mathUtils.h File Reference

#include <vector>
#include <cmath>
#include <iostream>
#include <sstream>
#include <string>
#include <map>
#include "debugUtils.h"
#include "cantera/base/ct_defs.h"
#include <eigen3/Eigen/Dense>

Include dependency graph for mathUtils.h:

This graph shows which files directly or indirectly include this file:

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

Macros
#define	_USE_MATH_DEFINES
#define	NOMINMAX

Typedefs
typedef Eigen::ArrayXXd	dmatrix
typedef Eigen::ArrayXd	dvec
typedef Eigen::ArrayXd::Index	index_t
typedef Eigen::Stride< Eigen::Dynamic, Eigen::Dynamic >	StrideXX
typedef Eigen::Stride< 1, Eigen::Dynamic >	Stride1X
typedef Eigen::Map< dmatrix, Eigen::Aligned, StrideXX >	MatrixMap
typedef Eigen::Map< dvec, Eigen::Unaligned, Stride1X >	VecMap
typedef std::vector< double >	dvector

Functions
void	remap (dmatrix &M, MatrixMap &A, index_t nRows, index_t nCols, index_t start)
void	remap (dmatrix &M, VecMap &A, index_t nVals, index_t start)
double	mathUtils::maxval (const dvector &v)
	Returns the value of the maximum element of a vector.
double	mathUtils::minval (const dvector &v)
	Returns the value of the minimum element of a vector.
double	mathUtils::range (const dvector &v)
	Returns the range (maximum - minimum) of a vector.
double	mathUtils::sum (const dvector &v)
	Returns the sum of all the elements in a vector.
double	mathUtils::mean (const dvector &v)
	Returns the arithemetic mean of the elements in a vector.
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]
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]
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]
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]
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]
size_t	mathUtils::minloc (const dvector &v)
	Returns the index of the minimum element of v.
size_t	mathUtils::maxloc (const dvector &v)
	Returns the index of the maximum element of v.
template<typename Derived >
bool	mathUtils::notnan (const Eigen::EigenBase< Derived > &v)
	Returns true if v does not contain any NaNs.
template<typename T >
bool	mathUtils::notnan (const vector< T > &v)
	Returns true if v does not contain any NaNs.
bool	mathUtils::notnan (const double &v)
	Returns true if v is not NaN.
bool	mathUtils::notnan (const sdVector &v)
	Returns true if v does not contain any NaNs.
size_t	mathUtils::nanloc (const dvector &v)
	Returns the index of first NaN component of v.
bool	mathUtils::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	mathUtils::abs (const dvector &v)
	Returns a vector containing the absolute values of the elements of v.
template<class T >
int	mathUtils::findFirst (const T &v)
	Returns the index of the first element of v which is true.
template<class T >
int	mathUtils::findLast (const T &v)
	Returns the index of the last element of v which is true.
vector< int >	mathUtils::find (vector< bool > &v)
	Returns a vector containing the indices of the elements of v which are true.
template<class T >
void	mathUtils::smooth (T &v)
	Applies a simple smoothing function to v which effectively filters out high-frequency components.
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]
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.
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.
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.
dvec	mathUtils::splines (const dvec &xIn, const dvec &yIn, const dvec &xOut)
	Cubic spline interpolation for a vector of desired outputs.
double	mathUtils::splines (const dvec &xIn, const dvec &yIn, const double xOut)
	Cubic spline interpolation for a single output point.
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.
template<class T1 , class T2 >
double	mathUtils::trapz (const T1 &x, const T2 &y)
	Trapezoidal rule integration.
void	mathUtils::vectorVectorToArray2D (const vector< dvector > &v, dmatrix &a)
void	mathUtils::array2DToVectorVector (const dmatrix &a, vector< dvector > &v)
std::string	mathUtils::stringify (double x)
std::string	mathUtils::stringify (double x, int nDigits)
std::string	mathUtils::stringify (int x)
int	mathUtils::sign (const double x)
int	mathUtils::sign (const int x)
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()
std::ostream &	operator<< (std::ostream &os, const dvector &v)
std::ostream &	operator<< (std::ostream &os, const vector< bool > &v)
std::ostream &	operator<< (std::ostream &os, const vector< int > &v)
dvector &	operator+= (dvector &v1, const dvector &v2)
dvector	operator+ (const dvector &v1, const dvector &v2)
dvector &	operator-= (dvector &v1, const dvector &v2)
dvector	operator- (const dvector &v1, const dvector &v2)
dvector &	operator+= (dvector &v1, const double s)
dvector	operator+ (const dvector &v1, const double s)
dvector &	operator-= (dvector &v1, const double s)
dvector	operator- (const dvector &v1, const double s)
dvector &	operator*= (dvector &v1, const dvector &v2)
dvector	operator* (const dvector &v1, const dvector &v2)
dvector &	operator*= (dvector &v1, const double s)
dvector	operator* (const dvector &v1, const double s)
dvector	operator* (const double s, const dvector &v1)
dvector &	operator/= (dvector &v1, const dvector &v2)
dvector	operator/ (const dvector &v1, const dvector &v2)
dvector &	operator/= (dvector &v1, const double s)
dvector	operator/ (const dvector &v1, const double s)
vector< bool >	operator> (const dvector &v1, const dvector &v2)
vector< bool >	operator< (const dvector &v1, const dvector &v2)
vector< bool >	operator>= (const dvector &v1, const dvector &v2)
vector< bool >	operator<= (const dvector &v1, const dvector &v2)
vector< bool >	operator== (const dvector &v1, const dvector &v2)
vector< bool >	operator!= (const dvector &v1, const dvector &v2)
vector< bool >	operator> (const dvector &v1, const double &s)
vector< bool >	operator< (const dvector &v1, const double &s)
vector< bool >	operator>= (const dvector &v1, const double &s)
vector< bool >	operator<= (const dvector &v1, const double &s)
vector< bool >	operator== (const dvector &v1, const double &s)
vector< bool >	operator!= (const dvector &v1, const double &s)
vector< bool >	operator! (const vector< bool > &v)
vector< bool >	operator&& (const vector< bool > &v1, const vector< bool > &v2)
vector< bool >	operator|| (const vector< bool > &v1, const vector< bool > &v2)

Variables
const double	NaN

Macro Definition Documentation

_USE_MATH_DEFINES

#define _USE_MATH_DEFINES

NOMINMAX

#define NOMINMAX

Typedef Documentation

dmatrix

typedef Eigen::ArrayXXd dmatrix

dvec

typedef Eigen::ArrayXd dvec

index_t

typedef Eigen::ArrayXd::Index index_t

StrideXX

typedef Eigen::Stride<Eigen::Dynamic,Eigen::Dynamic> StrideXX

Stride1X

typedef Eigen::Stride<1,Eigen::Dynamic> Stride1X

MatrixMap

typedef Eigen::Map<dmatrix, Eigen::Aligned, StrideXX > MatrixMap

VecMap

typedef Eigen::Map<dvec, Eigen::Unaligned, Stride1X> VecMap

dvector

typedef std::vector<double> dvector

Function Documentation

remap() [1/2]

void remap ( dmatrix &  M, MatrixMap &  A, index_t  nRows, index_t  nCols, index_t  start  )

inline

remap() [2/2]

void remap ( dmatrix &  M, VecMap &  A, index_t  nVals, index_t  start  )

inline

operator<<() [1/3]

std::ostream & operator<<	(	std::ostream &	os,
		const dvector &	v
	)

operator<<() [2/3]

std::ostream & operator<<	(	std::ostream &	os,
		const vector< bool > &	v
	)

operator<<() [3/3]

std::ostream & operator<<	(	std::ostream &	os,
		const vector< int > &	v
	)

operator+=() [1/2]

dvector & operator+=	(	dvector &	v1,
		const dvector &	v2
	)

operator+() [1/2]

dvector operator+	(	const dvector &	v1,
		const dvector &	v2
	)

operator-=() [1/2]

dvector & operator-=	(	dvector &	v1,
		const dvector &	v2
	)

operator-() [1/2]

dvector operator-	(	const dvector &	v1,
		const dvector &	v2
	)

operator+=() [2/2]

dvector & operator+=	(	dvector &	v1,
		const double	s
	)

operator+() [2/2]

dvector operator+	(	const dvector &	v1,
		const double	s
	)

operator-=() [2/2]

dvector & operator-=	(	dvector &	v1,
		const double	s
	)

operator-() [2/2]

dvector operator-	(	const dvector &	v1,
		const double	s
	)

operator*=() [1/2]

dvector & operator*=	(	dvector &	v1,
		const dvector &	v2
	)

operator*() [1/3]

dvector operator*	(	const dvector &	v1,
		const dvector &	v2
	)

operator*=() [2/2]

dvector & operator*=	(	dvector &	v1,
		const double	s
	)

operator*() [2/3]

dvector operator*	(	const dvector &	v1,
		const double	s
	)

operator*() [3/3]

dvector operator*	(	const double	s,
		const dvector &	v1
	)

operator/=() [1/2]

dvector & operator/=	(	dvector &	v1,
		const dvector &	v2
	)

operator/() [1/2]

dvector operator/	(	const dvector &	v1,
		const dvector &	v2
	)

operator/=() [2/2]

dvector & operator/=	(	dvector &	v1,
		const double	s
	)

operator/() [2/2]

dvector operator/	(	const dvector &	v1,
		const double	s
	)

operator>() [1/2]

vector< bool > operator>	(	const dvector &	v1,
		const dvector &	v2
	)

operator<() [1/2]

vector< bool > operator<	(	const dvector &	v1,
		const dvector &	v2
	)

operator>=() [1/2]

vector< bool > operator>=	(	const dvector &	v1,
		const dvector &	v2
	)

operator<=() [1/2]

vector< bool > operator<=	(	const dvector &	v1,
		const dvector &	v2
	)

operator==() [1/2]

vector< bool > operator==	(	const dvector &	v1,
		const dvector &	v2
	)

operator!=() [1/2]

vector< bool > operator!=	(	const dvector &	v1,
		const dvector &	v2
	)

operator>() [2/2]

vector< bool > operator>	(	const dvector &	v1,
		const double &	s
	)

operator<() [2/2]

vector< bool > operator<	(	const dvector &	v1,
		const double &	s
	)

operator>=() [2/2]

vector< bool > operator>=	(	const dvector &	v1,
		const double &	s
	)

operator<=() [2/2]

vector< bool > operator<=	(	const dvector &	v1,
		const double &	s
	)

operator==() [2/2]

vector< bool > operator==	(	const dvector &	v1,
		const double &	s
	)

operator!=() [2/2]

vector< bool > operator!=	(	const dvector &	v1,
		const double &	s
	)

operator!()

vector< bool > operator!

(

const vector< bool > &

v

)

operator&&()

vector< bool > operator&&	(	const vector< bool > &	v1,
		const vector< bool > &	v2
	)

operator||()

vector< bool > operator||	(	const vector< bool > &	v1,
		const vector< bool > &	v2
	)

Variable Documentation

NaN

const double NaN

extern