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An Object Oriented Finite Element Library

Files | Classes | Macros | Typedefs | Functions
Utilities
OFELI

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  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< real_t > &a, const Point< real_t > &b, real_t toler=OFELI_TOLERANCE)
 Return true if both instances of class Point<double> are distant with less then toler More...
 
real_t SqrDistance (const Point< real_t > &a, const Point< real_t > &b)
 Return squared euclidean distance between points a and b More...
 
real_t Distance (const Point< real_t > &a, const Point< real_t > &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 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 Sgn (real_t a, real_t b)
 Return |a| if b>0, -|a| if not.
 
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
 
string out_complex (complex_t z)
 Return string to conveniently display a complex number. More...
 
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.
 
template<class T_ >
const T_ & Max (const T_ &a, const T_ &b)
 Return maximum value of elements a and b
 
template<class T_ >
const T_ & Min (const T_ &a, const T_ &b)
 Return minimum value of elements a and b
 
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 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

◆ CATCH_EXCEPTION

#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.

◆ OFELI_E

#define OFELI_E   2.71828182845904523536028747135

Value of e or exp (with 28 digits)

◆ OFELI_EPSMCH

#define OFELI_EPSMCH   DBL_EPSILON

Value of Machine Epsilon

◆ OFELI_GAUSS2

#define OFELI_GAUSS2   0.57735026918962576450914878050196

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

◆ OFELI_IMAG

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

= Unit imaginary number (i)

◆ OFELI_ONEOVERPI

#define OFELI_ONEOVERPI   0.31830988618379067153776752675

Value of 1/Pi (with 28 digits)

◆ OFELI_PI

#define OFELI_PI   3.14159265358979323846264338328

Value of Pi (with 28 digits)

◆ OFELI_SIXTH

#define OFELI_SIXTH   0.16666666666666666666666666667

Value of 1/6 (with 28 digits)

◆ OFELI_SQRT2

#define OFELI_SQRT2   1.41421356237309504880168872421

Value of sqrt(2) (with 28 digits)

◆ OFELI_SQRT3

#define OFELI_SQRT3   1.73205080756887729352744634151

Value of sqrt(3) (with 28 digits)

◆ OFELI_THIRD

#define OFELI_THIRD   0.33333333333333333333333333333

Value of 1/3 (with 28 digits)

◆ OFELI_TOLERANCE

#define OFELI_TOLERANCE   OFELI_EPSMCH*10000

Default tolerance for an iterative process = OFELI_EPSMCH * 10000

◆ OFELI_TWELVETH

#define OFELI_TWELVETH   0.08333333333333333333333333333

Value of 1/12 (with 28 digits)

◆ VLG

#define VLG   1.e10

Very large number: A real number for penalty

Function Documentation

◆ areClose()

bool areClose ( const Point< real_t > &  a,
const Point< real_t > &  b,
real_t  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

◆ Axpy() [1/2]

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.

◆ Axpy() [2/2]

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_>

◆ banner()

void banner ( const string &  prog = " ")

Outputs a banner as header of any developed program.

Parameters
[in]progCalling program name. Enables writing a copyright notice accompanying the program.
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ BSpline()

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]nNumber of control points minus 1.
[in]tDegree of the polynomial plus 1.
[in]controlControl point array made up of Point stucture.
[out]outputVector in which the calculated spline points are to be put.
[in]num_outputHow 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

◆ clear() [1/2]

void clear ( Vect< T_ > &  v)

Assign 0 to all entries of a vector.

Parameters
[in]vVector to clear

◆ clear() [2/2]

void clear ( vector< T_ > &  v)

Assign 0 to all entries of a vector.

Parameters
[in]vVector to clear

◆ Discrepancy() [1/2]

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]xFirst vector (Instance of class Vect). On output, x is assigned the vector y
[in]ySecond vector (Instance of class Vect)
[in]nType of norm
  • 1: Weighted 1-Norm
  • 2: Weighted 2-Norm
  • 0: Max-Norm
[in]typeDiscrepancy type (0: Absolute, 1: Relative [Default])
Returns
Computed discrepancy value

◆ Discrepancy() [2/2]

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]xFirst vector (Instance of class Vect). On output, x is assigned the vector y
[in]ySecond vector (Instance of class Vect)
[in]nType of norm
  • 1: Weighted 1-Norm
  • 2: Weighted 2-Norm
  • 0: Max-Norm
[in]typeDiscrepancy type (0: Absolute, 1: Relative [Default])
Returns
Computed discrepancy value

◆ Distance() [1/2]

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

◆ Distance() [2/2]

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

Return euclidean distance between points a and b

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ Dot() [1/2]

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>

◆ Dot() [2/2]

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

Return dot product of arrays x and y

n is the arrays size.

◆ Equal()

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

◆ getBamg()

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]fileName 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]meshMesh instance created by the function.
[in]nb_dofNumber 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

◆ getEasymesh()

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]fileName 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]meshMesh instance created by the function.
[in]nb_dofNumber 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

◆ getGambit()

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]fileName of a file written in the Gambit neutral format.
[out]meshMesh instance created by the function.
[in]nb_dofNumber 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

◆ getGmsh()

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]fileName of a file written in the Gmsh format.
[out]meshMesh instance created by the function.
[in]nb_dofNumber 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

◆ getMatlab()

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]fileName of a file created by Matlab by executing the script file Matlab2OFELI.m
[out]meshMesh instance created by the function.
[in]nb_dofNumber 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

◆ getMesh()

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]fileInput mesh file name.
[in]formFormat of the mesh file. This one can be chosen among the enumerated values:
[out]meshMesh instance created by the function.
[in]nb_dofNumber 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

◆ getNetgen()

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]fileName of a file written in the Netgen format.
[out]meshMesh instance created by the function.
[in]nb_dofNumber 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

◆ getTetgen()

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]fileName of a file written in the Tetgen format.
[out]meshMesh instance created by the function.
[in]nb_dofNumber 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

◆ getTriangle()

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]fileName of a file written in the Tetgen format.
[out]meshMesh instance created by the function.
[in]nb_dofNumber 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

◆ Nrm2()

real_t Nrm2 ( size_t  n,
real_t *  x 
)

Return 2-norm of array x

Parameters
[in]nis Array length
[in]xArray to treat

◆ operator*() [1/10]

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

◆ operator*() [2/10]

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

◆ operator*() [3/10]

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

◆ operator*() [4/10]

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

◆ operator*() [5/10]

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

◆ operator*() [6/10]

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

◆ operator*() [7/10]

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

◆ operator*() [8/10]

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

Operator /

Return point b multiplied by constant a

◆ operator*() [9/10]

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

◆ operator*() [10/10]

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

◆ operator+() [1/4]

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

◆ operator+() [2/4]

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

Operator +.

Translate a by x

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator+() [3/4]

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

◆ operator+() [4/4]

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

Operator +

Translate a by x

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator-() [1/6]

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

Unary Operator -

Return minus a

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator-() [2/6]

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

◆ operator-() [3/6]

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

Operator -

Translate a by -x

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator-() [4/6]

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

Unary Operator -

Return minus a

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator-() [5/6]

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

◆ operator-() [6/6]

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

Operator -

Translate a by -x

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator/() [1/2]

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

◆ operator/() [2/2]

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

◆ operator<()

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

◆ operator<<() [1/7]

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

Output a complex number.

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator<<() [2/7]

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

Output a vector instance.

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator<<() [3/7]

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

Output a pair instance.

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator<<() [4/7]

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

Output a string.

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator<<() [5/7]

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

Output a vector instance.

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator<<() [6/7]

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

Output point coordinates.

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator<<() [7/7]

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

Output point coordinates.

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ operator==() [1/2]

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

◆ operator==() [2/2]

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

◆ out_complex()

string out_complex ( complex_t  z)

Return string to conveniently display a complex number.

Parameters
[in]zComplex number

◆ qksort() [1/2]

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]aVector to sort.
[in]beginindex of starting index (default value is 0)
[in]endindex of ending index (default value is the vector size - 1)
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ qksort() [2/2]

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]aVector to sort.
[in]beginindex of starting index (0 for the beginning of the vector)
[in]endindex of ending index
[in]compareA 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

◆ QuickSort()

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]aVector to sort.
[in]beginindex of starting iterator
[in]endindex 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

◆ saveField() [1/3]

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]vVect instance to save
[in]meshMesh instance
[in]output_fileOutput file where to save the vector
[in]optOption 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

◆ saveField() [2/3]

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]vVect instance to save
[in]gGrid instance
[in]output_fileOutput file where to save the vector
[in]optOption to choose file format to save. This is to be chosen among enumerated values: GMSH, VTK
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveField() [3/3]

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]vVect instance to save
[in]output_fileOutput file where to save the vector
[in]optOption 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

◆ saveGmsh() [1/3]

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
[in]fileOutput file in Gmsh format.
[in]meshMesh instance to save.
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveGmsh() [2/3]

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]meshReference to Mesh instance
[in]input_fileInput file (OFELI XML file containing a field).
[in]output_fileOutput file (Gmsh format file)
[in]fField is stored each f time step [Default: 1]
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveGmsh() [3/3]

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_fileInput file (OFELI XML file containing a field).
[in]output_fileOutput file (Gmsh format file)
[in]mesh_fileFile containing mesh data
[in]fField is stored each f time step [Default: 1]
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveGnuplot() [1/3]

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]fileOutput file in Gnuplot format.
[in]meshMesh instance to save.
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveGnuplot() [2/3]

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]meshReference to Mesh instance
[in]input_fileInput file (OFELI XML file containing a field).
[in]output_fileOutput file (gnuplot format file)
[in]fField is stored each f time step [Default: 1]
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveGnuplot() [3/3]

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_fileInput file (OFELI XML file containing a field).
[in]output_fileOutput file (gnuplot format file)
[in]mesh_fileFile containing mesh data
[in]fField is stored each f time step [Default: 1
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveMatlab()

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]fileOutput file in Matlab format.
[in]meshMesh instance to save.
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveMesh()

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

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

Parameters
[in]fileFile where to store mesh
[in]meshMesh instance to save
[in]formFormat of the mesh file. This one can be chosen among the enumerated values:
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveTecplot() [1/3]

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]fileOutput file in Tecplot format.
[in]meshMesh instance to save.
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveTecplot() [2/3]

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]meshReference to Mesh instance
[in]input_fileInput file (OFELI XML file containing a field).
[in]output_fileOutput file (gnuplot format file)
[in]fField is stored each f time step [Default: 1]
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveTecplot() [3/3]

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_fileInput file (OFELI XML file containing a field).
[in]output_fileOutput file (gnuplot format file)
[in]mesh_fileFile containing mesh data
[in]fField is stored each f time step [Default: 1]
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveVTK() [1/3]

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]fileOutput file in VTK format.
[in]meshMesh instance to save.
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveVTK() [2/3]

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]meshReference to Mesh instance
[in]input_fileInput file (OFELI XML file containing a field).
[in]output_fileOutput file (VTK format file)
[in]fField is stored each f time step [Default: 1]
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ saveVTK() [3/3]

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_fileInput file (OFELI XML file containing a field).
[in]output_fileOutput file (VTK format file)
[in]mesh_fileFile containing mesh data
[in]fField is stored each f time step [Default: 1]
Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ Scale() [1/3]

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_>

◆ Scale() [2/3]

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_>

◆ Scale() [3/3]

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

Mutiply vector x by a

x is an instance of class vector<T_>

◆ SqrDistance() [1/2]

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

◆ SqrDistance() [2/2]

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

Return squared euclidean distance between points a and b

Author
Rachid Touzani
Copyright
GNU Lesser Public License

◆ Xpy()

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

Add vector x to y

x and y are instances of class vector<T_>






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