Euler's method for neuroscience in C [closed] - c

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I need to estimate for my internship the firing rate of neurons that follows an ODE. I code at first in python and it goes pretty well but for better performance, my supervisor told to write the same code in C. However, I never coded in C so I am a very beginner and the file in which i want to have the values for the firing rate is full of zero... Can someone help me ?
Thank you very much
So here is my 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
eps = 0.05
f = 0.215
mu = 1.1
D = 0.001
DeltaT = 0.01
timewindow = 40
num_points = int(timewindow/DeltaT)
T = np.linspace(0, timewindow, num_points)
#signal
s = [sin(2*3.14*f*t) for t in T]
N=30000
compteur=np.zeros(num_points)
v = np.zeros((num_points,N))
samples = np.random.normal(0, 1, (num_points,N))
for i in range(1,num_points):
for j in range(N):
v[i,j] = v[i-1,j] + DeltaT *(-v[i-1,j]+ mu + eps*s[i-1]) + \
sqrt(2*D*DeltaT)*samples[i,j]
if v[i,j]>1:
v[i,j]=0
compteur[i]+=1/DeltaT/N
plt.plot(T,compteur)
plt.show()
and here is my "translation" in C :
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define PI 3.1415926536
float s(float x, float);
double AWGN_generator();
FILE* fopen(const char* nomDuFichier, const char* modeOuverture);
int fclose(FILE* pointeurSurFichier);
int main(int argc, char *argv[])
{
//parameters
double eps = 0.05;
float f = 0.215 ;
double mu = 1.1 ;
double D = 0.001 ;
int time_window = 90;
int num_points = 1000;
long num_neurons = 1000;
double deltaT = time_window/num_points;
int i ;
//time
double Time[num_points] ;
Time[0]= 0.0;
for (i = 1 ; i < num_points ; i++ )
{ Time[i] = Time[i-1] + deltaT;
}
//opening file for saving data
FILE* fichier = NULL;
fichier = fopen("challala.txt", "w");
if (fichier != NULL)
{
double v[num_points][num_neurons] ;
memset(v, 0, num_points*num_neurons*sizeof(long) );
long compteur[num_points];
memset( compteur, 0, num_points*sizeof(long) );
int pos_1 ;
int pos_2 ;
//Euler's method
for (pos_1 = 1 ; pos_1 < num_points ; pos_1 ++)
{
for (pos_2 = 0 ; pos_2<num_neurons ; pos_2 ++)
{
float t = Time[pos_1-1] ;
v[pos_1][pos_2] = v[pos_1-1][pos_2] + deltaT *(-v[pos_1-1]
[pos_2]+ mu + eps*s(t, f))+ sqrt(2*D*deltaT)*AWGN_generator();
if (v[pos_1][pos_2]>1)
{
v[pos_1][pos_2]=0 ;
compteur[pos_1]+=1/deltaT/num_neurons ;
}
}
fprintf(fichier, "%ld",compteur[pos_1]);
}
fclose(fichier);
printf("ca a marche test.txt");
}
else
{
// On affiche un message d'erreur si on veut
printf("Impossible d'ouvrir le fichier test.txt");
}
return 0;
}
float s(float x, float f)
{
return sin(2*M_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

Code repaired as able with old code commented out. See comments for change details.
Need to see challala.txt for a definitive test.
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
// Why use a coarse approximation?
//#define PI 3.1415926536
#define PI 3.1415926535897932384626433832795
// Let us stick to double only.
//float s(float x, float);
double s(double x, double);
// Add void, else declaration does not check the parameters.
//double AWGN_generator();
double AWGN_generator(void);
// These should have already been declared in <stdio.h>
// FILE* fopen(const char* nomDuFichier, const char* modeOuverture);
// int fclose(FILE* pointeurSurFichier);
int main(int argc, char *argv[]) {
//parameters
double eps = 0.05;
// float f = 0.215;
double f = 0.215;
double mu = 1.1;
double D = 0.001;
int time_window = 90;
// Unclear why `int/long` used here. size_t would be idiomatic for array sizing.
int num_points = 1000;
long num_neurons = 1000;
// Avoid integer division when a FP quotinet is desired
// double deltaT = time_window / num_points;
double deltaT = 1.0*time_window / num_points;
int i;
//time
double Time[num_points];
Time[0] = 0.0;
for (i = 1; i < num_points; i++)
{
Time[i] = Time[i - 1] + deltaT;
}
//opening file for saving data
FILE* fichier = NULL;
fichier = fopen("challala.txt", "w");
if (fichier != NULL) {
double v[num_points][num_neurons];
// zero fill use wrong type in sizeof.
// Avoid type in sizeof, better to use sizeof object
// memset(v, 0, num_points * num_neurons * sizeof(long));
memset(v, 0, sizeof v);
// Let us use FP here.
//long compteur[num_points];
double compteur[num_points];
memset(compteur, 0, sizeof compteur);
int pos_1;
int pos_2;
//Euler's method
for (pos_1 = 1; pos_1 < num_points; pos_1++)
{
for (pos_2 = 0; pos_2 < num_neurons; pos_2++) {
// float t = Time[pos_1 - 1];
double t = Time[pos_1 - 1];
v[pos_1][pos_2] = v[pos_1 - 1][pos_2]
+ deltaT * (-v[pos_1 - 1][pos_2] + mu + eps * s(t, f))
+ sqrt(2 * D * deltaT) * AWGN_generator();
if (v[pos_1][pos_2] > 1) {
v[pos_1][pos_2] = 0;
compteur[pos_1] += 1 / deltaT / num_neurons;
}
}
// Change of type
// fprintf(fichier, "%ld", compteur[pos_1]);
fprintf(fichier, " %g", compteur[pos_1]);
}
fclose(fichier);
printf("ca a marche test.txt");
} else {
// Was not the file another name?
// printf("Impossible d'ouvrir le fichier test.txt");
printf("Impossible d'ouvrir le fichier \"%s\"\n", challala.txt);
}
return 0;
}
//float s(float x, float f) {
double s(double x, double f) {
// M_PI is not defined in the standard C library, although common in extensions.
//return sin(2 * M_PI * f * x);
return sin(2 * PI * f * x);
}
double AWGN_generator() {
double temp1;
double temp2;
double result;
int p;
p = 1;
while (p > 0) {
temp2 = (rand() / ((double) RAND_MAX));
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
}
Minor and advanced numeric issue:
Realize that quotient 1.0*time_window / num_points maybe be a little different than mathematical expected due to finite precision of double. This is, at worst, expected to be a very small amount, maybe about 0.5 parts in 253.
Yet the repetitive additions accumulate the error.
double deltaT = 1.0*time_window / num_points;
int i;
double Time[num_points];
Time[0] = 0.0;
for (i = 1; i < num_points; i++) {
Time[i] = Time[i - 1] + deltaT;
}
To avoid that accumulated error, code can re-calculate Time[i] anew on each iteration.
double deltaT = 1.0*time_window / num_points;
double Time[num_points];
for (int i = 0; i < num_points; i++) {
Time[i] = deltaT*i;
}
Of course, such small errors are often ignorable, but mayne not when num_points is large enough. This happens when your good code is applied to ever larger tasks.

Answer 2

regarding the following 3 statements
int time_window = 90;
int num_points = 1000;
double deltaT = time_window/num_points;
Since time_window and num_points are integers, the division is performed as an integer divide.
In an integer divide, all fractions are truncated.
the expression: time_window/num_points is actually:
90 / 1000
the resulting fraction has everything right of the decimal point truncated, so the result is 0
so: Time[0] + 0 results in 0.0.
The same (calculated) value: 0.0 is then propagated thorough the whole array
suggest changing:
int time_window = 90;
int num_points = 1000;
to
double time_window = 90.0;
double num_points = 1000.0;
regarding:
memset(v, 0, num_points*num_neurons*sizeof(long) );
this statement may (or may not) perform the desired functionality. It depends on if the size of double is the same as the size of long
Suggest using:
memset( v, 0, sizeof( v ) );