Added semi-analytical approximations to the dynamical Lorentz LF class.
This commit is contained in:
Bastian M. Wojek
@ -24,7 +24,6 @@ LDFLAGS +=
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# some definitions: headers (used to generate *Dict* stuff), sources, objects,...
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OBJS =
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OBJS += TIntegrator.o
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OBJS += TLFRelaxation.o TLFRelaxationDict.o
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SHLIB = libLFRelaxation.so
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30
src/external/libLFRelaxation/TIntegrator.cpp
vendored
30
src/external/libLFRelaxation/TIntegrator.cpp
vendored
@ -1,30 +0,0 @@
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/***************************************************************************
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TIntegrator.cpp
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Author: Bastian M. Wojek
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e-mail: bastian.wojek@psi.ch
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2008/12/24
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***************************************************************************/
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#include "TIntegrator.h"
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using namespace std;
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TIntegrator::TIntegrator() : fFunc(0) {
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ROOT::Math::GSLIntegrator *integrator = new ROOT::Math::GSLIntegrator(ROOT::Math::Integration::kADAPTIVE,ROOT::Math::Integration::kGAUSS51);
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fIntegrator = integrator;
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integrator = 0;
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delete integrator;
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}
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TIntegrator::~TIntegrator(){
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delete fIntegrator;
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fIntegrator=0;
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fFunc=0;
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}
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15
src/external/libLFRelaxation/TIntegrator.h
vendored
15
src/external/libLFRelaxation/TIntegrator.h
vendored
@ -15,7 +15,7 @@
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#include "Math/GSLIntegrator.h"
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#include "TMath.h"
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#include<vector>
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#include <vector>
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using namespace std;
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@ -38,6 +38,19 @@ class TIntegrator {
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mutable double (*fFunc)(double, void *);
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};
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inline TIntegrator::TIntegrator() : fFunc(0) {
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ROOT::Math::GSLIntegrator *integrator = new ROOT::Math::GSLIntegrator(ROOT::Math::Integration::kADAPTIVE,ROOT::Math::Integration::kGAUSS31);
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fIntegrator = integrator;
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integrator = 0;
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delete integrator;
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}
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inline TIntegrator::~TIntegrator(){
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delete fIntegrator;
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fIntegrator=0;
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fFunc=0;
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}
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inline double TIntegrator::FuncAtXgsl(double x, void *obj)
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{
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return ((TIntegrator*)obj)->FuncAtX(x);
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154
src/external/libLFRelaxation/TLFRelaxation.cpp
vendored
154
src/external/libLFRelaxation/TLFRelaxation.cpp
vendored
@ -10,17 +10,24 @@
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***************************************************************************/
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#include <cassert>
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#include <sys/time.h>
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#include <iostream>
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#include "TIntegrator.h"
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#include "TLFRelaxation.h"
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using namespace std;
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#define PI 3.14159265358979323846
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#define TWOPI 6.28318530717958647692
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ClassImp(TLFStatGssKT)
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ClassImp(TLFStatLorKT)
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ClassImp(TLFDynGssKT)
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ClassImp(TLFDynLorKT)
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// LF Static Gaussian KT
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TLFStatGssKT::TLFStatGssKT() {
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@ -94,10 +101,10 @@ double TLFStatLorKT::operator()(double t, const vector<double> &par) const {
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// LF Dynamic Gaussian KT
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TLFDynGssKT::TLFDynGssKT() : fCalcNeeded(true), fFirstCall(true), fWisdom("/home/l_wojek/analysis/WordsOfWisdom.dat"), fNSteps(524288), fDt(0.000040), fCounter(0) {
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TLFDynGssKT::TLFDynGssKT() : fCalcNeeded(true), fFirstCall(true), fWisdom("/home/l_wojek/analysis/WordsOfWisdom.dat"), fNSteps(524288), fDt(0.00004), fCounter(0) {
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// Calculate d_omega and C for given NFFT and dt
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fDw = TMath::Pi()/fNSteps/fDt;
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fC = 2.0*TMath::Log(double(fNSteps))/(double(fNSteps-1)*fDt);
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fDw = PI/fNSteps/fDt;
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fC = 2.0*gsl_sf_log(double(fNSteps))/(double(fNSteps-1)*fDt);
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// Load FFTW Wisdom
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int wisdomLoaded(0);
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@ -120,8 +127,8 @@ TLFDynGssKT::TLFDynGssKT() : fCalcNeeded(true), fFirstCall(true), fWisdom("/home
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fFFTtime = (double *)malloc(sizeof(double) * fNSteps);
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fFFTfreq = (fftw_complex *)fftw_malloc(sizeof(fftw_complex) * (fNSteps/2+1));
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fFFTplanFORW = fftw_plan_dft_r2c_1d(fNSteps, fFFTtime, fFFTfreq, FFTW_EXHAUSTIVE);
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fFFTplanBACK = fftw_plan_dft_c2r_1d(fNSteps, fFFTfreq, fFFTtime, FFTW_EXHAUSTIVE);
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fFFTplanFORW = fftw_plan_dft_r2c_1d(fNSteps, fFFTtime, fFFTfreq, FFTW_ESTIMATE);
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fFFTplanBACK = fftw_plan_dft_c2r_1d(fNSteps, fFFTfreq, fFFTtime, FFTW_ESTIMATE);
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}
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TLFDynGssKT::~TLFDynGssKT() {
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@ -167,39 +174,53 @@ double TLFDynGssKT::operator()(double t, const vector<double> &par) const {
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}
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double sigsq(par[1]*par[1]); // sigma^2
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double omegaL(TMath::TwoPi()*par[0]); // Larmor frequency
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double omegaL(TWOPI*par[0]); // Larmor frequency
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double nusq(par[2]*par[2]); // nu^2
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double nut(par[2]*t); // nu*t
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double omegaLsq(omegaL*omegaL); // omega^2
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double omegaLnusqp(omegaLsq+nusq); //omega^2+nu^2
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double omegaLnusqm(omegaLsq-nusq); //omega^2-nu^2
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double wt(omegaL*t); // omega*t
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double enut(exp(-nut)); // exp(-nu*t)
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if(par[1]){
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if(par[2]/par[1] > 5. || omegaL > 20.0*par[1]){
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if(TMath::Abs(par[0])<0.00135538817){
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return TMath::Exp(-2.0*sigsq/nusq*(TMath::Exp(-par[2]*t)-1.0+par[2]*t)); // ZF Abragam Delta^2->2*Delta^2
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}
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double omegaLnusqp(omegaL*omegaL+nusq);
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double omegaLnusqm(omegaL*omegaL-nusq);
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return TMath::Exp(-2.0*sigsq/(omegaLnusqp*omegaLnusqp)*(omegaLnusqp*par[2]*t+omegaLnusqm*(1.0-TMath::Exp(-par[2]*t)*TMath::Cos(omegaL*t))-2.0*par[2]*omegaL*TMath::Exp(-par[2]*t)*TMath::Sin(omegaL*t))); // Keren
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if(fabs(par[0])<0.00135538817){ // Zero Field
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if(!nusq){
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double sigsqtsq(sigsq*t*t);
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return 0.33333333333333333333+0.66666666666666666667*(1.0-sigsqtsq)*exp(-0.5*sigsqtsq); // ZF static Gauss KT
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}
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return exp(-2.0*sigsq/nusq*(enut-1.0+nut)); // ZF Abragam Delta^2->2*Delta^2
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}
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if(fCalcNeeded){
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if((par[2] >= 5.0*par[1]) || (omegaL >= 10.0*par[1])) {
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return exp(-2.0*sigsq/(omegaLnusqp*omegaLnusqp)*(omegaLnusqp*nut+omegaLnusqm*(1.0-enut*gsl_sf_cos(wt))-2.0*par[2]*omegaL*enut*gsl_sf_sin(wt))); // Keren
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}
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double tt(0.);
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if(fCalcNeeded) {
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if(TMath::Abs(par[0])<0.00135538817){
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double t1,t2;
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// get start time
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struct timeval tv_start, tv_stop;
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gettimeofday(&tv_start, 0);
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double tt(0.),sigsqtsq(0.);
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if(fabs(par[0])<0.00135538817) {
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double mcplusnu(-(fC+par[2]));
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for(unsigned int i(0); i<fNSteps; i++) {
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tt=double(i)*fDt;
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fFFTtime[i]=(0.33333333333333333333+0.66666666666666666667*(1.0-sigsq*tt*tt)*TMath::Exp(-0.5*sigsq*tt*tt))*TMath::Exp(-(fC+par[2])*tt)*fDt;
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sigsqtsq=sigsq*tt*tt;
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fFFTtime[i]=(0.33333333333333333333+0.66666666666666666667*(1.0-sigsqtsq)*exp(-0.5*sigsqtsq))*exp(mcplusnu*tt)*fDt;
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}
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} else {
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double mcplusnu(-(fC+par[2]));
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double coeff1(2.0*sigsq/omegaLsq);
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double coeff2(coeff1*sigsq/omegaL);
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double coeff1(2.0*sigsq/(omegaL*omegaL));
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double coeff2(2.0*sigsq*sigsq/(omegaL*omegaL*omegaL));
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fFFTtime[0] = 1.0*fDt;
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fFFTtime[0] = fDt;
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for(unsigned int i(1); i<fNSteps; i++) {
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tt=(double(i)-0.5)*fDt;
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fFFTtime[i]=(TMath::Sin(omegaL*tt) * TMath::Exp(-0.5*sigsq*tt*tt))*fDt;
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fFFTtime[i]=(gsl_sf_sin(omegaL*tt) * exp(-0.5*sigsq*tt*tt))*fDt;
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}
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double totoIntegrale(0.);
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@ -207,22 +228,27 @@ double TLFDynGssKT::operator()(double t, const vector<double> &par) const {
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for(unsigned int i(1); i<fNSteps; i++) {
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tt=double(i)*fDt;
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totoIntegrale+=fFFTtime[i];
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fFFTtime[i]=(1.0-(coeff1*(1.0-TMath::Exp(-0.5*sigsq*tt*tt)*TMath::Cos(omegaL*tt)))+(coeff2*totoIntegrale))*TMath::Exp(-(fC+par[2])*tt)*fDt;
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fFFTtime[i]=(1.0-(coeff1*(1.0-exp(-0.5*sigsq*tt*tt)*gsl_sf_cos(omegaL*tt)))+(coeff2*totoIntegrale))*exp(mcplusnu*tt)*fDt;
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}
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}
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gettimeofday(&tv_stop, 0);
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t1 = (tv_stop.tv_sec - tv_start.tv_sec)*1000.0 + (tv_stop.tv_usec - tv_start.tv_usec)/1000.0;
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// Transform to frequency domain
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fftw_execute(fFFTplanFORW);
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// calculate F(s)
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double denom(1.0);
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double denom(1.0), imagsq(0.0), oneMINrealnu(1.0);
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for (unsigned int i(0); i<fNSteps/2+1; i++) {
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denom=(1.0-(par[2]*fFFTfreq[i][0]))*(1.0-(par[2]*fFFTfreq[i][0])) + (nusq*fFFTfreq[i][1]*fFFTfreq[i][1]);
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fFFTfreq[i][0] = (fFFTfreq[i][0]-(par[2]*fFFTfreq[i][0]*fFFTfreq[i][0])-(par[2]*fFFTfreq[i][1]*fFFTfreq[i][1]))/denom;
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fFFTfreq[i][1] = fFFTfreq[i][1]/denom;
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imagsq=fFFTfreq[i][1]*fFFTfreq[i][1];
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oneMINrealnu=1.0-(par[2]*fFFTfreq[i][0]);
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denom=oneMINrealnu*oneMINrealnu + (nusq*imagsq);
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fFFTfreq[i][0] = (oneMINrealnu*fFFTfreq[i][0]-(par[2]*imagsq))/denom;
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fFFTfreq[i][1] /= denom;
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}
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// Transform back to time domain
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@ -234,14 +260,19 @@ double TLFDynGssKT::operator()(double t, const vector<double> &par) const {
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// }
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fCalcNeeded=false;
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fCounter++;
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gettimeofday(&tv_stop, 0);
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t2 = (tv_stop.tv_sec - tv_start.tv_sec)*1000.0 + (tv_stop.tv_usec - tv_start.tv_usec)/1000.0;
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cout << "# Calculation times: " << t1 << " (ms), " << t2 << " (ms)" << endl;
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}
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// return fFFTtime[int(t/fDt)];
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return fDw*TMath::Exp(fC*t)/TMath::Pi()*fFFTtime[int(t/fDt)];
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return fDw*exp(fC*t)/PI*fFFTtime[int(t/fDt)];
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}
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// LF Dynamic Lorentz KT
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TLFDynLorKT::TLFDynLorKT() : fCalcNeeded(true), fFirstCall(true), fWisdom("/home/l_wojek/analysis/WordsOfWisdom.dat"), fNSteps(524288), fDt(0.000040), fCounter(0) {
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TLFDynLorKT::TLFDynLorKT() : fCalcNeeded(true), fFirstCall(true), fWisdom("/home/l_wojek/analysis/WordsOfWisdom.dat"), fNSteps(524288), fDt(0.000040), fCounter(0), fA(1.0), fL1(0.0), fL2(0.0) {
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// Calculate d_omega and C for given NFFT and dt
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fDw = TMath::Pi()/fNSteps/fDt;
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fC = 2.0*TMath::Log(double(fNSteps))/(double(fNSteps-1)*fDt);
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@ -252,14 +283,14 @@ TLFDynLorKT::TLFDynLorKT() : fCalcNeeded(true), fFirstCall(true), fWisdom("/home
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FILE *wordsOfWisdomR;
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wordsOfWisdomR = fopen(fWisdom.c_str(), "r");
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if (wordsOfWisdomR == NULL) {
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cout << "TLFDynGssKT::TLFDynGssKT: Couldn't open wisdom file ..." << endl;
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cout << "TLFDynLorKT::TLFDynGssKT: Couldn't open wisdom file ..." << endl;
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} else {
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wisdomLoaded = fftw_import_wisdom_from_file(wordsOfWisdomR);
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fclose(wordsOfWisdomR);
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}
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if (!wisdomLoaded) {
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cout << "TLFDynGssKT::TLFDynGssKT: No wisdom is imported..." << endl;
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cout << "TLFDynLorKT::TLFDynGssKT: No wisdom is imported..." << endl;
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}
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// END of WisdomLoading
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@ -291,6 +322,10 @@ TLFDynLorKT::~TLFDynLorKT() {
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cout << "TLFDynLorKT::~TLFDynLorKT(): " << fCounter << " full FFT cyles needed..." << endl;
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}
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const double TLFDynLorKT::fX[16]={1.61849, 1.27059, 0.890315, 6.72608, 0.327258, 0.981975, 1.5964, 2.31023, 2.37689, 5.63945, 0.235734, 1.10617, 1.1664, 0.218402, 0.266562, 0.471331};
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const double TLFDynLorKT::fY[20]={1.54699, 0.990321, 0.324923, 0.928399, 2.11155, 0.615106, 1.49907, 0.679423, 6.17621, 1.38907, 0.979608, 0.0593631, 0.806427, 3.33144, 1.05059, 1.29922, 0.254661, 0.284348, 0.991419, 0.375213};
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double TLFDynLorKT::operator()(double t, const vector<double> &par) const {
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assert(par.size() == 3); // three parameters nuL=gbar*B,sigma,fluct.rate nu
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@ -313,6 +348,50 @@ double TLFDynLorKT::operator()(double t, const vector<double> &par) const {
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}
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}
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double omegaL(TWOPI*par[0]); // Larmor frequency
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if(fabs(par[0])<0.00135538817){ // Zero Field
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if(!par[2]){ // nu=0
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double at(par[1]*t);
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return 0.33333333333333333333+0.66666666666666666667*(1.0-at)*exp(-at); // ZF static Lorentz KT
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}
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}
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// semi-analytical approximations for {nu >= 4a} and {omegaL >= 10a}
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if(par[2]){ // nu!=0
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if(par[2] >= 4.0*par[1]){ // nu >= 4a
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if(fCalcNeeded){
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double wLnu(omegaL/par[2]); // omegaL/nu
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double wLnusq(wLnu*wLnu); // (omegaL/nu)^2
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double anu(par[1]/par[2]); // a/nu
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fA=1.0+wLnu*anu*(-fX[0]/(wLnusq+fX[1])+fX[2]/(wLnusq*wLnu+fX[3])+fX[4]/(wLnusq*wLnusq+fX[5]));
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fL1=par[1]*(fX[6]/(wLnu+fX[7])+fX[8]/(wLnusq+fX[9])+fX[10]/(wLnusq*wLnusq+fX[11]));
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fL2=par[2]*(fX[12]*tanh(fX[13]*wLnu)+fX[14]*wLnu+fX[15]);
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fCalcNeeded=false;
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}
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return fA*exp(-fL1*t)+(1.0-fA)*exp(-fL2*t)*cos(omegaL*t);
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}
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if(omegaL >= 10.0*par[1]){ // omegaL >= 10a
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if(fCalcNeeded){
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double wLnu(omegaL/par[2]); // omegaL/nu
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double wLnusq(wLnu*wLnu); // (omegaL/nu)^2
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double anu(par[1]/par[2]); // a/nu
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fA=1.0-fY[0]*pow(anu,fY[1])/(wLnu+fY[2])+fY[3]*pow(anu,fY[4])/(wLnusq-fY[5])+fY[6]*pow(anu,fY[7])/(wLnusq*wLnu+fY[8]);
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fL1=par[1]*(fY[9]/(pow(wLnu,fY[10])+fY[11])-fY[12]/(pow(wLnu,fY[13])+fY[14]));
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fL2=par[2]*(fY[15]*tanh(fY[16]*wLnu)+fY[17]*pow(wLnu,fY[18])+fY[19]);
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fCalcNeeded=false;
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}
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return fA*exp(-fL1*t)+(1.0-fA)*exp(-fL2*t)*cos(omegaL*t);
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}
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}
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// if no approximation can be used -> Laplace transform
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if(fCalcNeeded){
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double tt(0.);
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@ -324,7 +403,6 @@ double TLFDynLorKT::operator()(double t, const vector<double> &par) const {
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}
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} else {
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double omegaL(TMath::TwoPi()*par[0]); // Larmor frequency
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double coeff1(par[1]/omegaL);
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double coeff2(coeff1*coeff1);
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double coeff3((1.0+coeff2)*par[1]);
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@ -351,13 +429,15 @@ double TLFDynLorKT::operator()(double t, const vector<double> &par) const {
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// calculate F(s)
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double denom(1.0);
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double nusq(par[2]*par[2]); // nu^2
|
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double denom(1.0), imagsq(0.0), oneMINrealnu(1.0);
|
||||
|
||||
for (unsigned int i(0); i<fNSteps/2+1; i++) {
|
||||
denom=(1.0-(par[2]*fFFTfreq[i][0]))*(1.0-(par[2]*fFFTfreq[i][0])) + (nusq*fFFTfreq[i][1]*fFFTfreq[i][1]);
|
||||
fFFTfreq[i][0] = (fFFTfreq[i][0]-(par[2]*fFFTfreq[i][0]*fFFTfreq[i][0])-(par[2]*fFFTfreq[i][1]*fFFTfreq[i][1]))/denom;
|
||||
fFFTfreq[i][1] = fFFTfreq[i][1]/denom;
|
||||
imagsq=fFFTfreq[i][1]*fFFTfreq[i][1];
|
||||
oneMINrealnu=1.0-(par[2]*fFFTfreq[i][0]);
|
||||
denom=oneMINrealnu*oneMINrealnu + (nusq*imagsq);
|
||||
fFFTfreq[i][0] = (oneMINrealnu*fFFTfreq[i][0]-(par[2]*imagsq))/denom;
|
||||
fFFTfreq[i][1] /= denom;
|
||||
}
|
||||
|
||||
// Transform back to time domain
|
||||
|
||||
15
src/external/libLFRelaxation/TLFRelaxation.h
vendored
15
src/external/libLFRelaxation/TLFRelaxation.h
vendored
@ -14,10 +14,17 @@
|
||||
|
||||
#include<vector>
|
||||
#include<cstdio>
|
||||
#include<cmath>
|
||||
|
||||
using namespace std;
|
||||
|
||||
#include "TMath.h"
|
||||
#include <gsl/gsl_math.h>
|
||||
#include <gsl/gsl_sf_exp.h>
|
||||
#include <gsl/gsl_sf_log.h>
|
||||
#include <gsl/gsl_sf_trig.h>
|
||||
#include <gsl/gsl_sf_bessel.h>
|
||||
|
||||
//#include "TMath.h"
|
||||
#include "PUserFcnBase.h"
|
||||
#include "fftw3.h"
|
||||
#include "TIntegrator.h"
|
||||
@ -98,8 +105,14 @@ private:
|
||||
double *fFFTtime;
|
||||
fftw_complex *fFFTfreq;
|
||||
mutable unsigned int fCounter;
|
||||
static const double fX[16];
|
||||
static const double fY[20];
|
||||
mutable double fA;
|
||||
mutable double fL1;
|
||||
mutable double fL2;
|
||||
|
||||
ClassDef(TLFDynLorKT,1)
|
||||
};
|
||||
|
||||
|
||||
#endif //_LFRelaxation_H_
|
||||
|
||||
Reference in New Issue
Block a user