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#include "cnumber.hpp"
#include "fractions.hpp"
#include "matrix.hpp"
#include "vector.hpp"
#include <iostream>
void cnumber_main() {
cnumber a(3, 2);
cnumber b(4, -3);
cout << "a = " << a << endl;
cout << "a* = " << a.conjugate() << endl;
cout << "a*a* = " << a * a.conjugate() << endl;
cout << "b = " << b << endl;
cout << "b* = " << b.conjugate() << endl;
cout << "b*b* = " << b * b.conjugate() << endl;
cout << "a + b = " << a + b << endl;
cout << "(a + b)* = " << (a + b).conjugate() << endl;
cout << "a - b = " << a - b << endl;
cout << "(a - b)* = " << (a - b).conjugate() << endl;
cout << "a * b = " << a * b << endl;
cout << "(a * b)* = " << (a * b).conjugate() << endl;
cout << "a / b = " << a / b << endl;
cout << "(a / b)* = " << (a / b).conjugate() << endl;
}
void fraction_main() {
int a = 7;
int b = 3;
int c = 1;
int d = 11;
double e = 0.75;
fraction q(a, b);
fraction q2(c, d);
fraction q3(e);
cout.precision(10);
cout << a << "/" << b << '=' << q << endl;
cout << a << "/" << b << '=' << q.to_double() << endl;
cout << c << "/" << d << '=' << q2 << endl;
cout << c << "/" << d << '=' << q2.to_double() << endl;
cout << q << "+" << q2 << '=' << q + q2 << endl;
cout << q << "+" << q2 << '=' << (q + q2).to_double() << endl;
cout << q << "-" << q2 << '=' << q - q2 << endl;
cout << q << "-" << q2 << '=' << (q - q2).to_double() << endl;
cout << q << "*" << q2 << '=' << q * q2 << endl;
cout << q << "*" << q2 << '=' << (q * q2).to_double() << endl;
cout << q << "/" << q2 << '=' << q / q2 << endl;
cout << q << "/" << q2 << '=' << (q / q2).to_double() << endl;
cout << e << '=' << q3 << endl;
}
void matrix_main() {
vector a = vector(2);
a[0] = 1;
a[1] = 1;
vector b = vector(2);
b[0] = 1;
b[1] = cnumber(1, 0);
vector c = vector(2);
c[0] = 2;
c[1] = cnumber(1, 1);
vector d = vector(2);
d[0] = cnumber(1, -1);
d[1] = 5;
matrix m = matrix(2, 2);
m[0] = a;
m[1] = b;
matrix n = matrix(2, 2);
n[0] = c;
n[1] = d;
cout << "The matrix m" << endl;
cout << m << endl;
cout << "The determinant of matrix m:" << endl;
cout << m.determinant() << endl;
cout << "The matrix n:" << endl;
cout << n << endl;
cout << "The matrix n roted by one pi radian:" << endl;
cout << n.rotate_by_one_pi() << endl;
cout << "The determinant of matrix n:" << endl;
cout << n.determinant() << endl;
cout << "The matrix n's transpose:" << endl;
cout << n.transpose() << endl;
cout << "The matrix n's diagonal:" << endl;
cout << n.get_diagonal() << endl;
cout << "The matrix n's off diagonal:" << endl;
cout << n.get_off_diagonal() << endl;
cout << "The vector d:" << endl;
cout << d << endl;
cout << "The matrix n * the vector d" << endl;
cout << n * d << endl;
cout << "The vector d * the matrix n" << endl;
cout << d * n << endl;
cout << "The matrix m * n" << endl;
cout << m * n << endl;
cout << "The matrix m + n" << endl;
cout << m + n << endl;
cout << "Is 2 an eigenvalue of m?" << endl;
if (m.is_eigenvalue(2)) {
cout << "Yes!" << endl;
} else {
cout << "No!" << endl;
}
if (n.is_hermitian()) {
cout << "The matrix n is hermitian, here is the hermitian conjugate:"
<< endl;
cout << n.hermitian_conjugate() << endl;
}
}
void vector_main() {
vector v = vector(3);
cnumber one(1, 0);
cnumber two(2, 0);
cnumber three(3, 0);
cnumber four(4, 0);
cnumber five(5, 0);
cnumber i(0, 1);
v[0] = one;
v[1] = two;
v[2] = i;
vector w = vector(3);
w[0] = three;
w[1] = four;
w[2] = five;
cout << "v:" << endl;
cout << v << endl;
cout << "w:" << endl;
cout << w << endl;
cout << "v + w:" << endl;
cout << v + w << endl;
cout << "v - w:" << endl;
cout << v - w << endl;
cout << "v * w:" << endl;
cout << v * w << endl;
cout << "w * i:" << endl;
cout << w * i << endl;
for (long long j = 0; j < v.get_dimention(); j++) {
cout << "Element " << j << " of v:" << endl;
cout << v[j] << endl;
}
cout << "A temp vector of dimension 3" << endl << vector(3) << endl;
vector k = vector(3);
k = w;
cout << "Assignment of w to k" << endl << k << endl;
cout << "Manually set elements of k to elements of v" << endl;
for (long long j = 0; j < v.get_dimention(); j++)
k[j] = v[j];
cout << k << endl;
}
int main() {
fraction_main();
cnumber_main();
vector_main();
matrix_main();
return 0;
}