C linear regression

regression.c

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

#define N 10

typedef struct {
	// Linear Function with form f(x)=a*x+b
	float a;
	float b;
} LinearFunction;

float a_derivative(const LinearFunction *f, const float xi, const float yi) {
	// Partial Derivative: df/da
	return (-2) * xi * (yi - (f->a * xi + f->b));
}

float b_derivative(const LinearFunction *f, const float xi, const float yi) {
	// Partial Derivative: df/db
	return (-2) * (yi - (f->a * xi + f->b));
}

void gradient_descent(LinearFunction *f, const float *x, const float *y, const float alpha) {
	// Gradient descent to minimise: (1/N)*sum((a*x+b - xi)^2)
	float aa = 0;
	float bb = 0;

	for (int i = 0; i < N; i++) {
		// Update the a & b values of the function
		aa += a_derivative(f, x[i], y[i]);
		bb += b_derivative(f, x[i], y[i]);
	}

	float progcoeff = (alpha/N); // (1.0/N) * alpha
	f->a -= progcoeff*aa;
	f->b -= progcoeff*bb;
}


void train_function(LinearFunction *f, const float *x, const float *y, const float epochs, const float alpha,	const int debug) {
	// Fit the function looping gradient descent for epochs
	// The more you add epochs the better the descent will be	

	for (int e = 0; e < epochs; e++) {
		gradient_descent(f, x, y, alpha);

		// Debug messages
		if (e % 100 == 0 && debug) {
			printf("Epoch: %i\t", e);
			printf("w: %f, b: %f\n", f->a, f->b);
		}
	}
}

float linear_predict(LinearFunction* f, const float x) {
	return (f->a * x) + f->b;
}

int main(int argc, char *argv[]) {
	// The dataset
	const float spending[N] = {1, 4, 15, 5, 8, 2, 13, 9, 6, 19};
	const float sales[N] = {1, 2, 10, 5, 9, 16, 4, 13, 8, 7};
	
	// Traine the LinearFunction to find (a*) * x + (b*)
	LinearFunction f = {0, 0};
	train_function(&f, spending, sales, 5000, .01, 1);	
	
	float predicted;
	if (argc == 2)
		predicted = linear_predict(&f, atoi(argv[1]));
	else
		predicted = linear_predict(&f, 1);
	printf("Predicted: %f", predicted);

	return 0;
}