newly added. First attempt for a numeric solution for the Gauss KT LF
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191
src/tests/dynGaussKT_LF/dynGaussKT_LF.cpp
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191
src/tests/dynGaussKT_LF/dynGaussKT_LF.cpp
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#include <sys/time.h>
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#include <unistd.h>
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#include <iostream>
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#include <iomanip>
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#include <vector>
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#include <cmath>
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using namespace std;
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typedef vector<double> PDoubleVector;
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#define PI 3.14159265359
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// NR p.797
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void voltra(const double h, PDoubleVector &t, PDoubleVector ¶m, PDoubleVector &f,
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double g(const int, const PDoubleVector &, const PDoubleVector &, const PDoubleVector &), PDoubleVector &gi)
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{
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int i,j;
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double sum;
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int n = f.size();
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double a;
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t[0] = 0.0;
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f[0]=g(0,t,param,gi);
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for (i=1; i<n; i++) {
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sum = g(i,t,param,gi);
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sum += 0.5*h*param[2]*g(i,t,param,gi)*f[0];
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for (j=1; j<i; j++) {
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sum += h*param[2]*g(i-j,t,param,gi)*f[j];
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}
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a = 1.0-0.5*h*param[2]*g(0,t,param,gi);
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f[i]=sum/a;
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}
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}
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double g(const int i, const PDoubleVector &tvec, const PDoubleVector ¶m, const PDoubleVector &gi)
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{
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// param: 0=w0, 1=Delta, 2=nu
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double result;
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double t = tvec[i];
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double Dt2 = pow(param[1]*t, 2.0)/2.0;
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if (param[0] == 0.0) {
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result = 0.333333333333333333333333 + 0.66666666666666666666 * (1.0-2.0*Dt2) * exp(-Dt2);
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} else {
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result = 1.0 - 2.0*param[1]*param[1]/(param[0]*param[0])*(1.0-exp(-Dt2)*cos(param[0]*t)) +
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2.0*pow(param[1],4.0)/pow(param[0],3.0)*gi[i];
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}
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result *= exp(-param[2]*t);
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return result;
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}
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void calc_gi(const double h, PDoubleVector &t, PDoubleVector ¶m, PDoubleVector &f)
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{
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// if w0=0 nothing to be done
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if (param[0] == 0.0)
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return;
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double dtHalf = h/2.0;
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PDoubleVector hh(t.size());
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hh[0] = 0.0;
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f[0] = 0.0;
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for (unsigned int i=1; i<t.size(); i++) {
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hh[i] = exp(-0.5*pow(param[1]*t[i],2.0))*sin(param[0]*t[i]);
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f[i] = f[i-1] + dtHalf*(hh[i]+hh[i-1]);
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}
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}
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int main(int argc, char *argv[])
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{
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bool useKeren = false;
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if (argc != 5) {
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cout << endl << "usage: dynGaussKT_LF w0 Delta nu [N]";
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cout << endl << " w0: external field in Mc/s";
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cout << endl << " Delta: static field width in Mc/s";
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cout << endl << " nu: hopping rate in Mc/s";
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cout << endl << " N: number of sampling points";
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cout << endl << " if N == -1 -> calc N internally";
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cout << endl << " if N is not given, N=1000";
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cout << endl << endl;
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return 0;
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}
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PDoubleVector param(4);
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const double Tmax = 15.0;
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// feed parameter vector
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param[0] = atof(argv[1]); // w0
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param[1] = atof(argv[2]); // Delta
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param[2] = atof(argv[3]); // nu
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if (argc == 5) {
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param[3] = atof(argv[4]); // N
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if (param[3] == -1.0) { // estimate N by itself
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// w0 criteria, i.e. w0 T = 2 pi, ts = T/16, N = Tmax/ts, if N < 300, N == 300
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double val = 8.0/PI*Tmax*param[0];
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if (val < 250)
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param[3] = 250;
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else
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param[3] = val;
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// nu/Delta criteria
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if (param[1] != 0.0) { // Delta != 0
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val = param[2]/param[1]; // nu/Delta
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if (val > 5.0) {
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useKeren = true;
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param[3] = 1000;
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}
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}
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}
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} else {
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param[3] = 1000;
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}
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const unsigned int N=static_cast<unsigned int>(param[3]);
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const double H = Tmax/N;
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PDoubleVector t(N);
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PDoubleVector f(N);
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PDoubleVector gi(N);
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PDoubleVector abragam(N);
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PDoubleVector keren(N);
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// get start time
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struct timeval tv_start, tv_stop;
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double t1, t2;
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gettimeofday(&tv_start, 0);
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// feed time vector
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for (unsigned int i=0; i<N; i++) {
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t[i] = H*i;
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}
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calc_gi(H, t, param, gi);
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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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gettimeofday(&tv_start, 0);
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voltra(H, t, param, f, g, gi);
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// get stop time
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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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bool abragam_present = false;
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if (param[1] != 0) {
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if (param[2]/param[1] >= 1.0) {
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for (unsigned int i=0; i<t.size(); i++)
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abragam[i] = exp(-2.0*pow(param[1]/param[2],2.0)*(exp(-param[2]*t[i])-1.0+param[2]*t[i]));
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abragam_present = true;
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}
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}
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// calculate keren LF
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double w02, nu2, Delta2, Gamma_t;
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for (unsigned int i=0; i<t.size(); i++) {
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w02 = pow(param[0], 2.0);
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Delta2 = pow(param[1], 2.0);
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nu2 = pow(param[2], 2.0);
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Gamma_t = 2.0*Delta2/pow(w02+nu2,2.0)*((w02+nu2)*param[2]*t[i]+(w02-nu2)*(1.0-exp(-param[2]*t[i])*cos(param[0]*t[i]))-2.0*param[2]*param[0]*exp(-param[2]*t[i])*sin(param[0]*t[i]));
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keren[i] = exp(-Gamma_t);
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}
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if (useKeren)
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cout << "# use Keren = true" << endl;
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else
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cout << "# use Keren = false" << endl;
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cout << "# N = " << param[3] << endl;
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cout << "# calculation time: t1 = " << t1 << " (ms), t2 = " << t2 << " (ms)" << endl;
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if (abragam_present)
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cout << setw(12) << "# time" << setw(13) << "Pz_dyn_LF" << setw(13) << "g" << setw(13) << "gi" << setw(13) << "agragam" << setw(13) << "keren" << endl;
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else
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cout << setw(12) << "# time" << setw(13) << "Pz_dyn_LF" << setw(13) << "g" << setw(13) << "gi" << setw(13) << "keren" << endl;
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cout << fixed << setprecision(6);
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for (unsigned int nn=0; nn<N; nn++) {
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if (abragam_present)
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cout << setw(12) << t[nn] << setw(13) << f[nn] << setw(13) << g(nn,t,param,gi) << setw(13) << gi[nn] << setw(13) << abragam[nn] << setw(13) << keren[nn];
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else
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cout << setw(12) << t[nn] << setw(13) << f[nn] << setw(13) << g(nn,t,param,gi) << setw(13) << gi[nn] << setw(13) << keren[nn];
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cout << endl;
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}
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return 0;
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}
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17
src/tests/dynGaussKT_LF/dynGaussKT_LF.pro
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src/tests/dynGaussKT_LF/dynGaussKT_LF.pro
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#------------------------------------------------------
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# dynGaussKT_LF.pro
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# qmake file for dynGaussKT_LF
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#
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# Andreas Suter, 2009/01/13
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#
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# $Id$
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#
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#------------------------------------------------------
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MAKEFILE = Makefile
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CONFIG += warn_on debug
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SOURCES = dynGaussKT_LF.cpp
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TARGET=dynGaussKT_LF
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24
src/tests/dynGaussKT_LF/nr/lubksb.cpp
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src/tests/dynGaussKT_LF/nr/lubksb.cpp
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#include "nr.h"
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void NR::lubksb(Mat_I_DP &a, Vec_I_INT &indx, Vec_IO_DP &b)
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{
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int i,ii=0,ip,j;
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DP sum;
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int n=a.nrows();
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for (i=0;i<n;i++) {
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ip=indx[i];
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sum=b[ip];
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b[ip]=b[i];
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if (ii != 0)
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for (j=ii-1;j<i;j++) sum -= a[i][j]*b[j];
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else if (sum != 0.0)
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ii=i+1;
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b[i]=sum;
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}
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for (i=n-1;i>=0;i--) {
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sum=b[i];
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for (j=i+1;j<n;j++) sum -= a[i][j]*b[j];
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b[i]=sum/a[i][i];
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}
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}
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53
src/tests/dynGaussKT_LF/nr/ludcmp.cpp
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src/tests/dynGaussKT_LF/nr/ludcmp.cpp
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#include <cmath>
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#include "nr.h"
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using namespace std;
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void NR::ludcmp(Mat_IO_DP &a, Vec_O_INT &indx, DP &d)
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{
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const DP TINY=1.0e-20;
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int i,imax,j,k;
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DP big,dum,sum,temp;
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int n=a.nrows();
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Vec_DP vv(n);
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d=1.0;
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for (i=0;i<n;i++) {
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big=0.0;
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for (j=0;j<n;j++)
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if ((temp=fabs(a[i][j])) > big) big=temp;
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if (big == 0.0) nrerror("Singular matrix in routine ludcmp");
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vv[i]=1.0/big;
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}
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for (j=0;j<n;j++) {
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for (i=0;i<j;i++) {
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sum=a[i][j];
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for (k=0;k<i;k++) sum -= a[i][k]*a[k][j];
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a[i][j]=sum;
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}
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big=0.0;
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for (i=j;i<n;i++) {
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sum=a[i][j];
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for (k=0;k<j;k++) sum -= a[i][k]*a[k][j];
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a[i][j]=sum;
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if ((dum=vv[i]*fabs(sum)) >= big) {
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big=dum;
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imax=i;
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}
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}
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if (j != imax) {
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for (k=0;k<n;k++) {
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dum=a[imax][k];
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a[imax][k]=a[j][k];
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a[j][k]=dum;
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}
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d = -d;
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vv[imax]=vv[j];
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}
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indx[j]=imax;
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if (a[j][j] == 0.0) a[j][j]=TINY;
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if (j != n-1) {
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dum=1.0/(a[j][j]);
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for (i=j+1;i<n;i++) a[i][j] *= dum;
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}
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}
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}
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36
src/tests/dynGaussKT_LF/nr/voltra.cpp
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36
src/tests/dynGaussKT_LF/nr/voltra.cpp
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#include "nr.h"
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void NR::voltra(const DP t0, const DP h, Vec_O_DP &t, Mat_O_DP &f,
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DP g(const int, const DP),
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DP ak(const int, const int, const DP, const DP))
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{
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int i,j,k,l;
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DP d,sum;
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int m=f.nrows();
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int n=f.ncols();
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Vec_INT indx(m);
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Vec_DP b(m);
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Mat_DP a(m,m);
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t[0]=t0;
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for (k=0;k<m;k++) f[k][0]=g(k,t[0]);
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for (i=1;i<n;i++) {
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t[i]=t[i-1]+h;
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for (k=0;k<m;k++) {
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sum=g(k,t[i]);
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for (l=0;l<m;l++) {
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sum += 0.5*h*ak(k,l,t[i],t[0])*f[l][0];
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for (j=1;j<i;j++)
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sum += h*ak(k,l,t[i],t[j])*f[l][j];
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if (k == l)
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a[k][l]=1.0-0.5*h*ak(k,l,t[i],t[i]);
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else
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a[k][l] = -0.5*h*ak(k,l,t[i],t[i]);
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}
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b[k]=sum;
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}
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ludcmp(a,indx,d);
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lubksb(a,indx,b);
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for (k=0;k<m;k++) f[k][i]=b[k];
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}
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}
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44
src/tests/dynGaussKT_LF/nr/xvoltra.cpp
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44
src/tests/dynGaussKT_LF/nr/xvoltra.cpp
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#include <iostream>
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#include <iomanip>
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#include <cmath>
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#include "nr.h"
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using namespace std;
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// Driver for routine voltra
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DP g(const int k, const DP t)
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{
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return (k == 0 ? cosh(t)+t*sin(t) :
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2.0*sin(t)+t*(SQR(sin(t))+exp(t)));
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}
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DP ak(const int k, const int l, const DP t, const DP s)
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{
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return ((k == 0) ?
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(l == 0 ? -exp(t-s) : -cos(t-s)) :
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(l == 0 ? -exp(t+s) : -t*cos(s)));
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}
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int main(void)
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{
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const int N=10,M=2;
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const DP H=0.05;
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int nn;
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DP t0=0.0;
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Vec_DP t(N);
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Mat_DP f(M,N);
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NR::voltra(t0,H,t,f,g,ak);
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// exact soln is f[1]=exp(-t), f[2]=2sin(t)
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cout << " abscissa voltra real";
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cout << " voltra real" << endl;
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cout << " answer1 answer1";
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cout << " answer2 answer2" << endl << endl;
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cout << fixed << setprecision(6);
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for (nn=0;nn<N;nn++) {
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cout << setw(12) << t[nn] << setw(13) << f[0][nn];
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cout << setw(13) << exp(-t[nn]) << setw(13) << f[1][nn];
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cout << setw(13) << 2.0*sin(t[nn]) << endl;
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}
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return 0;
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}
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