ziko/src/math/complex/index.js

A versatile JavaScript library offering a rich set of Hyperscript Based UI components, advanced mathematical utilities, interactivity ,animations, client side routing and more ...

// import {sum,prod,deg2rad} from "../utils/index.js";
// Should avoid CD
class Complex{
    constructor(a = 0, b = 0) {
        if(a instanceof Complex){
            this.a=a.a;
            this.b=a.b;
        }
        else if(typeof(a)==="object"){
            if(("a" in a && "b" in a)){
                this.a = a.a;
                this.b = a.b;
            }
            else if(("a" in a && "z" in a)){
                this.a = a.a;
                this.b = Math.sqrt((a.z**2)-(a.a**2));
            }
            else if(("a" in a && "phi" in a)){
                this.a = a.a;
                this.b = a.a * Math.tan(a.phi);
            }
            else if(("b" in a && "z" in a)){
                this.b = a.b;
                this.a = Math.sqrt((a.z**2)-(a.b**2));
            }
            else if(("b" in a && "phi" in a)){
                this.b = b;
                this.a = a.b / Math.tan(a.phi);
            }
            else if(("z" in a && "phi" in a)){
                this.a = + a.z * Math.cos(a.phi).toFixed(15);
                this.b = + a.z * Math.sin(a.phi).toFixed(15);
            }
        }
        else if(typeof(a)==="number" && typeof(b)==="number"){
            this.a = + a.toFixed(32);
            this.b = + b.toFixed(32);
        }
    }
    get __mapfun__(){
        return true
    }
    isComplex(){
        return true
    }
    toString(){
        let str = "";
        if (this.a !== 0)
          this.b >= 0
            ? (str = `${this.a}+${this.b}*i`)
            : (str = `${this.a}-${Math.abs(this.b)}*i`);
        else
          this.b >= 0
            ? (str = `${this.b}*i`)
            : (str = `-${Math.abs(this.b)}*i`);
        return str;
    }
      
    clone() {
        return new Complex(this.a, this.b);
    }
    get z(){
        return Math.hypot(this.a,this.b);    
    }
    get phi(){
        return Math.atan2(this.b , this.a);        
    }
    static Zero() {
        return new Complex(0, 0);
    }
    get conj() {
        return new Complex(this.a, -this.b);
    }
    get inv() {
        return new Complex(
            this.a / Math.hypot(this.a, this.b),
            -this.b / Math.hypot(this.a, this.b)
        );
    }
    add(...c) {
        for (let i = 0; i < c.length; i++) {
            if (typeof c[i] === "number") c[i] = new Complex(c[i], 0);
            this.a += c[i].a;
            this.b += c[i].b;
        }
        return this;
    }
    sub(...c) {
        for (let i = 0; i < c.length; i++) {
            if (typeof c[i] === "number") c[i] = new Complex(c[i], 0);
            this.a -= c[i].a;
            this.b -= c[i].b;
        }
        return this;
    }
    mul(...c){
        let {z, phi} = this;
        for (let i = 0; i < c.length; i++) {
            if (typeof c[i] === "number") c[i] = new Complex(c[i], 0);
            z *= c[i].z;
            phi += c[i].z;
        }
        this.a = z*Math.cos(phi)
        this.b = z*Math.sin(phi)  
        return this;
    }
    div(...c){
        let {z, phi} = this;
        for (let i = 0; i < c.length; i++) {
            if (typeof c[i] === "number") c[i] = new Complex(c[i], 0);
            z /= c[i].z;
            phi -= c[i].z;
        }
        this.a = z*Math.cos(phi)
        this.b = z*Math.sin(phi)  
        return this;
    }
    modulo(...c) {
        for (let i = 0; i < c.length; i++) {
            if (typeof c[i] === "number") c[i] = new Complex(c[i], 0);
            this.a %= c[i].a;
            this.b %= c[i].b;
        }
        return this;
    }
    static fromExpo(z, phi) {
        return new Complex(
            +(z * cos(phi)).toFixed(13), 
            +(z * sin(phi)).toFixed(13)
            );
    }
    get expo() {
        return [this.z, this.phi];
    }
    static add(c,...z) {
        return c.clone().add(...z);
    }
    static sub(c,...z) {
        return c.clone().sub(...z);
    }
    static mul(c,...z) {
        return c.clone().mul(...z);
    }
    static div(c,...z) {
        return c.clone().div(...z);
    }

    nthr(n=2){
        return complex({z: this.z ** (1/n), phi: this.phi / n});
    }
    get sqrt(){
        return this.nrth(2);
    }
    get cbrt(){
        return this.nrth(3);
    }
    get log(){
        return complex(this.z, this.phi);
    }
    get cos(){
        return complex(
            Math.cos(this.a) * Math.cosh(this.b),
            Math.sin(this.a) * Math.sinh(this.b)
        )
    }
    get sin(){
        return complex(
            Math.sin(this.a) * Math.cosh(this.b),
            Math.cos(this.a) * Math.sinh(this.b)
        )
    }
    get tan(){
        const D=cos(this.a*2)+cosh(this.b*2);
        return complex(
            Math.sin(2 * this.a) / D,
            Math.sinh(2 * this.b) / D
        );
    }
}
const complex=(a,b)=>{
    if((a instanceof Array||ArrayBuffer.isView(a)) && (b instanceof Array||ArrayBuffer.isView(a)))return a.map((n,i)=>complex(a[i],b[i]));
    if(a.isMatrix?.() && b.isMatrix?.()){
        if((a.shape[0]!==b.shape[0])||(a.shape[1]!==b.shape[1]))return Error(0)
        const arr=a.arr.map((n,i)=>complex(a.arr[i],b.arr[i]))
        return new a.constructor(a.rows,a.cols,...arr)
    }
    return new Complex(a,b)
}
export{complex,Complex}