Coefficient Fit

// Fit y = coefficient * x using an explicitly written squared-error gradient.
pure funcra loss(inputs: vector, targets: vector, coefficient: float) -> float
    needs len(inputs) > 0;
    needs len(inputs) == len(targets);
{
    return mse(scale(inputs, coefficient), targets);
}

bind inputs = [1.0, 2.0, 3.0];
bind targets = [2.0, 4.0, 6.0];
var coefficient = 0.0;
repeat 40 as iteration {
    bind residuals = add(scale(inputs, coefficient), scale(targets, -1.0));
    bind gradient = 2.0 * dot(inputs, residuals) / 3.0;
    coefficient -= 0.05 * gradient;
}
print(coefficient > 1.999999999 and coefficient < 2.000000001);
print(loss(coefficient: coefficient, targets: targets, inputs: inputs) < 1e-18);