27 lines
9.3 KiB
JavaScript
27 lines
9.3 KiB
JavaScript
/*
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Complex.js v2.4.2 11/5/2024
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https://raw.org/article/complex-numbers-in-javascript/
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Copyright (c) 2024, Robert Eisele (https://raw.org/)
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Licensed under the MIT license.
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*/
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'use strict';(function(r){function l(a,b){if(void 0===a||null===a)f.re=f.im=0;else if(void 0!==b)f.re=a,f.im=b;else switch(typeof a){case "object":if("im"in a&&"re"in a)f.re=a.re,f.im=a.im;else if("abs"in a&&"arg"in a){if(!isFinite(a.abs)&&isFinite(a.arg))return c.INFINITY;f.re=a.abs*Math.cos(a.arg);f.im=a.abs*Math.sin(a.arg)}else if("r"in a&&"phi"in a){if(!isFinite(a.r)&&isFinite(a.phi))return c.INFINITY;f.re=a.r*Math.cos(a.phi);f.im=a.r*Math.sin(a.phi)}else 2===a.length?(f.re=a[0],f.im=a[1]):m();
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break;case "string":f.im=f.re=0;a=a.replace(/_/g,"").match(/\d+\.?\d*e[+-]?\d+|\d+\.?\d*|\.\d+|./g);b=1;let d=0;null===a&&m();for(let e=0;e<a.length;e++){const g=a[e];" "!==g&&"\t"!==g&&"\n"!==g&&("+"===g?b++:"-"===g?d++:("i"===g||"I"===g?(0===b+d&&m()," "===a[e+1]||isNaN(a[e+1])?f.im+=parseFloat((d%2?"-":"")+"1"):(f.im+=parseFloat((d%2?"-":"")+a[e+1]),e++)):((0===b+d||isNaN(g))&&m(),"i"===a[e+1]||"I"===a[e+1]?(f.im+=parseFloat((d%2?"-":"")+g),e++):f.re+=parseFloat((d%2?"-":"")+g)),b=d=0))}0<b+d&&
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m();break;case "number":f.im=0;f.re=a;break;default:m()}return f}function m(){throw SyntaxError("Invalid Param");}function n(a,b){a=Math.abs(a);b=Math.abs(b);a<b&&([a,b]=[b,a]);if(1E8>a)return Math.sqrt(a*a+b*b);b/=a;return a*Math.sqrt(1+b*b)}function p(a,b){const d=Math.abs(a),e=Math.abs(b);if(0===a)return Math.log(e);if(0===b)return Math.log(d);if(3E3>d&&3E3>e)return.5*Math.log(a*a+b*b);a*=.5;b*=.5;return.5*Math.log(a*a+b*b)+Math.LN2}function c(a,b){if(!(this instanceof c))return new c(a,b);a=l(a,
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b);this.re=a.re;this.im=a.im}const h=Math.cosh||function(a){return 1E-9>Math.abs(a)?1-a:.5*(Math.exp(a)+Math.exp(-a))},k=Math.sinh||function(a){return 1E-9>Math.abs(a)?a:.5*(Math.exp(a)-Math.exp(-a))},f={re:0,im:0};c.prototype={re:0,im:0,sign:function(){const a=n(this.re,this.im);return new c(this.re/a,this.im/a)},add:function(a,b){a=l(a,b);b=this.isInfinite();const d=!(isFinite(a.re)&&isFinite(a.im));return b||d?b&&d?c.NAN:c.INFINITY:new c(this.re+a.re,this.im+a.im)},sub:function(a,b){a=l(a,b);b=
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this.isInfinite();const d=!(isFinite(a.re)&&isFinite(a.im));return b||d?b&&d?c.NAN:c.INFINITY:new c(this.re-a.re,this.im-a.im)},mul:function(a,b){a=l(a,b);b=this.isInfinite();const d=!(isFinite(a.re)&&isFinite(a.im)),e=0===this.re&&0===this.im,g=0===a.re&&0===a.im;return b&&g||d&&e?c.NAN:b||d?c.INFINITY:0===a.im&&0===this.im?new c(this.re*a.re,0):new c(this.re*a.re-this.im*a.im,this.re*a.im+this.im*a.re)},div:function(a,b){a=l(a,b);b=this.isInfinite();const d=!(isFinite(a.re)&&isFinite(a.im)),e=0===
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this.re&&0===this.im,g=0===a.re&&0===a.im;if(e&&g||b&&d)return c.NAN;if(g||b)return c.INFINITY;if(e||d)return c.ZERO;if(0===a.im)return new c(this.re/a.re,this.im/a.re);if(Math.abs(a.re)<Math.abs(a.im))return b=a.re/a.im,a=a.re*b+a.im,new c((this.re*b+this.im)/a,(this.im*b-this.re)/a);b=a.im/a.re;a=a.im*b+a.re;return new c((this.re+this.im*b)/a,(this.im-this.re*b)/a)},pow:function(a,b){a=l(a,b);b=0===this.re&&0===this.im;if(0===a.re&&0===a.im)return c.ONE;if(0===a.im){if(0===this.im&&0<this.re)return new c(Math.pow(this.re,
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a.re),0);if(0===this.re)switch((a.re%4+4)%4){case 0:return new c(Math.pow(this.im,a.re),0);case 1:return new c(0,Math.pow(this.im,a.re));case 2:return new c(-Math.pow(this.im,a.re),0);case 3:return new c(0,-Math.pow(this.im,a.re))}}if(b&&0<a.re)return c.ZERO;const d=Math.atan2(this.im,this.re),e=p(this.re,this.im);b=Math.exp(a.re*e-a.im*d);a=a.im*e+a.re*d;return new c(b*Math.cos(a),b*Math.sin(a))},sqrt:function(){const a=this.re,b=this.im;if(0===b)return 0<=a?new c(Math.sqrt(a),0):new c(0,Math.sqrt(-a));
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var d=n(a,b);d=Math.sqrt(.5*(d+Math.abs(a)));let e=Math.abs(b)/(2*d);return 0<=a?new c(d,0>b?-e:e):new c(e,0>b?-d:d)},exp:function(){const a=Math.exp(this.re);return 0===this.im?new c(a,0):new c(a*Math.cos(this.im),a*Math.sin(this.im))},expm1:function(){const a=this.re,b=this.im;var d=Math.expm1(a)*Math.cos(b);var e=Math.PI/4;-e>b||b>e?e=Math.cos(b)-1:(e=b*b,e*=e*(e*(e*(e*(e*(e*(e/20922789888E3-1/87178291200)+1/479001600)-1/3628800)+1/40320)-1/720)+1/24)-.5);return new c(d+e,Math.exp(a)*Math.sin(b))},
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log:function(){const a=this.re,b=this.im;return 0===b&&0<a?new c(Math.log(a),0):new c(p(a,b),Math.atan2(b,a))},abs:function(){return n(this.re,this.im)},arg:function(){return Math.atan2(this.im,this.re)},sin:function(){const a=this.re,b=this.im;return new c(Math.sin(a)*h(b),Math.cos(a)*k(b))},cos:function(){const a=this.re,b=this.im;return new c(Math.cos(a)*h(b),-Math.sin(a)*k(b))},tan:function(){const a=2*this.re,b=2*this.im,d=Math.cos(a)+h(b);return new c(Math.sin(a)/d,k(b)/d)},cot:function(){const a=
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2*this.re,b=2*this.im,d=Math.cos(a)-h(b);return new c(-Math.sin(a)/d,k(b)/d)},sec:function(){const a=this.re,b=this.im,d=.5*h(2*b)+.5*Math.cos(2*a);return new c(Math.cos(a)*h(b)/d,Math.sin(a)*k(b)/d)},csc:function(){const a=this.re,b=this.im,d=.5*h(2*b)-.5*Math.cos(2*a);return new c(Math.sin(a)*h(b)/d,-Math.cos(a)*k(b)/d)},asin:function(){var a=this.re;const b=this.im,d=(new c(b*b-a*a+1,-2*a*b)).sqrt();a=(new c(d.re-b,d.im+a)).log();return new c(a.im,-a.re)},acos:function(){var a=this.re;const b=
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this.im,d=(new c(b*b-a*a+1,-2*a*b)).sqrt();a=(new c(d.re-b,d.im+a)).log();return new c(Math.PI/2-a.im,a.re)},atan:function(){var a=this.re;const b=this.im;if(0===a){if(1===b)return new c(0,Infinity);if(-1===b)return new c(0,-Infinity)}const d=a*a+(1-b)*(1-b);a=(new c((1-b*b-a*a)/d,-2*a/d)).log();return new c(-.5*a.im,.5*a.re)},acot:function(){const a=this.re,b=this.im;if(0===b)return new c(Math.atan2(1,a),0);const d=a*a+b*b;return 0!==d?(new c(a/d,-b/d)).atan():(new c(0!==a?a/0:0,0!==b?-b/0:0)).atan()},
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asec:function(){const a=this.re,b=this.im;if(0===a&&0===b)return new c(0,Infinity);const d=a*a+b*b;return 0!==d?(new c(a/d,-b/d)).acos():(new c(0!==a?a/0:0,0!==b?-b/0:0)).acos()},acsc:function(){const a=this.re,b=this.im;if(0===a&&0===b)return new c(Math.PI/2,Infinity);const d=a*a+b*b;return 0!==d?(new c(a/d,-b/d)).asin():(new c(0!==a?a/0:0,0!==b?-b/0:0)).asin()},sinh:function(){const a=this.re,b=this.im;return new c(k(a)*Math.cos(b),h(a)*Math.sin(b))},cosh:function(){const a=this.re,b=this.im;return new c(h(a)*
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Math.cos(b),k(a)*Math.sin(b))},tanh:function(){const a=2*this.re,b=2*this.im,d=h(a)+Math.cos(b);return new c(k(a)/d,Math.sin(b)/d)},coth:function(){const a=2*this.re,b=2*this.im,d=h(a)-Math.cos(b);return new c(k(a)/d,-Math.sin(b)/d)},csch:function(){const a=this.re,b=this.im,d=Math.cos(2*b)-h(2*a);return new c(-2*k(a)*Math.cos(b)/d,2*h(a)*Math.sin(b)/d)},sech:function(){const a=this.re,b=this.im,d=Math.cos(2*b)+h(2*a);return new c(2*h(a)*Math.cos(b)/d,-2*k(a)*Math.sin(b)/d)},asinh:function(){let a=
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this.im;this.im=-this.re;this.re=a;const b=this.asin();this.re=-this.im;this.im=a;a=b.re;b.re=-b.im;b.im=a;return b},acosh:function(){const a=this.acos();if(0>=a.im){var b=a.re;a.re=-a.im;a.im=b}else b=a.im,a.im=-a.re,a.re=b;return a},atanh:function(){var a=this.re,b=this.im;const d=1<a&&0===b,e=1-a,g=1+a,q=e*e+b*b;a=0!==q?new c((g*e-b*b)/q,(b*e+g*b)/q):new c(-1!==a?a/0:0,0!==b?b/0:0);b=a.re;a.re=p(a.re,a.im)/2;a.im=Math.atan2(a.im,b)/2;d&&(a.im=-a.im);return a},acoth:function(){const a=this.re,b=
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this.im;if(0===a&&0===b)return new c(0,Math.PI/2);const d=a*a+b*b;return 0!==d?(new c(a/d,-b/d)).atanh():(new c(0!==a?a/0:0,0!==b?-b/0:0)).atanh()},acsch:function(){const a=this.re,b=this.im;if(0===b)return new c(0!==a?Math.log(a+Math.sqrt(a*a+1)):Infinity,0);const d=a*a+b*b;return 0!==d?(new c(a/d,-b/d)).asinh():(new c(0!==a?a/0:0,0!==b?-b/0:0)).asinh()},asech:function(){const a=this.re,b=this.im;if(this.isZero())return c.INFINITY;const d=a*a+b*b;return 0!==d?(new c(a/d,-b/d)).acosh():(new c(0!==
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a?a/0:0,0!==b?-b/0:0)).acosh()},inverse:function(){if(this.isZero())return c.INFINITY;if(this.isInfinite())return c.ZERO;const a=this.re,b=this.im,d=a*a+b*b;return new c(a/d,-b/d)},conjugate:function(){return new c(this.re,-this.im)},neg:function(){return new c(-this.re,-this.im)},ceil:function(a){a=Math.pow(10,a||0);return new c(Math.ceil(this.re*a)/a,Math.ceil(this.im*a)/a)},floor:function(a){a=Math.pow(10,a||0);return new c(Math.floor(this.re*a)/a,Math.floor(this.im*a)/a)},round:function(a){a=
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Math.pow(10,a||0);return new c(Math.round(this.re*a)/a,Math.round(this.im*a)/a)},equals:function(a,b){a=l(a,b);return Math.abs(a.re-this.re)<=c.EPSILON&&Math.abs(a.im-this.im)<=c.EPSILON},clone:function(){return new c(this.re,this.im)},toString:function(){let a=this.re,b=this.im,d="";if(this.isNaN())return"NaN";if(this.isInfinite())return"Infinity";Math.abs(a)<c.EPSILON&&(a=0);Math.abs(b)<c.EPSILON&&(b=0);if(0===b)return d+a;0!==a?(d=d+a+" ",0>b?(b=-b,d+="-"):d+="+",d+=" "):0>b&&(b=-b,d+="-");1!==
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b&&(d+=b);return d+"i"},toVector:function(){return[this.re,this.im]},valueOf:function(){return 0===this.im?this.re:null},isNaN:function(){return isNaN(this.re)||isNaN(this.im)},isZero:function(){return 0===this.im&&0===this.re},isFinite:function(){return isFinite(this.re)&&isFinite(this.im)},isInfinite:function(){return!this.isFinite()}};c.ZERO=new c(0,0);c.ONE=new c(1,0);c.I=new c(0,1);c.PI=new c(Math.PI,0);c.E=new c(Math.E,0);c.INFINITY=new c(Infinity,Infinity);c.NAN=new c(NaN,NaN);c.EPSILON=1E-15;
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"function"===typeof define&&define.amd?define([],function(){return c}):"object"===typeof exports?(Object.defineProperty(c,"__esModule",{value:!0}),c["default"]=c,c.Complex=c,module.exports=c):r.Complex=c})(this);
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