* provided "as is" without express or implied warranty. *
**************************************************************************/
-/* $Id$ */
-
-// Author: ruben.shahoyan@cern.ch 09/09/2006
-//
-////////////////////////////////////////////////////////////////////////////////
-// //
-// AliCheb3D produces the interpolation of the user 3D->NDimOut arbitrary //
-// function supplied in "void (*fcn)(float* inp,float* out)" format //
-// either in a separate macro file or as a function pointer. //
-// Only coefficients needed to guarantee the requested precision are kept. //
-// //
-// The user-callable methods are: //
-// To create the interpolation use: //
-// AliCheb3D(const char* funName, // name of the file with user function //
-// or //
-// AliCheb3D(void (*ptr)(float*,float*),// pointer on the user function //
-// Int_t DimOut, // dimensionality of the function's output //
-// Float_t *bmin, // lower 3D bounds of interpolation domain //
-// Float_t *bmax, // upper 3D bounds of interpolation domain //
-// Int_t *npoints, // number of points in each of 3 input //
-// // dimension, defining the interpolation grid //
-// Float_t prec=1E-6); // requested max.absolute difference between //
-// // the interpolation and any point on grid //
-// //
-// To test obtained parameterization use the method //
-// TH1* TestRMS(int idim,int npoints = 1000,TH1* histo=0); //
-// it will compare the user output of the user function and interpolation //
-// for idim-th output dimension and fill the difference in the supplied //
-// histogram. If no histogram is supplied, it will be created. //
-// //
-// To save the interpolation data: //
-// SaveData(const char* filename, Bool_t append ) //
-// write text file with data. If append is kTRUE and the output file already //
-// exists, data will be added in the end of the file. //
-// Alternatively, SaveData(FILE* stream) will write the data to //
-// already existing stream. //
-// //
-// To read back already stored interpolation use either the constructor //
-// AliCheb3D(const char* inpFile); //
-// or the default constructor AliCheb3D() followed by //
-// AliCheb3D::LoadData(const char* inpFile); //
-// //
-// To compute the interpolation use Eval(float* par,float *res) method, with //
-// par being 3D vector of arguments (inside the validity region) and res is //
-// the array of DimOut elements for the output. //
-// //
-// If only one component (say, idim-th) of the output is needed, use faster //
-// Float_t Eval(Float_t *par,int idim) method. //
-// //
-// void Print(option="") will print the name, the ranges of validity and //
-// the absolute precision of the parameterization. Option "l" will also print //
-// the information about the number of coefficients for each output //
-// dimension. //
-// //
-// NOTE: during the evaluation no check is done for parameter vector being //
-// outside the interpolation region. If there is such a risk, use //
-// Bool_t IsInside(float *par) method. Chebyshev parameterization is not //
-// good for extrapolation! //
-// //
-// For the properties of Chebyshev parameterization see: //
-// H.Wind, CERN EP Internal Report, 81-12/Rev. //
-// //
-////////////////////////////////////////////////////////////////////////////////
-
+#include <cstdlib>
+#include <TSystem.h>
#include "AliCheb3DCalc.h"
ClassImp(AliCheb3DCalc)
-
-AliCheb3DCalc::AliCheb3DCalc():
- TNamed("", ""),
- fNCoefs(0),
- fNRows(0),
- fNCols(0),
- fNElemBound2D(0),
- fNColsAtRow(0),
- fColAtRowBg(0),
- fCoefBound2D0(0),
- fCoefBound2D1(0),
- fCoefs(0),
- fTmpCf1(0),
- fTmpCf0(0)
+//__________________________________________________________________________________________
+AliCheb3DCalc::AliCheb3DCalc() :
+ fNCoefs(0),
+ fNRows(0),
+ fNCols(0),
+ fNElemBound2D(0),
+ fNColsAtRow(0),
+ fColAtRowBg(0),
+ fCoefBound2D0(0),
+ fCoefBound2D1(0),
+ fCoefs(0),
+ fTmpCf1(0),
+ fTmpCf0(0)
{
- // Default constructor
- Init0();
+ // default constructor
}
-AliCheb3DCalc::AliCheb3DCalc(FILE* stream):
- TNamed("", ""),
- fNCoefs(0),
- fNRows(0),
- fNCols(0),
- fNElemBound2D(0),
- fNColsAtRow(0),
- fColAtRowBg(0),
- fCoefBound2D0(0),
- fCoefBound2D1(0),
- fCoefs(0),
- fTmpCf1(0),
- fTmpCf0(0)
+//__________________________________________________________________________________________
+AliCheb3DCalc::AliCheb3DCalc(const AliCheb3DCalc& src) :
+ TNamed(src),
+ fNCoefs(src.fNCoefs),
+ fNRows(src.fNRows),
+ fNCols(src.fNCols),
+ fNElemBound2D(src.fNElemBound2D),
+ fNColsAtRow(0),
+ fColAtRowBg(0),
+ fCoefBound2D0(0),
+ fCoefBound2D1(0),
+ fCoefs(0),
+ fTmpCf1(0),
+ fTmpCf0(0)
{
- // Default constructor
- Init0();
- LoadData(stream);
+ // copy constructor
+ //
+ if (src.fNColsAtRow) {
+ fNColsAtRow = new UShort_t[fNRows];
+ for (int i=fNRows;i--;) fNColsAtRow[i] = src.fNColsAtRow[i];
+ }
+ if (src.fColAtRowBg) {
+ fColAtRowBg = new UShort_t[fNRows];
+ for (int i=fNRows;i--;) fColAtRowBg[i] = src.fColAtRowBg[i];
+ }
+ if (src.fCoefBound2D0) {
+ fCoefBound2D0 = new UShort_t[fNElemBound2D];
+ for (int i=fNElemBound2D;i--;) fCoefBound2D0[i] = src.fCoefBound2D0[i];
+ }
+ if (src.fCoefBound2D1) {
+ fCoefBound2D1 = new UShort_t[fNElemBound2D];
+ for (int i=fNElemBound2D;i--;) fCoefBound2D1[i] = src.fCoefBound2D1[i];
+ }
+ if (src.fCoefs) {
+ fCoefs = new Float_t[fNCoefs];
+ for (int i=fNCoefs;i--;) fCoefs[i] = src.fCoefs[i];
+ }
+ if (src.fTmpCf1) fTmpCf1 = new Float_t[fNCols];
+ if (src.fTmpCf0) fTmpCf0 = new Float_t[fNRows];
}
+//__________________________________________________________________________________________
+AliCheb3DCalc::AliCheb3DCalc(FILE* stream) :
+ fNCoefs(0),
+ fNRows(0),
+ fNCols(0),
+ fNElemBound2D(0),
+ fNColsAtRow(0),
+ fColAtRowBg(0),
+ fCoefBound2D0(0),
+ fCoefBound2D1(0),
+ fCoefs(0),
+ fTmpCf1(0),
+ fTmpCf0(0)
+{
+ // constructor from coeffs. streem
+ LoadData(stream);
+}
-AliCheb3DCalc::AliCheb3DCalc(const AliCheb3DCalc& src) :
- TNamed(src),
- fNCoefs(src.fNCoefs),
- fNRows(src.fNRows),
- fNCols(src.fNCols),
- fNElemBound2D(src.fNElemBound2D),
- fNColsAtRow(0),
- fColAtRowBg(0),
- fCoefBound2D0(0),
- fCoefBound2D1(0),
- fCoefs(0),
- fTmpCf1(0),
- fTmpCf0(0)
+//__________________________________________________________________________________________
+AliCheb3DCalc& AliCheb3DCalc::operator=(const AliCheb3DCalc& rhs)
{
- // Copy constructor
- if (src.fNColsAtRow) {
- fNColsAtRow = new Int_t[fNRows];
- for (int i=fNRows;i--;) fNColsAtRow[i] = src.fNColsAtRow[i];
+ // assignment operator
+ if (this != &rhs) {
+ Clear();
+ SetName(rhs.GetName());
+ SetTitle(rhs.GetTitle());
+ fNCoefs = rhs.fNCoefs;
+ fNRows = rhs.fNRows;
+ fNCols = rhs.fNCols;
+ if (rhs.fNColsAtRow) {
+ fNColsAtRow = new UShort_t[fNRows];
+ for (int i=fNRows;i--;) fNColsAtRow[i] = rhs.fNColsAtRow[i];
}
- if (src.fColAtRowBg) {
- fColAtRowBg = new Int_t[fNRows];
- for (int i=fNRows;i--;) fColAtRowBg[i] = src.fColAtRowBg[i];
+ if (rhs.fColAtRowBg) {
+ fColAtRowBg = new UShort_t[fNRows];
+ for (int i=fNRows;i--;) fColAtRowBg[i] = rhs.fColAtRowBg[i];
}
- if (src.fCoefBound2D0) {
- fCoefBound2D0 = new Int_t[fNElemBound2D];
- for (int i=fNElemBound2D;i--;) fCoefBound2D0[i] = src.fCoefBound2D0[i];
+ if (rhs.fCoefBound2D0) {
+ fCoefBound2D0 = new UShort_t[fNElemBound2D];
+ for (int i=fNElemBound2D;i--;) fCoefBound2D0[i] = rhs.fCoefBound2D0[i];
}
- if (src.fCoefBound2D1) {
- fCoefBound2D1 = new Int_t[fNElemBound2D];
- for (int i=fNElemBound2D;i--;) fCoefBound2D1[i] = src.fCoefBound2D1[i];
+ if (rhs.fCoefBound2D1) {
+ fCoefBound2D1 = new UShort_t[fNElemBound2D];
+ for (int i=fNElemBound2D;i--;) fCoefBound2D1[i] = rhs.fCoefBound2D1[i];
}
- if (src.fCoefs) {
- fCoefs = new Float_t[fNCoefs];
- for (int i=fNCoefs;i--;) fCoefs[i] = src.fCoefs[i];
- }
- if (src.fTmpCf1) fTmpCf1 = new Float_t[fNCols];
- if (src.fTmpCf0) fTmpCf0 = new Float_t[fNRows];
-}
-
-AliCheb3DCalc& AliCheb3DCalc::operator=(const AliCheb3DCalc& rhs)
-{
- // Assignment operator
- if (this != &rhs) {
- Clear();
- SetName(rhs.GetName());
- SetTitle(rhs.GetTitle());
- fNCoefs = rhs.fNCoefs;
- fNRows = rhs.fNRows;
- fNCols = rhs.fNCols;
- if (rhs.fNColsAtRow) {
- fNColsAtRow = new Int_t[fNRows];
- for (int i=fNRows;i--;) fNColsAtRow[i] = rhs.fNColsAtRow[i];
- }
- if (rhs.fColAtRowBg) {
- fColAtRowBg = new Int_t[fNRows];
- for (int i=fNRows;i--;) fColAtRowBg[i] = rhs.fColAtRowBg[i];
- }
- if (rhs.fCoefBound2D0) {
- fCoefBound2D0 = new Int_t[fNElemBound2D];
- for (int i=fNElemBound2D;i--;) fCoefBound2D0[i] = rhs.fCoefBound2D0[i];
- }
- if (rhs.fCoefBound2D1) {
- fCoefBound2D1 = new Int_t[fNElemBound2D];
- for (int i=fNElemBound2D;i--;) fCoefBound2D1[i] = rhs.fCoefBound2D1[i];
- }
- if (rhs.fCoefs) {
- fCoefs = new Float_t[fNCoefs];
- for (int i=fNCoefs;i--;) fCoefs[i] = rhs.fCoefs[i];
- }
- if (rhs.fTmpCf1) fTmpCf1 = new Float_t[fNCols];
- if (rhs.fTmpCf0) fTmpCf0 = new Float_t[fNRows];
+ if (rhs.fCoefs) {
+ fCoefs = new Float_t[fNCoefs];
+ for (int i=fNCoefs;i--;) fCoefs[i] = rhs.fCoefs[i];
}
- return *this;
+ if (rhs.fTmpCf1) fTmpCf1 = new Float_t[fNCols];
+ if (rhs.fTmpCf0) fTmpCf0 = new Float_t[fNRows];
+ }
+ return *this;
}
//__________________________________________________________________________________________
-void AliCheb3DCalc::Clear(Option_t*)
+void AliCheb3DCalc::Clear(const Option_t*)
{
// delete all dynamycally allocated structures
if (fTmpCf1) { delete[] fTmpCf1; fTmpCf1 = 0;}
}
//__________________________________________________________________________________________
-void AliCheb3DCalc::Init0()
+void AliCheb3DCalc::Print(const Option_t* ) const
{
- // reset everything to 0
- fNCoefs = fNRows = fNCols = fNElemBound2D = 0;
- fCoefs = 0;
- fCoefBound2D0 = fCoefBound2D1 = 0;
- fNColsAtRow = fColAtRowBg = 0;
- fTmpCf0 = fTmpCf1 = 0;
-}
-
-//__________________________________________________________________________________________
-void AliCheb3DCalc::Print(Option_t* ) const
-{
- // Print the Chebychev paramterization data
+ // print info
printf("Chebyshev parameterization data %s for 3D->1 function.\n",GetName());
int nmax3d = 0;
for (int i=fNElemBound2D;i--;) if (fCoefBound2D0[i]>nmax3d) nmax3d = fCoefBound2D0[i];
}
//__________________________________________________________________________________________
-Float_t AliCheb3DCalc::Eval(Float_t *par) const
+Float_t AliCheb3DCalc::EvalDeriv(int dim, const Float_t *par) const
+{
+ // evaluate Chebyshev parameterization derivative in given dimension for 3D function.
+ // VERY IMPORTANT: par must contain the function arguments ALREADY MAPPED to [-1:1] interval
+ //
+ int ncfRC;
+ for (int id0=fNRows;id0--;) {
+ int nCLoc = fNColsAtRow[id0]; // number of significant coefs on this row
+ if (!nCLoc) {fTmpCf0[id0]=0; continue;}
+ //
+ int col0 = fColAtRowBg[id0]; // beginning of local column in the 2D boundary matrix
+ for (int id1=nCLoc;id1--;) {
+ int id = id1+col0;
+ if (!(ncfRC=fCoefBound2D0[id])) { fTmpCf1[id1]=0; continue;}
+ if (dim==2) fTmpCf1[id1] = ChebEval1Deriv(par[2],fCoefs + fCoefBound2D1[id], ncfRC);
+ else fTmpCf1[id1] = ChebEval1D(par[2],fCoefs + fCoefBound2D1[id], ncfRC);
+ }
+ if (dim==1) fTmpCf0[id0] = ChebEval1Deriv(par[1],fTmpCf1,nCLoc);
+ else fTmpCf0[id0] = ChebEval1D(par[1],fTmpCf1,nCLoc);
+ }
+ return (dim==0) ? ChebEval1Deriv(par[0],fTmpCf0,fNRows) : ChebEval1D(par[0],fTmpCf0,fNRows);
+ //
+}
+
+//__________________________________________________________________________________________
+Float_t AliCheb3DCalc::EvalDeriv2(int dim1,int dim2, const Float_t *par) const
{
- // evaluate Chebyshev parameterization for 3D function.
+ // evaluate Chebyshev parameterization 2n derivative in given dimensions for 3D function.
// VERY IMPORTANT: par must contain the function arguments ALREADY MAPPED to [-1:1] interval
- Float_t &z = par[2];
- Float_t &y = par[1];
- Float_t &x = par[0];
//
+ Bool_t same = dim1==dim2;
int ncfRC;
for (int id0=fNRows;id0--;) {
int nCLoc = fNColsAtRow[id0]; // number of significant coefs on this row
+ if (!nCLoc) {fTmpCf0[id0]=0; continue;}
+ //
int col0 = fColAtRowBg[id0]; // beginning of local column in the 2D boundary matrix
for (int id1=nCLoc;id1--;) {
int id = id1+col0;
- fTmpCf1[id1] = (ncfRC=fCoefBound2D0[id]) ? ChebEval1D(z,fCoefs + fCoefBound2D1[id], ncfRC) : 0.0;
+ if (!(ncfRC=fCoefBound2D0[id])) { fTmpCf1[id1]=0; continue;}
+ if (dim1==2||dim2==2) fTmpCf1[id1] = same ? ChebEval1Deriv2(par[2],fCoefs + fCoefBound2D1[id], ncfRC)
+ : ChebEval1Deriv(par[2],fCoefs + fCoefBound2D1[id], ncfRC);
+ else fTmpCf1[id1] = ChebEval1D(par[2],fCoefs + fCoefBound2D1[id], ncfRC);
}
- fTmpCf0[id0] = nCLoc>0 ? ChebEval1D(y,fTmpCf1,nCLoc):0.0;
+ if (dim1==1||dim2==1) fTmpCf0[id0] = same ? ChebEval1Deriv2(par[1],fTmpCf1,nCLoc):ChebEval1Deriv(par[1],fTmpCf1,nCLoc);
+ else fTmpCf0[id0] = ChebEval1D(par[1],fTmpCf1,nCLoc);
}
- return ChebEval1D(x,fTmpCf0,fNRows);
+ return (dim1==0||dim2==0) ? (same ? ChebEval1Deriv2(par[0],fTmpCf0,fNRows):ChebEval1Deriv(par[0],fTmpCf0,fNRows)) :
+ ChebEval1D(par[0],fTmpCf0,fNRows);
//
}
if (fColAtRowBg) delete[] fColAtRowBg;
if (fTmpCf0) delete[] fTmpCf0;
fNRows = nr;
- fNColsAtRow = new Int_t[fNRows];
+ fNColsAtRow = new UShort_t[fNRows];
fTmpCf0 = new Float_t [fNRows];
- fColAtRowBg = new Int_t[fNRows];
+ fColAtRowBg = new UShort_t[fNRows];
for (int i=fNRows;i--;) fNColsAtRow[i] = fColAtRowBg[i] = 0;
}
if (fCoefBound2D0) delete[] fCoefBound2D0;
if (fCoefBound2D1) delete[] fCoefBound2D1;
fNElemBound2D = ne;
- fCoefBound2D0 = new Int_t[fNElemBound2D];
- fCoefBound2D1 = new Int_t[fNElemBound2D];
+ fCoefBound2D0 = new UShort_t[fNElemBound2D];
+ fCoefBound2D1 = new UShort_t[fNElemBound2D];
for (int i=fNElemBound2D;i--;) fCoefBound2D0[i] = fCoefBound2D1[i] = 0;
}
for (int i=fNCoefs;i--;) fCoefs[i] = 0.0;
}
+//__________________________________________________________________________________________
+Float_t AliCheb3DCalc::ChebEval1Deriv(Float_t x, const Float_t * array, int ncf )
+{
+ // evaluate 1D Chebyshev parameterization's derivative. x is the argument mapped to [-1:1] interval
+ if (--ncf<1) return 0;
+ Float_t b0, b1, b2;
+ Float_t x2 = x+x;
+ b1 = b2 = 0;
+ float dcf0=0,dcf1,dcf2=0;
+ b0 = dcf1 = 2*ncf*array[ncf];
+ if (!(--ncf)) return b0/2;
+ //
+ for (int i=ncf;i--;) {
+ b2 = b1;
+ b1 = b0;
+ dcf0 = dcf2 + 2*(i+1)*array[i+1];
+ b0 = dcf0 + x2*b1 -b2;
+ dcf2 = dcf1;
+ dcf1 = dcf0;
+ }
+ //
+ return b0 - x*b1 - dcf0/2;
+}
+
+//__________________________________________________________________________________________
+Float_t AliCheb3DCalc::ChebEval1Deriv2(Float_t x, const Float_t * array, int ncf )
+{
+ // evaluate 1D Chebyshev parameterization's 2nd derivative. x is the argument mapped to [-1:1] interval
+ if (--ncf<2) return 0;
+ Float_t b0, b1, b2;
+ Float_t x2 = x+x;
+ b1 = b2 = 0;
+ float dcf0=0,dcf1=0,dcf2=0;
+ float ddcf0=0,ddcf1,ddcf2=0;
+ //
+ dcf2 = 2*ncf*array[ncf];
+ --ncf;
+
+ dcf1 = 2*ncf*array[ncf];
+ b0 = ddcf1 = 2*ncf*dcf2;
+ //
+ if (!(--ncf)) return b0/2;
+ //
+ for (int i=ncf;i--;) {
+ b2 = b1;
+ b1 = b0;
+ dcf0 = dcf2 + 2*(i+1)*array[i+1];
+ ddcf0 = ddcf2 + 2*(i+1)*dcf1;
+ b0 = ddcf0 + x2*b1 -b2;
+ //
+ ddcf2 = ddcf1;
+ ddcf1 = ddcf0;
+ //
+ dcf2 = dcf1;
+ dcf1 = dcf0;
+ //
+ }
+ //
+ return b0 - x*b1 - ddcf0/2;
+}
+//__________________________________________________________________________________________
+Int_t AliCheb3DCalc::GetMaxColsAtRow() const
+{
+ int nmax3d = 0;
+ for (int i=fNElemBound2D;i--;) if (fCoefBound2D0[i]>nmax3d) nmax3d = fCoefBound2D0[i];
+ return nmax3d;
+}
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff