Utilities

Utility functions and classes. More...

Files
file	OFELI.h
	Header file that includes all kernel classes of the library.
file	OFELI_Config.h
	File that contains some macros.
file	constants.h
	File that contains some widely used constants.

Classes
class	Funct
	A simple class to parse real valued functions. More...
class	Tabulation
	To read and manipulate tabulated functions. More...
class	Point< T_ >
	Defines a point with arbitrary type coordinates. More...
class	Point2D< T_ >
	Defines a 2-D point with arbitrary type coordinates. More...
class	OFELIException
	To handle exceptions in OFELI. More...
class	Gauss
	Calculate data for Gauss integration. More...
class	Timer
	To handle elapsed time counting. More...

Macros
#define	OFELI_E   2.71828182845904523536028747135
#define	OFELI_PI   3.14159265358979323846264338328
#define	OFELI_THIRD   0.33333333333333333333333333333
#define	OFELI_SIXTH   0.16666666666666666666666666667
#define	OFELI_TWELVETH   0.08333333333333333333333333333
#define	OFELI_SQRT2   1.41421356237309504880168872421
#define	OFELI_SQRT3   1.73205080756887729352744634151
#define	OFELI_ONEOVERPI   0.31830988618379067153776752675
#define	OFELI_GAUSS2   0.57735026918962576450914878050196
#define	OFELI_EPSMCH   DBL_EPSILON
#define	OFELI_TOLERANCE   OFELI_EPSMCH*10000
#define	VLG   1.e10
#define	OFELI_IMAG   std::complex<double>(0.,1.);
#define	CATCH_EXCEPTION

Typedefs
typedef unsigned long	lsize_t
	This type stands for type unsigned long.
typedef double	real_t
	This type stands for double.
typedef std::complex< double >	complex_t
	This type stands for type std::complex<double>

Functions
ostream &	operator<< (ostream &s, const complex_t &x)
	Output a complex number. More...
ostream &	operator<< (ostream &s, const std::string &c)
	Output a string. More...
template<class T_ >
ostream &	operator<< (ostream &s, const vector< T_ > &v)
	Output a vector instance. More...
template<class T_ >
ostream &	operator<< (ostream &s, const std::list< T_ > &l)
	Output a vector instance. More...
template<class T_ >
ostream &	operator<< (ostream &s, const std::pair< T_, T_ > &a)
	Output a pair instance. More...
void	saveField (Vect< real_t > &v, string output_file, int opt)
	Save a vector to an output file in a given file format. More...
void	saveField (const Vect< real_t > &v, const Mesh &mesh, string output_file, int opt)
	Save a vector to an output file in a given file format. More...
void	saveField (Vect< real_t > &v, const Grid &g, string output_file, int opt)
	Save a vector to an output file in a given file format, for a structured grid data. More...
void	saveGnuplot (string input_file, string output_file, string mesh_file, int f=1)
	Save a vector to an input Gnuplot file. More...
void	saveGnuplot (Mesh &mesh, string input_file, string output_file, int f=1)
	Save a vector to an input Gnuplot file. More...
void	saveTecplot (string input_file, string output_file, string mesh_file, int f=1)
	Save a vector to an output file to an input Tecplot file. More...
void	saveTecplot (Mesh &mesh, string input_file, string output_file, int f=1)
	Save a vector to an output file to an input Tecplot file. More...
void	saveVTK (string input_file, string output_file, string mesh_file, int f=1)
	Save a vector to an output VTK file. More...
void	saveVTK (Mesh &mesh, string input_file, string output_file, int f=1)
	Save a vector to an output VTK file. More...
void	saveGmsh (string input_file, string output_file, string mesh_file, int f=1)
	Save a vector to an output Gmsh file. More...
void	saveGmsh (Mesh &mesh, string input_file, string output_file, int f=1)
	Save a vector to an output Gmsh file. More...
ostream &	operator<< (ostream &s, const Tabulation &t)
	Output Tabulated function data.
template<class T_ >
bool	operator== (const Point< T_ > &a, const Point< T_ > &b)
	Operator == More...
template<class T_ >
Point< T_ >	operator+ (const Point< T_ > &a, const Point< T_ > &b)
	Operator + More...
template<class T_ >
Point< T_ >	operator+ (const Point< T_ > &a, const T_ &x)
	Operator + More...
template<class T_ >
Point< T_ >	operator- (const Point< T_ > &a)
	Unary Operator - More...
template<class T_ >
Point< T_ >	operator- (const Point< T_ > &a, const Point< T_ > &b)
	Operator - More...
template<class T_ >
Point< T_ >	operator- (const Point< T_ > &a, const T_ &x)
	Operator - More...
template<class T_ >
Point< T_ >	operator* (const T_ &a, const Point< T_ > &b)
	Operator * More...
template<class T_ >
Point< T_ >	operator* (const int &a, const Point< T_ > &b)
	Operator *. More...
template<class T_ >
Point< T_ >	operator* (const Point< T_ > &b, const T_ &a)
	Operator / More...
template<class T_ >
Point< T_ >	operator* (const Point< T_ > &b, const int &a)
	Operator * More...
template<class T_ >
T_	operator* (const Point< T_ > &a, const Point< T_ > &b)
	Operator * More...
template<class T_ >
Point< T_ >	operator/ (const Point< T_ > &b, const T_ &a)
	Operator / More...
bool	areClose (const Point< double > &a, const Point< double > &b, double toler=OFELI_TOLERANCE)
	Return true if both instances of class Point<double> are distant with less then toler More...
double	SqrDistance (const Point< double > &a, const Point< double > &b)
	Return squared euclidean distance between points a and b More...
double	Distance (const Point< double > &a, const Point< double > &b)
	Return euclidean distance between points a and b More...
bool	operator< (const Point< size_t > &a, const Point< size_t > &b)
	Comparison operator. Returns true if all components of first vector are lower than those of second one. More...
template<class T_ >
std::ostream &	operator<< (std::ostream &s, const Point< T_ > &a)
	Output point coordinates. More...
template<class T_ >
bool	operator== (const Point2D< T_ > &a, const Point2D< T_ > &b)
	Operator ==. More...
template<class T_ >
Point2D< T_ >	operator+ (const Point2D< T_ > &a, const Point2D< T_ > &b)
	Operator +. More...
template<class T_ >
Point2D< T_ >	operator+ (const Point2D< T_ > &a, const T_ &x)
	Operator +. More...
template<class T_ >
Point2D< T_ >	operator- (const Point2D< T_ > &a)
	Unary Operator - More...
template<class T_ >
Point2D< T_ >	operator- (const Point2D< T_ > &a, const Point2D< T_ > &b)
	Operator - More...
template<class T_ >
Point2D< T_ >	operator- (const Point2D< T_ > &a, const T_ &x)
	Operator - More...
template<class T_ >
Point2D< T_ >	operator* (const T_ &a, const Point2D< T_ > &b)
	Operator *. More...
template<class T_ >
Point2D< T_ >	operator* (const int &a, const Point2D< T_ > &b)
template<class T_ >
Point2D< T_ >	operator* (const Point2D< T_ > &b, const T_ &a)
	Operator / More...
template<class T_ >
Point2D< T_ >	operator* (const Point2D< T_ > &b, const int &a)
	Operator * More...
template<class T_ >
T_	operator* (const Point2D< T_ > &b, const Point2D< T_ > &a)
	Operator *. More...
template<class T_ >
Point2D< T_ >	operator/ (const Point2D< T_ > &b, const T_ &a)
	Operator / More...
bool	areClose (const Point2D< real_t > &a, const Point2D< real_t > &b, real_t toler=OFELI_TOLERANCE)
	Return true if both instances of class Point2D<real_t> are distant with less then toler [Default: OFELI_EPSMCH].
real_t	SqrDistance (const Point2D< real_t > &a, const Point2D< real_t > &b)
	Return squared euclidean distance between points a and b More...
real_t	Distance (const Point2D< real_t > &a, const Point2D< real_t > &b)
	Return euclidean distance between points a and b More...
template<class T_ >
std::ostream &	operator<< (std::ostream &s, const Point2D< T_ > &a)
	Output point coordinates. More...
real_t	Discrepancy (Vect< real_t > &x, const Vect< real_t > &y, int n, int type=1)
	Return discrepancy between 2 vectors x and y More...
real_t	Discrepancy (Vect< complex_t > &x, const Vect< complex_t > &y, int n, int type=1)
	Return discrepancy between 2 vectors x and y More...
void	getMesh (string file, ExternalFileFormat form, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in an external file format. More...
void	getBamg (string file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Bamg format. More...
void	getEasymesh (string file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Easymesh format. More...
void	getGambit (string file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Gambit neutral format. More...
void	getGmsh (string file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Gmsh format. More...
void	getMatlab (string file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a Matlab mesh data. More...
void	getNetgen (string file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Netgen format. More...
void	getTetgen (string file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Tetgen format. More...
void	getTriangle (string file, Mesh &mesh, size_t nb_dof=1)
	Construct an instance of class Mesh from a mesh file stored in Triangle format. More...
void	saveMesh (const string &file, const Mesh &mesh, ExternalFileFormat form)
	This function saves mesh data a file for a given external format. More...
void	saveGmsh (const string &file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in Gmsh format. More...
void	saveGnuplot (const string &file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in Gmsh format. More...
void	saveMatlab (const string &file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in Matlab format. More...
void	saveTecplot (const string &file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in Tecplot format. More...
void	saveVTK (const string &file, const Mesh &mesh)
	This function outputs a Mesh instance in a file in VTK format. More...
void	saveBamg (const string &file, Mesh &mesh)
	This function outputs a Mesh instance in a file in Bamg format. More...
void	BSpline (size_t n, size_t t, Vect< Point< real_t > > &control, Vect< Point< real_t > > &output, size_t num_output)
	Function to perform a B-spline interpolation. More...
void	banner (const string &prog=" ")
	Outputs a banner as header of any developed program. More...
template<class T_ >
void	QuickSort (std::vector< T_ > &a, int begin, int end)
	Function to sort a vector. More...
template<class T_ >
void	qksort (std::vector< T_ > &a, int begin, int end)
	Function to sort a vector. More...
template<class T_ , class C_ >
void	qksort (std::vector< T_ > &a, int begin, int end, C_ compare)
	Function to sort a vector according to a key function. More...
int	Sgn (real_t a)
	Return sign of a: -1 or 1.
real_t	Abs2 (complex_t a)
	Return square of modulus of complex number a
real_t	Abs2 (real_t a)
	Return square of real number a
real_t	Abs (real_t a)
	Return absolute value of a
real_t	Abs (complex_t a)
	Return modulus of complex number a
real_t	Abs (const Point< real_t > &p)
	Return Norm of vector a
real_t	Conjg (real_t a)
	Return complex conjugate of real number a
complex_t	Conjg (complex_t a)
	Return complex conjugate of complex number a
real_t	Max (real_t a, real_t b, real_t c)
	Return maximum value of real numbers a, b and c
int	Kronecker (int i, int j)
	Return Kronecker delta of i and j.
int	Max (int a, int b, int c)
	Return maximum value of integer numbers a, b and c
real_t	Min (real_t a, real_t b, real_t c)
	Return minimum value of real numbers a, b and c
int	Min (int a, int b, int c)
	Return minimum value of integer numbers a, b and c
real_t	Max (real_t a, real_t b, real_t c, real_t d)
	Return maximum value of integer numbers a, b, c and d
int	Max (int a, int b, int c, int d)
	Return maximum value of integer numbers a, b, c and d
real_t	Min (real_t a, real_t b, real_t c, real_t d)
	Return minimum value of real numbers a, b, c and d
int	Min (int a, int b, int c, int d)
	Return minimum value of integer numbers a, b, c and d
real_t	Arg (complex_t x)
	Return argument of complex number x
complex_t	Log (complex_t x)
	Return principal determination of logarithm of complex number x
template<class T_ >
T_	Sqr (T_ x)
	Return square of value x
template<class T_ >
void	Scale (T_ a, const vector< T_ > &x, vector< T_ > &y)
	Mutiply vector x by a and save result in vector y More...
template<class T_ >
void	Scale (T_ a, const Vect< T_ > &x, Vect< T_ > &y)
	Mutiply vector x by a and save result in vector y More...
template<class T_ >
void	Scale (T_ a, vector< T_ > &x)
	Mutiply vector x by a More...
template<class T_ >
void	Xpy (size_t n, T_ *x, T_ *y)
	Add array x to y
template<class T_ >
void	Xpy (const vector< T_ > &x, vector< T_ > &y)
	Add vector x to y More...
template<class T_ >
void	Axpy (size_t n, T_ a, T_ *x, T_ *y)
	Multiply array x by a and add result to y More...
template<class T_ >
void	Axpy (T_ a, const vector< T_ > &x, vector< T_ > &y)
	Multiply vector x by a and add result to y More...
template<class T_ >
void	Axpy (T_ a, const Vect< T_ > &x, Vect< T_ > &y)
	Multiply vector x by a and add result to y More...
template<class T_ >
void	Copy (size_t n, T_ *x, T_ *y)
	Copy array x to y n is the arrays size.
real_t	Error2 (const vector< real_t > &x, const vector< real_t > &y)
	Return absolute L2 error between vectors x and y
real_t	RError2 (const vector< real_t > &x, const vector< real_t > &y)
	Return absolute L2 error between vectors x and y
real_t	ErrorMax (const vector< real_t > &x, const vector< real_t > &y)
	Return absolute Max. error between vectors x and y
real_t	RErrorMax (const vector< real_t > &x, const vector< real_t > &y)
	Return relative Max. error between vectors x and y
template<class T_ >
T_	Dot (size_t n, T_ *x, T_ *y)
	Return dot product of arrays x and y More...
real_t	Dot (const vector< real_t > &x, const vector< real_t > &y)
	Return dot product of vectors x and y. More...
template<class T_ >
T_	Dot (const Point< T_ > &x, const Point< T_ > &y)
	Return dot product of x and y
real_t	exprep (real_t x)
	Compute the exponential function with avoiding over and underflows.
template<class T_ >
void	Assign (vector< T_ > &v, const T_ &a)
	Assign the value a to all entries of a vector v
template<class T_ >
void	clear (vector< T_ > &v)
	Assign 0 to all entries of a vector. More...
template<class T_ >
void	clear (Vect< T_ > &v)
	Assign 0 to all entries of a vector. More...
real_t	Nrm2 (size_t n, real_t *x)
	Return 2-norm of array x More...
real_t	Nrm2 (const vector< real_t > &x)
	Return 2-norm of vector x
template<class T_ >
real_t	Nrm2 (const Point< T_ > &a)
	Return 2-norm of a
bool	Equal (real_t x, real_t y, real_t toler=OFELI_EPSMCH)
	Function to return true if numbers x and y are close up to a given tolerance toler More...
char	itoc (int i)
	Function to convert an integer to a character.
template<class T_ >
T_	stringTo (const std::string &s)
	Function to convert a string to a template type parameter.

Detailed Description

Utility functions and classes.

Macro Definition Documentation

#define OFELI_E   2.71828182845904523536028747135

Value of e or exp (with 28 digits)

#define OFELI_PI   3.14159265358979323846264338328

Value of Pi (with 28 digits)

#define OFELI_THIRD   0.33333333333333333333333333333

Value of 1/3 (with 28 digits)

#define OFELI_SIXTH   0.16666666666666666666666666667

Value of 1/6 (with 28 digits)

#define OFELI_TWELVETH   0.08333333333333333333333333333

Value of 1/12 (with 28 digits)

#define OFELI_SQRT2   1.41421356237309504880168872421

Value of sqrt(2) (with 28 digits)

#define OFELI_SQRT3   1.73205080756887729352744634151

Value of sqrt(3) (with 28 digits)

#define OFELI_ONEOVERPI   0.31830988618379067153776752675

Value of 1/Pi (with 28 digits)

#define OFELI_GAUSS2   0.57735026918962576450914878050196

Value of 1/sqrt(3) (with 32 digits)

#define OFELI_EPSMCH   DBL_EPSILON

Value of Machine Epsilon

#define OFELI_TOLERANCE   OFELI_EPSMCH*10000

Default tolerance for an iterative process = OFELI_EPSMCH * 10000

#define VLG   1.e10

Very large number: A real number for penalty

#define OFELI_IMAG   std::complex<double>(0.,1.);

= Unit imaginary number (i)

#define CATCH_EXCEPTION

Value:

catch(OFELIException &e) {                                   \
      std::cout << "OFELI error: " << e.what() << endl;         \
      return 1;                                                 \
   }                                                            \
   catch(runtime_error &e) {                                    \
      std::cout << "OFELI Runtime error: " << e.what() << endl; \
      return 1;                                                 \
   }                                                            \
   catch( ... ) {                                               \
      std::cout << "OFELI Unexpected error: " << endl;          \
      return 1;                                                 \
   }

This macro can be inserted after a try loop to catch a thrown exception.

Function Documentation

ostream & operator<<	(	ostream &	s,
		const complex_t &	x
	)

Output a complex number.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

ostream & operator<<	(	ostream &	s,
		const std::string &	c
	)

Output a string.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

ostream & operator<<	(	ostream &	s,
		const vector< T_ > &	v
	)

Output a vector instance.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

ostream & operator<<	(	ostream &	s,
		const std::list< T_ > &	l
	)

Output a vector instance.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

ostream & operator<<	(	ostream &	s,
		const std::pair< T_, T_ > &	a
	)

Output a pair instance.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveField	(	Vect< real_t > &	v,
		string	output_file,
		int	opt
	)

Save a vector to an output file in a given file format.

Case where the vector contains mesh information

Parameters

[in]	v	Vect instance to save
[in]	output_file	Output file where to save the vector
[in]	opt	Option to choose file format to save. This is to be chosen among enumerated values: GMSH GNUPLOT MATLAB TECPLOT VTK

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveField	(	const Vect< real_t > &	v,
		const Mesh &	mesh,
		string	output_file,
		int	opt
	)

Save a vector to an output file in a given file format.

Case where the vector does not contain mesh information

Parameters

[in]	v	Vect instance to save
[in]	mesh	Mesh instance
[in]	output_file	Output file where to save the vector
[in]	opt	Option to choose file format to save. This is to be chosen among enumerated values: GMSH, GNUPLOT, MATLAB, TECPLOT, VTK

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveField	(	Vect< real_t > &	v,
		const Grid &	g,
		string	output_file,
		int	opt = VTK
	)

Save a vector to an output file in a given file format, for a structured grid data.

Parameters

[in]	v	Vect instance to save
[in]	g	Grid instance
[in]	output_file	Output file where to save the vector
[in]	opt	Option to choose file format to save. This is to be chosen among enumerated values: GMSH, VTK

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveGnuplot	(	string	input_file,
		string	output_file,
		string	mesh_file,
		int	f = 1
	)

Save a vector to an input Gnuplot file.

Gnuplot is a command-line driven program for producing 2D and 3D plots. It is under the GNU General Public License. Available information can be found in the site:
http://www.gnuplot.info/

Parameters

[in]	input_file	Input file (OFELI XML file containing a field).
[in]	output_file	Output file (gnuplot format file)
[in]	mesh_file	File containing mesh data
[in]	f	Field is stored each f time step [Default: 1

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveGnuplot	(	Mesh &	mesh,
		string	input_file,
		string	output_file,
		int	f = 1
	)

Save a vector to an input Gnuplot file.

Gnuplot is a command-line driven program for producing 2D and 3D plots. It is under the GNU General Public License. Available information can be found in the site:
http://www.gnuplot.info/

Parameters

[in]	mesh	Reference to Mesh instance
[in]	input_file	Input file (OFELI XML file containing a field).
[in]	output_file	Output file (gnuplot format file)
[in]	f	Field is stored each f time step [Default: 1]

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveTecplot	(	string	input_file,
		string	output_file,
		string	mesh_file,
		int	f = 1
	)

Save a vector to an output file to an input Tecplot file.

Tecplot is high quality post graphical commercial processing program developed by Amtec. Available information can be found in the site: http://www.tecplot.com

Parameters

[in]	input_file	Input file (OFELI XML file containing a field).
[in]	output_file	Output file (gnuplot format file)
[in]	mesh_file	File containing mesh data
[in]	f	Field is stored each f time step [Default: 1]

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveTecplot	(	Mesh &	mesh,
		string	input_file,
		string	output_file,
		int	f = 1
	)

Save a vector to an output file to an input Tecplot file.

Tecplot is high quality post graphical commercial processing program developed by Amtec. Available information can be found in the site: http://www.tecplot.com

Parameters

[in]	mesh	Reference to Mesh instance
[in]	input_file	Input file (OFELI XML file containing a field).
[in]	output_file	Output file (gnuplot format file)
[in]	f	Field is stored each f time step [Default: 1]

Author

Rachid Touzani

Copyright

GNU Lesser Public License

saveVTK	(	string	input_file,
		string	output_file,
		string	mesh_file,
		int	f = 1
	)

Save a vector to an output VTK file.

The Visualization ToolKit (VTK) is an open source, freely available software system for 3D computer graphics. Available information can be found in the site:
http://public.kitware.com/VTK/

Parameters

[in]	input_file	Input file (OFELI XML file containing a field).
[in]	output_file	Output file (VTK format file)
[in]	mesh_file	File containing mesh data
[in]	f	Field is stored each f time step [Default: 1]

Author

Rachid Touzani

Copyright

GNU Lesser Public License

saveVTK	(	Mesh &	mesh,
		string	input_file,
		string	output_file,
		int	f = 1
	)

Save a vector to an output VTK file.

The Visualization ToolKit (VTK) is an open source, freely available software system for 3D computer graphics. Available information can be found in the site:
http://public.kitware.com/VTK/

Parameters

[in]	mesh	Reference to Mesh instance
[in]	input_file	Input file (OFELI XML file containing a field).
[in]	output_file	Output file (VTK format file)
[in]	f	Field is stored each f time step [Default: 1]

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveGmsh	(	string	input_file,
		string	output_file,
		string	mesh_file,
		int	f = 1
	)

Save a vector to an output Gmsh file.

Gmsh is a free mesh generator and postprocessor that can be downloaded from the site:
http://www.geuz.org/gmsh/

Parameters

[in]	input_file	Input file (OFELI XML file containing a field).
[in]	output_file	Output file (Gmsh format file)
[in]	mesh_file	File containing mesh data
[in]	f	Field is stored each f time step [Default: 1]

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveGmsh	(	Mesh &	mesh,
		string	input_file,
		string	output_file,
		int	f = 1
	)

Save a vector to an output Gmsh file.

Gmsh is a free mesh generator and postprocessor that can be downloaded from the site:
http://www.geuz.org/gmsh/

Parameters

[in]	mesh	Reference to Mesh instance
[in]	input_file	Input file (OFELI XML file containing a field).
[in]	output_file	Output file (Gmsh format file)
[in]	f	Field is stored each f time step [Default: 1]

Author

Rachid Touzani

Copyright

GNU Lesser Public License

bool operator==	(	const Point< T_ > &	a,
		const Point< T_ > &	b
	)

Operator ==

Return true if a=b, false if not.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point< T_ > operator+	(	const Point< T_ > &	a,
		const Point< T_ > &	b
	)

Operator +

Return sum of two points a and b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point< T_ > operator+	(	const Point< T_ > &	a,
		const T_ &	x
	)

Operator +

Translate a by x

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point< T_ > operator-

(

const Point< T_ > &

a

)

Unary Operator -

Return minus a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point< T_ > operator-	(	const Point< T_ > &	a,
		const Point< T_ > &	b
	)

Operator -

Return point a minus point b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point< T_ > operator-	(	const Point< T_ > &	a,
		const T_ &	x
	)

Operator -

Translate a by -x

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point< T_ > operator*	(	const T_ &	a,
		const Point< T_ > &	b
	)

Operator *

Return point b premultiplied by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point< T_ > operator*	(	const int &	a,
		const Point< T_ > &	b
	)

Operator *.

Return point b divided by integer constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point< T_ > operator*	(	const Point< T_ > &	b,
		const T_ &	a
	)

Operator /

Return point b multiplied by constant a

Point< T_ > operator*	(	const Point< T_ > &	b,
		const int &	a
	)

Operator *

Return point b postmultiplied by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

T_ operator*	(	const Point< T_ > &	b,
		const Point< T_ > &	a
	)

Operator *

Return inner (scalar) product of points a and b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point< T_ > operator/	(	const Point< T_ > &	b,
		const T_ &	a
	)

Operator /

Return point b divided by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

bool areClose	(	const Point< double > &	a,
		const Point< double > &	b,
		double	toler = OFELI_TOLERANCE
	)

Return true if both instances of class Point<double> are distant with less then toler

Author

Rachid Touzani

Copyright

GNU Lesser Public License

double SqrDistance	(	const Point< double > &	a,
		const Point< double > &	b
	)

Return squared euclidean distance between points a and b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

double Distance	(	const Point< double > &	a,
		const Point< double > &	b
	)

Return euclidean distance between points a and b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

bool operator<	(	const Point< size_t > &	a,
		const Point< size_t > &	b
	)

Comparison operator. Returns true if all components of first vector are lower than those of second one.

Return minus a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

ostream & operator<<	(	std::ostream &	s,
		const Point< T_ > &	a
	)

Output point coordinates.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

bool operator==	(	const Point2D< T_ > &	a,
		const Point2D< T_ > &	b
	)

Operator ==.

Return true if a=b, false if not.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point2D< T_ > operator+	(	const Point2D< T_ > &	a,
		const Point2D< T_ > &	b
	)

Operator +.

Return sum of two points a and b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point2D< T_ > operator+	(	const Point2D< T_ > &	a,
		const T_ &	x
	)

Operator +.

Translate a by x

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point2D< T_ > operator-

(

const Point2D< T_ > &

a

)

Unary Operator -

Return minus a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point2D< T_ > operator-	(	const Point2D< T_ > &	a,
		const Point2D< T_ > &	b
	)

Operator -

Return point a minus point b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point2D< T_ > operator-	(	const Point2D< T_ > &	a,
		const T_ &	x
	)

Operator -

Translate a by -x

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point2D< T_ > operator*	(	const T_ &	a,
		const Point2D< T_ > &	b
	)

Operator *.

Return point b premultiplied by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point2D< T_ > operator*	(	const int &	a,
		const Point2D< T_ > &	b
	)

Operator *.

Return point b divided by integer constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point2D< T_ > operator*	(	const Point2D< T_ > &	b,
		const T_ &	a
	)

Operator /

Return point b postmultiplied by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point2D< T_ > operator*	(	const Point2D< T_ > &	b,
		const int &	a
	)

Operator *

Return point b postmultiplied by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

T_ operator*	(	const Point2D< T_ > &	b,
		const Point2D< T_ > &	a
	)

Operator *.

Return point b postmultiplied by integer constant a.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Point2D< T_ > operator/	(	const Point2D< T_ > &	b,
		const T_ &	a
	)

Operator /

Return point b divided by constant a

Author

Rachid Touzani

Copyright

GNU Lesser Public License

real_t SqrDistance	(	const Point2D< real_t > &	a,
		const Point2D< real_t > &	b
	)

Return squared euclidean distance between points a and b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

real_t Distance	(	const Point2D< real_t > &	a,
		const Point2D< real_t > &	b
	)

Return euclidean distance between points a and b

Author

Rachid Touzani

Copyright

GNU Lesser Public License

ostream & operator<<	(	std::ostream &	s,
		const Point2D< T_ > &	a
	)

Output point coordinates.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

real_t Discrepancy	(	Vect< real_t > &	x,
		const Vect< real_t > &	y,
		int	n,
		int	type = 1
	)

Return discrepancy between 2 vectors x and y

Parameters

[in,out]	x	First vector (Instance of class Vect). On output, x is assigned the vector y
[in]	y	Second vector (Instance of class Vect)
[in]	n	Type of norm 1: Weighted 1-Norm 2: Weighted 2-Norm 0: Max-Norm
[in]	type	Discrepancy type (0: Absolute, 1: Relative [Default])

Returns

Computed discrepancy value

real_t Discrepancy	(	Vect< complex_t > &	x,
		const Vect< complex_t > &	y,
		int	n,
		int	type = 1
	)

Return discrepancy between 2 vectors x and y

Parameters

[in,out]	x	First vector (Instance of class Vect). On output, x is assigned the vector y
[in]	y	Second vector (Instance of class Vect)
[in]	n	Type of norm 1: Weighted 1-Norm 2: Weighted 2-Norm 0: Max-Norm
[in]	type	Discrepancy type (0: Absolute, 1: Relative [Default])

Returns

Computed discrepancy value

void getMesh	(	string	file,
		ExternalFileFormat	form,
		Mesh &	mesh,
		size_t	nb_dof = 1
	)

Construct an instance of class Mesh from a mesh file stored in an external file format.

Parameters

[in]	file	Input mesh file name.
[in]	form	Format of the mesh file. This one can be chosen among the enumerated values: GMSH: Mesh generator Gmsh, see site: http://www.geuz.org/gmsh/ MATLAB: Matlab file, see site: http://www.mathworks.com/products/matlab/ EASYMESH: Easymesh is a 2-D mesh generator, see site: http://web.mit.edu/easymesh_v1.4/www/easymesh.html GAMBIT: Gambit is a mesh generator associated to Fluent http://www.stanford.edu/class/me469b/gambit_download.html BAMG: Mesh generator Bamg, see site: http://raweb.inria.fr/rapportsactivite/RA2002/gamma/uid25.html NETGEN: Netgen is a 3-D mesh generator, see site: http://www.hpfem.jku.at/netgen/ TETGEN: Tetgen is a 3-D mesh generator, see site: http://tetgen.berlios.de/ TRIANGLE_FF: Triangle is a 2-D mesh generator, see site: http://www.cs.cmu.edu/~quake/triangle.html
[out]	mesh	Mesh instance created by the function.
[in]	nb_dof	Number of degrees of freedom for each node. This information is not provided, in general, by mesh generators. Its default value here is 1.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void getBamg	(	string	file,
		Mesh &	mesh,
		size_t	nb_dof = 1
	)

Construct an instance of class Mesh from a mesh file stored in Bamg format.

Parameters

[in]

file

Name of a file written in the Bamg format.

Note

Bamg is a 2-D mesh generator. It allows to construct adapted meshes from a given metric. It was developed at INRIA, France. Available information can be found in the site:
http://raweb.inria.fr/rapportsactivite/RA2002/gamma/uid25.html

Parameters

[out]	mesh	Mesh instance created by the function.
[in]	nb_dof	Number of degrees of freedom for each node. This information is not provided, in general, by mesh generators. Its default value here is 1.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void getEasymesh	(	string	file,
		Mesh &	mesh,
		size_t	nb_dof = 1
	)

Construct an instance of class Mesh from a mesh file stored in Easymesh format.

Parameters

[in]

file

Name of a file (without extension) written in Easymesh format. Actually, the function Easymesh2MDF attempts to read mesh data from files file.e, file.n and file.s produced by Easymesh.

Note

Easymesh is a free program that generates 2-D, unstructured, Delaunay and constrained Delaunay triangulations in general domains. It can be downloaded from the site:
http://www-dinma.univ.trieste.it/nirftc/research/easymesh/Default.htm

Parameters

[in]	mesh	Mesh instance created by the function.
[in]	nb_dof	Number of degrees of freedom for each node. This information is not provided, in general, by mesh generators. Its default value here is 1.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void getGambit	(	string	file,
		Mesh &	mesh,
		size_t	nb_dof = 1
	)

Construct an instance of class Mesh from a mesh file stored in Gambit neutral format.

Note

Gambit is a commercial mesh generator associated to the CFD code Fluent. Informations about Gambit can be found in the site:
http://www.fluent.com/software/gambit/

Parameters

[in]	file	Name of a file written in the Gambit neutral format.
[out]	mesh	Mesh instance created by the function.
[in]	nb_dof	Number of degrees of freedom for each node. This information is not provided, in general, by mesh generators. Its default value here is 1.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void getGmsh	(	string	file,
		Mesh &	mesh,
		size_t	nb_dof = 1
	)

Construct an instance of class Mesh from a mesh file stored in Gmsh format.

Note

Gmsh is a free mesh generator that can be downloaded from the site:
http://www.geuz.org/gmsh/

Parameters

[in]	file	Name of a file written in the Gmsh format.
[out]	mesh	Mesh instance created by the function.
[in]	nb_dof	Number of degrees of freedom for each node. This information is not provided, in general, by mesh generators. Its default value here is 1.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void getMatlab	(	string	file,
		Mesh &	mesh,
		size_t	nb_dof = 1
	)

Construct an instance of class Mesh from a Matlab mesh data.

Note

Matlab is a language of scientific computing including visualization. It is developed by MathWorks. Available information can be found in the site:
http://www.mathworks.com/products/matlab/

Parameters

[in]	file	Name of a file created by Matlab by executing the script file Matlab2OFELI.m
[out]	mesh	Mesh instance created by the function.
[in]	nb_dof	Number of degrees of freedom for each node. This information is not provided, in general, by mesh generators. Its default value here is 1.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void getNetgen	(	string	file,
		Mesh &	mesh,
		size_t	nb_dof = 1
	)

Construct an instance of class Mesh from a mesh file stored in Netgen format.

Note

Netgen is a tetrahedral mesh generator that can be downloaded from the site:
http://www.hpfem.jku.at/netgen/

Parameters

[in]	file	Name of a file written in the Netgen format.
[out]	mesh	Mesh instance created by the function.
[in]	nb_dof	Number of degrees of freedom for each node. This information is not provided, in general, by mesh generators. [ default = 1 ]

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void getTetgen	(	string	file,
		Mesh &	mesh,
		size_t	nb_dof = 1
	)

Construct an instance of class Mesh from a mesh file stored in Tetgen format.

Note

Tetgen is a free three-dimensional mesh generator that can be downloaded in the site:
http://tetgen.berlios.de/

Parameters

[in]	file	Name of a file written in the Tetgen format.
[out]	mesh	Mesh instance created by the function.
[in]	nb_dof	Number of degrees of freedom for each node. This information is not provided, in general, by mesh generators. Its default value here is 1.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void getTriangle	(	string	file,
		Mesh &	mesh,
		size_t	nb_dof = 1
	)

Construct an instance of class Mesh from a mesh file stored in Triangle format.

Note

TRIANGLE is a C program that can generate meshes, Delaunay triangulations and Voronoi diagrams for 2D pointsets that can be downloaded in the site:
http://people.scs.fsu.edu/~burkardt/c_src/triangle/triangle.html/

Parameters

[in]	file	Name of a file written in the Tetgen format.
[out]	mesh	Mesh instance created by the function.
[in]	nb_dof	Number of degrees of freedom for each node. This information is not provided, in general, by mesh generators. Its default value here is 1.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveMesh	(	const string &	file,
		const Mesh &	mesh,
		ExternalFileFormat	form
	)

This function saves mesh data a file for a given external format.

Parameters

[in]	file	File where to store mesh
[in]	mesh	Mesh instance to save
[in]	form	Format of the mesh file. This one can be chosen among the enumerated values: GMSH: Mesh generator and graphical postprocessor Gmsh: http://www.geuz.org/gmsh/ GNUPLOT: Well known graphics software: http://www.gnuplot.info/ MATLAB: Matlab file: http://www.mathworks.com/products/matlab/ TECPLOT: Commercial graphics software: http://www.tecplot.com VTK: Graphics format for the free postprocessor ParaView: http://public.kitware.com/VTK/

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveGmsh	(	const string &	file,
		const Mesh &	mesh
	)

This function outputs a Mesh instance in a file in Gmsh format.

Note

Gmsh is a free mesh generator that can be downloaded from the site: http://www.geuz.org/gmsh/

Parameters

[out]	file	Output file in Gmsh format.
[in]	mesh	Mesh instance to save.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveGnuplot	(	const string &	file,
		const Mesh &	mesh
	)

This function outputs a Mesh instance in a file in Gmsh format.

Note

Gnuplot is a command-line driven program for producing 2D and 3D plots. It is under the GNU General Public License. Available information can be found in the site:
http://www.gnuplot.info/

Parameters

[out]	file	Output file in Gnuplot format.
[in]	mesh	Mesh instance to save.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveMatlab	(	const string &	file,
		const Mesh &	mesh
	)

This function outputs a Mesh instance in a file in Matlab format.

Note

Matlab is a language of scientific computing including visualization. It is developed by MathWorks. Available information can be found in the site:
http://www.mathworks.com/products/matlab/

Parameters

[out]	file	Output file in Matlab format.
[in]	mesh	Mesh instance to save.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveTecplot	(	const string &	file,
		const Mesh &	mesh
	)

This function outputs a Mesh instance in a file in Tecplot format.

Note

Tecplot is high quality post graphical commercial processing program developed by Amtec. Available information can be found in the site:
http://www.tecplot.com

Parameters

[out]	file	Output file in Tecplot format.
[in]	mesh	Mesh instance to save.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveVTK	(	const string &	file,
		const Mesh &	mesh
	)

This function outputs a Mesh instance in a file in VTK format.

Note

The Visualization ToolKit (VTK) is an open source, freely available software system for 3D computer graphics. Available information can be found in the site:
http://public.kitware.com/VTK/

Parameters

[out]	file	Output file in VTK format.
[in]	mesh	Mesh instance to save.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void saveBamg	(	const string &	file,
		Mesh &	mesh
	)

This function outputs a Mesh instance in a file in Bamg format.

Parameters

[in]

file

Name of a file written in the Bamg format.

Note

Bamg is a 2-D mesh generator. It allows to construct adapted meshes from a given metric. It was developed at INRIA, France. Available information can be found in the site:
http://raweb.inria.fr/rapportsactivite/RA2002/gamma/uid25.html

Parameters

[in]

mesh

Mesh instance.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

BSpline	(	size_t	n,
		size_t	t,
		Vect< Point< real_t > > &	control,
		Vect< Point< real_t > > &	output,
		size_t	num_output
	)

Function to perform a B-spline interpolation.

This program is adapted from a free program ditributed by Keith Vertanen (verta.nosp@m.nkd@.nosp@m.cda.m.nosp@m.rs.u.nosp@m.mn.ed.nosp@m.u) in 1994.

Parameters

[in]	n	Number of control points minus 1.
[in]	t	Degree of the polynomial plus 1.
[in]	control	Control point array made up of Point stucture.
[out]	output	Vector in which the calculated spline points are to be put.
[in]	num_output	How many points on the spline are to be calculated.

Note

Condition: n+2>t (No curve results if n+2<=t) Control vector contains the number of points specified by n Output array is the proper size to hold num_output point structures

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void banner

(

const string &

prog = " "

)

Outputs a banner as header of any developed program.

Parameters

[in]

prog

Calling program name. Enables writing a copyright notice accompanying the program.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void QuickSort	(	std::vector< T_ > &	a,
		int	begin,
		int	end
	)

Function to sort a vector.

qksort uses the famous quick sorting algorithm.

Parameters

[in,out]	a	Vector to sort.
[in]	begin	index of starting iterator
[in]	end	index of ending iterator

The calling program must provide an overloading of the operator < for the type T_

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void qksort	(	std::vector< T_ > &	a,
		int	begin,
		int	end
	)

Function to sort a vector.

qksort uses the famous quick sorting algorithm.

Parameters

[in,out]	a	Vector to sort.
[in]	begin	index of starting index (default value is 0)
[in]	end	index of ending index (default value is the vector size - 1)

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void qksort	(	std::vector< T_ > &	a,
		int	begin,
		int	end,
		C_	compare
	)

Function to sort a vector according to a key function.

qksort uses the famous quick sorting algorithm.

Parameters

[in,out]	a	Vector to sort.
[in]	begin	index of starting index (0 for the beginning of the vector)
[in]	end	index of ending index
[in]	compare	A function object that implements the ordering. The user must provide this function that returns a boolean function that is true if the first argument is less than the second and false if not.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

void Scale	(	T_	a,
		const vector< T_ > &	x,
		vector< T_ > &	y
	)

Mutiply vector x by a and save result in vector y

x and y are instances of class vector<T_>

void Scale	(	T_	a,
		const Vect< T_ > &	x,
		Vect< T_ > &	y
	)

Mutiply vector x by a and save result in vector y

x and y are instances of class Vect<T_>

void Scale	(	T_	a,
		vector< T_ > &	x
	)

Mutiply vector x by a

x is an instance of class vector<T_>

void Xpy	(	const vector< T_ > &	x,
		vector< T_ > &	y
	)

Add vector x to y

x and y are instances of class vector<T_>

void Axpy	(	size_t	n,
		T_	a,
		T_ *	x,
		T_ *	y
	)

Multiply array x by a and add result to y

n is the arrays size.

void Axpy	(	T_	a,
		const vector< T_ > &	x,
		vector< T_ > &	y
	)

Multiply vector x by a and add result to y

x and y are instances of class vector<T_>

void Axpy	(	T_	a,
		const Vect< T_ > &	x,
		Vect< T_ > &	y
	)

Multiply vector x by a and add result to y

x and y are instances of class Vect<T_>

T_ Dot	(	size_t	n,
		T_ *	x,
		T_ *	y
	)

Return dot product of arrays x and y

n is the arrays size.

double Dot	(	const vector< real_t > &	x,
		const vector< real_t > &	y
	)

Return dot product of vectors x and y.

x and y are instances of class vector<double>

void clear

(

vector< T_ > &

v

)

Assign 0 to all entries of a vector.

Parameters

[in]

v

Vector to clear

void clear

(

Vect< T_ > &

v

)

Assign 0 to all entries of a vector.

Parameters

[in]

v

Vector to clear

real_t Nrm2	(	size_t	n,
		real_t *	x
	)

Return 2-norm of array x

Parameters

[in]	n	is Array length
[in]	x	Array to treat

bool Equal	(	real_t	x,
		real_t	y,
		real_t	toler = OFELI_EPSMCH
	)

Function to return true if numbers x and y are close up to a given tolerance toler

Default value of tolerance is the constant OFELI_EPSMCH