A namespace for math functions relating to linear least squares regression. More...

Namespaces
	Baseline

	Clustering

	DimensionReduction
	A namespace for math functions relating to dimension reduction.

	LinLeastSq

	NonLinLeastSq

	Normalization
	A namespace for math functions relating to normalization.

	PeakFinding
	A namespace for math functions relating to peak detection and counting.

	Quantification
	A namespace for math functions relating to peak quantification.

	Smoothing

	Stats

	Transform

Classes
class	DistanceMetricWrapper

class	KMeansWrapper
	The KMeansWrapper class mlpack relies heavily on template metaprogramming. This means that you only need to compile what you actually use. But Vespucci must be precompiled with all possible options availible at runtime. Here, we instantiate supported combinations of template parameters for the kmeans class in mlpack. More...

Functions
VESPUCCI_EXPORT arma::uword	LocalMaximum (const arma::vec &X, double &value)
	Vespucci::Math::LocalMaximum. More...

VESPUCCI_EXPORT arma::uword	LocalMaximum (const arma::vec &dX, const arma::vec &d2X, double &value)

VESPUCCI_EXPORT arma::uword	LocalMaximum (const arma::vec &X, const arma::vec &dX, const arma::vec &d2X, double &value)
	Vespucci::Math::LocalMaximum. More...

VESPUCCI_EXPORT arma::uword	LocalMinimum (const arma::mat &X, double &value)
	Vespucci::Math::LocalMinimum. More...

VESPUCCI_EXPORT arma::uword	LocalMinimum (const arma::vec &dX, const arma::vec &d2X, double &value)

VESPUCCI_EXPORT arma::uword	LocalMinimum (const arma::vec &X, const arma::vec &dX, const arma::mat &d2X, double &value)
	Vespucci::Math::LocalMinimum. More...

VESPUCCI_EXPORT arma::sp_mat	LocalMaxima (const arma::mat &X)
	Vespucci::Math::LocalMaxima. More...

VESPUCCI_EXPORT arma::sp_mat	LocalMaxima (const arma::mat &X, const arma::mat &dX, const arma::mat &d2X)
	Vespucci::Math::LocalMaxima. More...

VESPUCCI_EXPORT arma::sp_mat	LocalMinima (const arma::mat &X)
	Vespucci::Math::LocalMinima. More...

VESPUCCI_EXPORT arma::sp_mat	LocalMinima (const arma::mat &X, const arma::mat &dX, const arma::mat &d2X)
	Vespucci::Math::LocalMinima. More...

VESPUCCI_EXPORT arma::sp_mat	LocalMinimaWindow (const arma::mat &X, const int window_size)
	Vespucci::Math::LocalMinimaWindow. More...

VESPUCCI_EXPORT arma::sp_mat	LocalMaximaWindow (const arma::mat &X, const int window_size)
	Vespucci::Math::LocalMaximaWindow "Cleans" local maximum by window search to remove extraneous values. More...

VESPUCCI_EXPORT arma::sp_mat	LocalMinimaCWT (arma::mat coefs, arma::uvec scales, arma::uword min_window_size, double amplitude_threshold)

VESPUCCI_EXPORT arma::sp_mat	LocalMaximaCWT (arma::mat coefs, arma::uvec scales, arma::uword min_window_size)

VESPUCCI_EXPORT double	quantile (arma::vec &data, double probs)

VESPUCCI_EXPORT arma::vec	ExtendToNextPow (arma::vec X, arma::uword n)

VESPUCCI_EXPORT arma::uword	NextPow (arma::uword number, arma::uword power)

VESPUCCI_EXPORT arma::mat	spdiags (arma::mat B, arma::ivec d, arma::uword m, arma::uword n)
	spdiags analgous to the Octave/arma::matLAB function A = spdiags(B, d, m, n). More...

VESPUCCI_EXPORT arma::mat	orth (arma::mat X)
	orth Returns an orthonormal basis of the range space of A More...

VESPUCCI_EXPORT arma::uword	min (arma::uword a, arma::uword b)
	Vespucci::Math::min. More...

VESPUCCI_EXPORT arma::uword	max (arma::uword a, arma::uword b)
	Vespucci::Math::max. More...

VESPUCCI_EXPORT void	position (arma::uword index, arma::uword n_rows, arma::uword n_cols, arma::uword &i, arma::uword &j)
	Vespucci::Math::position Find row and column numbers for index. More...

VESPUCCI_EXPORT arma::umat	to_row_column (arma::uvec indices, arma::uword n_rows, arma::uword n_cols)

VESPUCCI_EXPORT double	RecalculateAverage (double new_value, double old_average, double old_count)
	Vespucci::Math::RecalculateAverage Recalculate the average value when a new value is added to a list for which only the previous means, stddevs and counts are known. More...

VESPUCCI_EXPORT double	RecalculateStdDev (double new_value, double old_mean, double old_stddev, double old_count)
	Vespucci::Math::RecalculateStdDev Recalculate a standard deviation when a new value is added to a list for which only the previous means, stddevs and counts are known. More...

VESPUCCI_EXPORT arma::umat	GetClosestValues (arma::vec query, arma::vec target, const arma::uword k=5)
	Vespucci::Math::GetClosestValues. More...

VESPUCCI_EXPORT double	CalcPoly (const double x, const arma::vec &coefs)
	Vespucci::Math::CalcPoly Calculate the value of a polynomial at particular point. More...

VESPUCCI_EXPORT arma::vec	RepresentativeSpectrum (const arma::mat &spectra, arma::uword &index, std::string metric_name="euclidean", std::string center="centroid")
	Vespucci::Math::RepresentativeSpectrum. More...

VESPUCCI_EXPORT arma::vec	WavelengthToFrequency (const arma::vec &x, double freq_factor, double wl_factor)
	Vespucci::Math::WavelengthToFrequency. More...

VESPUCCI_EXPORT arma::vec	FrequencyToWavelength (const arma::vec &x, double wl_factor, double freq_factor)
	Vespucci::Math::FrequencyToWavelength. More...

VESPUCCI_EXPORT arma::vec	FrequencyToEnergy (const arma::vec &x, double energy_factor, double freq_factor)
	Vespucci::Math::FrequencyToEnergy. More...

VESPUCCI_EXPORT arma::vec	EnergyToFrequency (const arma::vec &x, double freq_factor, double energy_factor)
	Vespucci::Math::EnergyToFrequency. More...

VESPUCCI_EXPORT arma::vec	WavenumberToFrequency (const arma::vec &x, double freq_factor, double wn_factor)
	Vespucci::Math::WavenumberToFrequency. More...

VESPUCCI_EXPORT arma::vec	FrequencyToWavenumber (const arma::vec &x, double wn_factor, double freq_factor)
	Vespucci::Math::FrequencyToWavenumber. More...

VESPUCCI_EXPORT arma::vec	WavenumberToWavelength (const arma::vec &x, double wn_factor, double wl_factor)
	Vespucci::Math::WavenumberToWavelength. More...

VESPUCCI_EXPORT arma::vec	WavelengthToWavenumber (const arma::vec &x, double wl_factor, double wn_factor)
	Vespucci::Math::WavelengthToWavenumber. More...

VESPUCCI_EXPORT arma::vec	WavelengthToEnergy (const arma::vec &x, double energy_factor, double wl_factor)
	Vespucci::Math::WavelengthToEnergy. More...

VESPUCCI_EXPORT arma::vec	EnergyToWavelength (const arma::vec &x, double wl_factor, double energy_factor)
	Vespucci::Math::EnergyToWavelength. More...

VESPUCCI_EXPORT arma::vec	EnergyToWavenumber (const arma::vec &x, double wn_factor, double energy_factor)
	Vespucci::Math::EnergyToWavenumber. More...

VESPUCCI_EXPORT arma::vec	WavenumberToEnergy (const arma::vec &x, double energy_factor, double wn_factor)
	Vespucci::Math::WavenumberToEnergy. More...

VESPUCCI_EXPORT bool	AreEqual (const arma::vec &a, const arma::vec &b)
	AreEqual. More...

VESPUCCI_EXPORT bool	IsMonotonic (const arma::vec &x)
	IsMonotonic. More...

VESPUCCI_EXPORT bool	IsIncreasing (const arma::vec &x)
	IsIncreasing. More...

VESPUCCI_EXPORT arma::cx_vec	cx_zeros (arma::uword n)
	Vespucci::Math::cx_zeros. More...

VESPUCCI_EXPORT arma::cx_mat	cx_zeros (arma::uword m, arma::uword n)
	Vespucci::Math::cx_zeros. More...

VESPUCCI_EXPORT arma::uword	ClosestIndex (double value, const arma::vec &vector)
	Vespucci::Math::ClosestIndex. More...

VESPUCCI_EXPORT arma::uvec	Intersection (arma::uvec &x, arma::uvec &y)
	Vespucci::Math::Intersection. More...

VESPUCCI_EXPORT double	CalculateRSquared (const arma::vec &data, const arma::vec &fit, arma::vec &residuals)
	Vespucci::Math::CalculateRSquared. More...

VESPUCCI_EXPORT arma::mat	SafeRows (const arma::mat &x, arma::uword a, arma::uword b)
	Vespucci::Math::SafeRows. More...

template<typename T >
T	conv_fft (const T &A, const T &B, std::string type)

template<typename T >
T	rotate (const T &X, arma::uword shift_by, bool slide_back=true)

template<typename T >
T	diff (const T &X, arma::uword deriv_order=1)
	Vespucci::Math::diff. More...

Detailed Description

A namespace for math functions relating to linear least squares regression.

A namespace for math functions.

:::LinLeastSq

Function Documentation

bool Vespucci::Math::AreEqual	(	const arma::vec &	a,
		const arma::vec &	b
	)

AreEqual.

Parameters

a
b

Returns: Whether or not all elements in the two vectors are equal

Definition at line 858 of file accessory.cpp.

double Vespucci::Math::CalcPoly	(	const double	x,
		const arma::vec &	coefs
	)

Vespucci::Math::CalcPoly Calculate the value of a polynomial at particular point.

Parameters

x	The value at which to evaluate a polynomial.
coefs	The coefficients of the polynomial ordered from constant to highest order

Returns: The value of the polynomial at x

Definition at line 599 of file accessory.cpp.

double Vespucci::Math::CalculateRSquared	(	const arma::vec &	data,
		const arma::vec &	fit,
		arma::vec &	residuals
	)

Vespucci::Math::CalculateRSquared.

Parameters

data
fit
residuals

Returns: calcuate residuals and R-squared from fit fit to data data.

Definition at line 1008 of file accessory.cpp.

arma::uword Vespucci::Math::ClosestIndex	(	double	value,
		const arma::vec &	vector
	)

Vespucci::Math::ClosestIndex.

Parameters

value
vector

Returns: Find the index of value in vector closest to the specified value

Definition at line 932 of file accessory.cpp.

template<typename T >

T Vespucci::Math::conv_fft	(	const T &	A,
		const T &	B,
		std::string	type
	)

Definition at line 102 of file accessory_impl.h.

arma::cx_vec Vespucci::Math::cx_zeros ( arma::uword n )

Vespucci::Math::cx_zeros.

Parameters

n

Returns

Definition at line 921 of file accessory.cpp.

arma::cx_mat Vespucci::Math::cx_zeros	(	arma::uword	m,
		arma::uword	n
	)

Vespucci::Math::cx_zeros.

Parameters

m
n

Returns: ]

Definition at line 911 of file accessory.cpp.

template<typename T >

T Vespucci::Math::diff	(	const T &	X,
		arma::uword	deriv_order = `1`
	)

Vespucci::Math::diff.

Parameters

X	A vector represetning a signal or a arma::matrix where each column is a signal
deriv_order	The derivative order to calculate

Returns: The deriv_order-th derivative of X, a vector with deriv_order fewer elements than X.

Perform arithmetic differentiation of a vector or arma::matrix (if X is a arma::matrix, the differentiation is performed to all the columns).

Definition at line 47 of file accessory_impl.h.

arma::vec Vespucci::Math::EnergyToFrequency	(	const arma::vec &	x,
		double	freq_factor,
		double	energy_factor
	)

Vespucci::Math::EnergyToFrequency.

Parameters

x
freq_factor
energy_factor

Returns

Definition at line 657 of file accessory.cpp.

arma::vec Vespucci::Math::EnergyToWavelength	(	const arma::vec &	x,
		double	wl_factor,
		double	energy_factor
	)

Vespucci::Math::EnergyToWavelength.

Parameters

x
wl_factor
energy_factor

Returns

Definition at line 746 of file accessory.cpp.

arma::vec Vespucci::Math::EnergyToWavenumber	(	const arma::vec &	x,
		double	wn_factor,
		double	energy_factor
	)

Vespucci::Math::EnergyToWavenumber.

Parameters

x
wn_factor
energy_factor

Returns

Definition at line 760 of file accessory.cpp.

arma::vec Vespucci::Math::ExtendToNextPow	(	arma::vec	X,
		arma::uword	n
	)

Definition at line 259 of file accessory.cpp.

arma::vec Vespucci::Math::FrequencyToEnergy	(	const arma::vec &	x,
		double	energy_factor,
		double	freq_factor
	)

Vespucci::Math::FrequencyToEnergy.

Parameters

x
energy_factor
freq_factor

Returns

Definition at line 643 of file accessory.cpp.

arma::vec Vespucci::Math::FrequencyToWavelength	(	const arma::vec &	x,
		double	wl_factor,
		double	freq_factor
	)

Vespucci::Math::FrequencyToWavelength.

Parameters

x
wl_factor
freq_factor

Returns

Definition at line 629 of file accessory.cpp.

arma::vec Vespucci::Math::FrequencyToWavenumber	(	const arma::vec &	x,
		double	wn_factor,
		double	freq_factor
	)

Vespucci::Math::FrequencyToWavenumber.

Parameters

x
wn_factor
freq_factor

Returns

Definition at line 686 of file accessory.cpp.

arma::umat Vespucci::Math::GetClosestValues	(	arma::vec	query,
		arma::vec	target,
		const arma::uword	k = `5`
	)

Vespucci::Math::GetClosestValues.

Parameters

query
target
k

Returns: The indices of the k values in target closest to each value in query k should be odd in case query and target contain equal values

Definition at line 576 of file accessory.cpp.

arma::uvec Vespucci::Math::Intersection	(	arma::uvec &	x,
		arma::uvec &	y
	)

Vespucci::Math::Intersection.

Parameters

x
y

Returns: Find the intersection between two sets of indices (the values in common between the two).

Definition at line 990 of file accessory.cpp.

bool Vespucci::Math::IsIncreasing ( const arma::vec & x )

IsIncreasing.

Parameters

x

Returns

Definition at line 894 of file accessory.cpp.

bool Vespucci::Math::IsMonotonic ( const arma::vec & x )

IsMonotonic.

Parameters

x

Returns

Definition at line 877 of file accessory.cpp.

arma::sp_mat Vespucci::Math::LocalMaxima ( const arma::mat & X )

Vespucci::Math::LocalMaxima.

Parameters

X	A matrix with signals as columns

Returns: A sparse matrix containing the value of each local maximum at the appropriate position. Find the local maxima of a matrix of signals using the first and second derivative tests. Works best with smooth signals (like CWT coeffs)

Definition at line 294 of file accessory.cpp.

arma::sp_mat Vespucci::Math::LocalMaxima	(	const arma::mat &	X,
		const arma::mat &	dX,
		const arma::mat &	d2X
	)

Vespucci::Math::LocalMaxima.

Parameters

X	A matrix of signals
dX	A matrix of first derivatives of signals (numerical, S-G, wavelet, etc)
d2X	A matrix of second derivatives of signals (numerical, S-G, wavelet, etc).

Returns

Definition at line 317 of file accessory.cpp.

arma::sp_mat Vespucci::Math::LocalMaximaCWT	(	arma::mat	coefs,
		arma::uvec	scales,
		arma::uword	min_window_size
	)

Definition at line 780 of file accessory.cpp.

arma::sp_mat Vespucci::Math::LocalMaximaWindow	(	const arma::mat &	X,
		const int	window_size
	)

Vespucci::Math::LocalMaximaWindow "Cleans" local maximum by window search to remove extraneous values.

Parameters

X
window_size

Returns

Definition at line 830 of file accessory.cpp.

arma::uword Vespucci::Math::LocalMaximum	(	const arma::vec &	X,
		double &	value
	)

Vespucci::Math::LocalMaximum.

Parameters

X
value

Returns

Definition at line 30 of file accessory.cpp.

VESPUCCI_EXPORT arma::uword Vespucci::Math::LocalMaximum	(	const arma::vec &	dX,
		const arma::vec &	d2X,
		double &	value
	)

arma::uword Vespucci::Math::LocalMaximum	(	const arma::vec &	X,
		const arma::vec &	dX,
		const arma::vec &	d2X,
		double &	value
	)

Vespucci::Math::LocalMaximum.

Parameters

X
dX
d2X
value

Returns

Definition at line 54 of file accessory.cpp.

arma::sp_mat Vespucci::Math::LocalMinima ( const arma::mat & X )

Vespucci::Math::LocalMinima.

Parameters

X

Returns

Definition at line 378 of file accessory.cpp.

arma::sp_mat Vespucci::Math::LocalMinima	(	const arma::mat &	X,
		const arma::mat &	dX,
		const arma::mat &	d2X
	)

Vespucci::Math::LocalMinima.

Parameters

X
dX
d2X

Returns

Definition at line 401 of file accessory.cpp.

VESPUCCI_EXPORT arma::sp_mat Vespucci::Math::LocalMinimaCWT	(	arma::mat	coefs,
		arma::uvec	scales,
		arma::uword	min_window_size,
		double	amplitude_threshold
	)

arma::sp_mat Vespucci::Math::LocalMinimaWindow	(	const arma::mat &	X,
		const int	window_size
	)

Vespucci::Math::LocalMinimaWindow.

Parameters

X
window_size

Returns

Definition at line 801 of file accessory.cpp.

arma::uword Vespucci::Math::LocalMinimum	(	const arma::mat &	X,
		double &	value
	)

Vespucci::Math::LocalMinimum.

Parameters

X
value

Returns

Definition at line 77 of file accessory.cpp.

VESPUCCI_EXPORT arma::uword Vespucci::Math::LocalMinimum	(	const arma::vec &	dX,
		const arma::vec &	d2X,
		double &	value
	)

arma::uword Vespucci::Math::LocalMinimum	(	const arma::vec &	X,
		const arma::vec &	dX,
		const arma::mat &	d2X,
		double &	value
	)

Vespucci::Math::LocalMinimum.

Parameters

X
dX
d2X
value

Returns

Definition at line 103 of file accessory.cpp.

arma::uword Vespucci::Math::max	(	arma::uword	a,
		arma::uword	b
	)

Vespucci::Math::max.

Parameters

a
b

Returns: std::max stopped working with arma::uwords for some reason, so I made a max function It might be a better idea to just cast uwords to int and use std::max

Definition at line 237 of file accessory.cpp.

arma::uword Vespucci::Math::min	(	arma::uword	a,
		arma::uword	b
	)

Vespucci::Math::min.

Parameters

a
b

Returns: std::min stopped working with arma::uwords for some reason, so I made a min function It might be a better idea to just cast uwords to int and use std::min

Definition at line 249 of file accessory.cpp.

arma::uword Vespucci::Math::NextPow	(	arma::uword	number,
		arma::uword	power
	)

Definition at line 281 of file accessory.cpp.

arma::mat Vespucci::Math::orth ( arma::mat X )

orth Returns an orthonormal basis of the range space of A

Parameters

X	arma::matrix

Returns: a arma::matrix whose columns form an orthonormal basis for X This function was written before MLPACK was used. The MLPACK method mlpack::math::Orthogonalize does the same thing

Definition at line 208 of file accessory.cpp.

void Vespucci::Math::position	(	arma::uword	index,
		arma::uword	n_rows,
		arma::uword	n_cols,
		arma::uword &	i,
		arma::uword &	j
	)

Vespucci::Math::position Find row and column numbers for index.

Parameters

index
n_rows	Number of rows
n_cols	Number of columns
i	Row number
j	Column number

Definition at line 469 of file accessory.cpp.

double Vespucci::Math::quantile	(	arma::vec &	data,
		double	probs
	)

Definition at line 503 of file accessory.cpp.

double Vespucci::Math::RecalculateAverage	(	double	new_value,
		double	old_average,
		double	old_count
	)

Vespucci::Math::RecalculateAverage Recalculate the average value when a new value is added to a list for which only the previous means, stddevs and counts are known.

Parameters

new_value
old_average
old_count

Returns

Definition at line 535 of file accessory.cpp.

double Vespucci::Math::RecalculateStdDev	(	double	new_value,
		double	old_mean,
		double	old_stddev,
		double	old_count
	)

Vespucci::Math::RecalculateStdDev Recalculate a standard deviation when a new value is added to a list for which only the previous means, stddevs and counts are known.

Parameters

new_value
old_mean
old_stddev
old_count

Returns

Definition at line 552 of file accessory.cpp.

arma::vec Vespucci::Math::RepresentativeSpectrum	(	const arma::mat &	spectra,
		arma::uword &	index,
		std::string	metric_name = `"euclidean"`,
		std::string	center_type = `"centroid"`
	)

Vespucci::Math::RepresentativeSpectrum.

Parameters

spectra
metric	Distance metric
center

Returns

Definition at line 953 of file accessory.cpp.

template<typename T >

T Vespucci::Math::rotate	(	const T &	X,
		arma::uword	shift_by,
		bool	slide_back = `true`
	)

Definition at line 65 of file accessory_impl.h.

arma::mat Vespucci::Math::SafeRows	(	const arma::mat &	x,
		arma::uword	a,
		arma::uword	b
	)

Vespucci::Math::SafeRows.

Parameters

x
a
b

Returns: An alternative to arma::mat::rows that allows a and b to be equal, a to be larger than b, and the range to be greater than the end of the vector (all things that are allowed in R). This makes translating from R easier.

Definition at line 1030 of file accessory.cpp.

arma::mat Vespucci::Math::spdiags	(	arma::mat	B,
		arma::ivec	d,
		arma::uword	m,
		arma::uword	n
	)

spdiags analgous to the Octave/arma::matLAB function A = spdiags(B, d, m, n).

Parameters

B	a arma::matrix containing the new diagonal vectors as columns
d	a vector containing the row numbers to set. The first column vector of B corresponds to the first entry in d.
m	the number of rows of the output arma::matrix
n	the number of columns of the output arma::matrix

Returns: a m by n sparase arma::matrix with the columns of B as diagonals A translation of the Octave/arma::matLAB function A = spdiags(B, d, m, n). For subdiagonals (entries of d < 0) vectors are truncated at the end when they are longer than the target diagonal. For superdiagonals, vectors are truncated at the beginning when they are longer than the target diagonal.

Definition at line 137 of file accessory.cpp.

arma::umat Vespucci::Math::to_row_column	(	arma::uvec	indices,
		arma::uword	n_rows,
		arma::uword	n_cols
	)

Definition at line 488 of file accessory.cpp.

arma::vec Vespucci::Math::WavelengthToEnergy	(	const arma::vec &	x,
		double	energy_factor,
		double	wl_factor
	)

Vespucci::Math::WavelengthToEnergy.

Parameters

x
energy_factor
wl_factor

Returns

Definition at line 731 of file accessory.cpp.

arma::vec Vespucci::Math::WavelengthToFrequency	(	const arma::vec &	x,
		double	freq_factor,
		double	wl_factor
	)

Vespucci::Math::WavelengthToFrequency.

Parameters

x
freq_factor
wl_factor

Returns

Definition at line 614 of file accessory.cpp.

arma::vec Vespucci::Math::WavelengthToWavenumber	(	const arma::vec &	x,
		double	wl_factor,
		double	wn_factor
	)

Vespucci::Math::WavelengthToWavenumber.

Parameters

x
wl_factor
wn_factor

Returns

Definition at line 716 of file accessory.cpp.

arma::vec Vespucci::Math::WavenumberToEnergy	(	const arma::vec &	x,
		double	energy_factor,
		double	wn_factor
	)

Vespucci::Math::WavenumberToEnergy.

Parameters

x
energy_factor
wn_factor

Returns

Definition at line 773 of file accessory.cpp.

arma::vec Vespucci::Math::WavenumberToFrequency	(	const arma::vec &	x,
		double	freq_factor,
		double	wn_factor
	)

Vespucci::Math::WavenumberToFrequency.

Parameters

x
freq_factor
wn_factor

Returns

Definition at line 671 of file accessory.cpp.

arma::vec Vespucci::Math::WavenumberToWavelength	(	const arma::vec &	x,
		double	wn_factor,
		double	wl_factor
	)

Vespucci::Math::WavenumberToWavelength.

Parameters

x
wn_factor
wl_factor

Returns

Definition at line 701 of file accessory.cpp.

Namespaces

Classes

Functions

Detailed Description

Function Documentation