#include <stdio.h> 

#include <stdlib.h> 

#include <math.h> 





struct complex 

{ 

double real , img; 

complex() {real = img = 0;}; 

complex(double r, double i) {real =r ; img = i;}; 

void set(double r, double i) {real=r ; img = i;}; 

void conjugate() {img *= -1;} 

complex operator + (complex c) 

{ 

	complex e;

	e.real = real + c.real; 

	e.img  = img  + c.img; 

	return e; 

} 

complex operator - (complex c) 

{ 

	complex e;

	e.real = real - c.real; 

	e.img  = img  - c.img ; 



	return e; 

} 

complex operator * (complex c) 

{ 

	complex e;

	e.real = real*c.real - img *c.img; 

	e.img  = img *c.real + real*c.img; 



	return e; 

} 

complex operator / (complex c) 

{ 

	complex e;

	double denominator = c.real*c.real + c.img*c.img; 



	e.real = (real * c.real + img * c.img) / denominator; 

	e.img = (img * c.real - real *c.img ) / denominator; 

	return e; 

} 

}; 







double probability (complex * c1, complex *c2 ) 

{ 

	complex c3[2], P; 



	c3[0] = c1[0]; 

	c3[1] = c1[1]; 

	c3[0].conjugate(); // c3 =  <c1| 

	c3[1].conjugate(); 



	P = c3[0]*c2[0] + c3[1]*c2[1]; // <c1|c2> 

	P = P*P; // ^2  



	return P.real; 

} 



complex sigma_z[2][2], sigma_x[2][2], sigma_y[2][2],spin_n[2], n[3]; 



void func(const char *str)

{

	complex  sigmaDOTn[2][2], v2[2]; 

	sigmaDOTn[0][0] = sigma_x[0][0]*n[0] + sigma_y[0][0]*n[1] + sigma_z[0][0]*n[2];   

	sigmaDOTn[0][1] = sigma_x[0][1]*n[0] + sigma_y[0][1]*n[1] + sigma_z[0][1]*n[2];   

	sigmaDOTn[1][0] = sigma_x[1][0]*n[0] + sigma_y[1][0]*n[1] + sigma_z[1][0]*n[2];   

	sigmaDOTn[1][1] = sigma_x[1][1]*n[0] + sigma_y[1][1]*n[1] + sigma_z[1][1]*n[2];   



	v2[0] = sigmaDOTn[0][0]*spin_n[0] + sigmaDOTn[0][1]*spin_n[1]; 

	v2[1] = sigmaDOTn[1][0]*spin_n[0] + sigmaDOTn[1][1]*spin_n[1]; 



	spin_n[0]=v2[0];

	spin_n[1]=v2[1];

	printf( "%s : %.2f/%.2f   %.2f/%.2f \n",str, spin_n[0].real, spin_n[0].img, spin_n[1].real, spin_n[1].img); 

}







int main () 

{ 

//Pauli matrices

	sigma_x[0][0].set(0,0); sigma_x[0][1].set(1,0); 

	sigma_x[1][0].set(1,0); sigma_x[1][1].set(0,0); 



	sigma_y[0][0].set(0,0); sigma_y[0][1].set(0, -1); 

	sigma_y[1][0].set(0,1); sigma_y[1][1].set(0,0); 



	sigma_z[0][0].set(1,0); sigma_z[0][1].set(0,0); 

	sigma_z[1][0].set(0,0); sigma_z[1][1].set(-1,0); 









//spin

	spin_n[0].set(1,0); 

	spin_n[1].set(0,0); 



	n[0].set(0, 0); 

	n[1].set(0, 0); 

	n[2].set(1, 0); 

	func("0  ");



	n[0].set(0, 0); 

	n[1].set(0, 0); 

	n[2].set(-1, 0); 

	func("180");



	n[0].set(0, 0); 

	n[1].set(0, 0); 

	n[2].set(1, 0); 

	func("360");



	n[0].set(0, 0); 

	n[1].set(0, 0); 

	n[2].set(-1, 0); 

	func("540");



	n[0].set(0, 0); 

	n[1].set(0, 0); 

	n[2].set(1, 0); 

	func("720");



} 





/*

the output:

0   : 1.00/0.00   0.00/0.00 

180 : -1.00/0.00   0.00/0.00 

360 : -1.00/0.00   -0.00/0.00 

540 : 1.00/0.00   -0.00/0.00 

720 : 1.00/0.00   0.00/0.00 

*/