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Renjian-buchaiPanquesito7realstealthninjatjgurwara99
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feat: add Quadratic equations complex numbers (#2451)
* Added quadratic_equations_complex_numbers.cpp * Added a demonstration * Added test cases * Added test cases * Revert "Added test cases" This reverts commit a1433a9. * Added test cases and made docs /// instead of // * test: Added test cases for quadraticEquation docs: Changed comment style * test: more test cases docs: added documentation * docs: Updated description * chore: removed redundant returns * chore: fixed formatting to pass Code Formatter checks * chore: apply suggestions from code review Co-authored-by: realstealthninja <[email protected]> * test: Added exception test * Update math/quadratic_equations_complex_numbers.cpp Co-authored-by: Taj <[email protected]> * Update math/quadratic_equations_complex_numbers.cpp Co-authored-by: Taj <[email protected]> * Update math/quadratic_equations_complex_numbers.cpp Co-authored-by: Taj <[email protected]> --------- Co-authored-by: David Leal <[email protected]> Co-authored-by: realstealthninja <[email protected]> Co-authored-by: Taj <[email protected]>
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‎math/quadratic_equations_complex_numbers.cpp

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/**
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* @file
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* @brief Calculate quadratic equation with complex roots, i.e. b^2 - 4ac < 0.
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*
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* @author [Renjian-buchai](https://github.com/Renjian-buchai)
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*
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* @description Calculates any quadratic equation in form ax^2 + bx + c.
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*
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* Quadratic equation:
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* x = (-b +/- sqrt(b^2 - 4ac)) / 2a
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*
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* @example
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* int main() {
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* using std::array;
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* using std::complex;
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* using std::cout;
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*
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* array<complex<long double, 2> solutions = quadraticEquation(1, 2, 1);
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* cout << solutions[0] << " " << solutions[1] << "\n";
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*
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* solutions = quadraticEquation(1, 1, 1); // Reusing solutions.
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* cout << solutions[0] << " " << solutions[1] << "\n";
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* return 0;
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* }
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*
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* Output:
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* (-1, 0) (-1, 0)
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* (-0.5,0.866025) (-0.5,0.866025)
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*/
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#include <array> /// std::array
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#include <cassert> /// assert
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#include <cmath> /// std::sqrt, std::trunc, std::pow
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#include <complex> /// std::complex
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#include <exception> /// std::invalid_argument
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#include <iomanip> /// std::setprecision
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#include <iostream> /// std::cout
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/**
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* @namespace
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* @brief Mathematical algorithms
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*/
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namespace math {
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/**
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* @brief Quadratic equation calculator.
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* @param a quadratic coefficient.
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* @param b linear coefficient.
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* @param c constant
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* @return Array containing the roots of quadratic equation, incl. complex
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* root.
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*/
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std::array<std::complex<long double>, 2> quadraticEquation(long double a,
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long double b,
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long double c) {
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if (a == 0) {
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throw std::invalid_argument("quadratic coefficient cannot be 0");
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}
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long double discriminant = b * b - 4 * a * c;
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std::array<std::complex<long double>, 2> solutions{0, 0};
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if (discriminant == 0) {
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solutions[0] = -b * 0.5 / a;
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solutions[1] = -b * 0.5 / a;
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return solutions;
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}
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// Complex root (discriminant < 0)
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// Note that the left term (-b / 2a) is always real. The imaginary part
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// appears when b^2 - 4ac < 0, so sqrt(b^2 - 4ac) has no real roots. So,
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// the imaginary component is i * (+/-)sqrt(abs(b^2 - 4ac)) / 2a.
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if (discriminant > 0) {
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// Since discriminant > 0, there are only real roots. Therefore,
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// imaginary component = 0.
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solutions[0] = std::complex<long double>{
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(-b - std::sqrt(discriminant)) * 0.5 / a, 0};
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solutions[1] = std::complex<long double>{
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(-b + std::sqrt(discriminant)) * 0.5 / a, 0};
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return solutions;
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}
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// Since b^2 - 4ac is < 0, for faster computation, -discriminant is
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// enough to make it positive.
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solutions[0] = std::complex<long double>{
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-b * 0.5 / a, -std::sqrt(-discriminant) * 0.5 / a};
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solutions[1] = std::complex<long double>{
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-b * 0.5 / a, std::sqrt(-discriminant) * 0.5 / a};
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return solutions;
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}
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} // namespace math
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/**
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* @brief Asserts an array of complex numbers.
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* @param input Input array of complex numbers. .
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* @param expected Expected array of complex numbers.
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* @param precision Precision to be asserted. Default=10
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*/
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void assertArray(std::array<std::complex<long double>, 2> input,
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std::array<std::complex<long double>, 2> expected,
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size_t precision = 10) {
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long double exponent = std::pow(10, precision);
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input[0].real(std::round(input[0].real() * exponent));
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input[1].real(std::round(input[1].real() * exponent));
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input[0].imag(std::round(input[0].imag() * exponent));
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input[1].imag(std::round(input[1].imag() * exponent));
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expected[0].real(std::round(expected[0].real() * exponent));
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expected[1].real(std::round(expected[1].real() * exponent));
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expected[0].imag(std::round(expected[0].imag() * exponent));
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expected[1].imag(std::round(expected[1].imag() * exponent));
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assert(input == expected);
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}
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/**
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* @brief Self-test implementations to test quadraticEquation function.
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* @note There are 4 different types of solutions: Real and equal, real,
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* complex, complex and equal.
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*/
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static void test() {
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// Values are equal and real.
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std::cout << "Input: \n"
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"a=1 \n"
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"b=-2 \n"
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"c=1 \n"
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"Expected output: \n"
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"(1, 0), (1, 0)\n\n";
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std::array<std::complex<long double>, 2> equalCase{
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std::complex<long double>{1, 0}, std::complex<long double>{1, 0}};
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assert(math::quadraticEquation(1, -2, 1) == equalCase);
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// Values are equal and complex.
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std::cout << "Input: \n"
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"a=1 \n"
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"b=4 \n"
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"c=5 \n"
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"Expected output: \n"
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"(-2, -1), (-2, 1)\n\n";
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std::array<std::complex<long double>, 2> complexCase{
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std::complex<long double>{-2, -1}, std::complex<long double>{-2, 1}};
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assert(math::quadraticEquation(1, 4, 5) == complexCase);
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// Values are real.
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std::cout << "Input: \n"
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"a=1 \n"
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"b=5 \n"
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"c=1 \n"
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"Expected output: \n"
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"(-4.7912878475, 0), (-0.2087121525, 0)\n\n";
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std::array<std::complex<long double>, 2> floatCase{
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std::complex<long double>{-4.7912878475, 0},
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std::complex<long double>{-0.2087121525, 0}};
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assertArray(math::quadraticEquation(1, 5, 1), floatCase);
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// Values are complex.
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std::cout << "Input: \n"
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"a=1 \n"
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"b=1 \n"
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"c=1 \n"
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"Expected output: \n"
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"(-0.5, -0.8660254038), (-0.5, 0.8660254038)\n\n";
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std::array<std::complex<long double>, 2> ifloatCase{
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std::complex<long double>{-0.5, -0.8660254038},
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std::complex<long double>{-0.5, 0.8660254038}};
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assertArray(math::quadraticEquation(1, 1, 1), ifloatCase);
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std::cout << "Exception test: \n"
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"Input: \n"
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"a=0 \n"
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"b=0 \n"
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"c=0\n"
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"Expected output: Exception thrown \n";
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try {
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math::quadraticEquation(0, 0, 0);
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} catch (std::invalid_argument& e) {
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std::cout << "Exception thrown successfully \n";
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}
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}
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/**
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* @brief Main function
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* @returns 0 on exit
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*/
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int main() {
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test(); // Run self-test implementation.
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return 0;
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}

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