Utilities for working with std::vector.

template<typename vectorT >
void	mx::math::vectorScale (vectorT &vec, size_t N=0, typename vectorT::value_type scale=0, typename vectorT::value_type offset=0)
	Fill in a vector with a regularly spaced scale. More...

template<typename memberT >
std::vector< size_t >	mx::math::vectorSortOrder (std::vector< memberT > const &values)
	Return the indices of the vector in sorted order, without altering the vector itself. More...

template<typename valueT >
valueT	mx::math::vectorSum (const valueT *vec, size_t sz)
	Calculate the sum of a vector. More...

template<typename vectorT >
vectorT::value_type	mx::math::vectorSum (const vectorT &vec)
	Calculate the sum of a vector. More...

template<typename valueT >
valueT	mx::math::vectorMean (const valueT *vec, size_t sz)
	Calculate the mean of a vector. More...

template<typename vectorT >
vectorT::value_type	mx::math::vectorMean (const vectorT &vec)
	Calculate the mean of a vector. More...

template<typename vectorT >
vectorT::value_type	mx::math::vectorMean (const vectorT &vec, const vectorT &w)
	Calculate the weighted mean of a vector. More...

template<typename vectorT >
vectorT::value_type	mx::math::vectorMedianInPlace (vectorT &vec)
	Calculate median of a vector in-place, altering the vector. More...

template<typename vectorT >
vectorT::value_type	mx::math::vectorMedian (const vectorT &vec, vectorT *work=0)
	Calculate median of a vector, leaving the vector unaltered. More...

template<typename valueT >
valueT	mx::math::vectorVariance (const valueT *vec, size_t sz, valueT mean)
	Calculate the variance of a vector relative to a supplied mean value. More...

template<typename vectorT >
vectorT::value_type	mx::math::vectorVariance (const vectorT &vec, const typename vectorT::value_type &mean)
	Calculate the variance of a vector relative to a supplied mean value. More...

template<typename valueT >
valueT	mx::math::vectorVariance (const valueT *vec, size_t sz)
	Calculate the variance of a vector. More...

template<typename vectorT >
vectorT::value_type	mx::math::vectorVariance (const vectorT &vec)
	Calculate the variance of a vector. More...

template<typename vectorT >
vectorT::value_type	mx::math::vectorSigmaMean (const vectorT &vec, const vectorT *weights, typename vectorT::value_type sigma, int &maxPasses)
	Calculate the sigma-clipped mean of a vector. More...

template<typename vectorT >
vectorT::value_type	mx::math::vectorSigmaMean (const vectorT &vec, typename vectorT::value_type sigma)

template<typename vectorT >
vectorT::value_type	mx::math::vectorSigmaMean (const vectorT &vec, const vectorT &weights, typename vectorT::value_type sigma, int &maxPasses)

template<typename vectorT >
vectorT::value_type	mx::math::vectorSigmaMean (const vectorT &vec, const vectorT &weights, typename vectorT::value_type sigma)

template<typename valueT , typename constT >
void	mx::math::vectorSub (valueT *vec, size_t sz, const constT &c)
	Subtract a constant value from a vector. More...

template<typename vecT , typename constT >
void	mx::math::vectorSub (vecT &vec, const constT &c)
	Subtract a constant value from a vector. More...

template<typename valueT >
void	mx::math::vectorMeanSub (valueT *vec, size_t sz)
	Subtract the mean from a vector. More...

template<typename vecT >
void	mx::math::vectorMeanSub (vecT &vec)
	Subtract the mean from a vector. More...

template<typename vecT >
void	mx::math::vectorMedianSub (vecT &vec)
	Subtract the median from a vector. More...

template<typename realT >
int	mx::math::vectorSmoothMean (realT smVec, realT vec, size_t vecSize, int win)
	Smooth a vector using the mean in a window specified by its full-width. More...

template<typename realT >
int	mx::math::vectorSmoothMean (std::vector< realT > &smVec, std::vector< realT > &vec, int win)
	Smooth a vector using the mean in a window specified by its full-width. More...

template<typename realT >
int	mx::math::vectorSmoothMean (std::vector< realT > &smVec, std::vector< realT > &vec, std::vector< int > &wins, bool norm=false)
	Smooth a vector using the mean in windows specified by their full-widths. More...

template<typename realT >
int	mx::math::vectorSmoothMedian (std::vector< realT > &smVec, std::vector< realT > &vec, int win)
	Smooth a vector using the median in a window specified by its full-width. More...

template<typename realT >
int	mx::math::vectorSmoothMax (std::vector< realT > &smVec, std::vector< realT > &vec, int win)
	Smooth a vector using the max in a window specified by its full-width. More...

template<typename vectorT >
int	mx::math::vectorRebin (vectorT &binv, const vectorT &v, unsigned n, bool binMean=false)
	Re-bin a vector by summing (or averaging) in bins of size n points. More...

template<typename vectorT , typename binVectorT >
int	mx::math::vectorBinMeans (std::vector< vectorT > &means, binVectorT &binSzs, const vectorT &v)
	Calculate and accumulate the means of a timeseries in bins of various sizes. More...

template<typename realT >
int	mx::math::vectorGaussConvolve (std::vector< realT > &dataOut, const std::vector< realT > &dataIn, const std::vector< realT > &scale, const realT fwhm, const int winhw)
	Convolve (smooth) a vector with a Gaussian. More...

template<typename floatT >
int	mx::math::vectorCumHist (std::vector< floatT > &svec, std::vector< floatT > &sum, std::vector< floatT > &vec)
	Calculate a cumulative histogram of a vector. More...

template<typename floatT >
int	mx::math::vectorCumHistReverse (std::vector< floatT > &svec, std::vector< floatT > &sum, std::vector< floatT > &vec)
	Calculate a reverse cumulative histogram of a vector. More...

Function Documentation

◆ vectorBinMeans()

template<typename vectorT , typename binVectorT >

int mx::math::vectorBinMeans	(	std::vector< vectorT > &	means,
		binVectorT &	binSzs,
		const vectorT &	v
	)

Calculate and accumulate the means of a timeseries in bins of various sizes.

Useful mainly to calculate the variance of the mean as a function of sample size. The output is a vector of vectors, where each element is a vector which contains the means in the unique bins of size corresponding to the same index in the in put binSzs vector.

Returns: 0 on success.

Parameters

[out]	means	the means in each distinct bin. Not cleared, but Will be resized with new means appended.
[in]	binSzs	the bin sizes in which to calculate the means
[in]	v	the input vector to bin .

Definition at line 730 of file vectorUtils.hpp.

References mx::math::vectorRebin().

◆ vectorCumHist()

template<typename floatT >

int mx::math::vectorCumHist	(	std::vector< floatT > &	svec,
		std::vector< floatT > &	sum,
		std::vector< floatT > &	vec
	)

Calculate a cumulative histogram of a vector.

Sorts the vector and sums.

Return values

0	on success, -1 otherwise.

Template Parameters

floatT the floating point type of the vector contens.

Parameters

[out]	svec	Contains the sorted vector.
[out]	sum	Contains the cumulative or running sum of the sorted vector
[in]	vec	The vector to sort and sum.

Definition at line 805 of file vectorUtils.hpp.

◆ vectorCumHistReverse()

template<typename floatT >

int mx::math::vectorCumHistReverse	(	std::vector< floatT > &	svec,
		std::vector< floatT > &	sum,
		std::vector< floatT > &	vec
	)

Calculate a reverse cumulative histogram of a vector.

Reverse-sorts the vector and sums.

Return values

0	on success, -1 otherwise.

Template Parameters

floatT the floating point type of the vector contens.

Parameters

[out]	svec	Contains the reverse-sorted vector.
[out]	sum	Contains the cumulative or running sum of the reverse-sorted vector
[in]	vec	The vector to reverse-sort and sum.

Definition at line 834 of file vectorUtils.hpp.

◆ vectorGaussConvolve()

template<typename realT >

int mx::math::vectorGaussConvolve	(	std::vector< realT > &	dataOut,
		const std::vector< realT > &	dataIn,
		const std::vector< realT > &	scale,
		const realT	fwhm,
		const int	winhw
	)

Convolve (smooth) a vector with a Gaussian.

Returns: 0 on success.; -1 on error.

Template Parameters

realT is the real floating point type of the data.

Parameters

[out]	dataOut	The smoothed data vector. Resized.
[in]	dataIn	The data vector to smooth.
[in]	scale	The scale vector used to calculate the kernel.
[in]	fwhm	The FWHM of the Gaussian kernel, same units as scale.
[in]	winhw	The window half-width in pixels.

Definition at line 758 of file vectorUtils.hpp.

References mx::astro::constants::G(), and mx::astro::constants::sigma().

◆ vectorMean() [1/3]

template<typename valueT >

valueT mx::math::vectorMean	(	const valueT *	vec,
		size_t	sz
	)

Calculate the mean of a vector.

Returns: the mean of vec

Template Parameters

vectorT the std::vector type of vec

Parameters

[in]	vec	the vector
[in]	sz	the size of the vector

Definition at line 150 of file vectorUtils.hpp.

Referenced by mx::improc::imCenterCircleSym< realT >::center(), mx::improc::eigenCube< dataT >::mean(), and mx::improc::sourceFinder< _realT >::operator()().

◆ vectorMean() [2/3]

template<typename vectorT >

vectorT::value_type mx::math::vectorMean ( const vectorT & vec )

Calculate the mean of a vector.

Returns: the mean of vec

Template Parameters

vectorT the std::vector type of vec

Parameters

[in] vec the vector

Definition at line 172 of file vectorUtils.hpp.

◆ vectorMean() [3/3]

template<typename vectorT >

vectorT::value_type mx::math::vectorMean	(	const vectorT &	vec,
		const vectorT &	w
	)

Calculate the weighted mean of a vector.

Returns: the weighted mean of vec

Template Parameters

vectorT the std::vector type of vec and w

Parameters

[in]	vec	the vector *‍/
[in]	w	the weights

Definition at line 191 of file vectorUtils.hpp.

Referenced by mx::math::vectorMeanSub(), mx::math::vectorSigmaMean(), and mx::math::vectorVariance().

◆ vectorMeanSub() [1/2]

template<typename valueT >

void mx::math::vectorMeanSub	(	valueT *	vec,
		size_t	sz
	)

Subtract the mean from a vector.

Parameters

	vec	[in.out] the vector, each element will have the mean subtracted from it
[in]	sz	the vector size

Definition at line 505 of file vectorUtils.hpp.

References mx::math::vectorMean(), and mx::math::vectorSub().

◆ vectorMeanSub() [2/2]

template<typename vecT >

void mx::math::vectorMeanSub ( vecT & vec )

Subtract the mean from a vector.

Parameters

vec	[in.out] the vector, each element will have the mean subtracted from it

Definition at line 515 of file vectorUtils.hpp.

◆ vectorMedian()

template<typename vectorT >

vectorT::value_type mx::math::vectorMedian	(	const vectorT &	vec,
		vectorT *	work = `0`
	)

Calculate median of a vector, leaving the vector unaltered.

Returns the center element if vec has an odd number of elements. Returns the mean of the center 2 elements if vec has an even number of elements.

Returns: the median of vec

Template Parameters

vectorT the std::vector type of vec

Parameters

[in]	vec	the vector for which the median is desired
[in]	work	[optional] an optional vector to use as workspace, use to avoid re-allocation

Definition at line 247 of file vectorUtils.hpp.

References mx::math::vectorMedianInPlace().

Referenced by mx::improc::aperturePhotometer< realT >::cumPhotWork(), mx::improc::sourceFinder< _realT >::operator()(), mx::math::vectorMedianSub(), and mx::math::vectorSigmaMean().

◆ vectorMedianInPlace()

template<typename vectorT >

vectorT::value_type mx::math::vectorMedianInPlace ( vectorT & vec )

Calculate median of a vector in-place, altering the vector.

Returns the center element if vec has an odd number of elements. Returns the mean of the center 2 elements if vec has an even number of elements.

Returns: the median of vec

Template Parameters

vectorT the std::vector type of vec

Parameters

[in] vec the vector, is altered by std::nth_element

Definition at line 218 of file vectorUtils.hpp.

Referenced by mx::improc::imageMedian(), mx::improc::medianSmooth(), mx::math::vectorMedian(), and mx::math::vectorSmoothMedian().

◆ vectorMedianSub()

template<typename vecT >

void mx::math::vectorMedianSub ( vecT & vec )

Subtract the median from a vector.

Parameters

vec	[in.out] the vector, each element will have the median subtracted from it

Definition at line 522 of file vectorUtils.hpp.

References mx::math::vectorMedian(), and mx::math::vectorSub().

◆ vectorRebin()

template<typename vectorT >

int mx::math::vectorRebin	(	vectorT &	binv,
		const vectorT &	v,
		unsigned	n,
		bool	binMean = `false`
	)

Re-bin a vector by summing (or averaging) in bins of size n points.

Returns: 0 on success; -1 on error

Template Parameters

vectorT is any vector-like type with resize(), size(), and the operator()[].

Parameters

[out]	binv	the re-binned vector. will be resized.
[in]	v	the vector to bin.
[in]	n	the size of the bins, in points
[in]	binMean	[optional] flag controlling whether sums (false) or means (true) are calculated.

Definition at line 691 of file vectorUtils.hpp.

Referenced by mx::math::vectorBinMeans().

◆ vectorScale()

template<typename vectorT >

void mx::math::vectorScale	(	vectorT &	vec,
		size_t	N = `0`,
		typename vectorT::value_type	scale = `0`,
		typename vectorT::value_type	offset = `0`
	)

Fill in a vector with a regularly spaced scale.

Fills in the vector with a 0....N-1 scale. The spacing of the points can be changed with the scale parameter, and the starting point can be changed with the offset.

Example:

std::vector vec;
 
mx::vectorScale(vec, 1000, 0.001, 0.001); // Produces a vector with values 0.001,0.002,.... 1.000

Template Parameters

vectorT is a std::vector type.

Parameters

[out]	vec	the vector to fill in, can be pre-allocated or not
[in]	N	[optional] if specified > 0, then vec is resize()-ed. Default is 0, and vec is not resize()-ed.
[in]	scale	[optional] if specified !=0, then the points are spaced by this value. Default spacing is 1.
[in]	offset	[optional] if specified !=0, then the starting point of the scale is this value.

Definition at line 62 of file vectorUtils.hpp.

Referenced by mx::AO::analysis::fourierTemporalPSD< _realT, aosysT >::makePSDGrid().

◆ vectorSigmaMean() [1/4]

template<typename vectorT >

vectorT::value_type mx::math::vectorSigmaMean	(	const vectorT &	vec,
		const vectorT &	weights,
		typename vectorT::value_type	sigma
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

[in]	vec	the vector (unaltered)
[in]	weights	[optional] the weights (unaltered)
[in]	sigma	the standard deviation threshold to apply.

Definition at line 473 of file vectorUtils.hpp.

References mx::astro::constants::sigma().

Referenced by mx::math::vectorSigmaMean().

◆ vectorSigmaMean() [2/4]

template<typename vectorT >

vectorT::value_type mx::math::vectorSigmaMean	(	const vectorT &	vec,
		const vectorT &	weights,
		typename vectorT::value_type	sigma,
		int &	maxPasses
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

[in]	vec	the vector (unaltered)
[in]	weights	[optional] the weights (unaltered)
[in]	sigma	the standard deviation threshold to apply.
	maxPasses	[in.out] [optional] the maximum number of sigma-clipping passes. Set to actual number of passes on return.

Definition at line 459 of file vectorUtils.hpp.

References mx::astro::constants::sigma(), and mx::math::vectorSigmaMean().

◆ vectorSigmaMean() [3/4]

template<typename vectorT >

vectorT::value_type mx::math::vectorSigmaMean	(	const vectorT &	vec,
		const vectorT *	weights,
		typename vectorT::value_type	sigma,
		int &	maxPasses
	)

Calculate the sigma-clipped mean of a vector.

Performas sigma-clipping relative to the median, removing any values with deviation from the median > sigma. Continues until either no values are removed, or maxPasses iterations. If maxPasses == 0, then it is ignored.

Returns: the sigma clipped mean of vec

Template Parameters

vectorT the std::vector type of vec

Parameters

[in]	vec	the vector (unaltered)
[in]	weights	[optional] the weights (unaltered)
[in]	sigma	the standard deviation threshold to apply.
	maxPasses	[in.out] [optional] the maximum number of sigma-clipping passes. Set to actual number of passes on return.

Definition at line 365 of file vectorUtils.hpp.

References mx::astro::constants::sigma(), mx::math::vectorMean(), mx::math::vectorMedian(), and mx::math::vectorVariance().

Referenced by mx::improc::eigenCube< dataT >::sigmaMean().

◆ vectorSigmaMean() [4/4]

template<typename vectorT >

vectorT::value_type mx::math::vectorSigmaMean	(	const vectorT &	vec,
		typename vectorT::value_type	sigma
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

[in]	vec	the vector (unaltered)
[in]	sigma	the standard deviation threshold to apply.

Definition at line 446 of file vectorUtils.hpp.

References mx::astro::constants::sigma(), and mx::math::vectorSigmaMean().

◆ vectorSmoothMax()

template<typename realT >

int mx::math::vectorSmoothMax	(	std::vector< realT > &	smVec,
		std::vector< realT > &	vec,
		int	win
	)

Smooth a vector using the max in a window specified by its full-width.

Parameters

[out]	smVec	the smoothed version of the vector
[in]	vec	the input vector, unaltered.
[in]	win	the full-width of the smoothing window

Definition at line 659 of file vectorUtils.hpp.

◆ vectorSmoothMean() [1/3]

template<typename realT >

int mx::math::vectorSmoothMean	(	realT *	smVec,
		realT *	vec,
		size_t	vecSize,
		int	win
	)

Smooth a vector using the mean in a window specified by its full-width.

Parameters

[out]	smVec	the smoothed version of the vector. At least as large as `vec`.
[in]	vec	the input vector, unaltered.
[in]	vecSize	the size of `vec`
[in]	win	the full-width of the smoothing window. Should be even. 0 results in a slow memcpy.

Definition at line 530 of file vectorUtils.hpp.

◆ vectorSmoothMean() [2/3]

template<typename realT >

int mx::math::vectorSmoothMean	(	std::vector< realT > &	smVec,
		std::vector< realT > &	vec,
		int	win
	)

Smooth a vector using the mean in a window specified by its full-width.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

[out]	smVec	the smoothed version of the vector. Will be resize()-ed.
[in]	vec	the input vector, unaltered.
[in]	win	the full-width of the smoothing window. Should be even. 0 results in a slow memcpy.

Definition at line 562 of file vectorUtils.hpp.

References mx::math::vectorSmoothMean().

◆ vectorSmoothMean() [3/3]

template<typename realT >

int mx::math::vectorSmoothMean	(	std::vector< realT > &	smVec,
		std::vector< realT > &	vec,
		std::vector< int > &	wins,
		bool	norm = `false`
	)

Smooth a vector using the mean in windows specified by their full-widths.

You supply a window width for each point. This is useful for, say, logarithmically growing bin sizes in a PSD.

Returns: 0 on success; -1 but who are we kidding it we don't check for errors

Parameters

[out]	smVec	the smoothed version of the vector
[in]	vec	the input vector, unaltered.
[in]	wins	the full-widths of the smoothing windows, same size as vec.
[in]	norm	if true the output will normalized to have the same integral as the input.

Definition at line 580 of file vectorUtils.hpp.

Referenced by mx::math::vectorSmoothMean().

◆ vectorSmoothMedian()

template<typename realT >

int mx::math::vectorSmoothMedian	(	std::vector< realT > &	smVec,
		std::vector< realT > &	vec,
		int	win
	)

Smooth a vector using the median in a window specified by its full-width.

Parameters

[out]	smVec	the smoothed version of the vector
[in]	vec	the input vector, unaltered.
[in]	win	the full-width of the smoothing window

Definition at line 629 of file vectorUtils.hpp.

References mx::math::vectorMedianInPlace().

◆ vectorSortOrder()

template<typename memberT >

std::vector<size_t> mx::math::vectorSortOrder ( std::vector< memberT > const & values )

Return the indices of the vector in sorted order, without altering the vector itself.

Example:

std::vector<double> x;
// -> fill in x with values
 
std::vector<size_t> idx;
idx = mx::sortOrder(x);
 
//Print x to stdout in sorted order
for(int i=0; i< x.size(); ++i) std::cout << x[idx[i]] << "\n";

Template Parameters

memberT is the member type of the vector. Must have < comparison defined.

Returns: the indices of the vector in sorted order.

Parameters

[in] values the vector to sort

Definition at line 92 of file vectorUtils.hpp.

Referenced by mx::astro::rewritePhoenixSpectrum().

◆ vectorSub() [1/2]

template<typename valueT , typename constT >

void mx::math::vectorSub	(	valueT *	vec,
		size_t	sz,
		const constT &	c
	)

Subtract a constant value from a vector.

Parameters

	vec	[in.out] the vector, each element will have the constant subtracted from it
[in]	sz	the size of the vector
[in]	c	the constant to subtract from each element

Definition at line 486 of file vectorUtils.hpp.

References mx::astro::constants::c().

◆ vectorSub() [2/2]

template<typename vecT , typename constT >

void mx::math::vectorSub	(	vecT &	vec,
		const constT &	c
	)

Subtract a constant value from a vector.

Parameters

	vec	[in.out] the vector, each element will have the constant subtracted from it
[in]	c	the constant to subtract from each element

Definition at line 496 of file vectorUtils.hpp.

References mx::astro::constants::c().

Referenced by mx::math::vectorMeanSub(), and mx::math::vectorMedianSub().

◆ vectorSum() [1/2]

template<typename valueT >

valueT mx::math::vectorSum	(	const valueT *	vec,
		size_t	sz
	)

Calculate the sum of a vector.

Returns: the sum of vec

Template Parameters

vectorT the std::vector type of vec

Parameters

[in]	vec	the vector
[in]	sz	the size of the vector

Definition at line 112 of file vectorUtils.hpp.

◆ vectorSum() [2/2]

template<typename vectorT >

vectorT::value_type mx::math::vectorSum ( const vectorT & vec )

Calculate the sum of a vector.

Returns: the sum of vec

Template Parameters

vectorT the std::vector type of vec

Parameters

[in] vec the vector

Definition at line 132 of file vectorUtils.hpp.

◆ vectorVariance() [1/4]

template<typename valueT >

valueT mx::math::vectorVariance	(	const valueT *	vec,
		size_t	sz
	)

Calculate the variance of a vector.

Returns: the variance of vec

Template Parameters

vectorT the std::vector type of vec

Parameters

[in]	vec	the vector
[in]	sz	the size of the vector

Definition at line 327 of file vectorUtils.hpp.

References mx::math::vectorMean(), and mx::math::vectorVariance().

◆ vectorVariance() [2/4]

template<typename valueT >

valueT mx::math::vectorVariance	(	const valueT *	vec,
		size_t	sz,
		valueT	mean
	)

Calculate the variance of a vector relative to a supplied mean value.

Returns: the variance of vec w.r.t. mean

Template Parameters

valueT the data type

Parameters

[in]	vec	the vector
[in]	sz	the size of the vector
[in]	mean	the mean value with which to calculate the variance

Definition at line 282 of file vectorUtils.hpp.

Referenced by mx::improc::imCenterCircleSym< realT >::center(), mx::improc::sourceFinder< _realT >::operator()(), mx::sigproc::averagePeriodogram< realT >::operator()(), SCENARIO(), and mx::improc::stddevImage().

◆ vectorVariance() [3/4]

template<typename vectorT >

vectorT::value_type mx::math::vectorVariance ( const vectorT & vec )

Calculate the variance of a vector.

Returns: the variance of vec

Template Parameters

vectorT the std::vector type of vec

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

[in] vec the vector

Definition at line 346 of file vectorUtils.hpp.

References mx::math::vectorMean().

Referenced by mx::math::vectorSigmaMean(), and mx::math::vectorVariance().

◆ vectorVariance() [4/4]

template<typename vectorT >

vectorT::value_type mx::math::vectorVariance	(	const vectorT &	vec,
		const typename vectorT::value_type &	mean
	)

Calculate the variance of a vector relative to a supplied mean value.

Returns: the variance of vec w.r.t. mean

Template Parameters

vectorT the std::vector type of vec

Parameters

[in]	vec	the vector
[in]	mean	the mean value with which to calculate the variance

Definition at line 305 of file vectorUtils.hpp.