Merge pull request #884 from tjgurwara99/master

Feat: Class implementation of complex numbers along with most complex number operations.

math/complex_numbers.cpp

@@ -0,0 +1,256 @@
+/**
+ * @author tjgurwara99
+ * @file
+ *
+ * A basic implementation of Complex Number field as a class with operators
+ * overloaded to accommodate (mathematical) field operations.
+ */
+
+#include <cassert>
+#include <cmath>
+#include <complex>
+#include <ctime>
+#include <iostream>
+#include <stdexcept>
+
+/**
+ * Class Complex to represent complex numbers as a field.
+ */
+class Complex {
+    // The real value of the complex number
+    double re;
+    // The imaginary value of the complex number
+    double im;
+
+ public:
+    /**
+     * Complex Constructor which initialises the complex number which takes two
+     * arguments.
+     * @param x If the third parameter is 'true' then this x is the absolute
+     * value of the complex number, if the third parameter is 'false' then this
+     * x is the real value of the complex number (optional).
+     * @param y If the third parameter is 'true' then this y is the argument of
+     * the complex number, if the third parameter is 'false' then this y is the
+     * imaginary value of the complex number (optional).
+     * @param is_polar 'false' by default. If we want to initialise our complex
+     * number using polar form then set this to true, otherwise set it to false
+     * to use initialiser which initialises real and imaginary values using the
+     * first two parameters (optional).
+     */
+    explicit Complex(double x = 0.f, double y = 0.f, bool is_polar = false) {
+        if (!is_polar) {
+            re = x;
+            im = y;
+            return;
+        }
+
+        re = x * std::cos(y);
+        im = x * std::sin(y);
+    }
+
+    /**
+     * Copy Constructor
+     * @param other The other number to equate our number to.
+     */
+    Complex(const Complex &other) : re(other.real()), im(other.imag()) {}
+
+    /**
+     * Member function (getter) to access the class' re value.
+     */
+    double real() const { return this->re; }
+
+    /**
+     * Member function (getter) to access the class' im value.
+     */
+    double imag() const { return this->im; }
+
+    /**
+     * Member function to which gives the absolute value (modulus) of our
+     * complex number
+     * @return \f$ \sqrt{z \dot \bar{z}} \f$ where \f$ z \f$ is our complex
+     * number.
+     */
+    double abs() const {
+        return std::sqrt(this->re * this->re + this->im * this->im);
+    }
+
+    /**
+     * Member function which gives the argument of our complex number.
+     * @return Argument of our Complex number in radians.
+     */
+    double arg() const { return std::atan2(this->im, this->re); }
+
+    /**
+     * Operator overload to be able to add two complex numbers.
+     * @param other The other number that is added to the current number.
+     * @return result current number plus other number
+     */
+    Complex operator+(const Complex &other) {
+        Complex result(this->re + other.re, this->im + other.im);
+        return result;
+    }
+
+    /**
+     * Operator overload to be able to subtract two complex numbers.
+     * @param other The other number being subtracted from the current number.
+     * @return result current number subtract other number
+     */
+    Complex operator-(const Complex &other) {
+        Complex result(this->re - other.re, this->im - other.im);
+        return result;
+    }
+
+    /**
+     * Operator overload to be able to multiple two complex numbers.
+     * @param other The other number to multiply the current number to.
+     * @return result current number times other number.
+     */
+    Complex operator*(const Complex &other) {
+        Complex result(this->re * other.re - this->im * other.im,
+                       this->re * other.im + this->im * other.re);
+        return result;
+    }
+
+    /**
+     * Operator overload of the BITWISE NOT which gives us the conjugate of our
+     * complex number. NOTE: This is overloading the BITWISE operator but its
+     * not a BITWISE operation in this definition.
+     * @return result The conjugate of our complex number.
+     */
+    Complex operator~() const {
+        Complex result(this->re, -(this->im));
+        return result;
+    }
+
+    /**
+     * Operator overload to be able to divide two complex numbers. This function
+     * would throw an exception if the other number is zero.
+     * @param other The other number we divide our number by.
+     * @return result Current number divided by other number.
+     */
+    Complex operator/(const Complex &other) {
+        Complex result = *this * ~other;
+        double denominator =
+            other.real() * other.real() + other.imag() * other.imag();
+        if (denominator != 0) {
+            result = Complex(result.real() / denominator,
+                             result.imag() / denominator);
+            return result;
+        } else {
+            throw std::invalid_argument("Undefined Value");
+        }
+    }
+
+    /**
+     * Operator overload to be able to copy RHS instance of Complex to LHS
+     * instance of Complex
+     */
+    const Complex &operator=(const Complex &other) {
+        this->re = other.real();
+        this->im = other.imag();
+        return *this;
+    }
+};
+
+/**
+ * Logical Equal overload for our Complex class.
+ * @param a Left hand side of our expression
+ * @param b Right hand side of our expression
+ * @return 'True' If real and imaginary parts of a and b are same
+ * @return 'False' Otherwise.
+ */
+bool operator==(const Complex &a, const Complex &b) {
+    return a.real() == b.real() && a.imag() == b.imag();
+}
+
+/**
+ * Overloaded insersion operator to accommodate the printing of our complex
+ * number in their standard form.
+ * @param os The console stream
+ * @param num The complex number.
+ */
+std::ostream &operator<<(std::ostream &os, const Complex &num) {
+    os << "(" << num.real();
+    if (num.imag() < 0) {
+        os << " - " << -num.imag();
+    } else {
+        os << " + " << num.imag();
+    }
+    os << "i)";
+    return os;
+}
+
+/**
+ * Function to get random numbers to generate our complex numbers for test
+ */
+double get_rand() { return (std::rand() % 100 - 50) / 100.f; }
+
+/**
+ * Tests Function
+ */
+void tests() {
+    std::srand(std::time(nullptr));
+    double x1 = get_rand(), y1 = get_rand(), x2 = get_rand(), y2 = get_rand();
+    Complex num1(x1, y1), num2(x2, y2);
+    std::complex<double> cnum1(x1, y1), cnum2(x2, y2);
+    Complex result;
+    std::complex<double> expected;
+    // Test for addition
+    result = num1 + num2;
+    expected = cnum1 + cnum2;
+    assert(((void)"1 + 1i + 1 + 1i is equal to 2 + 2i but the addition doesn't "
+                  "add up \n",
+            (result.real() == expected.real() &&
+             result.imag() == expected.imag())));
+    std::cout << "First test passes." << std::endl;
+    // Test for subtraction
+    result = num1 - num2;
+    expected = cnum1 - cnum2;
+    assert(((void)"1 + 1i - 1 - 1i is equal to 0 but the program says "
+                  "otherwise. \n",
+            (result.real() == expected.real() &&
+             result.imag() == expected.imag())));
+    std::cout << "Second test passes." << std::endl;
+    // Test for multiplication
+    result = num1 * num2;
+    expected = cnum1 * cnum2;
+    assert(((void)"(1 + 1i) * (1 + 1i) is equal to 2i but the program says "
+                  "otherwise. \n",
+            (result.real() == expected.real() &&
+             result.imag() == expected.imag())));
+    std::cout << "Third test passes." << std::endl;
+    // Test for division
+    result = num1 / num2;
+    expected = cnum1 / cnum2;
+    assert(((void)"(1 + 1i) / (1 + 1i) is equal to 1 but the program says "
+                  "otherwise.\n",
+            (result.real() == expected.real() &&
+             result.imag() == expected.imag())));
+    std::cout << "Fourth test passes." << std::endl;
+    // Test for conjugates
+    result = ~num1;
+    expected = std::conj(cnum1);
+    assert(((void)"(1 + 1i) has a conjugate which is equal to (1 - 1i) but the "
+                  "program says otherwise.\n",
+            (result.real() == expected.real() &&
+             result.imag() == expected.imag())));
+    std::cout << "Fifth test passes.\n";
+    // Test for Argument of our complex number
+    assert(((void)"(1 + 1i) has argument PI / 4 but the program differs from "
+                  "the std::complex result.\n",
+            (num1.arg() == std::arg(cnum1))));
+    std::cout << "Sixth test passes.\n";
+    // Test for absolute value of our complex number
+    assert(((void)"(1 + 1i) has absolute value sqrt(2) but the program differs "
+                  "from the std::complex result. \n",
+            (num1.abs() == std::abs(cnum1))));
+    std::cout << "Seventh test passes.\n";
+}
+
+/**
+ * Main function
+ */
+int main() {
+    tests();
+    return 0;
+}