C array of functions - c

Question

I have a problem with a series of functions. I have an array of 'return values' (i compute them through matrices) from a single function sys which depends on a integer variable, lets say, j, and I want to return them according to this j , i mean, if i want the equation number j, for example, i just write sys(j)
For this, i used a for loop but i don't know if it's well defined, because when i run my code, i don't get the right values.
Is there a better way to have an array of functions and call them in a easy way? That would make easier to work with a function in a Runge Kutta method to solve a diff equation.
I let this part of the code here: (c is just the j integer i used to explain before)
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int N=3;
double s=10.;
//float r=28.;
double b=8.0/3.0;
/ * Define functions * /
double sys(int c,double r,double y[])
{
int l,m,n,p=0;
double tmp;
double t[3][3]={0};
double j[3][3]={{-s,s,0},{r-y[2],-1,-y[0]},{y[1],y[0],-b}}; //Jacobiano
double id[3][3] = { {y[3],y[6],y[9]} , {y[4],y[7],y[10]} , {y[5],y[8],y[11]} };
double flat[N*(N+1)];
// Multiplication of matrices J * Y
for(l=0;l<N;l++)
{
for(m=0;m<N;m++)
{
for(n=0;n<N;n++)
{
t[l][m] += j[l][n] * id[n][m];
}
}
}
// Transpose the matrix (J * Y) -> () t
for(l=0;l<N;l++)
{
for(m=l+1;m<N;m++)
{
tmp = t[l][m];
t[l][m] = t[m][l];
t[m][l] = tmp;
}
}
// We flatten the array to be left in one array
for(l=0;l<N;l++)
{
for(m=0;m<N;m++)
{
flat[p+N] = t[l][m];
}
}
flat[0] = s*(y[1]-y[0]);
flat[1] = y[0]*(r-y[2])-y[1];
flat[2] = y[0]*y[1]-b*y[2];
for(l=0;l<(N*(N+1));l++)
{
if(c==l)
{
return flat[c];
}
}
}
EDIT ----------------------------------------------------------------
Ok, this is the part of the code where i use the function
int main(){
output = fopen("lyapcoef.dat","w");
int j,k;
int N2 = N*N;
int NN = N*(N+1);
double r;
double rmax = 29;
double t = 0;
double dt = 0.05;
double tf = 50;
double z[NN]; // Temporary matrix for RK4
double k1[N2],k2[N2],k3[N2],k4[N2];
double y[NN]; // Matrix for all variables
/* Initial conditions */
double u[N];
double phi[N][N];
double phiu[N];
double norm;
double lyap;
//Here we integrate the system using Runge-Kutta of fourth order
for(r=28;r<rmax;r++){
y[0]=19;
y[1]=20;
y[2]=50;
for(j=N;j<NN;j++) y[j]=0;
for(j=N;j<NN;j=j+3) y[j]=1; // Identity matrix for y from 3 to 11
while(t<tf){
/* RK4 step 1 */
for(j=0;j<NN;j++){
k1[j] = sys(j,r,y)*dt;
z[j] = y[j] + k1[j]*0.5;
}
/* RK4 step 2 */
for(j=0;j<NN;j++){
k2[j] = sys(j,r,z)*dt;
z[j] = y[j] + k2[j]*0.5;
}
/* RK4 step 3 */
for(j=0;j<NN;j++){
k3[j] = sys(j,r,z)*dt;
z[j] = y[j] + k3[j];
}
/* RK4 step 4 */
for(j=0;j<NN;j++){
k4[j] = sys(j,r,z)*dt;
}
/* Updating y matrix with new values */
for(j=0;j<NN;j++){
y[j] += (k1[j]/6.0 + k2[j]/3.0 + k3[j]/3.0 + k4[j]/6.0);
}
printf("%lf %lf %lf \n",y[0],y[1],y[2]);
t += dt;
}

Answer 1

Since you're actually computing all these values at the same time, what you really want is for the function to return them all together. The easiest way to do this is to pass in a pointer to an array, into which the function will write the values. Or perhaps two arrays; it looks to me as if the output of your function is (conceptually) a 3x3 matrix together with a length-3 vector.
So the declaration of sys would look something like this:
void sys(double v[3], double JYt[3][3], double r, const double y[12]);
where v would end up containing the first three elements of your flat and JYt would contain the rest. (More informative names are probably possible.)
Incidentally, the for loop at the end of your code is exactly equivalent to just saying return flat[c]; except that if c happens not to be >=0 and <N*(N+1) then control will just fall off the end of your function, which in practice means that it will return some random number that almost certainly isn't what you want.

Answer 2

Your function sys() does an O(N3) calculation to multiply two matrices, then does a couple of O(N2) operations, and finally selects a single number to return. Then it is called the next time and goes through most of the same processing. It feels a tad wasteful unless (even if?) the matrices are really small.
The final loop in the function is a little odd, too:
for(l=0;l<(N*(N+1));l++)
{
if(c==l)
{
return flat[c];
}
}
Isn't that more simply written as:
return flat[c];
Or, perhaps:
if (c < N * (N+1))
return flat[c];
else
...do something on disastrous error other than fall off the end of the
...function without returning a value as the code currently does...

Answer 3

I don't see where you are selecting an algorithm by the value of j. If that's what you're trying to describe, in C you can have an array of pointers to functions; you could use a numerical index to choose a function from the array, but you can also pass a pointer-to-a-function to another function that will call it.
That said: Judging from your code, you should keep it simple. If you want to use a number to control which code gets executed, just use an if or switch statement.
switch (c) {
case 0:
/* Algorithm 0 */
break;
case 1:
/* Algorithm 1 */
etc.