How to use properly FFTW in C++ with vectors? - c++

Question

I am a very beginner in C++ and for my internship I have to use the fftw library to get the fourier transform of a signal.
Actually, at first, I use python for my programm and then I tried to translate it into C++. However, it doesn't work and I really cannot understand why... I am not really used to pointers and stuff like that so maybe that is the problem. First, I would like to know why programms (the one in python and the in C++) do not give the same results ?
Moreover, I would be very grateful if someone could explain me how to use FFTW with vectors ? I would like to better understand things. Thank you very much :)
The python Code
import numpy as np
import matplotlib.pyplot as plt
from math import cos, sin, sqrt, pi, exp as cos, sin, sqrt, pi, exp
#parameters (suprathresold case)\
eps = 0.05
f = 0.215
mu = 1.1
D = 0.001
DeltaT = 0.001
period = int(1.0 / f / DeltaT)
num_periods_4_transient = 10
num_periods_4_spectrum = 100
#timewindow = 2 * period * DeltaT #quite long to be independant of the transient
l_transient = num_periods_4_transient * period
l_measure = num_periods_4_spectrum * period
#num_points = int(timewindow/DeltaT)
N = 100 # number of realization (number of neurons) should be at the end 10^8
DeltaT_ratio = 100
#signal that modulates the firing rate
#s = [sin(2*3.14*f*t) for t in T]
ts_transient = np.arange(l_transient)*DeltaT
ts_measure = np.arange(l_measure)*DeltaT
s = np.sin(2.0 * np.pi * f * ts_transient)
#Euler's method with FFT
v0 = np.zeros(N)
v = np.zeros((l_transient,N))
samples = np.random.normal(0, 1, (l_transient,N))
DeltaF = 1.0 / (l_measure * DeltaT)
#print "running transient..."
for i in range(1,l_transient):
v[i,:] = v[i-1,:] + DeltaT *(-v[i-1,:]+ mu + eps*s[i-1])+ sqrt(2*D*DeltaT)*samples[i,:]
mask_sp = v[i,:] > 1
v[i, mask_sp ] = 0
v0 = v[-1,:]
v = np.zeros((l_measure,N))
v[0,:] = v0
s = np.sin(2.0 * np.pi * f * ts_measure)
samples = np.random.normal(0, 1, (l_measure,N))
l_compteur = l_measure // DeltaT_ratio + 1
compteur=np.zeros((l_compteur, N))
DeltaT_prime = DeltaT * DeltaT_ratio
#print l_measure,l_measure // DeltaT_ratio
#print "running for measure..."
for i in range(1,l_measure):
v[i,:] = v[i-1,:] + DeltaT *(-v[i-1,:]+ mu + eps*s[i-1])+ sqrt(2*D*DeltaT)*samples[i,:]
mask_sp = v[i,:] > 1
compteur[ int(i / DeltaT_ratio), mask_sp ] = 1.0 / DeltaT_prime
v[i, mask_sp ] = 0
l_freq = int(l_compteur / 2) + 1
spectrum_matrix = np.abs(np.fft.rfft(compteur,axis=0)*DeltaT_prime)**2
powerspectra = np.mean(spectrum_matrix,axis=1)
powerspectra /= (l_measure*DeltaT)
powerspectra[0] = 0.0
plt.plot(np.arange(l_freq)*DeltaF, powerspectra )
plt.show()
The C++ Code
#include <iostream>
#include <cmath>
#include <complex>
#include <fstream>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <fstream>
#include <fftw3.h>
#define PI 3.1415926535897932384626433832795
#include <vector>
using namespace std;
double s(double x, double );
double AWGN_generator(void);
std::string double2str(const double x)
{
stringstream sss;
sss<<x;
return sss.str();
}
int main()
{
// srand (time(NULL));
//parameters
double eps = 0.05;
double f_1 = 0.215 ;
//double f_2 = 0.33;
double mu = 1.1 ;
double D = 0.001 ;
double deltaT = 0.001;
long period = 1.0 / f_1 / deltaT;
int N = 1000; //# number of realization (number of neurons) should be at the end 10^8
long DeltaT_ratio = 100;
double DeltaT_prime = DeltaT_ratio*deltaT;
int num_periods_4_transient = 10;
int num_periods_4_spectrum = 20;
long l_transient = num_periods_4_transient * period;
long l_measure = num_periods_4_spectrum * period;
long l_compteur = l_measure / DeltaT_ratio + 1 ;
long l_freq = int(l_compteur / 2) + 1;
double deltaf = 1.0 / (l_compteur * DeltaT_prime);
vector<double> powerspectrum(l_freq,0);
cout<<l_measure<<l_measure / DeltaT_ratio<<endl;
double a = 1.0;
ofstream m_out ;
string outfile = "/Users/Pierrot/powerspectrum_test.txt";
m_out.open(outfile.c_str());
vector< double > compteur(l_compteur,0);
std::vector< std::complex<double> > out(l_freq,0);
fftw_plan p;
p = fftw_plan_dft_r2c_1d(l_compteur, &compteur[0], reinterpret_cast<fftw_complex*>(&out[0]), FFTW_MEASURE);
//cout<<"test1"<<endl;
// Transient
vector< double > v(l_transient,0.0 );
vector<double> Time(l_transient, 0) ;
for (int i = 0 ; i < l_transient ; i++ )
{ Time[i] = deltaT*i ;
}
int pos_1 ;
for (pos_1 = 1 ; pos_1<l_transient ; pos_1 ++)
{
double t = Time[pos_1-1] ;
v[pos_1] = v[pos_1-1] + deltaT*(-v[pos_1-1]+ mu + eps*s(t, f_1)) + sqrt(2*D*deltaT)*AWGN_generator();
if (v[pos_1]>1)
{
v[pos_1]=0 ;
}
}
vector< double > v_bis(l_measure, v[l_transient-1]);
// v_bis[0]=v[l_transient-1];
for( int k=0; k<N ; k++)
{
//copy last value of transient in the new v
v_bis[0] = v_bis[l_measure-1];
double DeltaT_prime = deltaT * DeltaT_ratio ;
vector<double> Time_bis(l_measure) ;
for (int i = 0 ; i < l_measure ; i++ )
{ Time_bis[i] = deltaT*i ;
}
//cout<<"test2"<<endl;
for (int pos_1_bis = 1 ; pos_1_bis<l_measure ; pos_1_bis ++)
{
double t = Time_bis[pos_1_bis-1] ;
v_bis[pos_1_bis] = v_bis[pos_1_bis-1] + deltaT*(-v_bis[pos_1_bis-1]+ mu + eps*s(deltaT*(pos_1_bis-1), f_1)) + sqrt(2*D*deltaT)*AWGN_generator();
//cout<<v_bis[pos_1_bis]<<endl;
if (v_bis[pos_1_bis]>1)
{
v_bis[pos_1_bis]=0 ;
compteur[pos_1_bis/DeltaT_ratio] = 1.0/DeltaT_prime ;
// cout<<pos_1_bis/DeltaT_ratio<<endl;
}
}
fftw_execute(p);
for (long m(0);m<l_freq;m++)
{
powerspectrum[m] += (real( out[m] * conj(out[m]) ) * DeltaT_prime*DeltaT_prime) / (l_measure*deltaT*N);
}
}
//powerspectrum = powerspectrum *DeltaT_prime*DeltaT_prime/(l_measure*deltaT*N)
fftw_destroy_plan(p);
fftw_cleanup();
for (long m(1);m<l_freq;m++)
{
m_out<<deltaf*m <<"\t"<<powerspectrum[m]<<"\n";
}
m_out.close();
printf("ca a marche test.txt");
return 0;
}
double s(double x, double f)
{
return sin(2*PI*f*x);
}
double AWGN_generator()
{/* Generates additive white Gaussian Noise samples with zero mean and a standard
deviation of 1. */
double temp1;
double temp2;
double result;
int p;
p = 1;
while( p > 0 )
{
temp2 = ( rand() / ( (double)RAND_MAX ) ); /* rand() function generates an
integer between 0 and RAND_MAX,
which is defined in stdlib.h.
*/
if ( temp2 == 0 )
{// temp2 is >= (RAND_MAX / 2)
p = 1;
}// end if
else
{// temp2 is < (RAND_MAX / 2)
p = -1;
}// end else
}// end while()
temp1 = cos( ( 2.0 * (double)PI ) * rand() / ( (double)RAND_MAX ) );
result = sqrt( -2.0 * log( temp2 ) ) * temp1;
return result; // return the generated random sample to the caller
}

Answer 1

You are probably invoking undefined behaviour here
reinterpret_cast<fftw_complex*>(&out[0])
That section should be
std::vector<double> compteur(l_compteur);
std::vector<fftw_complex> out(l_freq);
fftw_plan p = fftw_plan_dft_r2c_1d(compteur.size(), compteur.data(), out.data(), FFTW_MEASURE);
This would be much easier to follow if you broke it up into functions, start by extracting each block of calculation that stands on it's own, but you can't go too far.
Other than that, you should avoid using namespace std;, consider using generators in <random>