#include <math.h>       /* sqrt, exp */

// class declaration
class Gaussian
{
	private:
		float mu, sigma2;

	public:
		
		// constructor functions
		Gaussian ();
		Gaussian (float, float);

		// change value of average and standard deviation 
		void setMu(float);
		void setSigma2(float);

		// output value of average and standard deviation
		float getMu();
		float getSigma2();

		// functions to evaluate 
		float evaluate (float);
		Gaussian mul (Gaussian);
		Gaussian add (Gaussian);
};


Gaussian::Gaussian() {
	mu = 0;
	sigma2 = 1;	
}

Gaussian::Gaussian (float average, float sigma) {
	mu = average;
	sigma2 = sigma;
}

void Gaussian::setMu (float average) {
	mu = average;
}

void Gaussian::setSigma2 (float sigma) {
	sigma2 = sigma;
}


float Gaussian::getMu () {
	return mu;
}

float Gaussian::getSigma2() {
	return sigma2;
}

float Gaussian::evaluate(float x) {
	float coefficient;
	float exponential;

	coefficient = 1.0 / sqrt (2.0 * M_PI * sigma2);
	exponential = exp ( pow (-0.5 * (x - mu), 2) / sigma2 );
	return coefficient * exponential;
}

Gaussian Gaussian::mul(Gaussian other) {
	float denominator;
	float numerator;
	float new_mu;
	float new_var;

	denominator = sigma2 + other.getSigma2();
	numerator = mu * other.getSigma2() + other.getMu() * sigma2;
	new_mu = numerator / denominator;

	new_var = 1.0 / ( (1.0 / sigma2) + (1.0 / other.sigma2) );

	return Gaussian(new_mu, new_var);
}

Gaussian Gaussian::add(Gaussian other) {

	float new_mu;
	float new_sigma2;

	new_mu = mu + other.getMu();
	new_sigma2 = sigma2 + other.getSigma2();

	return Gaussian(new_mu, new_sigma2);
}

int main ()
{
 /*
TODO: Instantiate a Gaussian object called gaussianone.The object
should have mean = 40.0 and variance (aka sigma2) = 225.0
*/

Gaussian gaussianone(40.0, 225.0);

/*
TODO: Instantiate another Gaussian object called gaussiantwo. 
The object should have mean = 35.6 and variance = 12.25
*/
Gaussian gaussiantwo(35.6, 12.25);

/*
TODO:
Output to the terminal the following:
- the probability density function value for gaussianone when x = 10.5
- the probability density function value for gaussianone when x = 55.4
- the probability density function value for gaussiantwo when x = 35.6
- the probability density function value for gaussiantwo when x = 29.4
*/

std::cout << gaussianone.evaluate(10.5) << "\n";
std::cout << gaussianone.evaluate(55.4) << "\n";
std::cout << gaussiantwo.evaluate(35.6) << "\n";
std::cout << gaussiantwo.evaluate(29.4) << "\n";

/*
TODO:
- Change the mean value of gaussianone to mean = 45
- Change the variance of gaussiantwo to variance = 15.4
- Output the mean of gaussianone to the terminal
- Output the variance of gaussiantwo to the terminal
*/

gaussianone.setMu(45.0);
gaussiantwo.setSigma2(15.4);
std::cout << gaussianone.getMu() << "\n";
std::cout << gaussiantwo.getSigma2() << "\n";

/*
TODO:
- Multiply gaussian one and gaussian two. Store the resulting gaussian
in a variable called gaussianthree
- Output the mean and variance of gaussianthree to the terminal
- Add gaussian one and gaussian two. Store the resulting gaussian in a 
variable called gaussianfour
- Output the mean and variance of gaussianfour to the terminal
*/
    
Gaussian gaussianthree = gaussianone.mul(gaussiantwo);
std::cout << gaussianthree.getMu() << "\n";
std::cout << gaussianthree.getSigma2() << "\n";

Gaussian gaussianfour = gaussianone.add(gaussiantwo);
std::cout << gaussianfour.getMu() << "\n";
std::cout << gaussianfour.getSigma2() << "\n";

    
}