complex.d

/*
Copyright (c) 2013-2025 Timur Gafarov

Boost Software License - Version 1.0 - August 17th, 2003

Permission is hereby granted, free of charge, to any person or organization
obtaining a copy of the software and accompanying documentation covered by
this license (the "Software") to use, reproduce, display, distribute,
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Software, and to permit third-parties to whom the Software is furnished to
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the above license grant, this restriction and the following disclaimer,
must be included in all copies of the Software, in whole or in part, and
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
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*/

/**
 * Complex numbers
 *
 * Copyright: Timur Gafarov 2013-2025.
 * License: $(LINK2 boost.org/LICENSE_1_0.txt, Boost License 1.0).
 * Authors: Timur Gafarov
 */
module dlib.math.complex;

import std.math;
import std.range;
import std.format;

/// Complex number representation
struct Complex(T)
{
    T re;
    T im;

    this(T r, T i)
    {
        re = r;
        im = i;
    }

    this(T r)
    {
        re = r;
        im = 0.0;
    }

    Complex!(T) opUnary(string op) () if (op == "-")
    {
        return Complex!(T)(re, -im);
    }

    Complex!(T) opBinary(string op)(Complex!(T) c) if (op == "+")
    {
        return Complex!(T)(re + c.re, im + c.im);
    }

    Complex!(T) opBinary(string op)(Complex!(T) c) if (op == "-")
    {
        return Complex!(T)(re - c.re, im - c.im);
    }

    Complex!(T) opBinary(string op)(Complex!(T) c) if (op == "*")
    {
        return Complex!(T)(
            re * c.re - im * c.im,
            re * c.im + im * c.re);
    }

    Complex!(T) opBinary(string op)(Complex!(T) c) if (op == "/")
    {
        T denominator = c.re * c.re + c.im * c.im;
        return Complex!(T)(
            (re * c.re + im * c.im) / denominator,
            (im * c.re - re * c.im) / denominator);
    }

    Complex!(T) opOpAssign(string op)(Complex!(T) c) if (op == "+")
    {
        re += c.re;
        im += c.im;
        return this;
    }

    Complex!(T) opOpAssign(string op)(Complex!(T) c) if (op == "-")
    {
        re -= c.re;
        im -= c.im;
        return this;
    }

    Complex!(T) opOpAssign(string op)(Complex!(T) c) if (op == "*")
    {
        T temp = re;
        re = re * c.re - im * c.im;
        im = im * c.re + temp * c.im;
        return this;
    }

    Complex!(T) opOpAssign(string op)(Complex!(T) c) if (op == "/")
    {
        T denominator = c.re * c.re + c.im * c.im;
        T temp = re;
        re = (re * c.re + im * c.im) / denominator;
        im = (im * c.re - temp * c.im) / denominator;
        return this;
    }

    Complex!(T) opBinary(string op)(T scalar) if (op == "+")
    {
        return Complex!(T)(re + scalar, im + scalar);
    }

    Complex!(T) opBinary(string op)(T scalar) if (op == "-")
    {
        return Complex!(T)(re + scalar, im + scalar);
    }

    Complex!(T) opBinary(string op)(T scalar) if (op == "*")
    {
        return Complex!(T)(re * scalar, im * scalar);
    }

    Complex!(T) opBinary(string op)(T scalar) if (op == "/")
    {
        return Complex!(T)(re / scalar, im / scalar);
    }

    Complex!(T) reciprocal()
    {
        T scale = re * re + im * im;
        return Complex!(T)(re / scale, -im / scale);
    }

    T magnitude()
    {
        return hypot(re, im);
    }

    T norm()
    {
        return (re * re + im * im);
    }

    string toString()
    {
        auto writer = appender!string();
        formattedWrite(writer, "%s + %si", re, im);
        return writer.data;
    }
}

///
unittest
{
    import dlib.math.utils;
    
    auto c1 = Complex!float(2, 1);
    auto c2 = Complex!float(1, 2);
    auto c3 = Complex!float(1);
    
    assert((c1 + c2) == Complex!float(3, 3));
    assert((c1 - c1) == Complex!float(0, 0));
    assert((c1 * c2) == Complex!float(0, 5));
    assert((c2 / c1) == Complex!float(0.8f, 0.6f));
    assert(c1.reciprocal == Complex!float(0.4f, -0.2f));
    assert(c3.magnitude == 1.0f);
    assert(c3.norm == 1.0f);
    assert(c1.toString == "2 + 1i");
}

/// Complex abs
T abs(T)(Complex!T x)
{
    return hypot(x.re, x.im);
}

///
unittest
{
    auto c1 = Complex!float(1);
    assert(abs(c1) == 1.0f);
}

/// Complex atan2
T atan2(T)(Complex!T x)
{
    return std.math.atan2(x.im, x.re);
}

///
unittest
{
    auto c1 = Complex!float(1);
    assert(atan2(c1) == 0.0f);
}

/// Complex pow
Complex!T pow(T)(Complex!T x, Complex!T n)
{
    T r = abs(x);
    T t = x.magnitude;
    T c = n.re;
    T d = n.im;

    Complex!T res;
    res.re = std.math.pow(r, c) * std.math.exp(-d*t) * cos(c*t + d*log(r));
    res.im = std.math.pow(r, c) * std.math.exp(-d*t) * sin(c*t + d*log(r));

    return res;
}

/// Complex exp
Complex!T exp(T)(Complex!T s)
{
    return Complex!T(
        std.math.exp(s.re) * cos(s.im),
        std.math.exp(s.re) * sin(s.im));
}

/*
 * Predefined complex type aliases
 */
alias Complexf = Complex!(float);
alias Complexd = Complex!(double);