Static helper functions for simple mathematical calculations. More...

#include <MathUtilities.h>

Public Types
enum	NormaliseType { NormaliseNone, NormaliseUnitSum, NormaliseUnitMax }

Static Public Member Functions
static double	round (double x)
	Round x to the nearest integer. More...

static void	getFrameMinMax (const double data, int len, double min, double *max)
	Return through min and max pointers the highest and lowest values in the given array of the given length. More...

static double	mean (const double *src, int len)
	Return the mean of the given array of the given length. More...

static double	mean (const std::vector< double > &data, int start, int count)
	Return the mean of the subset of the given vector identified by start and count. More...

static double	sum (const double *src, int len)
	Return the sum of the values in the given array of the given length. More...

static double	median (const double *src, int len)
	Return the median of the values in the given array of the given length. More...

static double	princarg (double ang)
	The principle argument function. More...

static double	mod (double x, double y)
	Floating-point division modulus: return x % y. More...

static void	getAlphaNorm (const double data, int len, int alpha, double ANorm)
	The alpha norm is the alpha'th root of the mean alpha'th power magnitude. More...

static double	getAlphaNorm (const std::vector< double > &data, int alpha)
	The alpha norm is the alpha'th root of the mean alpha'th power magnitude. More...

static void	normalise (double *data, int length, NormaliseType n=NormaliseUnitMax)

static void	normalise (std::vector< double > &data, NormaliseType n=NormaliseUnitMax)

static double	getLpNorm (const std::vector< double > &data, int p)
	Calculate the L^p norm of a vector. More...

static std::vector< double >	normaliseLp (const std::vector< double > &data, int p, double threshold=1e-6)
	Normalise a vector by dividing through by its L^p norm. More...

static void	adaptiveThreshold (std::vector< double > &data)
	Threshold the input/output vector data against a moving-mean average filter. More...

static void	circShift (double *data, int length, int shift)

static int	getMax (double data, int length, double max=0)

static int	getMax (const std::vector< double > &data, double *max=0)

static int	compareInt (const void a, const void b)

static bool	isPowerOfTwo (int x)
	Return true if x is 2^n for some integer n >= 0. More...

static int	nextPowerOfTwo (int x)
	Return the next higher integer power of two from x, e.g. More...

static int	previousPowerOfTwo (int x)
	Return the next lower integer power of two from x, e.g. More...

static int	nearestPowerOfTwo (int x)
	Return the nearest integer power of two to x, e.g. More...

static double	factorial (int x)
	Return x! More...

static int	gcd (int a, int b)
	Return the greatest common divisor of natural numbers a and b. More...

Detailed Description

Static helper functions for simple mathematical calculations.

Definition at line 26 of file MathUtilities.h.

Member Enumeration Documentation

enum MathUtilities::NormaliseType

Enumerator
NormaliseNone
NormaliseUnitSum
NormaliseUnitMax

Definition at line 93 of file MathUtilities.h.

Member Function Documentation

double MathUtilities::round ( double x )

static

Round x to the nearest integer.

Definition at line 75 of file MathUtilities.cpp.

Referenced by TempoTrack::beatPredict(), TempoTrack::createPhaseExtractor(), TempoTrack::findMeter(), and TempoTrack::phaseMM().

void MathUtilities::getFrameMinMax	(	const double *	data,
		int	len,
		double *	min,
		double *	max
	)

static

Return through min and max pointers the highest and lowest values in the given array of the given length.

Definition at line 140 of file MathUtilities.cpp.

Referenced by TempoTrack::createPhaseExtractor(), DFProcess::removeDCNormalize(), and Chromagram::unityNormalise().

double MathUtilities::mean	(	const double *	src,
		int	len
	)

static

Return the mean of the given array of the given length.

Definition at line 112 of file MathUtilities.cpp.

Referenced by GetKeyMode::GetKeyMode(), GetKeyMode::process(), and TempoTrack::tempoMM().

static double MathUtilities::mean	(	const std::vector< double > &	data,
		int	start,
		int	count
	)

static

Return the mean of the subset of the given vector identified by start and count.

double MathUtilities::sum	(	const double *	src,
		int	len
	)

static

Return the sum of the values in the given array of the given length.

Definition at line 100 of file MathUtilities.cpp.

double MathUtilities::median	(	const double *	src,
		int	len
	)

static

Return the median of the values in the given array of the given length.

If the array is even in length, the returned value will be half-way between the two values adjacent to median.

Definition at line 84 of file MathUtilities.cpp.

Referenced by DFProcess::medianFilter().

double MathUtilities::princarg ( double ang )

static

The principle argument function.

Map the phase angle ang into the range [-pi,pi).

Definition at line 33 of file MathUtilities.cpp.

Referenced by DetectionFunction::complexSD(), DetectionFunction::phaseDev(), and PhaseVocoder::unwrapPhases().

double MathUtilities::mod	(	double	x,
		double	y
	)

static

Floating-point division modulus: return x % y.

Definition at line 25 of file MathUtilities.cpp.

void MathUtilities::getAlphaNorm	(	const double *	data,
		int	len,
		int	alpha,
		double *	ANorm
	)

static

The alpha norm is the alpha'th root of the mean alpha'th power magnitude.

For example if alpha = 2 this corresponds to the RMS of the input data, and when alpha = 1 this is the mean magnitude.

Definition at line 42 of file MathUtilities.cpp.

Referenced by DFProcess::removeDCNormalize().

static double MathUtilities::getAlphaNorm	(	const std::vector< double > &	data,
		int	alpha
	)

static

The alpha norm is the alpha'th root of the mean alpha'th power magnitude.

For example if alpha = 2 this corresponds to the RMS of the input data, and when alpha = 1 this is the mean magnitude.

void MathUtilities::normalise	(	double *	data,
		int	length,
		NormaliseType	n = `NormaliseUnitMax`
	)

static

Definition at line 235 of file MathUtilities.cpp.

Referenced by Chromagram::process().

static void MathUtilities::normalise	(	std::vector< double > &	data,
		NormaliseType	n = `NormaliseUnitMax`
	)

static

double MathUtilities::getLpNorm	(	const std::vector< double > &	data,
		int	p
	)

static

Calculate the L^p norm of a vector.

Equivalent to MATLAB's norm(data, p).

Definition at line 305 of file MathUtilities.cpp.

vector< double > MathUtilities::normaliseLp	(	const std::vector< double > &	data,
		int	p,
		double	threshold = `1e-6`
	)

static

Normalise a vector by dividing through by its L^p norm.

If the norm is below the given threshold, the unit vector for that norm is returned. p may be 0, in which case no normalisation happens and the data is returned unchanged.

Definition at line 314 of file MathUtilities.cpp.

void MathUtilities::adaptiveThreshold ( std::vector< double > & data )

static

Threshold the input/output vector data against a moving-mean average filter.

Definition at line 331 of file MathUtilities.cpp.

Referenced by DownBeat::findDownBeats(), and TempoTrackV2::get_rcf().

void MathUtilities::circShift	(	double *	data,
		int	length,
		int	shift
	)

static

Definition at line 212 of file MathUtilities.cpp.

int MathUtilities::getMax	(	double *	data,
		int	length,
		double *	max = `0`
	)

static

Definition at line 165 of file MathUtilities.cpp.

Referenced by DownBeat::findDownBeats(), and GetKeyMode::process().

static int MathUtilities::getMax	(	const std::vector< double > &	data,
		double *	max = `0`
	)

static

int MathUtilities::compareInt	(	const void *	a,
		const void *	b
	)

static

Definition at line 230 of file MathUtilities.cpp.

Referenced by GetKeyMode::process().

bool MathUtilities::isPowerOfTwo ( int x )

static

Return true if x is 2^n for some integer n >= 0.

Definition at line 356 of file MathUtilities.cpp.

Referenced by DecimatorB::initialise().

int MathUtilities::nextPowerOfTwo ( int x )

static

Return the next higher integer power of two from x, e.g.

1300 -> 2048, 2048 -> 2048.

Definition at line 364 of file MathUtilities.cpp.

Referenced by DownBeat::DownBeat(), and ConstantQ::initialise().

int MathUtilities::previousPowerOfTwo ( int x )

static

Return the next lower integer power of two from x, e.g.

1300 -> 1024, 2048 -> 2048.

Definition at line 374 of file MathUtilities.cpp.

int MathUtilities::nearestPowerOfTwo ( int x )

static

Return the nearest integer power of two to x, e.g.

1300 -> 1024, 12 -> 16 (not 8; if two are equidistant, the higher is returned).

Definition at line 385 of file MathUtilities.cpp.

double MathUtilities::factorial ( int x )

static

Return x!

Definition at line 395 of file MathUtilities.cpp.

Referenced by besselTerm().

int MathUtilities::gcd	(	int	a,
		int	b
	)

static

Return the greatest common divisor of natural numbers a and b.

Definition at line 406 of file MathUtilities.cpp.

Referenced by Resampler::initialise().

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

QM-DSP

Public Types

Static Public Member Functions

Detailed Description

Member Enumeration Documentation

Member Function Documentation