WSpr Class Reference

#include <wspr.h>

List of all members.

Public Member Functions

 WSpr (char *configFileName)
 WSpr (int numberOfElementsX, int numberOfElementsY, double threshold=0.001, int minLevel=3, int interpOrder=4, int boundaryCodeSpr=1111, char *initialConditionFileName="InitialCondition.cfg")
void testLocalDerivate (void)
void testSprWithBoundaries (void)
void testViewMeshTransforms (void)
void testTransformTimeLocalPoints (void)
void testTransformsTime (void)
void testExtendMesh (void)
void testTimeEvolution (void)
void testMaxwellTimeEvolution (void)
void drawPhi (void)
Array2D computeRK4 (double dt, Array2D &u, Array2D(WSpr::*rhsEval)(Array2D &fu, double dX, double dY))
void compute_RK4 (double dt, Array2D &u, Array2D &v, Array2D &w, Array2D(WSpr::*rhsEval1)(Array2D &w, double epsilon0), Array2D(WSpr::*rhsEval2)(Array2D &w, double epsilon0), Array2D(WSpr::*rhsEval3)(Array2D &u, double epsilon0, Array2D &v, double mu0), double epsilon0, double mu0)
void compute_RK4Complete (double dt, Array2D &u, Array2D &v, Array2D &w, Array2D &sigma, Array2D(WSpr::*rhsEval1)(Array2D &w, Array2D &u, Array2D &v, double par1), Array2D(WSpr::*rhsEval2)(Array2D &w, Array2D &u, Array2D &v, double par2), Array2D(WSpr::*rhsEval3)(Array2D &u, double par1, Array2D &v, double par3), double par1, double par2)
double computeRKFCashKarp45 (double timeStep, int numberOfSteps, Array2D &u, Array2D(WSpr::*rhsEval)(Array2D &f, double dX, double dY))
double computeRKFCashKarp45 (double timeStep, int numberOfSteps, Array2D &u, Array2D &v, Array2D &w, Array2D(WSpr::*rhsEval1)(Array2D &w, double par1), Array2D(WSpr::*rhsEval2)(Array2D &w, double par2), Array2D(WSpr::*rhsEval3)(Array2D &u, double par1, Array2D &v, double par3), double par1, double par2)
double computeRKCashKarp45 (double dt, Array2D &u, Array2D(WSpr::*rhsEval)(Array2D &f, double dX, double dY))
double computeRKCashKarp45 (double dt, Array2D &u, Array2D &v, Array2D &w, Array2D(WSpr::*rhsEval1)(Array2D &w, double par1), Array2D(WSpr::*rhsEval2)(Array2D &w, double par2), Array2D(WSpr::*rhsEval3)(Array2D &u, double par1, Array2D &v, double par3), double par1, double par2)
Array2D advRHS (Array2D &u, double dx, double dy)
Array2D exRHS (Array2D &u, double epsilon0)
 last update: 23/jun/2006
Array2D eyRHS (Array2D &u, double epsilon0)
Array2D hzRHS (Array2D &u, double epsilon0, Array2D &v, double mu0)
Array2D exRHS (Array2D &hz, Array2D &ex, Array2D &sigma, double epsilon)
 last update: 8/jan/2007
Array2D eyRHS (Array2D &hz, Array2D &ey, Array2D &sigma, double epsilon)
 last update: 8/jan/2007
void dataToSparse (void)
void sparseToData (void)
void dataToSparseInnerGrid (int numberOfBorderPoints)
void extendMesh (int numberOfNeighbors=1, int numberOfGenerations=1)
void applyConeCondition (void)
 Use: findLevel, findStride.
void verifySpr (void)
void verifySprInnerGrid (int numberOfBordersPoints)
void plotDataGnuplot (char *title)
void plotDataGnuplot (char *title, char *grfFileNameOutput)
void plotDataGnuplot (char *title, char *grfFileName, char *grfFileNameCfg)
void plotGridGnuplot (char *title)
void plotGridGnuplot (char *title, char *grfFileNameOutput)
void plotGridGnuplot (char *title, char *grfFileName, char *grfFileNameCfg)
void computeSameMesh (WSpr &U, WSpr &V)
void initArray (void)
void infoNAN (void)
long getNumberOfNANs (void)
Array2D computeFirstDerivativeInSpr (int direction, int kind)
Array2D computeFirstDerivativeInSpr (Array2D &u, int direction, int kind)
int getNumberOfElements (int dimension)
double getThreshold (void)
void forceSprFlag (bool flag)

Public Attributes

Array2D _mat
Array2D _matDer

Protected Member Functions

void setWSpr (void)
void setWaveletFilter (void)
void setBoundarySpr (void)
void setDerivativeCoefficients (void)
int logTwo (int n)
 Auxiliary tools from class WSpr.
int powerTwo (int n)
int getNumberOfLevels (int n)
void recoverGrid (Array2D &tmp)
void interpGrid (Array2D &tmp)
double interpPoint (Array2D &u, int m, int n, bool isToUseOrigMeshPoints=true)
 --------------------------------------------------------Interpolation of point values
void interpInnerCol (Array2D &u)
void interpInnerRow (Array2D &u)
void interpLowerColRigid (Array2D &u)
void interpUpperColRigid (Array2D &u)
void interpLowerRowRigid (Array2D &u)
void interpUpperRowRigid (Array2D &u)
void interpLowerColSymmetric (Array2D &u)
void interpUpperColSymmetric (Array2D &u)
void interpLowerRowSymmetric (Array2D &u)
void interpUpperRowSymmetric (Array2D &u)
void interpLowerColAntisymmetric (Array2D &u)
void interpUpperColAntisymmetric (Array2D &u)
void interpLowerRowAntisymmetric (Array2D &u)
void interpUpperRowAntisymmetric (Array2D &u)
void recoverInnerCol (Array2D &u)
void recoverInnerRow (Array2D &u)
void recoverLowerColRigid (Array2D &u)
void recoverUpperColRigid (Array2D &u)
void recoverLowerRowRigid (Array2D &u)
void recoverUpperRowRigid (Array2D &u)
void recoverLowerColSymmetric (Array2D &u)
void recoverUpperColSymmetric (Array2D &u)
void recoverLowerRowSymmetric (Array2D &u)
void recoverUpperRowSymmetric (Array2D &u)
void recoverLowerColAntisymmetric (Array2D &u)
void recoverUpperColAntisymmetric (Array2D &u)
void recoverLowerRowAntisymmetric (Array2D &u)
void recoverUpperRowAntisymmetric (Array2D &u)
double interpInnerColPoint (Array2D &u, int m, int n)
double interpInnerRowPoint (Array2D &u, int m, int n)
double interpLowerColPointRigid (Array2D &u, int m, int n)
double interpUpperRowPointRigid (Array2D &u, int m, int n)
double interpUpperColPointRigid (Array2D &u, int m, int n)
double interpLowerRowPointRigid (Array2D &u, int m, int n)
double interpLowerColPointSymmetric (Array2D &u, int m, int n)
double interpUpperRowPointSymmetric (Array2D &u, int m, int n)
double interpUpperColPointSymmetric (Array2D &u, int m, int n)
double interpLowerRowPointSymmetric (Array2D &u, int m, int n)
double interpLowerColPointAntisymmetric (Array2D &u, int m, int n)
double interpUpperRowPointAntisymmetric (Array2D &u, int m, int n)
double interpUpperColPointAntisymmetric (Array2D &u, int m, int n)
double interpLowerRowPointAntisymmetric (Array2D &u, int m, int n)
void writeMessage (const char *message, const char *fileName, int ExiT=1, int App=0)
double computeFirstDerivativeInfBoundary (Array2D &u, int m, int n, int stride, int direction, int kind)
 last update: 20/jun/2006
double computeFirstDerivativeSupBoundary (Array2D &u, int m, int n, int stride, int direction, int kind)
 last update: 20/jun/2006
double computeFirstDerivativeLocalScaleX (Array2D &u, int m, int n, int kind)
double computeFirstDerivativeLocalScaleY (Array2D &u, int m, int n, int kind)
double computeFirstDerivativeInLocalScale (Array2D &u, int m, int n, int direction)
int computeDistanceOfNearestNeighbor (Array2D &u, int m, int n, int direction)
void dataToSparse (Array2D &u)
void sparseToData (Array2D &u)
void extendMesh (Array2D &u, int numberOfNeighbors=1, int numberOfGenerations=1)
void applyConeCondition (Array2D &u)
void verifySpr (Array2D &u)
void verifySprInnerGrid (Array2D &u, int numberOfBordersPoints)
void computeSameMesh (Array2D &u, Array2D &v, Array2D &w)
void plotDataGnuplot (Array2D &u, char *title)
 Visualization tools from class WSpr.
void plotDataGnuplot (Array2D &u, char *title, char *grfFileNameOutput)
void plotDataGnuplot (Array2D &u, char *title, char *grfFileName, char *grfFileNameCfg)
void plotGridGnuplot (Array2D &u, char *title)
void plotGridGnuplot (Array2D &u, char *title, char *grfFileNameOutput)
void plotGridGnuplot (Array2D &u, char *title, char *grfFileName, char *grfFileNameCfg)
int findLevel (int m, int n, int meshLevel)
int findLevel (int m, int n, int meshLevel, int *mPosition, int *nPosition)
int findLocalSpacing (int m, int n)
int findStride (int m, int n)
int findPointPosition (Array2D &u, int m, int n)
int findPositionInMesh (int m, int n, int level, int *mPosition, int *nPosition)
int findMaxDecompositionLevel (Array2D &u)
void initArray (Array2D &u, char *confFileName)
void dataAsciiToBlitz (char *fileNameIn, char *fileNameOut, int sizeX, int sizeY)
void infoNAN (Array2D &u)
long countNAN (Array2D &u)

Protected Attributes

bool _isInSpr
bool _isLocalDerivative
char _initialConditionFileName [301]
char _functionName [301]
int _minLevel
int _maxLevel
int _interpOrder
int _boundaryCodeSpr
int _numberOfElementsX
int _numberOfElementsY
int _meshLevel
double _threshold
Array1D _waveletFilter
Array1D _interpFilterRigidBoundary
Array1D _interpFilterSymmetricBoundary
Array1D _interpFilterAntiSymmetricBoundary
Array1D _coefFirstDerivative

Detailed Description

This class computes the sparse point representation. to be applied in EDPs solvers with finite difference and RK methods.

Member Function Documentation

Array2D WSpr::advRHS (  Array2D &  u,
double  dx,
double  dy
) 
 

Function advRHS Compute the rhs of the advection equation ut= -ux-uy last update: 23/jun/2006

-(Ux+Uy) central diff 4th order

void WSpr::applyConeCondition (  void   ) 
 

Use: findLevel, findStride.

Function applyConeCondition Compute and apply the cone condition for each significative point in the grid last update: 25/jul/2006

int WSpr::computeDistanceOfNearestNeighbor (  Array2D &  u,
int  m,
int  n,
int  direction
)  [protected]
 

Function computeDistanceOfNearestNeighbor Compute distance of the nearest neighbor if _isLocalDerivative is true last update: 21/jul/2006

double WSpr::computeFirstDerivativeInfBoundary (  Array2D &  u,
int  m,
int  n,
int  stride,
int  direction,
int  kind
)  [protected]
 

last update: 20/jun/2006

Function computeFirstDerivativeInfBoundary Compute the local scale derivative for inferior boundaries It uses a 4th order direction is 1 for x derivative direction is 2 for y derivative kind is 1 for symmetric boundary kind is 2 for antisymmetric boundary

Array2D WSpr::computeFirstDerivativeInSpr (  int  direction,
int  kind
) 
 

Function computeFirstDerivativeInSpr Compute the derivative only when u is !nan It uses a 4th order direction is 1 for x derivative direction is 2 for y derivative kind is 1 for symmetric boundary kind is 2 for antisymmetric boundary last update: 20/jun/2006

double WSpr::computeFirstDerivativeLocalScaleX (  Array2D &  u,
int  m,
int  n,
int  kind
)  [protected]
 

Function computeFirstDerivativeLocalScaleX Compute the local scale derivative if _isLocalDerivative is true last update: 21/jul/2006

double WSpr::computeFirstDerivativeLocalScaleY (  Array2D &  u,
int  m,
int  n,
int  kind
)  [protected]
 

Function computeFirstDerivativeLocalScaleY Compute the local scale derivative if _isLocalDerivative is true last update: 20/jun/2006

double WSpr::computeFirstDerivativeSupBoundary (  Array2D &  u,
int  m,
int  n,
int  stride,
int  direction,
int  kind
)  [protected]
 

last update: 20/jun/2006

Function computeFirstDerivativeSupBoundary Compute the local scale derivative for superior boundaries It uses a 4th order direction is 1 for x derivative direction is 2 for y derivative kind is 1 for symmetric boundary kind is 2 for antisymmetric boundary

double WSpr::computeRKCashKarp45 (  double  dt,
Array2D &  u,
Array2D &  v,
Array2D &  w,
Array2D(WSpr::*)(Array2D &w, double par1)  rhsEval1,
Array2D(WSpr::*)(Array2D &w, double par2)  rhsEval2,
Array2D(WSpr::*)(Array2D &u, double par1, Array2D &v, double par3)  rhsEval3,
double  par1,
double  par2
) 
 

Function compute RK Felhberg method order 4(5) Compute Runge Kutta 4(5) method using Cash and Karp coefficients It updates the solution u and returns the error between the two RK last update: 6/aug/2006 For a 3 equation system

double WSpr::computeRKCashKarp45 (  double  dt,
Array2D &  u,
Array2D(WSpr::*)(Array2D &f, double dX, double dY)  rhsEval
) 
 

Function compute RK Felhberg method order 4(5) Compute Runge Kutta 4(5) method using Cash and Karp coefficients It updates the solution u and returns the error between the two RK last update: 3/aug/2006

void WSpr::computeSameMesh (  WSpr &  U,
WSpr &  V
) 
 

Function computeSameMesh Merge the not nan points if one of the three arrays has in this position a not nan point last update: 23/jun/2006

long WSpr::countNAN (  Array2D &  u  )  [protected]
 

Function countNAN Compute the number of NAN in a transformed matrix last update: 12/may/2006

void WSpr::dataAsciiToBlitz (  char *  fileNameIn,
char *  fileNameOut,
int  sizeX,
int  sizeY
)  [protected]
 

Function dataAsciiToBlitz This function converts ascii matrix data file in a BLITZ format data file last update: 12/may/2006

void WSpr::dataToSparse (  Array2D &  u  )  [protected]
 

Copy A(2k,2m) and

Build all odd points

All points associated to the interpolatory wavelet coefficients that are not significant (less than the treshold) are set NAN

All odd points are recursively checked

void WSpr::dataToSparse (  void   ) 
 

Function dataToSparse 2D Compute 2d interpolatory multilevel SPR decomposition and set the non significant coefficients to NAN. N is considered a even number and the matrix is [0,N], so it has N+1 elements Calling functions: getNumberOfLevels interpGrid last update: 10/may/2006

void WSpr::dataToSparseInnerGrid (  int  numberOfPointsBorder  ) 
 

Function dataToSparse 2D Inner Grid Compute 2d interpolatory multilevel SPR decomposition and set the non significant coefficients to NAN. N is considered a even number and the matrix is [0,N], so it has N+1 elements Calling functions: getNumberOfLevels interpGridInnerMesh last update: 11/aug/2006

Array2D WSpr::exRHS (  Array2D &  hz,
Array2D &  ex,
Array2D &  sigma,
double  epsilon
) 
 

last update: 8/jan/2007

Function exRHS - TE mode complete Compute the rhs of the advection equation ex_t= 1/epsilon0 * Hz/partial y - sigma e_x

Array2D WSpr::exRHS (  Array2D &  hz,
double  epsilon
) 
 

last update: 23/jun/2006

Function exRHS Compute the rhs of the advection equation ex_t= 1/epsilon0 * Hz/partial y

void WSpr::extendMesh (  int  numberOfNeighbors = 1,
int  numberOfGenerations = 1
) 
 

Function extendMesh(Array2D u, int numberOfNeibors, int numberOfGenerations) This insert neighbor point for each significative point in the grid at the same level of the point and in the upper levels last update: 6/jul/2006

Array2D WSpr::eyRHS (  Array2D &  hz,
Array2D &  ey,
Array2D &  sigma,
double  epsilon
) 
 

last update: 8/jan/2007

Function eyRHS - TE mode complete Compute the rhs of the advection equation ey_t= 1/epsilon0 * Hz/partial x + sigma e_y

Array2D WSpr::eyRHS (  Array2D &  hz,
double  epsilon
) 
 

Function eyRHS Compute the rhs of the advection equation ey_t= - 1/epsilon0 * Hz/partial x last update: 23/jun/2006

int WSpr::findLevel (  int  m,
int  n,
int  level,
int *  mPosition,
int *  nPosition
)  [protected]
 

returns the point (m,n) level for a square matrix (isotropic decomposition) and the parity of the coordinate points last update: 10/may/2006

int WSpr::findLevel (  int  m,
int  n,
int  level
)  [protected]
 

Function findLevel returns the point (m,n) level for a square matrix (isotropic decomposition) last update: 10/may/2006

int WSpr::findMaxDecompositionLevel (  Array2D &  A  )  [protected]
 

Function findMaxDecompositionLevel Find max decomposition level that is not NAN It uses: findLevel last update: 12/may/2006

int WSpr::findPointPosition (  Array2D &  A,
int  m,
int  n
)  [protected]
 

return code: 0 - the point is not in the right mesh, ie it is a (even,even) point 1 - the point needs an inner column inperpolation 2 - the point needs a lower column inperpolation 3 - the point needs an upper column inperpolation 4 - the point needs an inner row inperpolation 5 - the point needs a lower row inperpolation 6 - the point needs an upper row inperpolation

int WSpr::findPositionInMesh (  int  m,
int  n,
int  level,
int *  mPosition,
int *  nPosition
)  [protected]
 

Function findPositionInMesh returns the point (m,n) position in the original mesh that this point belongs to and the level of that mesh. last update: 9/jul/2006

int WSpr::findStride (  int  m,
int  n
)  [protected]
 

Function findStride returns the stride associated with the local level of the point (m,n) last update: 10/may/2006

int WSpr::getNumberOfLevels (  int  n  )  [protected]
 

Function getNumberOfLevels Verify in which level the decomposition is last update: 6/may/2006

long WSpr::getNumberOfNANs (  void   ) 
 

Function getNumberOfNANs Compute the number of NAN in _mat last update: 29/aug/2006

Array2D WSpr::hzRHS (  Array2D &  ex,
double  epsilon0,
Array2D &  ey,
double  mu
) 
 

Function hzRHS Compute the rhs of the advection equation hz_t= 1/mu0 * ex/partial y - ey/partial x last update: 26/jun/2006

void WSpr::infoNAN (  void   ) 
 

Function infoNAN Print on screen info about number of NAN It uses: countNAN, findMaxDecompositionLevel last update: 12/may/2006

void WSpr::initArray (  void   ) 
 

Function initArray This function generate the initial value function or read it from a file in BLITZ format last update: 12/may/2006

void WSpr::interpGrid (  Array2D &  u  )  [protected]
 

Function interpGrid This function interpolates the (odd,even), (odd,odd) and (odd, even) points of a grid given the (even,even) points in a recursive way until minLevel. The boundary points are treated as rigid, symmetric or antisymetric Must be implemented the periodic boundary. last update: 10/may/2006

void WSpr::interpInnerCol (  Array2D &  u  )  [protected]
 

Function interpInnerCol This function interpolates the inner column points of a grid It uses a 4th order Lagrangian interpolation scheme. last update: 14/may/2006

double WSpr::interpInnerColPoint (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpInnerColPoint This function interpolates a point in the inner grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 16/may/2006

void WSpr::interpInnerRow (  Array2D &  u  )  [protected]
 

Function interpInnerRow This function interpolates the inner row points of a grid It uses a 4th order Lagrangian interpolation scheme. last update: 14/may/2006

double WSpr::interpInnerRowPoint (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpInnerRowPoint This function interpolate a point in the inner grid using row interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 16/may/2006

void WSpr::interpLowerColAntisymmetric (  Array2D &  u  )  [protected]
 

Function interpLowerColAntisymmetric This function interpolates the lower boundary column points of a grid using a antisymmetric boundary It uses a 4th order Lagrangian interpolation scheme. last update: 02/aug/2006

double WSpr::interpLowerColPointAntisymmetric (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpLowerColPointAntisymmetric This function interpolate a point in the lower column grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

double WSpr::interpLowerColPointRigid (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpLowerColPointRigid This function interpolate a point in the lower column grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 16/may/2006

double WSpr::interpLowerColPointSymmetric (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpLowerColPointSymmetric This function interpolate a point in the lower column grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

void WSpr::interpLowerColRigid (  Array2D &  u  )  [protected]
 

Function interpLowerColRigid This function interpolates the lower boundary column points of a grid using a rigid boundary It uses a 4th order Lagrangian interpolation scheme. last update: 14/may/2006

void WSpr::interpLowerColSymmetric (  Array2D &  u  )  [protected]
 

Function interpLowerColSymmetric This function interpolates the lower boundary column points of a grid using a antisymmetric boundary It uses a 4th order Lagrangian interpolation scheme. last update: 02/aug/2006

void WSpr::interpLowerRowAntisymmetric (  Array2D &  u  )  [protected]
 

Function interpLowerRowAntisymmetric This function interpolates the lower boundary row points of a grid using a antisymmetric boundary It uses a 4th order Lagrangian interpolation scheme. last update: 2/aug/2006

double WSpr::interpLowerRowPointAntisymmetric (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpLowerRowPointAntisymmetric This function interpolate a point in the lower row grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

double WSpr::interpLowerRowPointRigid (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpLowerRowPointRigid This function interpolate a point in the lower row grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 16/may/2006

double WSpr::interpLowerRowPointSymmetric (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpLowerRowPointSymmetric This function interpolate a point in the lower row grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

void WSpr::interpLowerRowRigid (  Array2D &  u  )  [protected]
 

Function interpLowerRowRigid This function interpolates the lower boundary row points of a grid using a rigid boundary It uses a 4th order Lagrangian interpolation scheme. last update: 14/may/2006

void WSpr::interpLowerRowSymmetric (  Array2D &  u  )  [protected]
 

Function interpLowerRowSymmetric This function interpolates the lower boundary row points of a grid using a antisymmetric boundary It uses a 4th order Lagrangian interpolation scheme. last update: 2/aug/2006

double WSpr::interpPoint (  Array2D &  u,
int  m,
int  n,
bool  isToUseOrigMeshPoints = true
)  [protected]
 

--------------------------------------------------------Interpolation of point values

Function interpPoint This function interpolate a point in the grid It uses: findpointPosition, interpPoint, interpInner(Col,Row)Point, interp(Lower,Upper)(Col,Row)Point last update: 16/may/2006

void WSpr::interpUpperColAntisymmetric (  Array2D &  u  )  [protected]
 

Function interpUpperColAntisymmetric This function interpolates the upper boundary column points of a grid using a antisymmetric boundary It uses a 4th order Lagrangian interpolation scheme. last update: 2/aug/2006

double WSpr::interpUpperColPointAntisymmetric (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpUpperColPointAntisymmetric This function interpolate a point in the upper column grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

double WSpr::interpUpperColPointRigid (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpUpperColPointRigid This function interpolate a point in the upper column grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 16/may/2006

double WSpr::interpUpperColPointSymmetric (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpUpperColPointSymmetric This function interpolate a point in the upper column grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

void WSpr::interpUpperColRigid (  Array2D &  u  )  [protected]
 

Function interpUpperColRigid This function interpolates the upper boundary column points of a grid using a rigid boundary It uses a 4th order Lagrangian interpolation scheme. last update: 14/may/2006

void WSpr::interpUpperColSymmetric (  Array2D &  u  )  [protected]
 

Function interpUpperColSymmetric This function interpolates the upper boundary column points of a grid using a antisymmetric boundary It uses a 4th order Lagrangian interpolation scheme. last update: 2/aug/2006

void WSpr::interpUpperRowAntisymmetric (  Array2D &  u  )  [protected]
 

Function interpUpperColAntisymmetric This function interpolates the upper boundary row points of a grid using a antisymmetric boundary It uses a 4th order Lagrangian interpolation scheme. last update: 2/aug/2006

double WSpr::interpUpperRowPointAntisymmetric (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpUpperRowPointAntisymmetric This function interpolate a point in the lower row grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

double WSpr::interpUpperRowPointRigid (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpUpperRowPointRigid This function interpolate a point in the lower row grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 16/may/2006

double WSpr::interpUpperRowPointSymmetric (  Array2D &  u,
int  m,
int  n
)  [protected]
 

Function interpUpperRowPointSymmetric This function interpolate a point in the lower row grid using column interpolation It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

void WSpr::interpUpperRowRigid (  Array2D &  u  )  [protected]
 

Function interpUpperColRigid This function interpolates the upper boundary row points of a grid using a rigid boundary It uses a 4th order Lagrangian interpolation scheme. last update: 14/may/2006

void WSpr::interpUpperRowSymmetric (  Array2D &  u  )  [protected]
 

Function interpUpperColSymmetric This function interpolates the upper boundary row points of a grid using a antisymmetric boundary It uses a 4th order Lagrangian interpolation scheme. last update: 2/aug/2006

int WSpr::logTwo (  int  n  )  [protected]
 

Auxiliary tools from class WSpr.

Function logTwo Compute Log2(n) last update: 6/may/2006

void WSpr::plotDataGnuplot (  Array2D &  u,
char *  title
)  [protected]
 

Visualization tools from class WSpr.

Function plotDataGnuplot This function plot the value of the solution in real time directly in gnuplot produce one screen shots or eps or png file last update: 31/jul/2006

void WSpr::plotGridGnuplot (  Array2D &  u,
char *  title
)  [protected]
 

Function plotGridGnuplot This function plot the grid points of the solution is Spr representation in real time directly in gnuplot produce two screen shots + eps file last update: 12/jun/2006

int WSpr::powerTwo (  int  n  )  [protected]
 

Function powerTwo Compute 2^j of a given number j last update: 6/may/2006

void WSpr::recoverGrid (  Array2D &  u  )  [protected]
 

Function recoverGrid This function recover the original grid interpolating the (odd,even), (odd,odd) and (odd, even) points of a grid given the (even,even) points in a recursive way from the minimum level. It uses a 4th order Lagrangian interpolation scheme. The bounday points are treated as rigid but the idea is a function call for it, to implemented it also for symetric and anti-simetric boundaries interpolations. last update: 10/may/2006

void WSpr::recoverInnerCol (  Array2D &  u  )  [protected]
 

Function recoverInnerCol This function interpolates the inner column points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 14/may/2006

void WSpr::recoverInnerRow (  Array2D &  u  )  [protected]
 

Function recoverInnerRow This function interpolates the inner row points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 14/may/2006

void WSpr::recoverLowerColAntisymmetric (  Array2D &  u  )  [protected]
 

Function recoverLowerColAntisymmetric This function interpolates the lower column points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

void WSpr::recoverLowerColRigid (  Array2D &  u  )  [protected]
 

Function recoverLowerColRigid This function interpolates the lower column points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 14/may/2006

void WSpr::recoverLowerColSymmetric (  Array2D &  u  )  [protected]
 

Function recoverLowerColSymmetric This function interpolates the lower column points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

void WSpr::recoverLowerRowAntisymmetric (  Array2D &  u  )  [protected]
 

Function recoverLowerRowAntisymmetric This function interpolates the lower row points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

void WSpr::recoverLowerRowRigid (  Array2D &  u  )  [protected]
 

Function recoverLowerRowRigid This function interpolates the lower row points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 14/may/2006

void WSpr::recoverLowerRowSymmetric (  Array2D &  u  )  [protected]
 

Function recoverLowerRowSymmetric This function interpolates the lower row points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

void WSpr::recoverUpperColAntisymmetric (  Array2D &  u  )  [protected]
 

Function recoverUpperColAntisymmetric This function interpolates the upper column points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

void WSpr::recoverUpperColRigid (  Array2D &  u  )  [protected]
 

Function recoverUpperColRigid This function interpolates the upper column points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 14/may/2006

void WSpr::recoverUpperColSymmetric (  Array2D &  u  )  [protected]
 

Function recoverUpperColSymmetric This function interpolates the upper column points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

void WSpr::recoverUpperRowAntisymmetric (  Array2D &  u  )  [protected]
 

Function recoverUpperRowAntisymmetric This function interpolates the upper row points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

void WSpr::recoverUpperRowRigid (  Array2D &  u  )  [protected]
 

Function recoverUpperRowRigid This function interpolates the upper row points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 14/may/2006

void WSpr::recoverUpperRowSymmetric (  Array2D &  u  )  [protected]
 

Function recoverUpperRowSymmetric This function interpolates the upper row points of a grid is they are NAN It uses a 4th order Lagrangian interpolation scheme. last update: 2/Aug/2006

void WSpr::setDerivativeCoefficients (  void   )  [protected]
 

Function setDerivativeCoefficients Puts the derivative coeficients - only first derivative implemented It uses a 4th order last update: 19/jun/2006

void WSpr::setWaveletFilter (  void   )  [protected]
 

Function setWaveletFilter This function set the interpolatory Wavelet filters for M=2,4,6 and 8 last update: 29/may/2006

void WSpr::setWSpr (  void   )  [protected]
 

Function setWSpr This function initialize the filters and boundaries last update: 29/may/2006

void WSpr::sparseToData (  void   ) 
 

Function sparseToData 2D This function is the interpolatory transform itself. Calling functions: getNumberOfLevels recoverGrid last update: 10/may/2006

void WSpr::testExtendMesh (  void   ) 
 

Function testextendMesh Teste the extend mesh function last update: 31/may/2006

void WSpr::testLocalDerivate (  void   ) 
 

Function testLocalDerivate Teste the first derivate function last update: 20/jun/2006

void WSpr::testMaxwellTimeEvolution (  void   ) 
 

Function testMaxwellTimeEvolution Teste Maxwell Equation in TE mode last update: 27/jun/2006

void WSpr::testSprWithBoundaries (  void   ) 
 

Function testSprWithBoundaries Test the spr with boundaries symmetric and antisymmetric in x and y last update: 2/aug/2006

void WSpr::testTimeEvolution (  void   ) 
 

Function testTimeEvolution Test the first derivate function last update: 20/jun/2006

void WSpr::testTransformsTime (  void   ) 
 

Function TestTransformsTime Teste the time duration of the pointwise and grid inverse transform last update: 30/may/2006

void WSpr::testTransformTimeLocalPoints (  void   ) 
 

Function TestTransformTimeLocalPoints Teste the time duration of the pointwise and grid inverse transform last update: 31/may/2006

void WSpr::testViewMeshTransforms (  void   ) 
 

Function testViewMeshTransform Plot function and mesh last update: 30/may/2006

void WSpr::verifySpr (  void   ) 
 

Function verifySpr Verify the sparse point representation, ie, verify if all points considered significative points are really significative last update: 1/jun/2006

void WSpr::verifySprInnerGrid (  int  numberOfBordersPoints  ) 
 

Function verifySprInnerMesh Verify the sparse point representation, ie, verify if all points considered significative points are really significative only in an inner submatrix that has a fix numbers of cells around it. In this case no boundary condition to the spr is necessary if the number of points is great of interpOrder/2. last update: 11/ago/2006

void WSpr::writeMessage (  const char *  message,
const char *  fileName,
int  ExiT = 1,
int  App = 0
)  [protected]
 

Function writeMessage Write a message in a log file and exit the program if necessary last update: 22/may/2006

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