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numbers.min.js

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  1. !function(r){if("object"==typeof exports&&"undefined"!=typeof module)module.exports=r();else if("function"==typeof define&&define.amd)define([],r);else{var t;"undefined"!=typeof window?t=window:"undefined"!=typeof global?t=global:"undefined"!=typeof self&&(t=self),t.numbers=r()}}(function(){return function r(t,e,n){function o(i,u){if(!e[i]){if(!t[i]){var f="function"==typeof require&&require;if(!u&&f)return f(i,!0);if(a)return a(i,!0);var s=new Error("Cannot find module '"+i+"'");throw s.code="MODULE_NOT_FOUND",s}var h=e[i]={exports:{}};t[i][0].call(h.exports,function(r){var e=t[i][1][r];return o(e?e:r)},h,h.exports,r,t,e,n)}return e[i].exports}for(var a="function"==typeof require&&require,i=0;i<n.length;i++)o(n[i]);return o}({1:[function(r,t){t.exports=r("./lib/numbers.js")},{"./lib/numbers.js":2}],2:[function(r,t,e){var n=e;n.basic=r("./numbers/basic"),n.calculus=r("./numbers/calculus"),n.complex=r("./numbers/complex"),n.dsp=r("./numbers/dsp"),n.matrix=r("./numbers/matrix"),n.prime=r("./numbers/prime"),n.statistic=r("./numbers/statistic"),n.generate=r("./numbers/generators"),n.random=r("./numbers/random"),n.EPSILON=.001},{"./numbers/basic":3,"./numbers/calculus":4,"./numbers/complex":5,"./numbers/dsp":6,"./numbers/generators":7,"./numbers/matrix":8,"./numbers/prime":9,"./numbers/random":10,"./numbers/statistic":11}],3:[function(r,t,e){var n=e;n.sum=function(r){if("[object Array]"===Object.prototype.toString.call(r)){for(var t=0,e=0;e<r.length;e++){if("number"!=typeof r[e])throw new Error("All elements in array must be numbers");t+=r[e]}return t}throw new Error("Input must be of type Array")},n.subtraction=function(r){if("[object Array]"===Object.prototype.toString.call(r)){var t=r[0];if("number"!=typeof t)throw new Error("All elements in array must be numbers");for(var e=1,n=r.length;n>e;e++){if("number"!=typeof r[e])throw new Error("All elements in array must be numbers");t-=r[e]}return t}throw new Error("Input must be of type Array")},n.product=function(r){if("[object Array]"===Object.prototype.toString.call(r)){var t=r[0];if("number"!=typeof t)throw new Error("All elements in array must be numbers");for(var e=1,n=r.length;n>e;e++){if("number"!=typeof r[e])throw new Error("All elements in array must be numbers");t*=r[e]}return t}throw new Error("Input must be of type Array")},n.square=function(r){if("number"!=typeof r)throw new Error("Input must be a number.");return r*r},n.binomial=function(r,t){function e(r,t){if("number"!=typeof r&&"number"!=typeof t)throw new Error("Input must be a number.");return r>=0&&0===t?1:0===r&&t>0?0:n[r]&&n[r][t]>0?n[r][t]:(n[r]||(n[r]=[]),n[r][t]=e(r-1,t-1)+e(r-1,t),n[r][t])}var n=[];return e(r,t)},n.factorial=function(r){if("number"!=typeof r)throw new Error("Input must be a number.");if(0>r)throw new Error("Input must not be negative.");for(var t=2,e=1;r>=t;)e*=t++;return e},n.gcd=function(r,t){var e;if(r=+r,t=+t,r!==r||t!==t)return 0/0;if(1/0===r||r===-1/0||1/0===t||t===-1/0)return 1/0;if(r%1!==0||t%1!==0)throw new Error("Can only operate on integers");for(;t;)e=r%t,r=t,t=e;return r>0?r:-r},n.lcm=function(r,t){return Math.abs(r*t)/n.gcd(r,t)},n.random=function(r,t,e){if(0===r.length)throw new Error("Empty array");if(t>r.length&&!e)throw new Error("Quantity requested exceeds size of array");if(e===!0){var o,a=[];for(o=0;t>o;o++)a[o]=r[Math.floor(Math.random()*r.length)];return a}return n.shuffle(r).slice(0,t)},n.shuffle=function(r){for(var t,e,n=r.length;n;)e=Math.floor(Math.random()*n--),t=r[n],r[n]=r[e],r[e]=t;return r},n.max=function(r){if(!Array.isArray(r))throw new Error("Input must be of type Array");for(var t,e=-1/0,n=0,o=r.length;o>n;n++)if(t=+r[n],t>e&&(e=t),t!==t)return 0/0;return e},n.min=function(r){if(!Array.isArray(r))throw new Error("Input must be of type Array");for(var t,e=+1/0,n=0,o=r.length;o>n;n++)if(t=+r[n],e>t&&(e=t),t!==t)return 0/0;return e},n.range=function(r,t,e){var n,o,a=0;for(arguments.length<=1&&(t=r||0,r=0),e=e||1,r>t&&(e=0-Math.abs(e)),o=Math.max(Math.ceil((t-r)/e)+1,0),n=new Array(o);o>a;)n[a++]=r,r+=e;return n},n.isInt=function(r){return r%1===0},n.divMod=function(r,t){if(0>=t)throw new Error("b cannot be zero. Undefined.");if(!n.isInt(r)||!n.isInt(t))throw new Error("A or B are not integers.");return[Math.floor(r/t),r%t]},n.powerMod=function(r,t,e){if("number"!=typeof r||"number"!=typeof t||"number"!=typeof e)throw new Error("Inputs must be numbers.");if(-1>t)return Math.pow(r,t)%e;if(0===t)return 1%e;if(t>=1){for(var o=1;t>0;)t%2===1&&(o=o*r%e),r=r*r%e,t>>=1;return o}return-1===t?n.modInverse(r,e):1>t?n.powerMod(r,Math.pow(t,-1),e):void 0},n.egcd=function(r,t){if(r=+r,t=+t,r!==r||t!==t)return[0/0,0/0,0/0];if(1/0===r||r===-1/0||1/0===t||t===-1/0)return[1/0,1/0,1/0];if(r%1!==0||t%1!==0)throw new Error("Can only operate on integers");var e,n,o,a,i=0>r?-1:1,u=0>t?-1:1,f=0,s=1,h=1,l=0;for(r=Math.abs(r),t=Math.abs(t);0!==r;)e=Math.floor(t/r),n=t%r,o=f-h*e,a=s-l*e,t=r,r=n,f=h,s=l,h=o,l=a;return[t,i*f,u*s]},n.modInverse=function(r,t){var e=n.egcd(r,t);if(1!==e[0])throw new Error("No modular inverse exists");return e[1]%t},n.numbersEqual=function(r,t,e){if("number"!=typeof r||"number"!=typeof t||"number"!=typeof e)throw new Error("First and Second must be numbers.");return e>r-t&&r-t>-e},n.fallingFactorial=function(r,t){var e=r-t+1,n=1;if(0>r)throw new Error("n cannot be negative.");if(t>r)throw new Error("k cannot be greater than n.");for(;r>=e;)n*=e++;return n},n.permutation=function(r,t){if(0>=r)throw new Error("n cannot be less than or equal to 0.");if(t>r)throw new Error("k cannot be greater than k.");var e=n.binomial(r,t),o=e*n.factorial(t);return o}},{}],4:[function(r,t,e){function n(r,t,e){var n=(t+e)/2,o=Math.abs(e-t)/6;return o*(r(t)+4*r(n)+r(e))}function o(r,t,e,a,i){var u=t+e,f=n(r,t,u),s=n(r,u,e);return Math.abs(f+s-a)<=15*i?f+s+(f+s-a)/15:o(r,t,u,i/2,f)+o(r,u,e,i/2,s)}var a=r("../numbers"),i=e;i.pointDiff=function(r,t){var e=r(t-.001),n=r(t+.001);return(n-e)/.002},i.Riemann=function(r,t,e,n,o){var a,i=(e-t)/n,u=0;if("function"==typeof o)for(a=t;e>a;a+=i)u+=r(o(a,a+i));else for(a=t;e>a;a+=i)u+=r(a);return u*i},i.adaptiveSimpson=function(r,t,e,i){return i="undefined"==typeof i?a.EPSILON:i,o(r,t,e,n(r,t,e),i)},i.limit=function(r,t,e){if("left"===e)return r(t-1e-15);if("right"===e)return r(t+1e-15);if("middle"===e)return(i.limit(r,t,"left")+i.limit(r,t,"right"))/2;throw new Error("Approach not provided")},i.StirlingGamma=function(r){return Math.sqrt(2*Math.PI/r)*Math.pow(r/Math.E,r)},i.LanczosGamma=function(r){var t,e=[.9999999999998099,676.5203681218851,-1259.1392167224028,771.3234287776531,-176.6150291621406,12.507343278686905,-.13857109526572012,9984369578019572e-21,1.5056327351493116e-7],n=7;if(.5>r)return Math.PI/(Math.sin(Math.PI*r)*i.LanczosGamma(1-r));r-=1;var o=e[0],a=r+n+.5;for(t=1;t<e.length;t++)o+=e[t]/(r+t);return Math.sqrt(2*Math.PI)*Math.pow(a,r+.5)*Math.exp(-a)*o},i.MonteCarlo=function(r,t){if(arguments.length<2)throw new Error("Please enter at least one interval.");if(0>=t)throw new Error("Please use a positive integer for N.");var e=[];t=Math.ceil(t);for(var n=2;n<arguments.length;n++)e.push(arguments[n]);var o=e.map(function(r){return r[1]-r[0]}).reduce(function(r,t){return r*t})/t,i=a.matrix.transpose(e.map(function(r){return a.statistic.randomSample(r[0],r[1],t)})).map(function(t){return r.apply(null,[t[0],t[1],t[2]])});return o*i.reduce(function(r,t){return r+t})}},{"../numbers":2}],5:[function(r,t){var e=r("../numbers"),n=e.basic,o=function(r,t){this.re=r,this.im=t,this.r=this.magnitude(),this.t=this.phase()};o.prototype.add=function(r){return new o(this.re+r.re,this.im+r.im)},o.prototype.subtract=function(r){return new o(this.re-r.re,this.im-r.im)},o.prototype.multiply=function(r){var t=this.re*r.re-this.im*r.im,e=this.im*r.re+this.re*r.im;return new o(t,e)},o.prototype.divide=function(r){var t=r.re*r.re+r.im*r.im,e=(this.re*r.re+this.im*r.im)/t,n=(this.im*r.re-this.re*r.im)/t;return new o(e,n)},o.prototype.magnitude=function(){return Math.sqrt(this.re*this.re+this.im*this.im)},o.prototype.phase=function(){return Math.atan2(this.im,this.re)},o.prototype.conjugate=function(){return new o(this.re,-1*this.im)},o.prototype.pow=function(r){var t=Math.pow(this.magnitude(),r);return new o(t*Math.cos(r*this.phase()),t*Math.sin(r*this.phase()))},o.prototype.complexPow=function(r){var t=Math.pow(this.re,2)+Math.pow(this.im,2),e=Math.pow(t,r.re/2)*Math.pow(Math.E,-r.im*this.phase()),n=r.re*this.phase()+.5*r.im*Math.log(t);return new o(e*Math.cos(n),e*Math.sin(n))},o.prototype.roots=function(r){for(var t=new Array(r),e=0;r>e;e++){var n=(this.phase()+2*Math.PI*e)/r,a=Math.pow(this.magnitude(),1/r);t[e]=new o(a*Math.cos(n),a*Math.sin(n))}return t},o.prototype.sin=function(){var r=new o(Math.E,0),t=new o(0,1),e=new o(0,-1),n=r.complexPow(t.multiply(this)).subtract(r.complexPow(e.multiply(this)));return n.divide(new o(0,2))},o.prototype.cos=function(){var r=new o(Math.E,0),t=new o(0,1),e=new o(0,-1),n=r.complexPow(t.multiply(this)).add(r.complexPow(e.multiply(this)));return n.divide(new o(2,0))},o.prototype.tan=function(){return this.sin().divide(this.cos())},o.prototype.equals=function(r,t){return n.numbersEqual(this.re,r.re,t)&&n.numbersEqual(this.im,r.im,t)},t.exports=o},{"../numbers":2}],6:[function(r,t,e){var n=r("../numbers"),o=n.complex,a=e;a.segment=function(r,t,e){for(var n=[],o=t;o<r.length;o+=e)n.push(r[o]);return n},a.fft=function(r){var t=r.length;if(1>=t)return[new o(r[0],0)];if(Math.log(t)/Math.LN2%1!==0)throw new Error("Array length must be integer power of 2");for(var e=a.fft(a.segment(r,0,2)),n=a.fft(a.segment(r,1,2)),i=[],u=t/2,f=0;t>f;f++){var s=-2*Math.PI*f/t,h=new o(Math.cos(s),Math.sin(s));i[f]=u>f?e[f].add(h.multiply(n[f])):e[f-u].subtract(h.multiply(n[f-u]))}return i}},{"../numbers":2}],7:[function(r,t,e){var n=e;n.fibonacci=function(r){for(var t,e=function(r){for(var t,e=[];r>0;)t=2>r?r:r%2,r=Math.floor(r/2),e.push(t);return e.reverse()},n=1,o=0,a=1,i=e(r),u=0;u<i.length;u++){var f=i[u];f?(t=[(n+a)*o,o*o+a*a],n=t[0],o=t[1]):(t=[n*n+o*o,(n+a)*o],n=t[0],o=t[1]),a=n+o}return o},n.collatz=function(r,t){t.push(r),1!==r&&(r%2===0?n.collatz(r/2,t):n.collatz(3*r+1,t))}},{}],8:[function(r,t,e){var n=e,o="Matrix must be square.",a="Only two dimensional operations are supported at this time.";n._check2DVector=function(r){if(2!==r.length)throw new Error(a)},n.deepCopy=function(r){if(!Array.isArray(r))throw new Error("Input must be a matrix.");if(void 0===r[0][0])throw new Error("Input cannot be a vector.");for(var t=new Array(r.length),e=0;e<r.length;e++)t[e]=r[e].slice();return t},n.isSquare=function(r){if(!Array.isArray(r))throw new Error("Input must be a matrix.");if(void 0===r[0][0])throw new Error("Input cannot be a vector.");for(var t=r.length,e=0;t>e;e++)if(r[e].length!==t)return!1;return!0},n.addition=function(r,t){if(r.length!==t.length||r[0].length!==t[0].length)throw new Error("Matrix mismatch");var e,n=new Array(r.length);if(r[0].length)for(e=0;e<r.length;e++){n[e]=new Array(r[e].length);for(var o=0;o<r[e].length;o++)n[e][o]=r[e][o]+t[e][o]}else 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Array(r.length),o=0;o<r.length;o++)e[o]=new Array(t[0].length);for(var a=n.transpose(t),i=0;i<e.length;i++)for(var u=0;u<e[i].length;u++)e[i][u]=n.dotproduct(r[i],a[u]);return e},n.determinant=function(r){var t,e,a,i,u=r.length,f=r[0].length,s=0;if(!n.isSquare(r))throw new Error(o);if(1===u)return r[0][0];if(2===u)return r[0][0]*r[1][1]-r[0][1]*r[1][0];for(e=0;f>e;e++){for(a=r[0][e],i=r[0][e],t=1;u>t;t++)i*=r[t][((e+t)%f+f)%f],a*=r[t][((e-t)%f+f)%f];s+=i-a}return s},n.lupDecomposition=function(r){if(!n.isSquare(r))throw new Error(o);var t,e=r.length,a=n.deepCopy(r),i=n.transpose(n.identity(e)),u=new Array(e);this.getL=function(r){for(var t=r[0].length,e=n.identity(t),o=0;t>o;o++)for(var a=0;t>a;a++)o>a&&(e[o][a]=r[o][a]);return e},this.getU=function(r){for(var t=r[0].length,e=n.identity(t),o=0;t>o;o++)for(var a=0;t>a;a++)a>=o&&(e[o][a]=r[o][a]);return e};for(var f=0;e>f;f++){var s;for(s=0;e>s;s++)u[s]=a[s][f];for(s=0;e>s;s++){t=a[s];for(var h=Math.min(s,f),l=0,c=0;h>c;c++)l+=t[c]*u[c];t[f]=u[s]-=l}var m=f;for(s=f+1;e>s;s++)Math.abs(u[s])>Math.abs(u[m])&&(m=s);if(m!==f&&(a=n.rowSwitch(a,m,f),i=n.rowSwitch(i,m,f)),e>f&&0!==a[f][f])for(s=f+1;e>s;s++)a[s][f]/=a[f][f]}return[this.getL(a),this.getU(a),i]},n.rotate=function(r,t,e){n._check2DVector(r);var o="clockwise"===e?-1:1,a=t*(Math.PI/180),i=[[Math.cos(a),-1*o*Math.sin(a)],[o*Math.sin(a),Math.cos(a)]];return n.multiply(i,r)},n.scale=function(r,t,e){n._check2DVector(r);var o=[[t,0],[0,e]];return n.multiply(o,r)},n.shear=function(r,t,e){n._check2DVector(r);var o="xaxis"===e?t:0,a="yaxis"===e?t:0,i=[[1,o],[a,1]];return n.multiply(i,r)},n.affine=function(r,t,e){n._check2DVector(r);var o=[[1,0,t],[0,1,e],[0,0,1]],a=[[r[0][0]],[r[1][0]],[1]],i=n.multiply(o,a);return[[i[0][0]],[i[1][0]]]},n.rowScale=function(r,t,e){for(var n=new Array(r.length),o=0;o<r.length;o++){n[o]=new Array(r[o].length);for(var a=0;a<r[o].length;a++)n[o][a]=o===t?e*r[o][a]:r[o][a]}return n},n.rowSwitch=function(r,t,e){for(var n=new Array(r.length),o=0;o<r.length;o++){n[o]=new Array(r[o].length);for(var a=0;a<r[o].length;a++)n[o][a]=o===t?r[e][a]:o===e?r[t][a]:r[o][a]}return n},n.rowAddMultiple=function(r,t,e,n){for(var o=new Array(r.length),a=0;a<r.length;a++){o[a]=new Array(r[a].length);for(var i=0;i<r[a].length;i++)a===e?o[e][i]=r[e][i]+n*r[t][i]:o[a][i]=r[a][i]}return o},n.GaussJordanEliminate=function(r,t){for(var e,n,o,a="undefined"==typeof t?1e-10:t,i=r.length,u=r[0].length,f=-1;++f<i;){var s=f;for(e=f;++e<i;)Math.abs(r[e][f])>Math.abs(r[s][f])&&(s=e);var h=r[f];if(r[f]=r[s],r[s]=h,Math.abs(r[f][f])<=a)return r;for(e=f;++e<i;)for(o=r[e][f]/r[f][f],n=f-1;++n<u;)r[e][n]-=r[f][n]*o}for(f=i;--f>=0;){for(o=r[f][f],e=-1;++e<f;)for(n=u;--n>=f;)r[e][n]-=r[f][n]*r[e][f]/o;for(r[f][f]/=o,n=i-1;++n<u;)r[f][n]/=o}return r},n.rowReduce=function(r,t){return n.GaussJordanEliminate(r,t)},n.inverse=function(r){if(!n.isSquare(r))throw new Error(o);var 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a=n.getCol(r,e),u=a[e],f=i(a,e);if(Math.abs(u)<f)return!1}return!0},n.isStrictlyColumnDD=function(r){if(!n.isSquare(r))throw new Error(o);for(var t=r.length,e=0;t>e;e++){var a=n.getCol(r,e),u=a[e],f=i(a,e);if(Math.abs(u)<=f)return!1}return!0}},{}],9:[function(r,t,e){var n=r("./basic"),o=e;o.simple=function(r){if(isNaN(r)||!isFinite(r)||r%1||2>r)return!1;if(r%2===0)return 2===r;if(r%3===0)return 3===r;for(var t=5,e=Math.sqrt(r);e>=t;t+=6)if(r%t===0||r%(t+2)===0)return!1;return!0},o.factorization=function(r){r=Math.floor(r);for(var t,e,n=[],o=Math.sqrt,a=r>1&&isFinite(r);a;){if(t=o(r),e=2,r%e)for(e=3;r%e&&(e+=2)<t;);e=e>t?r:e,n.push(e),a=e!==r,r/=e}return n},o.millerRabin=function(r,t){if(1===arguments.length&&(t=20),2===r)return!0;if(!n.isInt(r)||1>=r||r%2===0)return!1;for(var e=0,o=r-1;;){var a=n.divMod(o,2),i=a[0],u=a[1];if(1===u)break;e+=1,o=i}for(var f=function(t){if(1===n.powerMod(t,o,r))return!1;for(var 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