I have a 2×2 matrix, called “one_elect”, which is a function of a variable “r” but I am a little confused as to how to apply the Trapezoidal Method for integrating onto this matrix. I am a decent beginner in C; essentially, I don’t know how to loop this matrix for that particular variable. Please see the code below for a beginner trapezoidal integration code and the code I am working on.

My Code containing the function I want to use for the integration Method:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define Z 1
#define BASISFUN 2
#define UPPER 100 // This is the Upper bound for the integral
#define LOWER 0   // This is the lower bound of the integral
#define SUBINT 50 // This is the number of subintervals for Integration

void makingmatrix(double a[][BASISFUN], double d[][BASISFUN], double alpha_coeff[BASISFUN], double d_coeff[BASISFUN]){
    
    for (int i = 0; i < BASISFUN; i++){
        for (int j = 0; j < BASISFUN; j++){
            a[i][j] = alpha_coeff[j];
            d[i][j] = d_coeff[j];
        }
    }

    printf("nAlpha 2x2 Coefficient Matrix is:n");
    for (int i = 0; i < BASISFUN; i++){
        for (int j = 0; j < BASISFUN; j++){
            printf("%.4ft", a[i][j]);
        }
        printf("n");
    }

   printf("nD 2x2 Coefficient Matrix is:n");
    for (int i = 0; i < BASISFUN; i++){
        for (int j = 0; j < BASISFUN; j++){
            printf("%.4ft", d[i][j]);
        }
        printf("n");    
    }
    printf("n------------------------------------------------------------------n");
};

void one_ele(double a[][BASISFUN], double d[][BASISFUN], double r, double one_electron[][BASISFUN]){

    double i_step = (UPPER-LOWER)/SUBINT;

    for (int i = 0; i < BASISFUN; i++){
            for (int j = 0; j < BASISFUN; j++){
                
                if (i != j){
                    one_electron[i][j] = (0.5) * (-2 * a[i][j] * r * exp(-a[i][j] * pow(r, 2))) * (-2 * a[j][i] * r * exp(-a[j][i] * pow(r, 2))) + (Z / r);
                } 
                
                else{
                    one_electron[i][i] = (0.5) * (-2 * a[i][i] * r * exp(-a[i][i] * pow(r, 2))) * (-2 * a[i][i] * r * exp(-a[i][i] * pow(r, 2))) + (Z / r);
                }
            }
    }
 printf("nOne Electron Hamiltonian Elements aren");
    for (int i = 0; i < BASISFUN; i++){
        for (int j = 0; j < BASISFUN; j++){
            printf("%.4ft", one_electron[i][j]);
        }
        printf("n");
    }

    printf("n------------------------------------------------------------------n");
}

int main(){
double A1 = 0.532149, A2 = 4.097728, D1 = 0.82559, D2 = 0.28317;
double r;

double alpha_coeff[BASISFUN] = {A1, A2};
double d_coeff[BASISFUN] = {D1, D2};
double a[BASISFUN][BASISFUN], d[BASISFUN][BASISFUN];

makingmatrix(a, d, alpha_coeff, d_coeff);
one_ele(a, d, r, one_electron);

return 0;
}

Sample code for Trapezoidal Rule:

#include <stdio.h>
#include <math.h>

#define BASISFUN 2 
#define Z 1.0
#define UPPER 100 // This is the Upper bound for the integral
#define LOWER 0   // This is the lower bound of the integral
#define SUBINT 50 // This is the number of subintervals for Integration 

double f(double r) {
    // Define your function here
    return (0.5) * (-2 * a[i][j] * r * exp(-a[i][j] * pow(r, 2))) * (-2 * a[i][j] * r * exp(-a[i][j] * pow(r, 2))) + (Z / r);
}

int main() {
    double stepSize = (UPPER - LOWER) / SUBINT;
    double integral = f(a) + f(b);

    for (int i = 1; i < SUBINT; i++) {
        double r = a + i * stepSize;
        integral += 2 * f(r);
    }

    integral *= stepSize / 2.0;

    printf("Required value of integration is: %.3fn", integral);
    return 0;
}