Various math functions performed on eisgenerator types . More...

Functions
std::complex< fvalue >	eis::absGrad (const std::vector< eis::DataPoint > &data, size_t index)
	Calculates the element wise absolute gradient at the given point of the data given.

fvalue	eis::grad (const std::vector< fvalue > &data, const std::vector< fvalue > &omega, size_t index)
	Calculates derivative at the given point of the data given.

std::complex< fvalue >	eis::grad (const std::vector< eis::DataPoint > &data, size_t index)
	Calculates the gradient at the given point of the data given.

fvalue	eis::mean (const std::vector< fvalue > &data)
	Calculates the mean of the given data.

std::complex< fvalue >	eis::mean (const std::vector< eis::DataPoint > &data)
	Calculates the mean of the given data.

fvalue	eis::median (std::vector< fvalue > data)
	Calculates the median of the given data.

std::complex< fvalue >	eis::median (const std::vector< eis::DataPoint > &data)
	Calculates the median of the given data.

void	eis::difference (std::vector< eis::DataPoint > &a, const std::vector< eis::DataPoint > &b)
	Calculates the difference between two spectra.

std::vector< eis::DataPoint >	eis::rescale (const std::vector< eis::DataPoint > &data, size_t outputSize)
	Resamples the data to the given amount of points.

fvalue	eis::pearsonCorrelation (const std::vector< eis::DataPoint > &data)
	Calculates the Pearson correlation between the imaginary and the real part of the data.

fvalue	eis::nyquistAreaVariance (const std::vector< eis::DataPoint > &data, eis::DataPoint *centroid=nullptr)
	Calculates the variance of the distance of the data from a centroid in the nyquist plane.

fvalue	eis::maximumNyquistJump (const std::vector< eis::DataPoint > &data)
	Finds the maximum distance between subsequent points in the data in the nyquist plane.

void	eis::noise (std::vector< eis::DataPoint > &data, double amplitude, bool relative)
	Adds white noise to the data.

void	eis::removeDuplicates (std::vector< eis::DataPoint > &data)
	Removes duplicate data points from the data.

bool	eis::fvalueEq (fvalue a, fvalue b, unsigned int ulp=4)
	Checks two fvalues for equality.

std::vector< eis::DataPoint >	eis::fitToFrequencies (std::vector< fvalue > omegas, const std::vector< eis::DataPoint > &data, bool linearExtrapolation=false)
	This function resamples, extrapolates and interpolates to fit the data given to the frequencies also given.

Detailed Description

Various math functions performed on eisgenerator types .

Function Documentation

◆ absGrad()

std::complex< fvalue > eis::absGrad	(	const std::vector< eis::DataPoint > &	data,
		size_t	index )

Calculates the element wise absolute gradient at the given point of the data given.

Parameters

data	The data to calculate the gradient on.
index	The position in the data to calculate the gradient at.

Returns: The element wise absolute gradient abs(re(grad(a)))+abs(im(grad(a)))i.

◆ difference()

void eis::difference	(	std::vector< eis::DataPoint > &	a,
		const std::vector< eis::DataPoint > &	b )

Calculates the difference between two spectra.

this function calculates an element wise a = a-b and ingores omega

Parameters

a	The first operand, where b is subtracted
b	The second operand that is subtracted from the first, must be the same size as a

◆ fitToFrequencies()

std::vector< eis::DataPoint > eis::fitToFrequencies	(	std::vector< fvalue >	omegas,
		const std::vector< eis::DataPoint > &	data,
		bool	linearExtrapolation = false )

This function resamples, extrapolates and interpolates to fit the data given to the frequencies also given.

Data is resampled to the target size, interpolation for data points is performed using linear interpolation, extrapolation is performed using linear or base 10 logarithmic extrapolation.

Parameters

omegas	The frequencies to resample the data to.
data	The data to resample.
linearExtrapolation	true if linear extrapolation is to be performed, otherwise base 10 logarithmic extrapolation is used.

Returns: The resampled data.

◆ fvalueEq()

bool eis::fvalueEq	(	fvalue	a,
		fvalue	b,
		unsigned int	ulp = 4 )

Checks two fvalues for equality.

Equality is considered given when the values are within ulp epsilons at the magnitude of the sum of operands.

Parameters

a	the first value to compare
b	the second value to compare

Returns: true if equal, false if unequal

◆ grad() [1/2]

std::complex< fvalue > eis::grad	(	const std::vector< eis::DataPoint > &	data,
		size_t	index )

Calculates the gradient at the given point of the data given.

Parameters

data	The data to calculate the gradient on.
index	The position in the data to calculate the gradient at.

Returns: The gradient.

◆ grad() [2/2]

fvalue eis::grad	(	const std::vector< fvalue > &	data,
		const std::vector< fvalue > &	omega,
		size_t	index )

Calculates derivative at the given point of the data given.

Parameters

data	The data to calculate the gradient on.
index	The position in the data to calculate the gradient at.

Returns: The derivative.

◆ maximumNyquistJump()

fvalue eis::maximumNyquistJump ( const std::vector< eis::DataPoint > & data )

Finds the maximum distance between subsequent points in the data in the nyquist plane.

Parameters

data	The data to use.

Returns: The largest distance.

◆ mean() [1/2]

std::complex< fvalue > eis::mean ( const std::vector< eis::DataPoint > & data )

Calculates the mean of the given data.

Parameters

data	The data to calculate the mean of.

Returns: The mean

◆ mean() [2/2]

fvalue eis::mean ( const std::vector< fvalue > & data )

Calculates the mean of the given data.

Parameters

data	The data to calculate the mean of.

Returns: The mean

◆ median() [1/2]

std::complex< fvalue > eis::median ( const std::vector< eis::DataPoint > & data )

Calculates the median of the given data.

Parameters

data	The data to calculate the median of.

Returns: The median.

◆ median() [2/2]

fvalue eis::median ( std::vector< fvalue > data )

Calculates the median of the given data.

Parameters

data	The data to calculate the median of.

Returns: The median.

◆ noise()

void eis::noise	(	std::vector< eis::DataPoint > &	data,
		double	amplitude,
		bool	relative )

Adds white noise to the data.

Parameters

data	The data to add noise to.
amplitude	The amplitude of the noise.
relative	If true, the amplitude will be taken as relative to the magnitude of the data, otherwise it will be taken as an absolute value.

◆ nyquistAreaVariance()

fvalue eis::nyquistAreaVariance	(	const std::vector< eis::DataPoint > &	data,
		eis::DataPoint *	centroid = nullptr )

Calculates the variance of the distance of the data from a centroid in the nyquist plane.

Parameters

data	The data to calculate on.
centroid	The centroid to use, if nullptr is passed here, the mean of the data will be used as the centroid.

Returns: The variance.

◆ pearsonCorrelation()

fvalue eis::pearsonCorrelation ( const std::vector< eis::DataPoint > & data )

Calculates the Pearson correlation between the imaginary and the real part of the data.

Parameters

data	Data to calculate the Pearson correlation on.

Returns: the Pearson correlation coefficient.

◆ removeDuplicates()

void eis::removeDuplicates ( std::vector< eis::DataPoint > & data )

Removes duplicate data points from the data.

Duplicates are detected by checking the value of omega for sameness using fvalueEq with the default ulp.

Parameters

data	the data to remove duplicates from

◆ rescale()

std::vector< eis::DataPoint > eis::rescale	(	const std::vector< eis::DataPoint > &	data,
		size_t	outputSize )

Resamples the data to the given amount of points.

Parameters

data	Data to resample.
outputSize	Size to resample to.

Returns: The resampled data.

Functions

Detailed Description

Function Documentation

◆ absGrad()

◆ difference()

◆ fitToFrequencies()

◆ fvalueEq()

◆ grad() [1/2]

◆ grad() [2/2]

◆ maximumNyquistJump()

◆ mean() [1/2]

◆ mean() [2/2]

◆ median() [1/2]

◆ median() [2/2]

◆ noise()

◆ nyquistAreaVariance()

◆ pearsonCorrelation()

◆ removeDuplicates()

◆ rescale()