mathUtils Namespace Reference

A collection of general-purpose mathematical functions for working with vectors. More...

Functions
double	maxval (const dvector &v)
	Returns the value of the maximum element of a vector.
double	minval (const dvector &v)
	Returns the value of the minimum element of a vector.
double	range (const dvector &v)
	Returns the range (maximum - minimum) of a vector.
double	sum (const dvector &v)
	Returns the sum of all the elements in a vector.
double	mean (const dvector &v)
	Returns the arithemetic mean of the elements in a vector.
double	maxval (const dvector &v, size_t iStart, size_t iEnd)
	Returns the value of the maximum element of the sub-vector of v with indices on the closed interval [iStart, iEnd]
double	minval (const dvector &v, size_t iStart, size_t iEnd)
	Returns the value of the minimum element of the sub-vector of v with indices on the closed interval [iStart, iEnd]
double	range (const dvector &v, size_t iStart, size_t iEnd)
	Returns the range (maximum - minimum) of the sub-vector of v with indices on the closed interval [iStart, iEnd]
double	sum (const dvector &v, size_t iStart, size_t iEnd)
	Returns the sum of all the elements in the sub-vector of v with indices on the closed interval [iStart, iEnd]
double	mean (const dvector &v, size_t iStart, size_t iEnd)
	Returns the arithemetic mean of the sub-vector of v with indices on the closed interval [iStart, iEnd]
size_t	minloc (const dvector &v)
	Returns the index of the minimum element of v.
size_t	maxloc (const dvector &v)
	Returns the index of the maximum element of v.
template<typename Derived >
bool	notnan (const Eigen::EigenBase< Derived > &v)
	Returns true if v does not contain any NaNs.
template<typename T >
bool	notnan (const vector< T > &v)
	Returns true if v does not contain any NaNs.
bool	notnan (const double &v)
	Returns true if v is not NaN.
bool	notnan (const sdVector &v)
	Returns true if v does not contain any NaNs.
size_t	nanloc (const dvector &v)
	Returns the index of first NaN component of v.
bool	almostEqual (double a, double b, double rtol=1e-10, double atol=1e-18)
	Returns true if a and b are equal to within the specified relative (rtol) and absolute (atol) tolerances.
dvector	abs (const dvector &v)
	Returns a vector containing the absolute values of the elements of v.
template<class T >
int	findFirst (const T &v)
	Returns the index of the first element of v which is true.
template<class T >
int	findLast (const T &v)
	Returns the index of the last element of v which is true.
vector< int >	find (vector< bool > &v)
	Returns a vector containing the indices of the elements of v which are true.
template<class T >
void	smooth (T &v)
	Applies a simple smoothing function to v which effectively filters out high-frequency components.
dvector	linspace (const double x1, const double x2, const int n)
	Returns a vector of n elements linearly spaced along the closed interval [x1, x2]
template<class T1 , class T2 >
vector< T1 >	computeSplines (const T1 &xIn, const T2 &yIn)
	Internal function for calculating cubic splines for a sequence of data points.
template<class T >
T	interp1 (const T &xIn, const T &yIn, const T &xOut, bool extrap=true)
	Linear interpolation for a vector of desired outputs.
template<class T >
double	interp1 (const T &xIn, const T &yIn, const double xOut, bool extrap=true)
	Linear interpolation for a single output point.
dvec	splines (const dvec &xIn, const dvec &yIn, const dvec &xOut)
	Cubic spline interpolation for a vector of desired outputs.
double	splines (const dvec &xIn, const dvec &yIn, const double xOut)
	Cubic spline interpolation for a single output point.
template<class T1 , class T2 >
double	integrate (const T1 &x, const T2 &y)
	Numerical integration using the cubic spline fit for the given data.
template<class T1 , class T2 >
double	trapz (const T1 &x, const T2 &y)
	Trapezoidal rule integration.
void	vectorVectorToArray2D (const vector< dvector > &v, dmatrix &a)
void	array2DToVectorVector (const dmatrix &a, vector< dvector > &v)
std::string	stringify (double x)
std::string	stringify (double x, int nDigits)
std::string	stringify (int x)
int	sign (const double x)
int	sign (const int x)
template<class Tx , class Ty >
void	uniqueSort (vector< Tx > &keys, vector< vector< Ty > > &values)
	Sort & remove duplicate entries from keys, and perform the same permutation on values Requires that keys.size() == values[i].size()

Detailed Description

A collection of general-purpose mathematical functions for working with vectors.

Function Documentation

maxval() [1/2]

double mathUtils::maxval

(

const dvector &

v

)

Returns the value of the maximum element of a vector.

minval() [1/2]

double mathUtils::minval

(

const dvector &

v

)

Returns the value of the minimum element of a vector.

range() [1/2]

double mathUtils::range

(

const dvector &

v

)

Returns the range (maximum - minimum) of a vector.

sum() [1/2]

double mathUtils::sum

(

const dvector &

v

)

Returns the sum of all the elements in a vector.

mean() [1/2]

double mathUtils::mean

(

const dvector &

v

)

Returns the arithemetic mean of the elements in a vector.

maxval() [2/2]

double mathUtils::maxval	(	const dvector &	v,
		size_t	iStart,
		size_t	iEnd
	)

Returns the value of the maximum element of the sub-vector of v with indices on the closed interval [iStart, iEnd]

minval() [2/2]

double mathUtils::minval	(	const dvector &	v,
		size_t	iStart,
		size_t	iEnd
	)

Returns the value of the minimum element of the sub-vector of v with indices on the closed interval [iStart, iEnd]

range() [2/2]

double mathUtils::range	(	const dvector &	v,
		size_t	iStart,
		size_t	iEnd
	)

Returns the range (maximum - minimum) of the sub-vector of v with indices on the closed interval [iStart, iEnd]

sum() [2/2]

double mathUtils::sum	(	const dvector &	v,
		size_t	iStart,
		size_t	iEnd
	)

Returns the sum of all the elements in the sub-vector of v with indices on the closed interval [iStart, iEnd]

mean() [2/2]

double mathUtils::mean	(	const dvector &	v,
		size_t	iStart,
		size_t	iEnd
	)

Returns the arithemetic mean of the sub-vector of v with indices on the closed interval [iStart, iEnd]

minloc()

size_t mathUtils::minloc

(

const dvector &

v

)

Returns the index of the minimum element of v.

maxloc()

size_t mathUtils::maxloc

(

const dvector &

v

)

Returns the index of the maximum element of v.

notnan() [1/4]

template<typename Derived >

bool mathUtils::notnan

(

const Eigen::EigenBase< Derived > &

v

)

Returns true if v does not contain any NaNs.

notnan() [2/4]

template<typename T >

bool mathUtils::notnan

(

const vector< T > &

v

)

Returns true if v does not contain any NaNs.

notnan() [3/4]

bool mathUtils::notnan ( const double &  v )

inline

Returns true if v is not NaN.

notnan() [4/4]

bool mathUtils::notnan

(

const sdVector &

v

)

Returns true if v does not contain any NaNs.

nanloc()

size_t mathUtils::nanloc

(

const dvector &

v

)

Returns the index of first NaN component of v.

Returns -1 if no elements are NaN.

almostEqual()

bool mathUtils::almostEqual ( double  a, double  b, double  rtol = 1e-10, double  atol = 1e-18  )

inline

Returns true if a and b are equal to within the specified relative (rtol) and absolute (atol) tolerances.

abs()

dvector mathUtils::abs

(

const dvector &

v

)

Returns a vector containing the absolute values of the elements of v.

findFirst()

template<class T >

int mathUtils::findFirst

(

const T &

v

)

Returns the index of the first element of v which is true.

Returns -1 if all elements of v are false.

findLast()

template<class T >

int mathUtils::findLast

(

const T &

v

)

Returns the index of the last element of v which is true.

Returns -1 if all elements of v are false.

find()

vector< int > mathUtils::find

(

vector< bool > &

v

)

Returns a vector containing the indices of the elements of v which are true.

smooth()

template<class T >

void mathUtils::smooth

(

T &

v

)

Applies a simple smoothing function to v which effectively filters out high-frequency components.

linspace()

dvector mathUtils::linspace	(	const double	x1,
		const double	x2,
		const int	n
	)

Returns a vector of n elements linearly spaced along the closed interval [x1, x2]

computeSplines()

template<class T1 , class T2 >

vector< T1 > mathUtils::computeSplines	(	const T1 &	xIn,
		const T2 &	yIn
	)

Internal function for calculating cubic splines for a sequence of data points.

interp1() [1/2]

template<class T >

T mathUtils::interp1	(	const T &	xIn,
		const T &	yIn,
		const T &	xOut,
		bool	extrap = true
	)

Linear interpolation for a vector of desired outputs.

T is a container of doubles, e.g. vector<double> or Eigen::ArrayXd.

Parameters

xIn	Input x-coordinates, length N. Must be monotonically increasing.
yIn	Input y-coordinates, length N
xOut	Target x-coordinates, length M
extrap	Linearly extrapolate outside the input interval. If false, clip to the nearest value.

Returns

Computed y-coordinates at the points defined in xOut, length M

interp1() [2/2]

template<class T >

double mathUtils::interp1	(	const T &	xIn,
		const T &	yIn,
		const double	xOut,
		bool	extrap = true
	)

Linear interpolation for a single output point.

T is a container of dobules, e.g. vector<double> or Eigen::ArrayXd.

Parameters

xIn	Input x-coordinates, length N. Must be monotonically increasing.
yIn	Input y-coordinates, length N
xOut	Target x-coordinate
extrap	Linearly extrapolate outside the input interval. If false, clip to the nearest value.

Returns

Computed y-coordinate at xOut

splines() [1/2]

dvec mathUtils::splines	(	const dvec &	xIn,
		const dvec &	yIn,
		const dvec &	xOut
	)

Cubic spline interpolation for a vector of desired outputs.

Parameters

xIn	Input x-coordinates, length N. Must be monotonically increasing.
yIn	Input y-coordinates, length N
xOut	Target x-coordinates, length M

Returns

Computed y-coordinates at the points defined in xOut, length M

splines() [2/2]

double mathUtils::splines	(	const dvec &	xIn,
		const dvec &	yIn,
		const double	xOut
	)

Cubic spline interpolation for a single output point.

Parameters

xIn	Input x-coordinates, length N. Must be monotonically increasing.
yIn	Input y-coordinates, length N
xOut	Target x-coordinate

Returns

Computed y-coordinate at xOut

integrate()

template<class T1 , class T2 >

double mathUtils::integrate	(	const T1 &	x,
		const T2 &	y
	)

Numerical integration using the cubic spline fit for the given data.

trapz()

template<class T1 , class T2 >

double mathUtils::trapz	(	const T1 &	x,
		const T2 &	y
	)

Trapezoidal rule integration.

vectorVectorToArray2D()

void mathUtils::vectorVectorToArray2D	(	const vector< dvector > &	v,
		dmatrix &	a
	)

array2DToVectorVector()

void mathUtils::array2DToVectorVector	(	const dmatrix &	a,
		vector< dvector > &	v
	)

stringify() [1/3]

std::string mathUtils::stringify

(

double

x

)

stringify() [2/3]

std::string mathUtils::stringify	(	double	x,
		int	nDigits
	)

stringify() [3/3]

std::string mathUtils::stringify

(

int

x

)

sign() [1/2]

int mathUtils::sign

(

const double

x

)

sign() [2/2]

int mathUtils::sign

(

const int

x

)

uniqueSort()

template<class Tx , class Ty >

void mathUtils::uniqueSort	(	vector< Tx > &	keys,
		vector< vector< Ty > > &	values
	)

Sort & remove duplicate entries from keys, and perform the same permutation on values Requires that keys.size() == values[i].size()