using System;
using System.Collections.Generic;
using System.Text;

namespace FftSharp
{
    public struct Complex
    {
        private double _real;
        public double Real { get => _real; set { _real = value; _magnitude = null; _magnitudeSquared = null; } }

        private double _imaginary;
        public double Imaginary { get => _imaginary; set { _imaginary = value; _magnitude = null; _magnitudeSquared = null; } }

        private double? _magnitudeSquared;
        public double MagnitudeSquared
        {
            get
            {
                if (null == _magnitudeSquared)
                    _magnitudeSquared = CalculateMagnitudeSquared(Real, Imaginary);
                return (double)_magnitudeSquared;
            }
        }

        private double? _magnitude;
        public double Magnitude
        {
            get
            {
                if (null == _magnitude)
                    _magnitude = CalculateMagnitude(Real, Imaginary);
                return (double)_magnitude;
            }
        }

        public static Complex Conjugate(Complex a)
        {
            return new Complex(a.Real, -a.Imaginary);
        }

        public Complex(double real, double imaginary)
        {
            _real = real;
            _imaginary = imaginary;
            _magnitude = CalculateMagnitude(real, imaginary);
            _magnitudeSquared = CalculateMagnitudeSquared(real, imaginary);
        }

        public override string ToString()
        {
            if (Imaginary < 0)
                return $"{Real}-{-Imaginary}j";
            else
                return $"{Real}+{Imaginary}j";
        }

        public static Complex operator +(Complex a, Complex b)
        {
            return new Complex(a.Real + b.Real, a.Imaginary + b.Imaginary);
        }

        public static Complex operator -(Complex a, Complex b)
        {
            return new Complex(a.Real - b.Real, a.Imaginary - b.Imaginary);
        }

        public static Complex operator *(Complex a, Complex b)
        {
            return new Complex(
                real: (a.Real * b.Real) - (a.Imaginary * b.Imaginary),
                imaginary: (a.Real * b.Imaginary) + (a.Imaginary * b.Real));
        }

        public static Complex operator *(Complex a, double b)
        {
            return new Complex(a.Real * b, a.Imaginary * b);
        }

        public static Complex[] FromReal(double[] real)
        {
            Complex[] complex = new Complex[real.Length];
            for (int i = 0; i < real.Length; i++)
                complex[i].Real = real[i];
            return complex;
        }

        private static double CalculateMagnitudeSquared(double real, double imaginary)
        {
            return real * real + imaginary * imaginary;
        }

        private static double CalculateMagnitude(double real, double imaginary)
        {
            return Math.Sqrt(CalculateMagnitudeSquared(real, imaginary));
        }

        public static double[] GetMagnitudes(Complex[] input)
        {
            double[] output = new double[input.Length];
            for (int i = 0; i < input.Length; i++)
                output[i] = input[i].Magnitude;
            return output;
        }
    }
}