template<class T >
static void	SWAP (T &a, T &b)
	exchange (swap) two values. More...

template<class T >
static const T	SQR (const T a)
	compute the square of a value More...

static void	linearFit (boost::numeric::ublas::vector< double > &_x, boost::numeric::ublas::vector< double > &_y, boost::numeric::ublas::vector< double > &_sig, boost::numeric::ublas::vector< double > &_a, boost::numeric::ublas::vector< bool > &_ia, boost::numeric::ublas::matrix< double > &_covar, double &_chisq, void _funcs(const double, boost::numeric::ublas::vector< double > &))

static void	gaussj (boost::numeric::ublas::matrix< double > &a, boost::numeric::ublas::matrix< double > &b)

static void	covsrt (boost::numeric::ublas::matrix< double > &_covar, boost::numeric::ublas::vector< bool > &_ia, const int _mfit)

template<typename T >
static std::vector< std::vector< int > >	subSets (T N, T m)

static Nice::SeqPoint	generateSpiral (const Nice::Circle &c, int type, double latConst)

Static Protected Member Functions
template<typename T >
static std::vector< std::vector< int > >	subSets (T N, T m, std::vector< int > fxd, T minm)
	construct subsets of size m out of n elements More...

template<typename T >
static std::vector< std::vector< int > >	subSets (T N, T m, std::vector< int > fxd, T minm)

Member Function Documentation

◆ covsrt() [1/2]

void Nice::Alg::covsrt	(	boost::numeric::ublas::matrix< double > &	covar,
		boost::numeric::ublas::vector< bool > &	ia,
		const int	mfit
	)

static

Sorts covariance matrix.

Parameters

_covar
_ia
_mfit

◆ covsrt() [2/2]

static void Nice::Alg::covsrt	(	boost::numeric::ublas::matrix< double > &	_covar,
		boost::numeric::ublas::vector< bool > &	_ia,
		const int	_mfit
	)

static

◆ gaussj() [1/2]

void Nice::Alg::gaussj	(	boost::numeric::ublas::matrix< double > &	a,
		boost::numeric::ublas::matrix< double > &	b
	)

static

Gauss-Jordan elimination.

Used e.g. by lfit to solve for the coefficients (and to find the covariance matrix)

Parameters

_a
_b

◆ gaussj() [2/2]

static void Nice::Alg::gaussj	(	boost::numeric::ublas::matrix< double > &	a,
		boost::numeric::ublas::matrix< double > &	b
	)

static

◆ generateSpiral() [1/2]

Nice::SeqPoint Nice::Alg::generateSpiral	(	const Nice::Circle &	c,
		int	type,
		double	latConst
	)

static

construct a chain of points on a c.c.w. spiral.

Parameters

c	A circle which will contain the spiral. The center of the circle defines the starting point of the spiral. The radius of the circle defines how far the spiral radius may reach out from the center.
type	Type of the discret underlying lattice. If type=0 the points are on a simple 2D quadratic lattice. If type=1 the points are on a simple triangular (a.k.a. hexagonal) lattice. There is no type for centered square lattices, because these are the same as quadratic lattices rotated by 45 degrees and shrunk by a factor sqrt(2). (So they may be derived by rotation and shrinking the vector of points returned by this function.)
latConst	The lattice constant in the same units as the circle center and radius. This is the shortest distance between two distinct points on the lattice. That value should not be an integer multiple of the lattice constant (to avoid fuzzy interpretation of which points on the spiral stay within the circle)

Returns: A sequence of points with increasing distance from the circle center.

Since: 2017-11-02

Author: R. J. Mathar

◆ generateSpiral() [2/2]

static Nice::SeqPoint Nice::Alg::generateSpiral	(	const Nice::Circle &	c,
		int	type,
		double	latConst
	)

static

◆ linearFit() [1/2]

void Nice::Alg::linearFit	(	boost::numeric::ublas::vector< double > &	_x,
		boost::numeric::ublas::vector< double > &	_y,
		boost::numeric::ublas::vector< double > &	_sig,
		boost::numeric::ublas::vector< double > &	_a,
		boost::numeric::ublas::vector< bool > &	_ia,
		boost::numeric::ublas::matrix< double > &	_covar,
		double &	_chisq,
		void	_funcsconst double, boost::numeric::ublas::vector< double > &
	)

static

linear least-square solver using normal equations

Given a set of data points _x[0..ndat-1], _y[0..ndat-1] with inidividual standard deviations sig[0..ndat-1], use chi-squared minimization to fit for some or all of the coefficeints a[0..ma-1] of a function that depends linearly on a, y=sum_i a_i*afunc_i(x). The boolean input array ia[0..ma-1] indicates by true entries those components of a that should be fitted for, and by false entries those components that should be held fixed at their input values. The program returns values for a[0..ma-1], chi-square=chisq, and the covariance matrix covar[0..ma-1][0..ma-1]. (Parameters held fixed will return zero covariances.) The user supplies a routine funcs(x,afunc) that returns the ma basis functions evaluated at x=x in the array afunc[0..ma-1]). (Excerpt of numerical recipies section 15.4)

Parameters

[in]	_x	data points (x)
[in]	_y	data points (y)
[in]	_sig	standard deviations of the data points
[out]	_a	coefficients
[in]	_ia	flags for each coefficient. if false, coefficient will be kept constant
[out]	_covar	covariance matrix will be returned
[out]	_chisq	chi^2 as return value
[in]	_funcs	the function that is linear to the coefficients a

◆ linearFit() [2/2]

static void Nice::Alg::linearFit	(	boost::numeric::ublas::vector< double > &	_x,
		boost::numeric::ublas::vector< double > &	_y,
		boost::numeric::ublas::vector< double > &	_sig,
		boost::numeric::ublas::vector< double > &	_a,
		boost::numeric::ublas::vector< bool > &	_ia,
		boost::numeric::ublas::matrix< double > &	_covar,
		double &	_chisq,
		void	_funcsconst double, boost::numeric::ublas::vector< double > &
	)

static

◆ SQR() [1/2]

template<class T >

static const T Nice::Alg::SQR ( const T a )

inlinestatic

compute the square of a value

Parameters

a	The value to be squared.

Returns: The square of a.

◆ SQR() [2/2]

template<class T >

static const T Nice::Alg::SQR ( const T a )

inlinestatic

compute the square of a value

Parameters

a	The value to be squared.

Returns: The square of a.

◆ subSets() [1/4]

template<typename T >

std::vector< std::vector< int > > Nice::Alg::subSets	(	T	N,
		T	m
	)

static

construct subsets of size m out of n elements

This is the standard combinatorial sub-set construction. For N=5 , m=3 we construct <0,1,2>, <0,1,3>, <0,1,4>, <0,2,3>, <0,2,4>...., <2,3,4>.

Parameters

N	The number of elements to choose from.
m	The number of elements selected in each element of the result.

Returns: ordered lists of numbers in the range 0..n-1 where each list has m elements. The cardinality of the outer vector is biomial(N,m).

Since: 2017-03-30

Author: R. J. Mathar

◆ subSets() [2/4]

template<typename T >

static std::vector< std::vector<int> > Nice::Alg::subSets	(	T	N,
		T	m
	)

static

◆ subSets() [3/4]

template<typename T >

static std::vector< std::vector<int> > Nice::Alg::subSets	(	T	N,
		T	m,
		std::vector< int >	fxd,
		T	minm
	)

staticprotected

◆ subSets() [4/4]

template<typename T >

std::vector< std::vector< int > > Nice::Alg::subSets	(	T	N,
		T	m,
		std::vector< int >	fxd,
		T	minm
	)

staticprotected

construct subsets of size m out of n elements

Parameters

	N	The number of elements to coose from.
	m	The number of elements selected in each element of the result.
[in]	fxd	The sublist of indices which are already fixed.
[in]	minm	A lower bound of the indices to be taken freely.

Returns: ordered lists of numbers in the range 0..n-1 where

Since: 2017-03-30

Author: R. J. Mathar

◆ SWAP() [1/2]

template<class T >

static void Nice::Alg::SWAP	(	T &	a,
		T &	b
	)

inlinestatic

exchange (swap) two values.

Parameters

[in,out]	a
[in,out]	b

◆ SWAP() [2/2]

template<class T >

static void Nice::Alg::SWAP	(	T &	a,
		T &	b
	)

inlinestatic

exchange (swap) two values.

Parameters

[in,out]	a
[in,out]	b

The documentation for this class was generated from the following files:

/home/nirva/insroot/include/Nice/Alg/Alg.h
TwiceAsNice/nice/src/libNice/Nice/Alg/Alg.cc

Static Public Member Functions

Static Protected Member Functions

Member Function Documentation

◆ covsrt() [1/2]

◆ covsrt() [2/2]

◆ gaussj() [1/2]

◆ gaussj() [2/2]

◆ generateSpiral() [1/2]

◆ generateSpiral() [2/2]

◆ linearFit() [1/2]

◆ linearFit() [2/2]

◆ SQR() [1/2]

◆ SQR() [2/2]

◆ subSets() [1/4]

◆ subSets() [2/4]

◆ subSets() [3/4]

◆ subSets() [4/4]

◆ SWAP() [1/2]

◆ SWAP() [2/2]