[u/mrichter/AliRoot.git] / STAT / Macros / pdfTest.C

#include <malloc.h>

#include "TSystem.h"
#include "TFile.h"
#include "TTree.h"
#include "TProfile.h"
#include "TF1.h"
#include "TF2.h"
#include "TF3.h"
#include "TLegend.h"
#include "TRandom.h"
#include "TString.h"
#include "TGraph.h"
#include "TMarker.h"
#include "TStopwatch.h"
#include "../src/TKDPDF.h"

void pdfTest(const Int_t ndim = 1);
Double_t interpolation(const int nstat, const int ndim, const int first);
void build(const int ndim, const int npoints);
Float_t Mem();

TF1 *f = 0x0;

//__________________________________________________________
void pdfTest(const Int_t ndim)
{
// Test interpolator on a variable dimension (ndim<=5) uncorrelated
// Gauss model. The macro displays the chi2 between interpolation and
// model for various statistics of experimental data.
//
// Check the worker function interpolation() to fine tune the
// algorithm.
// 
// Attention:
// The macro works in compiled mode !

	// define model
	switch(ndim){
	case 1:
		f=new TF1("f1", "gaus(0);x;f(x)", -5., 5.);
		f->SetParameter(0, 1.);
		f->SetParameter(1, 0.);
		f->SetParameter(2, 1.);
		f->SetParameter(0, 1./f->Integral(-5., 5.));
		break;
	case 2:
		f=new TF2("f2", "[0]*exp(-0.5*((x-[1])/[2])**2)*exp(-0.5*((y-[3])/[4])**2)", -5., 5., -5., 5.);
		f->SetParameter(0, 1.);
		f->SetParameter(1, 0.);
		f->SetParameter(2, 1.);
		f->SetParameter(3, 0.);
		f->SetParameter(4, 1.);
		f->SetParameter(0, 1./f->Integral(-5., 5., -5., 5.));
		break;
	case 3:
	case 4:
	case 5:
		f=new TF3("f3", "[0]*exp(-0.5*((x-[1])/[2])**2)*exp(-0.5*((y-[3])/[4])**2)*exp(-0.5*((z-[5])/[6])**2)", -5., 5., -5., 5., -5., 5.);
		f->SetParameter(0, 1.);
		f->SetParameter(1, 0.);
		f->SetParameter(2, 1.);
		f->SetParameter(3, 0.);
		f->SetParameter(4, 1.);
		f->SetParameter(5, 0.);
		f->SetParameter(6, 1.);
		f->SetParameter(0, 1./f->Integral(-5., 5., -5., 5., -5., 5.));
		if(ndim>3) printf("Warning : chi2 results are unreliable !\n");
		break;
	default:
		printf("%dD not supported in this macro.\n", ndim);
		return;
	}

	Double_t chi2;
	const Int_t nchi2 = 18;
	const Int_t nfirst = 1;
 	//TProfile *hp = new TProfile("hp", "", 100, 1.E4, 1.E6);
 	//hp->SetMarkerStyle(24);
	TGraph *gChi2 = new TGraph(nchi2);
 	gChi2->SetMarkerStyle(24);
	Int_t ip = 0, nstat, first;
	for(int ifirst=0; ifirst<nfirst; ifirst++){
		first = 0;//Int_t(gRandom->Uniform(1.E4));
		for(int i=2; i<10; i++){
			nstat = 10000*i;
			chi2 = interpolation(nstat, ndim, first);
			gChi2->SetPoint(ip++, TMath::Log10(float(nstat)), chi2);
			//hp->Fill(float(nstat), chi2);
		}
		for(int i=1; i<10; i++){
			nstat = 100000*i;
			chi2 = interpolation(nstat, ndim, first);
			gChi2->SetPoint(ip++, TMath::Log10(float(nstat)), chi2);
			//hp->Fill(float(nstat), chi2);
		}
		gChi2->Draw("apl");
	}
	//hp->Draw("pl");
}


//__________________________________________________________
Double_t interpolation(const int nstat, const int ndim, const int first)
{
// Steer interpolation of a nD (n<=5) uncorrelated Gauss distribution.
// The user is suppose to give the experimental statistics (nstat) the
// dimension of the experimental point (ndim). The entry from which the
// data base is being read is steered by "first".

 	const int bs = 400;
 	const int npoints = 100;
	// switch on chi2 calculation between interpolation and model.
	// Default calculates distance.
	const Bool_t kCHI2 = kFALSE; 
	const Bool_t kINT  = kTRUE; // switch on integral interpolator

	// open data base
	TString fn("5D_Gauss.root");
	if(!gSystem->FindFile(".", fn)) build(5, 1000000);
	TFile::Open("5D_Gauss.root");
	TTree *t = (TTree*)gFile->Get("db");

	// build interpolator
	TString var = "x0"; for(int idim=1; idim<ndim; idim++) var += Form(":x%d", idim);
	TKDPDF pdf(t, var.Data(), "", bs, nstat, first);
	pdf.SetInterpolationMethod(kINT);
	pdf.SetStore();
	
	// define testing grid
	Double_t x[5];
	Double_t dx[5] = {4., 4., 4., 4., 4.};
	Double_t chi2, theor, result, err;
	for(int idim=0; idim<ndim; idim++){
		dx[idim] = (ndim<<2)/float(npoints);
		x[idim]  = -2.+dx[idim]/2.;
	}
	
	// setup the integral interpolator and do memory test
	Float_t start, stop;
	start = Mem();
	Float_t *c, v, ve;
	for(int ip=0; ip<pdf.GetNTNodes(); ip++){
		pdf.GetCOGPoint(ip, c, v, ve);
		for(int idim=0; idim<ndim; idim++) x[idim] = (Double_t)c[idim];
		pdf.Eval(x, result, err);
	}
	stop  = Mem();
	printf("\nInterpolating %d data points in %dD ...\n", nstat, ndim);
	printf("\tbucket size %d\n", bs);
	printf("\tmemory usage in Eval() %6.4fKB\n", stop-start);
	printf("\tstarting interpolation ...\n");
	//return stop-start;

	// evaluate relative error
	for(int idim=0; idim<ndim; idim++) x[idim] = 0.;
	pdf.Eval(x, result, err);
	Double_t threshold = err/result;
	
	// starting interpolation over the testing grid
	chi2 = 0.; Int_t nsample = 0;
	x[4]  = -2.+dx[4]/2.;
	do{
		x[3]  = -2.+dx[3]/2.;
		do{
			x[2]  = -2.+dx[2]/2.;
			do{
				x[1]  = -2.+dx[1]/2.;
				do{
					x[0]  = -2.+dx[0]/2.;
					do{
						pdf.Eval(x, result, err);
						if(err/TMath::Abs(result) < 1.1*threshold){
							theor = f->Eval(x[0], x[1], x[2]);
							Double_t tmp = result - theor; tmp *= tmp;
							chi2 += tmp/(kCHI2 ? err*err : theor);
							nsample++;
						}
					} while((x[0] += dx[0]) < 2.);
				} while((x[1] += dx[1]) < 2.);
			} while((x[2] += dx[2]) < 2.);
		} while((x[3] += dx[3]) < 2.);
	} while((x[4] += dx[4]) < 2.);
	chi2 /= float(nsample);
	printf("\tinterpolation quality (chi2) %f\n", chi2);
	
	return kCHI2 ? chi2 : TMath::Sqrt(chi2);
}


//___________________________________________________________
void build(const int ndim, const int npoints)
{
	printf("Building DB ...\n");
	Float_t data[ndim];
	TFile::Open(Form("%dD_Gauss.root", ndim), "RECREATE");
	TTree *t = new TTree("db", Form("%dD data base for kD statistics", ndim));
	for(int idim=0; idim<ndim; idim++) t->Branch(Form("x%d", idim), &data[idim], Form("x%d/F", idim));

	for (Int_t ip=0; ip<npoints; ip++){
		for (Int_t id=0; id<ndim; id++) data[id]= gRandom->Gaus();
		t->Fill();
	}

	t->Write();
	gFile->Close();
	delete gFile;
}

//______________________________________________________________
Float_t Mem()
{
  // size in KB
  static struct mallinfo debug;
  debug = mallinfo();
	//printf("arena[%d] usmblks[%d] uordblks[%d] fordblks[%d]\n", debug.arena, debug.usmblks, debug.uordblks, debug.fordblks);
  return debug.uordblks/1024.;
}
Commit	Line	Data
8a8f8274	1	#include <malloc.h>
	2
	3	#include "TSystem.h"
	4	#include "TFile.h"
	5	#include "TTree.h"
	6	#include "TProfile.h"
	7	#include "TF1.h"
	8	#include "TF2.h"
	9	#include "TF3.h"
	10	#include "TLegend.h"
	11	#include "TRandom.h"
	12	#include "TString.h"
	13	#include "TGraph.h"
	14	#include "TMarker.h"
	15	#include "TStopwatch.h"
	16	#include "../src/TKDPDF.h"
	17
	18	void pdfTest(const Int_t ndim = 1);
	19	Double_t interpolation(const int nstat, const int ndim, const int first);
	20	void build(const int ndim, const int npoints);
	21	Float_t Mem();
	22
	23	TF1 *f = 0x0;
	24
	25	//__________________________________________________________
	26	void pdfTest(const Int_t ndim)
	27	{
	28	// Test interpolator on a variable dimension (ndim<=5) uncorrelated
	29	// Gauss model. The macro displays the chi2 between interpolation and
	30	// model for various statistics of experimental data.
	31	//
	32	// Check the worker function interpolation() to fine tune the
	33	// algorithm.
	34	//
	35	// Attention:
	36	// The macro works in compiled mode !
	37
	38	// define model
	39	switch(ndim){
	40	case 1:
	41	f=new TF1("f1", "gaus(0);x;f(x)", -5., 5.);
	42	f->SetParameter(0, 1.);
	43	f->SetParameter(1, 0.);
	44	f->SetParameter(2, 1.);
	45	f->SetParameter(0, 1./f->Integral(-5., 5.));
	46	break;
	47	case 2:
	48	f=new TF2("f2", "[0]exp(-0.5((x-[1])/[2])*2)exp(-0.5((y-[3])/[4])*2)", -5., 5., -5., 5.);
	49	f->SetParameter(0, 1.);
	50	f->SetParameter(1, 0.);
	51	f->SetParameter(2, 1.);
	52	f->SetParameter(3, 0.);
	53	f->SetParameter(4, 1.);
	54	f->SetParameter(0, 1./f->Integral(-5., 5., -5., 5.));
	55	break;
	56	case 3:
	57	case 4:
	58	case 5:
	59	f=new TF3("f3", "[0]exp(-0.5((x-[1])/[2])*2)exp(-0.5((y-[3])/[4])2)exp(-0.5((z-[5])/[6])*2)", -5., 5., -5., 5., -5., 5.);
	60	f->SetParameter(0, 1.);
	61	f->SetParameter(1, 0.);
	62	f->SetParameter(2, 1.);
	63	f->SetParameter(3, 0.);
	64	f->SetParameter(4, 1.);
65	f->SetParameter(5, 0.);
66	f->SetParameter(6, 1.);
67	f->SetParameter(0, 1./f->Integral(-5., 5., -5., 5., -5., 5.));
68	if(ndim>3) printf("Warning : chi2 results are unreliable !\n");
69	break;
70	default:
71	printf("%dD not supported in this macro.\n", ndim);
72	return;
73	}
74
75	Double_t chi2;
76	const Int_t nchi2 = 18;
77	const Int_t nfirst = 1;
78	//TProfile *hp = new TProfile("hp", "", 100, 1.E4, 1.E6);
79	//hp->SetMarkerStyle(24);
80	TGraph *gChi2 = new TGraph(nchi2);
81	gChi2->SetMarkerStyle(24);
82	Int_t ip = 0, nstat, first;
83	for(int ifirst=0; ifirst<nfirst; ifirst++){
84	first = 0;//Int_t(gRandom->Uniform(1.E4));
85	for(int i=2; i<10; i++){
86	nstat = 10000*i;
87	chi2 = interpolation(nstat, ndim, first);
88	gChi2->SetPoint(ip++, TMath::Log10(float(nstat)), chi2);
89	//hp->Fill(float(nstat), chi2);
90	}
91	for(int i=1; i<10; i++){
92	nstat = 100000*i;
93	chi2 = interpolation(nstat, ndim, first);
94	gChi2->SetPoint(ip++, TMath::Log10(float(nstat)), chi2);
95	//hp->Fill(float(nstat), chi2);
96	}
97	gChi2->Draw("apl");
98	}
99	//hp->Draw("pl");
100	}
101
102
103	//__________________________________________________________
104	Double_t interpolation(const int nstat, const int ndim, const int first)
105	{
106	// Steer interpolation of a nD (n<=5) uncorrelated Gauss distribution.
107	// The user is suppose to give the experimental statistics (nstat) the
108	// dimension of the experimental point (ndim). The entry from which the
109	// data base is being read is steered by "first".
110
111	const int bs = 400;
112	const int npoints = 100;
113	// switch on chi2 calculation between interpolation and model.
114	// Default calculates distance.
115	const Bool_t kCHI2 = kFALSE;
116	const Bool_t kINT = kTRUE; // switch on integral interpolator
117
118	// open data base
119	TString fn("5D_Gauss.root");
120	if(!gSystem->FindFile(".", fn)) build(5, 1000000);
121	TFile::Open("5D_Gauss.root");
122	TTree t = (TTree)gFile->Get("db");
123
124	// build interpolator
125	TString var = "x0"; for(int idim=1; idim<ndim; idim++) var += Form(":x%d", idim);
126	TKDPDF pdf(t, var.Data(), "", bs, nstat, first);
127	pdf.SetInterpolationMethod(kINT);
128	pdf.SetStore();
129
130	// define testing grid
131	Double_t x[5];
132	Double_t dx[5] = {4., 4., 4., 4., 4.};
133	Double_t chi2, theor, result, err;
134	for(int idim=0; idim<ndim; idim++){
135	dx[idim] = (ndim<<2)/float(npoints);
136	x[idim] = -2.+dx[idim]/2.;
137	}
138
139	// setup the integral interpolator and do memory test
140	Float_t start, stop;
141	start = Mem();
142	Float_t *c, v, ve;
143	for(int ip=0; ip<pdf.GetNTNodes(); ip++){
144	pdf.GetCOGPoint(ip, c, v, ve);
145	for(int idim=0; idim<ndim; idim++) x[idim] = (Double_t)c[idim];
146	pdf.Eval(x, result, err);
147	}
148	stop = Mem();
149	printf("\nInterpolating %d data points in %dD ...\n", nstat, ndim);
150	printf("\tbucket size %d\n", bs);
151	printf("\tmemory usage in Eval() %6.4fKB\n", stop-start);
152	printf("\tstarting interpolation ...\n");
153	//return stop-start;
154
155	// evaluate relative error
156	for(int idim=0; idim<ndim; idim++) x[idim] = 0.;
157	pdf.Eval(x, result, err);
158	Double_t threshold = err/result;
159
160	// starting interpolation over the testing grid
161	chi2 = 0.; Int_t nsample = 0;
162	x[4] = -2.+dx[4]/2.;
163	do{
164	x[3] = -2.+dx[3]/2.;
165	do{
166	x[2] = -2.+dx[2]/2.;
167	do{
168	x[1] = -2.+dx[1]/2.;
169	do{
170	x[0] = -2.+dx[0]/2.;
171	do{
172	pdf.Eval(x, result, err);
173	if(err/TMath::Abs(result) < 1.1*threshold){
174	theor = f->Eval(x[0], x[1], x[2]);
175	Double_t tmp = result - theor; tmp *= tmp;
176	chi2 += tmp/(kCHI2 ? err*err : theor);
177	nsample++;
178	}
179	} while((x[0] += dx[0]) < 2.);
180	} while((x[1] += dx[1]) < 2.);
181	} while((x[2] += dx[2]) < 2.);
182	} while((x[3] += dx[3]) < 2.);
183	} while((x[4] += dx[4]) < 2.);
184	chi2 /= float(nsample);
185	printf("\tinterpolation quality (chi2) %f\n", chi2);
186
187	return kCHI2 ? chi2 : TMath::Sqrt(chi2);
188	}
189
190
191	//___________________________________________________________
192	void build(const int ndim, const int npoints)
193	{
194	printf("Building DB ...\n");
195	Float_t data[ndim];
196	TFile::Open(Form("%dD_Gauss.root", ndim), "RECREATE");
197	TTree *t = new TTree("db", Form("%dD data base for kD statistics", ndim));
198	for(int idim=0; idim<ndim; idim++) t->Branch(Form("x%d", idim), &data[idim], Form("x%d/F", idim));
199
200	for (Int_t ip=0; ip<npoints; ip++){
201	for (Int_t id=0; id<ndim; id++) data[id]= gRandom->Gaus();
202	t->Fill();
203	}
204
205	t->Write();
206	gFile->Close();
207	delete gFile;
208	}
209
210	//______________________________________________________________
211	Float_t Mem()
212	{
213	// size in KB
214	static struct mallinfo debug;
215	debug = mallinfo();
216	//printf("arena[%d] usmblks[%d] uordblks[%d] fordblks[%d]\n", debug.arena, debug.usmblks, debug.uordblks, debug.fordblks);
217	return debug.uordblks/1024.;
218	}
219