Utility.hpp File Reference

#include "constant.hpp"

Go to the source code of this file.

Functions
double *	vector2array (const std::vector< double > &a)
	copy the content of the vector to an array, which can be directly written to the h5 file.
double *	vector2array (const std::vector< double > &a, const unsigned size)
	copy the content of the vector to an array, specified by size.
int *	vector2array (const std::vector< int > &a)
double **	vector2array (const std::vector< double > &a, const unsigned M, const unsigned N)
	copy the content of the vector to a MxN 2-D array.
void	deleteArray (double *data)
	Free the memory space created by vector2array()
void	deleteArray (double **data)
	Free the memory space created by vector2array()
std::vector< std::vector < double > >	vector2vector (const std::vector< double > &a, const int N, const int M)
std::vector< double >	array2vector (const double *a, const int size)
std::vector< std::vector < double > >	array2vector (const double *a, const int N, const int M)
	create a 2-D array from a 1-D array specified by N rows and M columns.
double	str2num (const std::string &s)
	Use the std::istd::stringstream to perform the conversion.
std::string	num2str (const double x)
	Use the std::ostd::stringstream to perform the conversion.
double	matlabfmod (const double x, const double y)
	c++ fmod() is not consistent with Matlab fmod() when handling negative number.
std::string	getRandomFileName (std::string &prefix)
	Generate a h5 file name in format of "prefix_year_month_day_hour_minute_random.h5".
int	getNextPower (int N, int base)
void	writeToTxtFile (const std::string file_name, const std::vector< double > &data)
void	writeToTxtFile (const std::string file_name, const std::vector< std::vector< double > > &data)
double	bandwidthToGaussianStdDev (unsigned bandwidth_defn, double bandwidth)
std::vector< double >	solveTridiagonalSystem (const std::vector< double > &a, const std::vector< double > &b, const std::vector< double > &c, const std::vector< double > &d)
	solve Ax = d problem, where A is a tri-diagonal system specified by its lower, main, and upper diagonal.
std::vector< double >	solveLinearSystem (const std::vector< std::vector< double > > &S, const std::vector< double > &rhs)
	Solve the linear system S x = t.
std::vector< double >	cubic_spline_interp (const std::vector< double > &x, const std::vector< double > &y, const std::vector< double > &xi)
	Use cubic spline to Interpolate xi based on the data (x, y).
double	linear_interp (const std::vector< double > &x, const std::vector< double > &y, const std::vector< std::vector< double > > &z, const double xi, const double yi)
	Bi-linear interpolation over one grid onto another point.
void	convertIndex (const int index, const int nZ, int j, int k)
	Convert the integer index to the indices of the two-dimensional vector.
void	convertIndex (const int index, const int nY, const int nZ, int i, int j, int k)
	Convert the integer index to the indices of the three-dimensional vector.
std::vector< int >	getBilinearInterpolationIndex (const std::vector< double > &z, const double zi)
std::vector< int >	getBilinearInterpolationIndex (const std::vector< double > &y, const std::vector< double > &z, const double yi, const double zi)
std::vector< int >	getBilinearInterpolationIndex (const std::vector< double > &x, const std::vector< double > &y, const std::vector< double > &z, const double xi, const double yi, const double zi)
	To be implemented.
std::vector< double >	getBilinearInterpolationCoefficient (const std::vector< double > &z, const double zi)
std::vector< double >	getBilinearInterpolationCoefficient (const std::vector< double > &y, const std::vector< double > &z, const double yi, const double zi)
std::vector< double >	getBilinearInterpolationCoefficient (const std::vector< double > &x, const std::vector< double > &y, const std::vector< double > &z, const double xi, const double yi, const double zi)
	To be implemented.
std::vector< std::vector < double > >	cubic_spline_interp (const std::vector< double > &x, const std::vector< double > &y, const std::vector< std::vector< double > > &z, const std::vector< double > &xi, const std::vector< double > &yi)
std::vector< double >	poly_interp (const std::vector< double > &x, const std::vector< double > &y, const std::vector< double > &xi)
	Polynomial interpolation.
int	findEqual (const std::vector< double > &reference, const double x, int i, int j)
	Find the index of the element which is equal to x.
std::vector< int >	findEqual (const std::vector< double > &reference, const double x)
	Find the index of the elements that are equal to x.
std::vector< int >	findEqual (const std::vector< std::vector< double > > &reference, const double x)
bool	approximatelyEqual (const double a, const double b, const double epsilon)
	See knuth book on double comparision.
bool	essentiallyEqual (const double a, const double b, const double epsilon)
	See knuth book.
bool	definitelyGreaterThan (const double a, const double b, const double epsilon)
	See knuth book.
bool	definitelyLessThan (const double a, const double b, const double epsilon)
	See knuth book.
std::string	secondToTime (int seconds)
	Parse the input to the string form of "XX hours XX minutes XX seconds".
std::vector< double >	estimateAmplitudePhase (const std::vector< double > &data, const double frequency, const double delta_t)
double	cot (const double x)
double	acot (const double x)
bool	isEven (unsigned n)
bool	isOdd (unsigned n)

Function Documentation

double acot

(

const double

x

)

bool approximatelyEqual	(	const double	a,
		const double	b,
		const double	epsilon
	)

See knuth book on double comparision.

Parameters

a	first parameter
b	second parameter
epsilon	depends on the context, and determines how equal you want the numbers to be.

std::vector<double> array2vector	(	const double *	a,
		const int	size
	)

std::vector<std::vector<double> > array2vector	(	const double *	a,
		const int	N,
		const int	M
	)

create a 2-D array from a 1-D array specified by N rows and M columns.

double bandwidthToGaussianStdDev	(	unsigned	bandwidth_defn,
		double	bandwidth
	)

void convertIndex	(	const int	index,
		const int	nZ,
		int	j,
		int	k
	)

Convert the integer index to the indices of the two-dimensional vector.

Parameters

&index
&nZ
&j	contain returned value
&k	contain returned value

void convertIndex	(	const int	index,
		const int	nY,
		const int	nZ,
		int	i,
		int	j,
		int	k
	)

Convert the integer index to the indices of the three-dimensional vector.

Parameters

&index
&nY
&nZ
&i	contain returned value
&j	contain returned value
&k	contain returned value

double cot

(

const double

x

)

std::vector<double> cubic_spline_interp	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		const std::vector< double > &	xi
	)

Use cubic spline to Interpolate xi based on the data (x, y).

From the end points of (x,y), it estimates the the second derivative and uses them as the boudnary boundary condition. If xi falls outside of x, return 0.

Parameters

x	Uniformly spaced sample point
y
xi	Can be nonuniformly spaced sample point

std::vector<std::vector<double> > cubic_spline_interp	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		const std::vector< std::vector< double > > &	z,
		const std::vector< double > &	xi,
		const std::vector< double > &	yi
	)

Parameters

x	Uniformly spaced sample point
y	Uniformly spaced sample point
z
xi	Can be non-uniformly spaced sample point
yi	Can be non-uniformly spaced sample point

bool definitelyGreaterThan	(	const double	a,
		const double	b,
		const double	epsilon
	)

See knuth book.

Parameters

a	first parameter
b	second parameter
epsilon	depends on the context, and determines how equal you want the numbers to be.

bool definitelyLessThan	(	const double	a,
		const double	b,
		const double	epsilon
	)

See knuth book.

Parameters

a	first parameter
b	second parameter
epsilon	depends on the context, and determines how equal you want the numbers to be.

void deleteArray

(

double *

data

)

Free the memory space created by vector2array()

void deleteArray

(

double **

data

)

Free the memory space created by vector2array()

bool essentiallyEqual	(	const double	a,
		const double	b,
		const double	epsilon
	)

See knuth book.

Parameters

a	first parameter
b	second parameter
epsilon	depends on the context, and determines how equal you want the numbers to be.

std::vector<double> estimateAmplitudePhase	(	const std::vector< double > &	data,
		const double	frequency,
		const double	delta_t
	)

int findEqual	(	const std::vector< double > &	reference,
		const double	x,
		int	i,
		int	j
	)

Find the index of the element which is equal to x.

Using binary search.

Parameters

reference	an increasing array without repeating element
x	specified value
i	starting index of reference to search
j	ending index of reference to search

Returns

the index of the element that is equal to x. -1 if otherwise

std::vector<int> findEqual	(	const std::vector< double > &	reference,
		const double	x
	)

Find the index of the elements that are equal to x.

std::vector<int> findEqual	(	const std::vector< std::vector< double > > &	reference,
		const double	x
	)

std::vector<double> getBilinearInterpolationCoefficient	(	const std::vector< double > &	z,
		const double	zi
	)

std::vector<double> getBilinearInterpolationCoefficient	(	const std::vector< double > &	y,
		const std::vector< double > &	z,
		const double	yi,
		const double	zi
	)

std::vector<double> getBilinearInterpolationCoefficient	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		const std::vector< double > &	z,
		const double	xi,
		const double	yi,
		const double	zi
	)

To be implemented.

std::vector<int> getBilinearInterpolationIndex	(	const std::vector< double > &	z,
		const double	zi
	)

Returns

the integer index of the left and right neighbour.

std::vector<int> getBilinearInterpolationIndex	(	const std::vector< double > &	y,
		const std::vector< double > &	z,
		const double	yi,
		const double	zi
	)

Returns

the integer index of the four neighbour. Should be used with Utility::convertIndex()

std::vector<int> getBilinearInterpolationIndex	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		const std::vector< double > &	z,
		const double	xi,
		const double	yi,
		const double	zi
	)

To be implemented.

int getNextPower	(	int	N,
		int	base
	)

std::string getRandomFileName

(

std::string &

prefix

)

Generate a h5 file name in format of "prefix_year_month_day_hour_minute_random.h5".

Returns

std::string the file name

bool isEven

(

unsigned

n

)

bool isOdd

(

unsigned

n

)

double linear_interp	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		const std::vector< std::vector< double > > &	z,
		const double	xi,
		const double	yi
	)

Bi-linear interpolation over one grid onto another point.

double matlabfmod	(	const double	x,
		const double	y
	)

c++ fmod() is not consistent with Matlab fmod() when handling negative number.

This function follows the Matlab convention.

std::string num2str

(

const double

x

)

Use the std::ostd::stringstream to perform the conversion.

std::vector<double> poly_interp	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		const std::vector< double > &	xi
	)

Polynomial interpolation.

Solving the linear sytem using Boost.

std::string secondToTime

(

int

seconds

)

Parse the input to the string form of "XX hours XX minutes XX seconds".

Parameters

seconds

std::difftime().

std::vector<double> solveLinearSystem	(	const std::vector< std::vector< double > > &	S,
		const std::vector< double > &	rhs
	)

Solve the linear system S x = t.

It actually uses LU in Boost to invert S' S, and compute x = inv(S' S) S' t.

Parameters

S	NxN matrix
rhs	right hand side

std::vector<double> solveTridiagonalSystem	(	const std::vector< double > &	a,
		const std::vector< double > &	b,
		const std::vector< double > &	c,
		const std::vector< double > &	d
	)

solve Ax = d problem, where A is a tri-diagonal system specified by its lower, main, and upper diagonal.

See [Schwarz1989] for the algorithm to perform LU decomposition on A and use backward/forwad substitution solve the system.

Parameters

a	main diagonal
b	lower diagonal
c	upper diagonal
d	right hand side

Returns

x

double str2num

(

const std::string &

s

)

Use the std::istd::stringstream to perform the conversion.

double* vector2array

(

const std::vector< double > &

a

)

copy the content of the vector to an array, which can be directly written to the h5 file.

This method dynamically creates an array using new and returns the pointer to it. Cannot be used too often to avoid allocating too much memory space.

Parameters

a	vector<double>

double* vector2array	(	const std::vector< double > &	a,
		const unsigned	size
	)

copy the content of the vector to an array, specified by size.

If size is longer than the size of the vector, 0 will be padded at the end.

int* vector2array

(

const std::vector< int > &

a

)

double** vector2array	(	const std::vector< double > &	a,
		const unsigned	M,
		const unsigned	N
	)

copy the content of the vector to a MxN 2-D array.

The array occupies an contiguous space in the memory.

std::vector<std::vector<double> > vector2vector	(	const std::vector< double > &	a,
		const int	N,
		const int	M
	)

void writeToTxtFile	(	const std::string	file_name,
		const std::vector< double > &	data
	)

void writeToTxtFile	(	const std::string	file_name,
		const std::vector< std::vector< double > > &	data
	)