added turacer video and neuroticus

6 files changed, 256 insertions, 2 deletions

diff --git a/00_blog/00030_Computer-Games/00150_TU-Racer/index.md b/00_blog/00030_Computer-Games/00150_TU-Racer/index.md
index 2cbbe1a..0fa52b7 100644
--- a/00_blog/00030_Computer-Games/00150_TU-Racer/index.md
+++ b/00_blog/00030_Computer-Games/00150_TU-Racer/index.md
@@ -6,10 +6,17 @@ legendary _Computergraphik_ II & III Courses.
 
 You participate in deadly races around the Technical University, as well
 as in psychodelic worlds to earn money for your tuition fees, which the 
-Austrian government just invented. (back then in 2005...)
+Austrian government just invented. (back then in 00s...)
 
 The game is using a custom game engine based on raw OpenGL. 
 
+<video controls>
+<source src="turacer.mp4" type="video/mp4">
+<source src="turacer.webm" type="video/webm">
+    Sorry, Your browser does not support the video tag.
+
+</video>
+
 ## Features
 
 * Precalculated Lightmaps
@@ -19,3 +26,4 @@ The game is using a custom game engine based on raw OpenGL.
 * Lights and Transparency
 * 3 Unique Levels
 * 4 Cars with individual physics
+* Smoke Particle Effect
diff --git a/00_blog/00030_Computer-Games/00150_TU-Racer/turacer.mp4 b/00_blog/00030_Computer-Games/00150_TU-Racer/turacer.mp4
new file mode 100644
index 0000000..24fcca5
--- /dev/null
+++ b/00_blog/00030_Computer-Games/00150_TU-Racer/turacer.mp4
diff --git a/00_blog/00030_Computer-Games/00150_TU-Racer/turacer.webm b/00_blog/00030_Computer-Games/00150_TU-Racer/turacer.webm
new file mode 100644
index 0000000..e4c44a7
--- /dev/null
+++ b/00_blog/00030_Computer-Games/00150_TU-Racer/turacer.webm
diff --git a/00_blog/00040_Haskell/00220_Neural-Networks/index.md b/00_blog/00040_Haskell/00220_Neural-Networks/index.md
index db69154..16b39d0 100644
--- a/00_blog/00040_Haskell/00220_Neural-Networks/index.md
+++ b/00_blog/00040_Haskell/00220_Neural-Networks/index.md
@@ -1,3 +1,4 @@
+    March 2019
 # Neural Networks
 
 ## Hello Sigmoid
@@ -10,7 +11,8 @@ reading the first two chapters of _Neural Networks and Deep Learning_ [1].
 
 Be warned that the following implementation aims at clarity and readability,
 but not performance! In another article I will probably discuss, how to 
-optimize it heavily, utilizing _Parallel Programming_ / _Tensor Flow (CUDA)_.
+optimize it heavily, utilizing _Parallel Programming_ / _Tensor Flow (CUDA)_. 
+We can even run it on a cluster someday...
 
 The source code below was auto-fetched from: 
 <https://gitweb.softwarefools.com/?p=miguel/haskell.git;a=blob;f=mnist/Neuronet.hs>
@@ -35,6 +37,11 @@ the first ten epochs. (The speed of the cast was increased quite a bit)
  
 <asciinema-player loop="1" preload="true" theme="solarized-dark" autoplay="true" src="mnist.cast"></asciinema-player>
 
+I created a little javascript version with 100 random test samples where 
+you can test the trained neuronal network inside your browser, if it
+supports HTML5. 
+
+* [link to neuroticus.html](neuroticus.html)
 
 ## Technical Vocublary
 
@@ -46,6 +53,8 @@ yourself familiar with, when learning about neural networks.
 * cost / loss / objective function
 * required assumptions about the cost function
 * quadratic cost function / mean squared error
+* cross-entropy cost function (recheck proof)
+* binary entropy
 * gradient descent 
 * gradient (vector of partial derivatives)
 * stochastic gradient descent 
diff --git a/00_blog/00040_Haskell/00220_Neural-Networks/math.min.js b/00_blog/00040_Haskell/00220_Neural-Networks/math.min.js
new file mode 100644
index 0000000..4a79ab6
--- /dev/null
+++ b/00_blog/00040_Haskell/00220_Neural-Networks/math.min.js
@@ -0,0 +1,56 @@
+/**
+ * math.js
+ * https://github.com/josdejong/mathjs
+ *
+ * Math.js is an extensive math library for JavaScript and Node.js,
+ * It features real and complex numbers, units, matrices, a large set of
+ * mathematical functions, and a flexible expression parser.
+ *
+ * @version 5.8.0
+ * @date    2019-03-20
+ *
+ * @license
+ * Copyright (C) 2013-2019 Jos de Jong <wjosdejong@gmail.com>
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License"); you may not
+ * use this file except in compliance with the License. You may obtain a copy
+ * of the License at
+ *
+ * https://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+ * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
+ * License for the specific language governing permissions and limitations under
+ * the License.
+ */
+!function(e,t){"object"==typeof exports&&"object"==typeof module?module.exports=t():"function"==typeof define&&define.amd?define([],t):"object"==typeof exports?exports.math=t():e.math=t()}(this,function(){return function(r){var n={};function i(e){if(n[e])return n[e].exports;var t=n[e]={i:e,l:!1,exports:{}};return r[e].call(t.exports,t,t.exports,i),t.l=!0,t.exports}return i.m=r,i.c=n,i.d=function(e,t,r){i.o(e,t)||Object.defineProperty(e,t,{enumerable:!0,get:r})},i.r=function(e){"undefined"!=typeof Symbol&&Symbol.toStringTag&&Object.defineProperty(e,Symbol.toStringTag,{value:"Module"}),Object.defineProperty(e,"__esModule",{value:!0})},i.t=function(t,e){if(1&e&&(t=i(t)),8&e)return t;if(4&e&&"object"==typeof t&&t&&t.__esModule)return t;var r=Object.create(null);if(i.r(r),Object.defineProperty(r,"default",{enumerable:!0,value:t}),2&e&&"string"!=typeof t)for(var n in t)i.d(r,n,function(e){return t[e]}.bind(null,n));return r},i.n=function(e){var t=e&&e.__esModule?function(){return 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+/**
+ * @license Complex.js v2.0.11 11/02/2016
+ *
+ * Copyright (c) 2016, Robert Eisele (robert@xarg.org)
+ * Dual licensed under the MIT or GPL Version 2 licenses.
+ **/
+/**
+ * @license Complex.js v2.0.11 11/02/2016
+ *
+ * Copyright (c) 2016, Robert Eisele (robert@xarg.org)
+ * Dual licensed under the MIT or GPL Version 2 licenses.
+ **/
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s=a(0);t.name="complex",t.factory=function(r,e,t,n){var i=a(4),o=n("complex",{"":function(){return r.Complex.ZERO},number:function(e){return new r.Complex(e,0)},"number, number":function(e,t){return new r.Complex(e,t)},"BigNumber, BigNumber":function(e,t){return new r.Complex(e.toNumber(),t.toNumber())},Complex:function(e){return e.clone()},string:function(e){return r.Complex(e)},null:function(e){return r.Complex(0)},Object:function(e){if("re"in e&&"im"in e)return new r.Complex(e.re,e.im);if("r"in e&&"phi"in e||"abs"in e&&"arg"in e)return new r.Complex(e);throw new Error("Expected object with properties (re and im) or (r and phi) or (abs and arg)")},"Array | Matrix":function(e){return s(e,o)}});return o.toTex={0:"0",1:"\\left(${args[0]}\\right)",2:"\\left(\\left(${args[0]}\\right)+".concat(i.symbols.i,"\\cdot\\left(${args[1]}\\right)\\right)")},o}},function(e,t,r){"use strict";var l=Object.assign||function(e){for(var t=1;t<arguments.length;t++){var r=arguments[t];for(var n in 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i=r(181);i.prototype.type="Fraction",i.prototype.isFraction=!0,i.prototype.toJSON=function(){return{mathjs:"Fraction",n:this.s*this.n,d:this.d}},i.fromJSON=function(e){return new i(e)},t.name="Fraction",t.path="type",t.factory=function(e,t,r,n){return i}},function(i,o,e){var a;
+/**
+ * @license Fraction.js v4.0.12 09/09/2015
+ * http://www.xarg.org/2014/03/rational-numbers-in-javascript/
+ *
+ * Copyright (c) 2015, Robert Eisele (robert@xarg.org)
+ * Dual licensed under the MIT or GPL Version 2 licenses.
+ **/
+/**
+ * @license Fraction.js v4.0.12 09/09/2015
+ * http://www.xarg.org/2014/03/rational-numbers-in-javascript/
+ *
+ * Copyright (c) 2015, Robert Eisele (robert@xarg.org)
+ * Dual licensed under the MIT or GPL Version 2 licenses.
+ **/
+!function(e){"use strict";var d={s:1,n:0,d:1};function t(t){function e(){var e=Error.apply(this,arguments);e.name=this.name=t,this.stack=e.stack,this.message=e.message}function r(){}return r.prototype=Error.prototype,e.prototype=new r,e}var y=c.DivisionByZero=t("DivisionByZero"),r=c.InvalidParameter=t("InvalidParameter");function g(e,t){return isNaN(e=parseInt(e,10))&&v(),e*t}function v(){throw new r}var n=function(e,t){var r,n=0,i=1,o=1,a=0,s=0,u=0,c=1,f=1,l=0,p=1,m=1,h=1;if(null==e);else if(void 0!==t)o=(n=e)*(i=t);else switch(typeof e){case"object":"d"in e&&"n"in e?(n=e.n,i=e.d,"s"in e&&(n*=e.s)):0 in e?(n=e[0],1 in e&&(i=e[1])):v(),o=n*i;break;case"number":if(e<0&&(e=-(o=e)),e%1==0)n=e;else 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d=0;for(u=0;u<p;u++){e._ptr[u]=e._ptr[u]-d;var y=e._ptr[u],g=e._ptr[u+1]-d;for(c=y;c<g;c++)t-1<(s=e._index[c])&&(e._values.splice(c,1),e._index.splice(c,1),d++)}e._ptr[u]=e._values.length}return e._size[0]=t,e._size[1]=r,e}function o(e,t,r,n,i){var o,a,s=n[0],u=n[1],c=[];for(o=0;o<s;o++)for(c[o]=[],a=0;a<u;a++)c[o][a]=0;for(a=0;a<u;a++)for(var f=r[a],l=r[a+1],p=f;p<l;p++)c[o=t[p]][a]=e?i?w.clone(e[p]):e[p]:1;return c}return(A.prototype=new r).type="SparseMatrix",A.prototype.isSparseMatrix=!0,A.prototype.getDataType=function(){return n(this._values)},A.prototype.storage=function(){return"sparse"},A.prototype.datatype=function(){return this._datatype},A.prototype.create=function(e,t){return new A(e,t)},A.prototype.density=function(){var e=this._size[0],t=this._size[1];return 0!==e&&0!==t?this._index.length/(e*t):0},A.prototype.subset=function(e,t,r){if(!this._values)throw new Error("Cannot invoke subset on a Pattern only matrix");switch(arguments.length){case 1:return function(e,t){if(!b.isIndex(t))throw new TypeError("Invalid index");if(t.isScalar())return e.get(t.min());var r,n,i,o,a=t.size();if(a.length!==e._size.length)throw new x(a.length,e._size.length);var s=t.min(),u=t.max();for(r=0,n=e._size.length;r<n;r++)B(s[r],e._size[r]),B(u[r],e._size[r]);var c=e._values,f=e._index,l=e._ptr,p=t.dimension(0),m=t.dimension(1),h=[],d=[];p.forEach(function(e,t){d[e]=t[0],h[e]=!0});var y=c?[]:void 0,g=[],v=[];return m.forEach(function(e){for(v.push(g.length),i=l[e],o=l[e+1];i<o;i++)r=f[i],!0===h[r]&&(g.push(d[r]),y&&y.push(c[i]))}),v.push(g.length),new A({values:y,index:g,ptr:v,size:a,datatype:e._datatype})}(this,e);case 2:case 3:return function(e,t,r,n){if(!t||!0!==t.isIndex)throw new TypeError("Invalid index");var i,o=t.size(),a=t.isScalar();if(b.isMatrix(r)?(i=r.size(),r=r.toArray()):i=y.size(r),a){if(0!==i.length)throw new TypeError("Scalar expected");e.set(t.min(),r,n)}else{if(1!==o.length&&2!==o.length)throw new x(o.length,e._size.length,"<");if(i.length<o.length){for(var s=0,u=0;1===o[s]&&1===i[s];)s++;for(;1===o[s];)u++,s++;r=y.unsqueeze(r,o.length,u,i)}if(!w.deepEqual(o,i))throw new x(o,i,">");for(var c=t.min()[0],f=t.min()[1],l=i[0],p=i[1],m=0;m<l;m++)for(var h=0;h<p;h++){var d=r[m][h];e.set([m+c,h+f],d,n)}}return e}(this,e,t,r);default:throw new SyntaxError("Wrong number of arguments")}},A.prototype.get=function(e){if(!O(e))throw new TypeError("Array expected");if(e.length!==this._size.length)throw new x(e.length,this._size.length);if(!this._values)throw new Error("Cannot invoke get on a Pattern only matrix");var t=e[0],r=e[1];B(t,this._size[0]),B(r,this._size[1]);var n=g(t,this._ptr[r],this._ptr[r+1],this._index);return n<this._ptr[r+1]&&this._index[n]===t?this._values[n]:0},A.prototype.set=function(e,t,r){if(!O(e))throw new TypeError("Array expected");if(e.length!==this._size.length)throw new x(e.length,this._size.length);if(!this._values)throw new Error("Cannot invoke set on a Pattern only matrix");var n=e[0],i=e[1],o=this._size[0],a=this._size[1],s=E,u=0;C(this._datatype)&&(s=M.find(E,[this._datatype,this._datatype])||E,u=M.convert(0,this._datatype)),(o-1<n||a-1<i)&&(f(this,Math.max(n+1,o),Math.max(i+1,a),r),o=this._size[0],a=this._size[1]),B(n,o),B(i,a);var c=g(n,this._ptr[i],this._ptr[i+1],this._index);return c<this._ptr[i+1]&&this._index[c]===n?s(t,u)?function(e,t,r,n,i){r.splice(e,1),n.splice(e,1);for(var o=t+1;o<i.length;o++)i[o]--}(c,i,this._values,this._index,this._ptr):this._values[c]=t:v(c,n,i,t,this._values,this._index,this._ptr),this},A.prototype.resize=function(t,e,r){if(!O(t))throw new TypeError("Array expected");if(2!==t.length)throw new Error("Only two dimensions matrix are supported");return t.forEach(function(e){if(!S.isNumber(e)||!S.isInteger(e)||e<0)throw new TypeError("Invalid size, must contain positive integers (size: "+N.format(t)+")")}),f(r?this.clone():this,t[0],t[1],e)},A.prototype.reshape=function(t,e){if(!O(t))throw new TypeError("Array expected");if(2!==t.length)throw new Error("Sparse matrices can only be reshaped in two dimensions");if(t.forEach(function(e){if(!S.isNumber(e)||!S.isInteger(e)||e<0)throw new TypeError("Invalid size, must contain positive integers (size: "+N.format(t)+")")}),this._size[0]*this._size[1]!=t[0]*t[1])throw new Error("Reshaping sparse matrix will result in the wrong number of elements");var r=e?this.clone():this;if(this._size[0]===t[0]&&this._size[1]===t[1])return r;for(var n=[],i=0;i<r._ptr.length;i++)for(var o=0;o<r._ptr[i+1]-r._ptr[i];o++)n.push(i);for(var a=r._values.slice(),s=r._index.slice(),u=0;u<r._index.length;u++){var c=s[u],f=n[u],l=c*r._size[1]+f;n[u]=l%t[1],s[u]=Math.floor(l/t[1])}r._values.length=0,r._index.length=0,r._ptr.length=t[1]+1,r._size=t.slice();for(var p=0;p<r._ptr.length;p++)r._ptr[p]=0;for(var m=0;m<a.length;m++){var h=s[m],d=n[m],y=a[m];v(g(h,r._ptr[d],r._ptr[d+1],r._index),h,d,y,r._values,r._index,r._ptr)}return r},A.prototype.clone=function(){return new A({values:this._values?w.clone(this._values):void 0,index:w.clone(this._index),ptr:w.clone(this._ptr),size:w.clone(this._size),datatype:this._datatype})},A.prototype.size=function(){return this._size.slice(0)},A.prototype.map=function(n,e){if(!this._values)throw new Error("Cannot invoke map on a Pattern only matrix");var i=this;return function(e,t,r,n,i,o,a){var s=[],u=[],c=[],f=E,l=0;C(e._datatype)&&(f=M.find(E,[e._datatype,e._datatype])||E,l=M.convert(0,e._datatype));for(var p=function(e,t,r){e=o(e,t,r),f(e,l)||(s.push(e),u.push(t))},m=n;m<=i;m++){c.push(s.length);var h=e._ptr[m],d=e._ptr[m+1];if(a)for(var y=h;y<d;y++){var g=e._index[y];t<=g&&g<=r&&p(e._values[y],g-t,m-n)}else{for(var v={},x=h;x<d;x++){var b=e._index[x];v[b]=e._values[x]}for(var w=t;w<=r;w++){var N=w in v?v[w]:0;p(N,w-t,m-n)}}}return c.push(s.length),new A({values:s,index:u,ptr:c,size:[r-t+1,i-n+1]})}(this,0,this._size[0]-1,0,this._size[1]-1,function(e,t,r){return n(e,[t,r],i)},e)},A.prototype.forEach=function(e,t){if(!this._values)throw new Error("Cannot invoke forEach on a Pattern only matrix");for(var r=this._size[0],n=this._size[1],i=0;i<n;i++){var o=this._ptr[i],a=this._ptr[i+1];if(t)for(var s=o;s<a;s++){var u=this._index[s];e(this._values[s],[u,i],this)}else{for(var c={},f=o;f<a;f++)c[this._index[f]]=this._values[f];for(var l=0;l<r;l++)e(l in c?c[l]:0,[l,i],this)}}},A.prototype.toArray=function(){return o(this._values,this._index,this._ptr,this._size,!0)},A.prototype.valueOf=function(){return o(this._values,this._index,this._ptr,this._size,!1)},A.prototype.format=function(e){for(var t=this._size[0],r=this._size[1],n=this.density(),i="Sparse Matrix ["+N.format(t,e)+" x "+N.format(r,e)+"] density: "+N.format(n,e)+"\n",o=0;o<r;o++)for(var a=this._ptr[o],s=this._ptr[o+1],u=a;u<s;u++){var c=this._index[u];i+="\n    ("+N.format(c,e)+", "+N.format(o,e)+") ==> "+(this._values?N.format(this._values[u],e):"X")}return i},A.prototype.toString=function(){return N.format(this.toArray())},A.prototype.toJSON=function(){return{mathjs:"SparseMatrix",values:this._values,index:this._index,ptr:this._ptr,size:this._size,datatype:this._datatype}},A.prototype.diagonal=function(e){if(e){if(b.isBigNumber(e)&&(e=e.toNumber()),!T(e)||!_(e))throw new TypeError("The parameter k must be an integer number")}else e=0;var t=0<e?e:0,r=e<0?-e:0,n=this._size[0],i=this._size[1],o=Math.min(n-r,i-t),a=[],s=[],u=[];u[0]=0;for(var c=t;c<i&&a.length<o;c++)for(var f=this._ptr[c],l=this._ptr[c+1],p=f;p<l;p++){var m=this._index[p];if(m===c-t+r){a.push(this._values[p]),s[a.length-1]=m-r;break}}return u.push(a.length),new A({values:a,index:s,ptr:u,size:[o,1]})},A.fromJSON=function(e){return new A(e)},A.diagonal=function(e,t,r,n,i){if(!O(e))throw new TypeError("Array expected, size parameter");if(2!==e.length)throw new Error("Only two dimensions matrix are supported");if(e=e.map(function(e){if(b.isBigNumber(e)&&(e=e.toNumber()),!T(e)||!_(e)||e<1)throw new Error("Size values must be positive integers");return e}),r){if(b.isBigNumber(r)&&(r=r.toNumber()),!T(r)||!_(r))throw new TypeError("The parameter k must be an integer number")}else r=0;var o=E,a=0;C(i)&&(o=M.find(E,[i,i])||E,a=M.convert(0,i));var s,u=0<r?r:0,c=r<0?-r:0,f=e[0],l=e[1],p=Math.min(f-c,l-u);if(O(t)){if(t.length!==p)throw new Error("Invalid value array length");s=function(e){return t[e]}}else if(b.isMatrix(t)){var m=t.size();if(1!==m.length||m[0]!==p)throw new Error("Invalid matrix length");s=function(e){return t.get([e])}}else s=function(){return t};for(var h=[],d=[],y=[],g=0;g<l;g++){y.push(h.length);var v=g-u;if(0<=v&&v<p){var x=s(v);o(x,a)||(d.push(v+c),h.push(x))}}return y.push(h.length),new A({values:h,index:d,ptr:y,size:[f,l]})},A.prototype.swapRows=function(e,t){if(!(T(e)&&_(e)&&T(t)&&_(t)))throw new Error("Row index must be positive integers");if(2!==this._size.length)throw new Error("Only two dimensional matrix is supported");return B(e,this._size[0]),B(t,this._size[0]),A._swapRows(e,t,this._size[1],this._values,this._index,this._ptr),this},A._forEachRow=function(e,t,r,n,i){for(var o=n[e],a=n[e+1],s=o;s<a;s++)i(r[s],t[s])},A._swapRows=function(e,t,r,n,i,o){for(var a=0;a<r;a++){var s=o[a],u=o[a+1],c=g(e,s,u,i),f=g(t,s,u,i);if(c<u&&f<u&&i[c]===e&&i[f]===t){if(n){var l=n[c];n[c]=n[f],n[f]=l}}else if(c<u&&i[c]===e&&(u<=f||i[f]!==t)){var p=n?n[c]:void 0;i.splice(f,0,t),n&&n.splice(f,0,p),i.splice(f<=c?c+1:c,1),n&&n.splice(f<=c?c+1:c,1)}else if(f<u&&i[f]===t&&(u<=c||i[c]!==e)){var m=n?n[f]:void 0;i.splice(c,0,e),n&&n.splice(c,0,m),i.splice(c<=f?f+1:f,1),n&&n.splice(c<=f?f+1:f,1)}}},b.Matrix._storage.sparse=A},t.lazy=!1},function(e,t,o){"use strict";t.name="Spa",t.path="type",t.factory=function(e,t,r){var n=r(o(14)),c=r(o(11));function i(){if(!(this instanceof i))throw new SyntaxError("Constructor must be called with the new operator");this._values=[],this._heap=new e.FibonacciHeap}return i.prototype.type="Spa",i.prototype.isSpa=!0,i.prototype.set=function(e,t){if(this._values[e])this._values[e].value=t;else{var r=this._heap.insert(e,t);this._values[e]=r}},i.prototype.get=function(e){var t=this._values[e];return t?t.value:0},i.prototype.accumulate=function(e,t){var r=this._values[e];r?r.value=n(r.value,t):(r=this._heap.insert(e,t),this._values[e]=r)},i.prototype.forEach=function(e,t,r){var n=this._heap,i=this._values,o=[],a=n.extractMinimum();for(a&&o.push(a);a&&a.key<=t;)a.key>=e&&(c(a.value,0)||r(a.key,a.value,this)),(a=n.extractMinimum())&&o.push(a);for(var s=0;s<o.length;s++){var u=o[s];i[(a=n.insert(u.key,u.value)).key]=a}},i.prototype.swap=function(e,t){var r=this._values[e],n=this._values[t];if(!r&&n)r=this._heap.insert(e,n.value),this._heap.remove(n),this._values[e]=r,this._values[t]=void 0;else if(r&&!n)n=this._heap.insert(t,r.value),this._heap.remove(r),this._values[t]=n,this._values[e]=void 0;else if(r&&n){var i=r.value;r.value=n.value,n.value=i}},i}},function(e,t,a){"use strict";t.name="FibonacciHeap",t.path="type",t.factory=function(e,t,r,n){var l=r(a(38)),p=r(a(33)),m=1/Math.log((1+Math.sqrt(5))/2);function i(){if(!(this instanceof i))throw new SyntaxError("Constructor must be called with the new operator");this._minimum=null,this._size=0}function o(e,t,r){t.left.right=t.right,t.right.left=t.left,r.degree--,r.child===t&&(r.child=t.right),0===r.degree&&(r.child=null),t.left=e,t.right=e.right,((e.right=t).right.left=t).parent=null,t.mark=!1}i.prototype.type="FibonacciHeap",i.prototype.isFibonacciHeap=!0,i.prototype.insert=function(e,t){var r={key:e,value:t,degree:0};if(this._minimum){var n=this._minimum;r.left=n,r.right=n.right,(n.right=r).right.left=r,l(e,n.key)&&(this._minimum=r)}else(r.left=r).right=r,this._minimum=r;return this._size++,r},i.prototype.size=function(){return this._size},i.prototype.clear=function(){this._minimum=null,this._size=0},i.prototype.isEmpty=function(){return 0===this._size},i.prototype.extractMinimum=function(){var e=this._minimum;if(null===e)return e;for(var t=this._minimum,r=e.degree,n=e.child;0<r;){var i=n.right;n.left.right=n.right,n.right.left=n.left,n.left=t,n.right=t.right,((t.right=n).right.left=n).parent=null,n=i,r--}return e.left.right=e.right,e.right.left=e.left,t=e===e.right?null:function(e,t){var r,n=Math.floor(Math.log(t)*m)+1,i=new Array(n),o=0,a=e;if(a)for(o++,a=a.right;a!==e;)o++,a=a.right;for(;0<o;){for(var s=a.degree,u=a.right;r=i[s];){if(p(a.key,r.key)){var c=r;r=a,a=c}h(r,a),i[s]=null,s++}i[s]=a,a=u,o--}e=null;for(var f=0;f<n;f++)(r=i[f])&&(e?(r.left.right=r.right,r.right.left=r.left,r.left=e,r.right=e.right,(e.right=r).right.left=r,l(r.key,e.key)&&(e=r)):e=r);return e}(t=e.right,this._size),this._size--,this._minimum=t,e},i.prototype.remove=function(e){this._minimum=function(e,t,r){t.key=r;var n=t.parent;return n&&l(t.key,n.key)&&(o(e,t,n),function e(t,r){var n=r.parent;n&&(r.mark?(o(t,r,n),e(n)):r.mark=!0)}(e,n)),l(t.key,e.key)&&(e=t),e}(this._minimum,e,-1),this.extractMinimum()};var h=function(e,t){e.left.right=e.right,e.right.left=e.left,(e.parent=t).child?(e.left=t.child,e.right=t.child.right,(t.child.right=e).right.left=e):((t.child=e).right=e).left=e,t.degree++,e.mark=!1};return i}},function(e,t,a){"use strict";var s=a(31),r=s.string,u=s.object,c=Array.isArray,f=r.isString;t.name="ImmutableDenseMatrix",t.path="type",t.factory=function(n,e,t){var i=t(a(49)),r=t(a(38));function o(e,t){if(!(this instanceof o))throw new SyntaxError("Constructor must be called with the new operator");if(t&&!f(t))throw new Error("Invalid datatype: "+t);if(n.isMatrix(e)||c(e)){var r=new i(e,t);this._data=r._data,this._size=r._size,this._datatype=r._datatype,this._min=null,this._max=null}else if(e&&c(e.data)&&c(e.size))this._data=e.data,this._size=e.size,this._datatype=e.datatype,this._min=void 0!==e.min?e.min:null,this._max=void 0!==e.max?e.max:null;else{if(e)throw new TypeError("Unsupported type of data ("+s.types.type(e)+")");this._data=[],this._size=[0],this._datatype=t,this._min=null,this._max=null}}return(o.prototype=new i).type="ImmutableDenseMatrix",o.prototype.isImmutableDenseMatrix=!0,o.prototype.subset=function(e){switch(arguments.length){case 1:var t=i.prototype.subset.call(this,e);return n.isMatrix(t)?new o({data:t._data,size:t._size,datatype:t._datatype}):t;case 2:case 3:throw new Error("Cannot invoke set subset on an Immutable Matrix instance");default:throw new SyntaxError("Wrong number of arguments")}},o.prototype.set=function(){throw new Error("Cannot invoke set on an Immutable Matrix instance")},o.prototype.resize=function(){throw new Error("Cannot 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Matrix A is decomposed in three matrices (L, U, P) where P * A = L * U",examples:["lup([[2, 1], [1, 4]])","lup(matrix([[2, 1], [1, 4]]))","lup(sparse([[2, 1], [1, 4]]))"],seealso:["lusolve","lsolve","usolve","matrix","sparse","slu","qr"]}},function(e,t){e.exports={name:"lusolve",category:"Algebra",syntax:["x=lusolve(A, b)","x=lusolve(lu, b)"],description:"Solves the linear system A * x = b where A is an [n x n] matrix and b is a [n] column vector.",examples:["a = [-2, 3; 2, 1]","b = [11, 9]","x = lusolve(a, b)"],seealso:["lup","slu","lsolve","usolve","matrix","sparse"]}},function(e,t){e.exports={name:"simplify",category:"Algebra",syntax:["simplify(expr)","simplify(expr, rules)"],description:"Simplify an expression tree.",examples:['simplify("3 + 2 / 4")','simplify("2x + x")','f = parse("x * (x + 2 + x)")',"simplified = simplify(f)","simplified.eval({x: 2})"],seealso:["derivative","parse","eval"]}},function(e,t){e.exports={name:"rationalize",category:"Algebra",syntax:["rationalize(expr)","rationalize(expr, scope)","rationalize(expr, scope, detailed)"],description:"Transform a rationalizable expression in a rational fraction. If rational fraction is one variable polynomial then converts the numerator and denominator in canonical form, with decreasing exponents, returning the coefficients of numerator.",examples:['rationalize("2x/y - y/(x+1)")','rationalize("2x/y - y/(x+1)", true)'],seealso:["simplify"]}},function(e,t){e.exports={name:"slu",category:"Algebra",syntax:["slu(A, order, threshold)"],description:"Calculate the Matrix LU decomposition with full pivoting. Matrix A is decomposed in two matrices (L, U) and two permutation vectors (pinv, q) where P * A * Q = L * U",examples:["slu(sparse([4.5, 0, 3.2, 0; 3.1, 2.9, 0, 0.9; 0, 1.7, 3, 0; 3.5, 0.4, 0, 1]), 1, 0.001)"],seealso:["lusolve","lsolve","usolve","matrix","sparse","lup","qr"]}},function(e,t){e.exports={name:"usolve",category:"Algebra",syntax:["x=usolve(U, b)"],description:"Solves the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.",examples:["x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])"],seealso:["lup","lusolve","lsolve","matrix","sparse"]}},function(e,t){e.exports={name:"qr",category:"Algebra",syntax:["qr(A)"],description:"Calculates the Matrix QR decomposition. Matrix `A` is decomposed in two matrices (`Q`, `R`) where `Q` is an orthogonal matrix and `R` is an upper triangular matrix.",examples:["qr([[1, -1,  4], [1,  4, -2], [1,  4,  2], [1,  -1, 0]])"],seealso:["lup","slu","matrix"]}},function(e,t){e.exports={name:"abs",category:"Arithmetic",syntax:["abs(x)"],description:"Compute the absolute value.",examples:["abs(3.5)","abs(-4.2)"],seealso:["sign"]}},function(e,t){e.exports={name:"add",category:"Operators",syntax:["x + y","add(x, y)"],description:"Add two values.",examples:["a = 2.1 + 3.6","a - 3.6","3 + 2i","3 cm + 2 inch",'"2.3" + "4"'],seealso:["subtract"]}},function(e,t){e.exports={name:"cbrt",category:"Arithmetic",syntax:["cbrt(x)","cbrt(x, allRoots)"],description:"Compute the cubic root value. If x = y * y * y, then y is the cubic root of x. When `x` is a number or complex number, an optional second argument `allRoots` can be provided to return all three cubic roots. If not provided, the principal root is returned",examples:["cbrt(64)","cube(4)","cbrt(-8)","cbrt(2 + 3i)","cbrt(8i)","cbrt(8i, true)","cbrt(27 m^3)"],seealso:["square","sqrt","cube","multiply"]}},function(e,t){e.exports={name:"ceil",category:"Arithmetic",syntax:["ceil(x)"],description:"Round a value towards plus infinity. If x is complex, both real and imaginary part are rounded towards plus infinity.",examples:["ceil(3.2)","ceil(3.8)","ceil(-4.2)"],seealso:["floor","fix","round"]}},function(e,t){e.exports={name:"cube",category:"Arithmetic",syntax:["cube(x)"],description:"Compute the cube of a value. The cube of x is x * x * x.",examples:["cube(2)","2^3","2 * 2 * 2"],seealso:["multiply","square","pow"]}},function(e,t){e.exports={name:"divide",category:"Operators",syntax:["x / y","divide(x, y)"],description:"Divide two values.",examples:["a = 2 / 3","a * 3","4.5 / 2","3 + 4 / 2","(3 + 4) / 2","18 km / 4.5"],seealso:["multiply"]}},function(e,t){e.exports={name:"dotDivide",category:"Operators",syntax:["x ./ y","dotDivide(x, y)"],description:"Divide two values element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","b = [2, 1, 1; 3, 2, 5]","a ./ b"],seealso:["multiply","dotMultiply","divide"]}},function(e,t){e.exports={name:"dotMultiply",category:"Operators",syntax:["x .* y","dotMultiply(x, y)"],description:"Multiply two values element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","b = [2, 1, 1; 3, 2, 5]","a .* b"],seealso:["multiply","divide","dotDivide"]}},function(e,t){e.exports={name:"dotpow",category:"Operators",syntax:["x .^ y","dotpow(x, y)"],description:"Calculates the power of x to y element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","a .^ 2"],seealso:["pow"]}},function(e,t){e.exports={name:"exp",category:"Arithmetic",syntax:["exp(x)"],description:"Calculate the exponent of a value.",examples:["exp(1.3)","e ^ 1.3","log(exp(1.3))","x = 2.4","(exp(i*x) == cos(x) + i*sin(x))   # Euler's formula"],seealso:["expm","expm1","pow","log"]}},function(e,t){e.exports={name:"expm",category:"Arithmetic",syntax:["exp(x)"],description:"Compute the matrix exponential, expm(A) = e^A. 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This is the same as calculating `log(x, 2)`.",examples:["log2(0.03125)","log2(16)","log2(16) / log2(2)","pow(2, 4)"],seealso:["exp","log1p","log","log10"]}},function(e,t){e.exports={name:"log1p",category:"Arithmetic",syntax:["log1p(x)","log1p(x, base)"],description:"Calculate the logarithm of a `value+1`",examples:["log1p(2.5)","exp(log1p(1.4))","pow(10, 4)","log1p(9999, 10)","log1p(9999) / log(10)"],seealso:["exp","log","log2","log10"]}},function(e,t){e.exports={name:"log10",category:"Arithmetic",syntax:["log10(x)"],description:"Compute the 10-base logarithm of a value.",examples:["log10(0.00001)","log10(10000)","10 ^ 4","log(10000) / log(10)","log(10000, 10)"],seealso:["exp","log"]}},function(e,t){e.exports={name:"mod",category:"Operators",syntax:["x % y","x mod y","mod(x, y)"],description:"Calculates the modulus, the remainder of an integer division.",examples:["7 % 3","11 % 2","10 mod 4","isOdd(x) = x % 2","isOdd(2)","isOdd(3)"],seealso:["divide"]}},function(e,t){e.exports={name:"multiply",category:"Operators",syntax:["x * y","multiply(x, y)"],description:"multiply two values.",examples:["a = 2.1 * 3.4","a / 3.4","2 * 3 + 4","2 * (3 + 4)","3 * 2.1 km"],seealso:["divide"]}},function(e,t){e.exports={name:"norm",category:"Arithmetic",syntax:["norm(x)","norm(x, p)"],description:"Calculate the norm of a number, vector or matrix.",examples:["abs(-3.5)","norm(-3.5)","norm(3 - 4i)","norm([1, 2, -3], Infinity)","norm([1, 2, -3], -Infinity)","norm([3, 4], 2)","norm([[1, 2], [3, 4]], 1)",'norm([[1, 2], [3, 4]], "inf")','norm([[1, 2], [3, 4]], "fro")']}},function(e,t){e.exports={name:"nthRoot",category:"Arithmetic",syntax:["nthRoot(a)","nthRoot(a, root)"],description:'Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation "x^root = A".',examples:["4 ^ 3","nthRoot(64, 3)","nthRoot(9, 2)","sqrt(9)"],seealso:["nthRoots","pow","sqrt"]}},function(e,t){e.exports={name:"nthRoots",category:"Arithmetic",syntax:["nthRoots(A)","nthRoots(A, root)"],description:'Calculate the nth roots of a value. An nth root of a positive real number A, is a positive real solution of the equation "x^root = A". This function returns an array of complex values.',examples:["nthRoots(1)","nthRoots(1, 3)"],seealso:["sqrt","pow","nthRoot"]}},function(e,t){e.exports={name:"pow",category:"Operators",syntax:["x ^ y","pow(x, y)"],description:"Calculates the power of x to y, x^y.",examples:["2^3","2*2*2","1 + e ^ (pi * i)"],seealso:["multiply","nthRoot","nthRoots","sqrt"]}},function(e,t){e.exports={name:"round",category:"Arithmetic",syntax:["round(x)","round(x, n)"],description:"round a value towards the nearest integer.If x is complex, both real and imaginary part are rounded towards the nearest integer. When n is specified, the value is rounded to n decimals.",examples:["round(3.2)","round(3.8)","round(-4.2)","round(-4.8)","round(pi, 3)","round(123.45678, 2)"],seealso:["ceil","floor","fix"]}},function(e,t){e.exports={name:"sign",category:"Arithmetic",syntax:["sign(x)"],description:"Compute the sign of a value. The sign of a value x is 1 when x>1, -1 when x<0, and 0 when x=0.",examples:["sign(3.5)","sign(-4.2)","sign(0)"],seealso:["abs"]}},function(e,t){e.exports={name:"sqrt",category:"Arithmetic",syntax:["sqrt(x)"],description:"Compute the square root value. If x = y * y, then y is the square root of x.",examples:["sqrt(25)","5 * 5","sqrt(-1)"],seealso:["square","sqrtm","multiply","nthRoot","nthRoots","pow"]}},function(e,t){e.exports={name:"sqrtm",category:"Arithmetic",syntax:["sqrtm(x)"],description:"Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.",examples:["sqrtm([[1, 2], [3, 4]])"],seealso:["sqrt","abs","square","multiply"]}},function(e,t){e.exports={name:"square",category:"Arithmetic",syntax:["square(x)"],description:"Compute the square of a value. The square of x is x * x.",examples:["square(3)","sqrt(9)","3^2","3 * 3"],seealso:["multiply","pow","sqrt","cube"]}},function(e,t){e.exports={name:"subtract",category:"Operators",syntax:["x - y","subtract(x, y)"],description:"subtract two values.",examples:["a = 5.3 - 2","a + 2","2/3 - 1/6","2 * 3 - 3","2.1 km - 500m"],seealso:["add"]}},function(e,t){e.exports={name:"unaryMinus",category:"Operators",syntax:["-x","unaryMinus(x)"],description:"Inverse the sign of a value. Converts booleans and strings to numbers.",examples:["-4.5","-(-5.6)",'-"22"'],seealso:["add","subtract","unaryPlus"]}},function(e,t){e.exports={name:"unaryPlus",category:"Operators",syntax:["+x","unaryPlus(x)"],description:"Converts booleans and strings to numbers.",examples:["+true",'+"2"'],seealso:["add","subtract","unaryMinus"]}},function(e,t){e.exports={name:"xgcd",category:"Arithmetic",syntax:["xgcd(a, b)"],description:"Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.",examples:["xgcd(8, 12)","gcd(8, 12)","xgcd(36163, 21199)"],seealso:["gcd","lcm"]}},function(e,t){e.exports={name:"bitAnd",category:"Bitwise",syntax:["x & y","bitAnd(x, y)"],description:"Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0",examples:["5 & 3","bitAnd(53, 131)","[1, 12, 31] & 42"],seealso:["bitNot","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]}},function(e,t){e.exports={name:"bitNot",category:"Bitwise",syntax:["~x","bitNot(x)"],description:"Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.",examples:["~1","~2","bitNot([2, -3, 4])"],seealso:["bitAnd","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]}},function(e,t){e.exports={name:"bitOr",category:"Bitwise",syntax:["x | y","bitOr(x, y)"],description:"Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.",examples:["5 | 3","bitOr([1, 2, 3], 4)"],seealso:["bitAnd","bitNot","bitXor","leftShift","rightArithShift","rightLogShift"]}},function(e,t){e.exports={name:"bitXor",category:"Bitwise",syntax:["bitXor(x, y)"],description:"Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.",examples:["bitOr(1, 2)","bitXor([2, 3, 4], 4)"],seealso:["bitAnd","bitNot","bitOr","leftShift","rightArithShift","rightLogShift"]}},function(e,t){e.exports={name:"leftShift",category:"Bitwise",syntax:["x << y","leftShift(x, y)"],description:"Bitwise left logical shift of a value x by y number of bits.",examples:["4 << 1","8 >> 1"],seealso:["bitAnd","bitNot","bitOr","bitXor","rightArithShift","rightLogShift"]}},function(e,t){e.exports={name:"rightArithShift",category:"Bitwise",syntax:["x >> y","rightArithShift(x, y)"],description:"Bitwise right arithmetic shift of a value x by y number of bits.",examples:["8 >> 1","4 << 1","-12 >> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightLogShift"]}},function(e,t){e.exports={name:"rightLogShift",category:"Bitwise",syntax:["x >>> y","rightLogShift(x, y)"],description:"Bitwise right logical shift of a value x by y number of bits.",examples:["8 >>> 1","4 << 1","-12 >>> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightArithShift"]}},function(e,t){e.exports={name:"bellNumbers",category:"Combinatorics",syntax:["bellNumbers(n)"],description:"The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["bellNumbers(3)","bellNumbers(8)"],seealso:["stirlingS2"]}},function(e,t){e.exports={name:"catalan",category:"Combinatorics",syntax:["catalan(n)"],description:"The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["catalan(3)","catalan(8)"],seealso:["bellNumbers"]}},function(e,t){e.exports={name:"composition",category:"Combinatorics",syntax:["composition(n, k)"],description:"The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.",examples:["composition(5, 3)"],seealso:["combinations"]}},function(e,t){e.exports={name:"stirlingS2",category:"Combinatorics",syntax:["stirlingS2(n, k)"],description:"he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.",examples:["stirlingS2(5, 3)"],seealso:["bellNumbers"]}},function(e,t){e.exports={name:"config",category:"Core",syntax:["config()","config(options)"],description:"Get configuration or change configuration.",examples:["config()","1/3 + 1/4",'config({number: "Fraction"})',"1/3 + 1/4"],seealso:[]}},function(e,t){e.exports={name:"import",category:"Core",syntax:["import(functions)","import(functions, options)"],description:"Import functions or constants from an object.",examples:["import({myFn: f(x)=x^2, myConstant: 32 })","myFn(2)","myConstant"],seealso:[]}},function(e,t){e.exports={name:"typed",category:"Core",syntax:["typed(signatures)","typed(name, signatures)"],description:"Create a typed function.",examples:['double = typed({ "number, number": f(x)=x+x })',"double(2)",'double("hello")'],seealso:[]}},function(e,t){e.exports={name:"arg",category:"Complex",syntax:["arg(x)"],description:"Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).",examples:["arg(2 + 2i)","atan2(3, 2)","arg(2 + 3i)"],seealso:["re","im","conj","abs"]}},function(e,t){e.exports={name:"conj",category:"Complex",syntax:["conj(x)"],description:"Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.",examples:["conj(2 + 3i)","conj(2 - 3i)","conj(-5.2i)"],seealso:["re","im","abs","arg"]}},function(e,t){e.exports={name:"re",category:"Complex",syntax:["re(x)"],description:"Get the real part of a complex number.",examples:["re(2 + 3i)","im(2 + 3i)","re(-5.2i)","re(2.4)"],seealso:["im","conj","abs","arg"]}},function(e,t){e.exports={name:"im",category:"Complex",syntax:["im(x)"],description:"Get the imaginary part of a complex number.",examples:["im(2 + 3i)","re(2 + 3i)","im(-5.2i)","im(2.4)"],seealso:["re","conj","abs","arg"]}},function(e,t){e.exports={name:"eval",category:"Expression",syntax:["eval(expression)","eval([expr1, expr2, expr3, ...])"],description:"Evaluate an expression or an array with expressions.",examples:['eval("2 + 3")','eval("sqrt(" + 4 + ")")'],seealso:[]}},function(e,t){e.exports={name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]}},function(e,t){e.exports={name:"distance",category:"Geometry",syntax:["distance([x1, y1], [x2, y2])","distance([[x1, y1], [x2, y2])"],description:"Calculates the Euclidean distance between two points.",examples:["distance([0,0], [4,4])","distance([[0,0], [4,4]])"],seealso:[]}},function(e,t){e.exports={name:"intersect",category:"Geometry",syntax:["intersect(expr1, expr2, expr3, expr4)","intersect(expr1, expr2, expr3)"],description:"Computes the intersection point of lines and/or planes.",examples:["intersect([0, 0], [10, 10], [10, 0], [0, 10])","intersect([1, 0, 1],  [4, -2, 2], [1, 1, 1, 6])"],seealso:[]}},function(e,t){e.exports={name:"and",category:"Logical",syntax:["x and y","and(x, y)"],description:"Logical and. Test whether two values are both defined with a nonzero/nonempty value.",examples:["true and false","true and true","2 and 4"],seealso:["not","or","xor"]}},function(e,t){e.exports={name:"not",category:"Logical",syntax:["not x","not(x)"],description:"Logical not. Flips the boolean value of given argument.",examples:["not true","not false","not 2","not 0"],seealso:["and","or","xor"]}},function(e,t){e.exports={name:"or",category:"Logical",syntax:["x or y","or(x, y)"],description:"Logical or. Test if at least one value is defined with a nonzero/nonempty value.",examples:["true or false","false or false","0 or 4"],seealso:["not","and","xor"]}},function(e,t){e.exports={name:"xor",category:"Logical",syntax:["x xor y","xor(x, y)"],description:"Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.",examples:["true xor false","false xor false","true xor true","0 xor 4"],seealso:["not","and","or"]}},function(e,t){e.exports={name:"concat",category:"Matrix",syntax:["concat(A, B, C, ...)","concat(A, B, C, ..., dim)"],description:"Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.",examples:["A = [1, 2; 5, 6]","B = [3, 4; 7, 8]","concat(A, B)","concat(A, B, 1)","concat(A, B, 2)"],seealso:["det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={name:"cross",category:"Matrix",syntax:["cross(A, B)"],description:"Calculate the cross product for two vectors in three dimensional space.",examples:["cross([1, 1, 0],  [0, 1, 1])","cross([3, -3, 1], [4, 9, 2])","cross([2, 3, 4],  [5, 6, 7])"],seealso:["multiply","dot"]}},function(e,t){e.exports={name:"transpose",category:"Matrix",syntax:["x'","ctranspose(x)"],description:"Complex Conjugate and Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","ctranspose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]}},function(e,t){e.exports={name:"det",category:"Matrix",syntax:["det(x)"],description:"Calculate the determinant of a matrix",examples:["det([1, 2; 3, 4])","det([-2, 2, 3; -1, 1, 3; 2, 0, -1])"],seealso:["concat","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={name:"diag",category:"Matrix",syntax:["diag(x)","diag(x, k)"],description:"Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.",examples:["diag(1:3)","diag(1:3, 1)","a = [1, 2, 3; 4, 5, 6; 7, 8, 9]","diag(a)"],seealso:["concat","det","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={name:"dot",category:"Matrix",syntax:["dot(A, B)","A * B"],description:"Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn",examples:["dot([2, 4, 1], [2, 2, 3])","[2, 4, 1] * [2, 2, 3]"],seealso:["multiply","cross"]}},function(e,t){e.exports={name:"getMatrixDataType",category:"Matrix",syntax:["getMatrixDataType(x)"],description:'Find the data type of all elements in a matrix or array, for example "number" if all items are a number and "Complex" if all values are complex numbers. If a matrix contains more than one data type, it will return "mixed".',examples:["getMatrixDataType([1, 2, 3])","getMatrixDataType([[5 cm], [2 inch]])",'getMatrixDataType([1, "text"])',"getMatrixDataType([1, bignumber(4)])"],seealso:["matrix","sparse","typeof"]}},function(e,t){e.exports={name:"identity",category:"Matrix",syntax:["identity(n)","identity(m, n)","identity([m, n])"],description:"Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.",examples:["identity(3)","identity(3, 5)","a = [1, 2, 3; 4, 5, 6]","identity(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={name:"filter",category:"Matrix",syntax:["filter(x, test)"],description:"Filter items in a matrix.",examples:["isPositive(x) = x > 0","filter([6, -2, -1, 4, 3], isPositive)","filter([6, -2, 0, 1, 0], x != 0)"],seealso:["sort","map","forEach"]}},function(e,t){e.exports={name:"flatten",category:"Matrix",syntax:["flatten(x)"],description:"Flatten a multi dimensional matrix into a single dimensional matrix.",examples:["a = [1, 2, 3; 4, 5, 6]","size(a)","b = flatten(a)","size(b)"],seealso:["concat","resize","size","squeeze"]}},function(e,t){e.exports={name:"forEach",category:"Matrix",syntax:["forEach(x, callback)"],description:"Iterates over all elements of a matrix/array, and executes the given callback function.",examples:["forEach([1, 2, 3], function(val) { console.log(val) })"],seealso:["map","sort","filter"]}},function(e,t){e.exports={name:"inv",category:"Matrix",syntax:["inv(x)"],description:"Calculate the inverse of a matrix",examples:["inv([1, 2; 3, 4])","inv(4)","1 / 4"],seealso:["concat","det","diag","identity","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={name:"kron",category:"Matrix",syntax:["kron(x, y)"],description:"Calculates the kronecker product of 2 matrices or vectors.",examples:["kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])","kron([1,1], [2,3,4])"],seealso:["multiply","dot","cross"]}},function(e,t){e.exports={name:"map",category:"Matrix",syntax:["map(x, callback)"],description:"Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.",examples:["map([1, 2, 3], square)"],seealso:["filter","forEach"]}},function(e,t){e.exports={name:"ones",category:"Matrix",syntax:["ones(m)","ones(m, n)","ones(m, n, p, ...)","ones([m])","ones([m, n])","ones([m, n, p, ...])"],description:"Create a matrix containing ones.",examples:["ones(3)","ones(3, 5)","ones([2,3]) * 4.5","a = [1, 2, 3; 4, 5, 6]","ones(size(a))"],seealso:["concat","det","diag","identity","inv","range","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={name:"partitionSelect",category:"Matrix",syntax:["partitionSelect(x, k)","partitionSelect(x, k, compare)"],description:"Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.",examples:["partitionSelect([5, 10, 1], 2)",'partitionSelect(["C", "B", "A", "D"], 1)'],seealso:["sort"]}},function(e,t){e.exports={name:"range",category:"Type",syntax:["start:end","start:step:end","range(start, end)","range(start, end, step)","range(string)"],description:"Create a range. Lower bound of the range is included, upper bound is excluded.",examples:["1:5","3:-1:-3","range(3, 7)","range(0, 12, 2)",'range("4:10")',"a = [1, 2, 3, 4; 5, 6, 7, 8]","a[1:2, 1:2]"],seealso:["concat","det","diag","identity","inv","ones","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={name:"resize",category:"Matrix",syntax:["resize(x, size)","resize(x, size, defaultValue)"],description:"Resize a matrix.",examples:["resize([1,2,3,4,5], [3])","resize([1,2,3], [5])","resize([1,2,3], [5], -1)","resize(2, [2, 3])",'resize("hello", [8], "!")'],seealso:["size","subset","squeeze","reshape"]}},function(e,t){e.exports={name:"reshape",category:"Matrix",syntax:["reshape(x, sizes)"],description:"Reshape a multi dimensional array to fit the specified dimensions.",examples:["reshape([1, 2, 3, 4, 5, 6], [2, 3])","reshape([[1, 2], [3, 4]], [1, 4])","reshape([[1, 2], [3, 4]], [4])"],seealso:["size","squeeze","resize"]}},function(e,t){e.exports={name:"size",category:"Matrix",syntax:["size(x)"],description:"Calculate the size of a matrix.",examples:["size(2.3)",'size("hello world")',"a = [1, 2; 3, 4; 5, 6]","size(a)","size(1:6)"],seealso:["concat","det","diag","identity","inv","ones","range","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={name:"sort",category:"Matrix",syntax:["sort(x)","sort(x, compare)"],description:'Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.',examples:["sort([5, 10, 1])",'sort(["C", "B", "A", "D"])',"sortByLength(a, b) = size(a)[1] - size(b)[1]",'sort(["Langdon", "Tom", "Sara"], sortByLength)','sort(["10", "1", "2"], "natural")'],seealso:["map","filter","forEach"]}},function(e,t){e.exports={name:"squeeze",category:"Matrix",syntax:["squeeze(x)"],description:"Remove inner and outer singleton dimensions from a matrix.",examples:["a = zeros(3,2,1)","size(squeeze(a))","b = zeros(1,1,3)","size(squeeze(b))"],seealso:["concat","det","diag","identity","inv","ones","range","size","subset","trace","transpose","zeros"]}},function(e,t){e.exports={name:"subset",category:"Matrix",syntax:["value(index)","value(index) = replacement","subset(value, [index])","subset(value, [index], replacement)"],description:"Get or set a subset of a matrix or string. Indexes are one-based. Both the ranges lower-bound and upper-bound are included.",examples:["d = [1, 2; 3, 4]","e = []","e[1, 1:2] = [5, 6]","e[2, :] = [7, 8]","f = d * e","f[2, 1]","f[:, 1]"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","trace","transpose","zeros"]}},function(e,t){e.exports={name:"trace",category:"Matrix",syntax:["trace(A)"],description:"Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.",examples:["A = [1, 2, 3; -1, 2, 3; 2, 0, 3]","trace(A)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","transpose","zeros"]}},function(e,t){e.exports={name:"transpose",category:"Matrix",syntax:["x'","transpose(x)"],description:"Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","transpose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]}},function(e,t){e.exports={name:"zeros",category:"Matrix",syntax:["zeros(m)","zeros(m, n)","zeros(m, n, p, ...)","zeros([m])","zeros([m, n])","zeros([m, n, p, ...])"],description:"Create a matrix containing zeros.",examples:["zeros(3)","zeros(3, 5)","a = [1, 2, 3; 4, 5, 6]","zeros(size(a))"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose"]}},function(e,t){e.exports={name:"combinations",category:"Probability",syntax:["combinations(n, k)"],description:"Compute the number of combinations of n items taken k at a time",examples:["combinations(7, 5)"],seealso:["permutations","factorial"]}},function(e,t){e.exports={name:"factorial",category:"Probability",syntax:["n!","factorial(n)"],description:"Compute the factorial of a value",examples:["5!","5 * 4 * 3 * 2 * 1","3!"],seealso:["combinations","permutations","gamma"]}},function(e,t){e.exports={name:"gamma",category:"Probability",syntax:["gamma(n)"],description:"Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.",examples:["gamma(4)","3!","gamma(1/2)","sqrt(pi)"],seealso:["factorial"]}},function(e,t){e.exports={name:"kldivergence",category:"Probability",syntax:["kldivergence(x, y)"],description:"Calculate the Kullback-Leibler (KL) divergence  between two distributions.",examples:["kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])"],seealso:[]}},function(e,t){e.exports={name:"multinomial",category:"Probability",syntax:["multinomial(A)"],description:"Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.",examples:["multinomial([1, 2, 1])"],seealso:["combinations","factorial"]}},function(e,t){e.exports={name:"permutations",category:"Probability",syntax:["permutations(n)","permutations(n, k)"],description:"Compute the number of permutations of n items taken k at a time",examples:["permutations(5)","permutations(5, 3)"],seealso:["combinations","factorial"]}},function(e,t){e.exports={name:"pickRandom",category:"Probability",syntax:["pickRandom(array)","pickRandom(array, number)","pickRandom(array, weights)","pickRandom(array, number, weights)","pickRandom(array, weights, number)"],description:"Pick a random entry from a given array.",examples:["pickRandom(0:10)","pickRandom([1, 3, 1, 6])","pickRandom([1, 3, 1, 6], 2)","pickRandom([1, 3, 1, 6], [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)"],seealso:["random","randomInt"]}},function(e,t){e.exports={name:"random",category:"Probability",syntax:["random()","random(max)","random(min, max)","random(size)","random(size, max)","random(size, min, max)"],description:"Return a random number.",examples:["random()","random(10, 20)","random([2, 3])"],seealso:["pickRandom","randomInt"]}},function(e,t){e.exports={name:"randomInt",category:"Probability",syntax:["randomInt(max)","randomInt(min, max)","randomInt(size)","randomInt(size, max)","randomInt(size, min, max)"],description:"Return a random integer number",examples:["randomInt(10, 20)","randomInt([2, 3], 10)"],seealso:["pickRandom","random"]}},function(e,t){e.exports={name:"compare",category:"Relational",syntax:["compare(x, y)"],description:"Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compare(2, 3)","compare(3, 2)","compare(2, 2)","compare(5cm, 40mm)","compare(2, [1, 2, 3])"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compareNatural","compareText"]}},function(e,t){e.exports={name:"compareNatural",category:"Relational",syntax:["compareNatural(x, y)"],description:"Compare two values of any type in a deterministic, natural way. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compareNatural(2, 3)","compareNatural(3, 2)","compareNatural(2, 2)","compareNatural(5cm, 40mm)",'compareNatural("2", "10")',"compareNatural(2 + 3i, 2 + 4i)","compareNatural([1, 2, 4], [1, 2, 3])","compareNatural([1, 5], [1, 2, 3])","compareNatural([1, 2], [1, 2])","compareNatural({a: 2}, {a: 4})"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare","compareText"]}},function(e,t){e.exports={name:"compareText",category:"Relational",syntax:["compareText(x, y)"],description:"Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:['compareText("B", "A")','compareText("A", "B")','compareText("A", "A")','compareText("2", "10")','compare("2", "10")',"compare(2, 10)",'compareNatural("2", "10")','compareText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural"]}},function(e,t){e.exports={name:"deepEqual",category:"Relational",syntax:["deepEqual(x, y)"],description:"Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.",examples:["deepEqual([1,3,4], [1,3,4])","deepEqual([1,3,4], [1,3])"],seealso:["equal","unequal","smaller","larger","smallerEq","largerEq","compare"]}},function(e,t){e.exports={name:"equal",category:"Relational",syntax:["x == y","equal(x, y)"],description:"Check equality of two values. Returns true if the values are equal, and false if not.",examples:["2+2 == 3","2+2 == 4","a = 3.2","b = 6-2.8","a == b","50cm == 0.5m"],seealso:["unequal","smaller","larger","smallerEq","largerEq","compare","deepEqual","equalText"]}},function(e,t){e.exports={name:"equalText",category:"Relational",syntax:["equalText(x, y)"],description:"Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.",examples:['equalText("Hello", "Hello")','equalText("a", "A")','equal("2e3", "2000")','equalText("2e3", "2000")','equalText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural","compareText","equal"]}},function(e,t){e.exports={name:"larger",category:"Relational",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns true if x is larger than y, and false if not.",examples:["2 > 3","5 > 2*2","a = 3.3","b = 6-2.8","(a > b)","(b < a)","5 cm > 2 inch"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare"]}},function(e,t){e.exports={name:"largerEq",category:"Relational",syntax:["x >= y","largerEq(x, y)"],description:"Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.",examples:["2 >= 1+1","2 > 1+1","a = 3.2","b = 6-2.8","(a >= b)"],seealso:["equal","unequal","smallerEq","smaller","compare"]}},function(e,t){e.exports={name:"smaller",category:"Relational",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not.",examples:["2 < 3","5 < 2*2","a = 3.3","b = 6-2.8","(a < b)","5 cm < 2 inch"],seealso:["equal","unequal","larger","smallerEq","largerEq","compare"]}},function(e,t){e.exports={name:"smallerEq",category:"Relational",syntax:["x <= y","smallerEq(x, y)"],description:"Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.",examples:["2 <= 1+1","2 < 1+1","a = 3.2","b = 6-2.8","(a <= b)"],seealso:["equal","unequal","larger","smaller","largerEq","compare"]}},function(e,t){e.exports={name:"unequal",category:"Relational",syntax:["x != y","unequal(x, y)"],description:"Check unequality of two values. Returns true if the values are unequal, and false if they are equal.",examples:["2+2 != 3","2+2 != 4","a = 3.2","b = 6-2.8","a != b","50cm != 0.5m","5 cm != 2 inch"],seealso:["equal","smaller","larger","smallerEq","largerEq","compare","deepEqual"]}},function(e,t){e.exports={name:"setCartesian",category:"Set",syntax:["setCartesian(set1, set2)"],description:"Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setCartesian([1, 2], [3, 4])"],seealso:["setUnion","setIntersect","setDifference","setPowerset"]}},function(e,t){e.exports={name:"setDifference",category:"Set",syntax:["setDifference(set1, set2)"],description:"Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setDifference([1, 2, 3, 4], [3, 4, 5, 6])","setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setSymDifference"]}},function(e,t){e.exports={name:"setDistinct",category:"Set",syntax:["setDistinct(set)"],description:"Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setDistinct([1, 1, 1, 2, 2, 3])"],seealso:["setMultiplicity"]}},function(e,t){e.exports={name:"setIntersect",category:"Set",syntax:["setIntersect(set1, set2)"],description:"Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIntersect([1, 2, 3, 4], [3, 4, 5, 6])","setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setDifference"]}},function(e,t){e.exports={name:"setIsSubset",category:"Set",syntax:["setIsSubset(set1, set2)"],description:"Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIsSubset([1, 2], [3, 4, 5, 6])","setIsSubset([3, 4], [3, 4, 5, 6])"],seealso:["setUnion","setIntersect","setDifference"]}},function(e,t){e.exports={name:"setMultiplicity",category:"Set",syntax:["setMultiplicity(element, set)"],description:"Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setMultiplicity(1, [1, 2, 2, 4])","setMultiplicity(2, [1, 2, 2, 4])"],seealso:["setDistinct","setSize"]}},function(e,t){e.exports={name:"setPowerset",category:"Set",syntax:["setPowerset(set)"],description:"Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setPowerset([1, 2, 3])"],seealso:["setCartesian"]}},function(e,t){e.exports={name:"setSize",category:"Set",syntax:["setSize(set)","setSize(set, unique)"],description:'Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',examples:["setSize([1, 2, 2, 4])","setSize([1, 2, 2, 4], true)"],seealso:["setUnion","setIntersect","setDifference"]}},function(e,t){e.exports={name:"setSymDifference",category:"Set",syntax:["setSymDifference(set1, set2)"],description:"Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])","setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setDifference"]}},function(e,t){e.exports={name:"setUnion",category:"Set",syntax:["setUnion(set1, set2)"],description:"Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setUnion([1, 2, 3, 4], [3, 4, 5, 6])","setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setIntersect","setDifference"]}},function(e,t){e.exports={name:"erf",category:"Special",syntax:["erf(x)"],description:"Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x",examples:["erf(0.2)","erf(-0.5)","erf(4)"],seealso:[]}},function(e,t){e.exports={name:"mad",category:"Statistics",syntax:["mad(a, b, c, ...)","mad(A)"],description:"Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.",examples:["mad(10, 20, 30)","mad([1, 2, 3])"],seealso:["mean","median","std","abs"]}},function(e,t){e.exports={name:"max",category:"Statistics",syntax:["max(a, b, c, ...)","max(A)","max(A, dim)"],description:"Compute the maximum value of a list of values.",examples:["max(2, 3, 4, 1)","max([2, 3, 4, 1])","max([2, 5; 4, 3])","max([2, 5; 4, 3], 1)","max([2, 5; 4, 3], 2)","max(2.7, 7.1, -4.5, 2.0, 4.1)","min(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["mean","median","min","prod","std","sum","var"]}},function(e,t){e.exports={name:"mean",category:"Statistics",syntax:["mean(a, b, c, ...)","mean(A)","mean(A, dim)"],description:"Compute the arithmetic mean of a list of values.",examples:["mean(2, 3, 4, 1)","mean([2, 3, 4, 1])","mean([2, 5; 4, 3])","mean([2, 5; 4, 3], 1)","mean([2, 5; 4, 3], 2)","mean([1.0, 2.7, 3.2, 4.0])"],seealso:["max","median","min","prod","std","sum","var"]}},function(e,t){e.exports={name:"median",category:"Statistics",syntax:["median(a, b, c, ...)","median(A)"],description:"Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.",examples:["median(5, 2, 7)","median([3, -1, 5, 7])"],seealso:["max","mean","min","prod","std","sum","var","quantileSeq"]}},function(e,t){e.exports={name:"min",category:"Statistics",syntax:["min(a, b, c, ...)","min(A)","min(A, dim)"],description:"Compute the minimum value of a list of values.",examples:["min(2, 3, 4, 1)","min([2, 3, 4, 1])","min([2, 5; 4, 3])","min([2, 5; 4, 3], 1)","min([2, 5; 4, 3], 2)","min(2.7, 7.1, -4.5, 2.0, 4.1)","max(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["max","mean","median","prod","std","sum","var"]}},function(e,t){e.exports={name:"mode",category:"Statistics",syntax:["mode(a, b, c, ...)","mode(A)","mode(A, a, b, B, c, ...)"],description:"Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.",examples:["mode(2, 1, 4, 3, 1)","mode([1, 2.7, 3.2, 4, 2.7])","mode(1, 4, 6, 1, 6)"],seealso:["max","mean","min","median","prod","std","sum","var"]}},function(e,t){e.exports={name:"prod",category:"Statistics",syntax:["prod(a, b, c, ...)","prod(A)"],description:"Compute the product of all values.",examples:["prod(2, 3, 4)","prod([2, 3, 4])","prod([2, 5; 4, 3])"],seealso:["max","mean","min","median","min","std","sum","var"]}},function(e,t){e.exports={name:"quantileSeq",category:"Statistics",syntax:["quantileSeq(A, prob[, sorted])","quantileSeq(A, [prob1, prob2, ...][, sorted])","quantileSeq(A, N[, sorted])"],description:"Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probablity are: Number, BigNumber. \n\nIn case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.",examples:["quantileSeq([3, -1, 5, 7], 0.5)","quantileSeq([3, -1, 5, 7], [1/3, 2/3])","quantileSeq([3, -1, 5, 7], 2)","quantileSeq([-1, 3, 5, 7], 0.5, true)"],seealso:["mean","median","min","max","prod","std","sum","var"]}},function(e,t){e.exports={name:"std",category:"Statistics",syntax:["std(a, b, c, ...)","std(A)","std(A, normalization)"],description:'Compute the standard deviation of all values, defined as std(A) = sqrt(var(A)). Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["std(2, 4, 6)","std([2, 4, 6, 8])",'std([2, 4, 6, 8], "uncorrected")','std([2, 4, 6, 8], "biased")',"std([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","min","prod","sum","var"]}},function(e,t){e.exports={name:"sum",category:"Statistics",syntax:["sum(a, b, c, ...)","sum(A)"],description:"Compute the sum of all values.",examples:["sum(2, 3, 4, 1)","sum([2, 3, 4, 1])","sum([2, 5; 4, 3])"],seealso:["max","mean","median","min","prod","std","sum","var"]}},function(e,t){e.exports={name:"var",category:"Statistics",syntax:["var(a, b, c, ...)","var(A)","var(A, normalization)"],description:'Compute the variance of all values. Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["var(2, 4, 6)","var([2, 4, 6, 8])",'var([2, 4, 6, 8], "uncorrected")','var([2, 4, 6, 8], "biased")',"var([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","min","prod","std","sum"]}},function(e,t){e.exports={name:"acos",category:"Trigonometry",syntax:["acos(x)"],description:"Compute the inverse cosine of a value in radians.",examples:["acos(0.5)","acos(cos(2.3))"],seealso:["cos","atan","asin"]}},function(e,t){e.exports={name:"acosh",category:"Trigonometry",syntax:["acosh(x)"],description:"Calculate the hyperbolic arccos of a value, defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.",examples:["acosh(1.5)"],seealso:["cosh","asinh","atanh"]}},function(e,t){e.exports={name:"acot",category:"Trigonometry",syntax:["acot(x)"],description:"Calculate the inverse cotangent of a value.",examples:["acot(0.5)","acot(cot(0.5))","acot(2)"],seealso:["cot","atan"]}},function(e,t){e.exports={name:"acoth",category:"Trigonometry",syntax:["acoth(x)"],description:"Calculate the hyperbolic arccotangent of a value, defined as `acoth(x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.",examples:["acoth(2)","acoth(0.5)"],seealso:["acsch","asech"]}},function(e,t){e.exports={name:"acsc",category:"Trigonometry",syntax:["acsc(x)"],description:"Calculate the inverse cotangent of a value.",examples:["acsc(2)","acsc(csc(0.5))","acsc(0.5)"],seealso:["csc","asin","asec"]}},function(e,t){e.exports={name:"acsch",category:"Trigonometry",syntax:["acsch(x)"],description:"Calculate the hyperbolic arccosecant of a value, defined as `acsch(x) = ln(1/x + sqrt(1/x^2 + 1))`.",examples:["acsch(0.5)"],seealso:["asech","acoth"]}},function(e,t){e.exports={name:"asec",category:"Trigonometry",syntax:["asec(x)"],description:"Calculate the inverse secant of a value.",examples:["asec(0.5)","asec(sec(0.5))","asec(2)"],seealso:["acos","acot","acsc"]}},function(e,t){e.exports={name:"asech",category:"Trigonometry",syntax:["asech(x)"],description:"Calculate the inverse secant of a value.",examples:["asech(0.5)"],seealso:["acsch","acoth"]}},function(e,t){e.exports={name:"asin",category:"Trigonometry",syntax:["asin(x)"],description:"Compute the inverse sine of a value in radians.",examples:["asin(0.5)","asin(sin(0.5))"],seealso:["sin","acos","atan"]}},function(e,t){e.exports={name:"asinh",category:"Trigonometry",syntax:["asinh(x)"],description:"Calculate the hyperbolic arcsine of a value, defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.",examples:["asinh(0.5)"],seealso:["acosh","atanh"]}},function(e,t){e.exports={name:"atan",category:"Trigonometry",syntax:["atan(x)"],description:"Compute the inverse tangent of a value in radians.",examples:["atan(0.5)","atan(tan(0.5))"],seealso:["tan","acos","asin"]}},function(e,t){e.exports={name:"atanh",category:"Trigonometry",syntax:["atanh(x)"],description:"Calculate the hyperbolic arctangent of a value, defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.",examples:["atanh(0.5)"],seealso:["acosh","asinh"]}},function(e,t){e.exports={name:"atan2",category:"Trigonometry",syntax:["atan2(y, x)"],description:"Computes the principal value of the arc tangent of y/x in radians.",examples:["atan2(2, 2) / pi","angle = 60 deg in rad","x = cos(angle)","y = sin(angle)","atan2(y, x)"],seealso:["sin","cos","tan"]}},function(e,t){e.exports={name:"cos",category:"Trigonometry",syntax:["cos(x)"],description:"Compute the cosine of x in radians.",examples:["cos(2)","cos(pi / 4) ^ 2","cos(180 deg)","cos(60 deg)","sin(0.2)^2 + cos(0.2)^2"],seealso:["acos","sin","tan"]}},function(e,t){e.exports={name:"cosh",category:"Trigonometry",syntax:["cosh(x)"],description:"Compute the hyperbolic cosine of x in radians.",examples:["cosh(0.5)"],seealso:["sinh","tanh","coth"]}},function(e,t){e.exports={name:"cot",category:"Trigonometry",syntax:["cot(x)"],description:"Compute the cotangent of x in radians. Defined as 1/tan(x)",examples:["cot(2)","1 / tan(2)"],seealso:["sec","csc","tan"]}},function(e,t){e.exports={name:"coth",category:"Trigonometry",syntax:["coth(x)"],description:"Compute the hyperbolic cotangent of x in radians.",examples:["coth(2)","1 / tanh(2)"],seealso:["sech","csch","tanh"]}},function(e,t){e.exports={name:"csc",category:"Trigonometry",syntax:["csc(x)"],description:"Compute the cosecant of x in radians. Defined as 1/sin(x)",examples:["csc(2)","1 / sin(2)"],seealso:["sec","cot","sin"]}},function(e,t){e.exports={name:"csch",category:"Trigonometry",syntax:["csch(x)"],description:"Compute the hyperbolic cosecant of x in radians. Defined as 1/sinh(x)",examples:["csch(2)","1 / sinh(2)"],seealso:["sech","coth","sinh"]}},function(e,t){e.exports={name:"sec",category:"Trigonometry",syntax:["sec(x)"],description:"Compute the secant of x in radians. Defined as 1/cos(x)",examples:["sec(2)","1 / cos(2)"],seealso:["cot","csc","cos"]}},function(e,t){e.exports={name:"sech",category:"Trigonometry",syntax:["sech(x)"],description:"Compute the hyperbolic secant of x in radians. Defined as 1/cosh(x)",examples:["sech(2)","1 / cosh(2)"],seealso:["coth","csch","cosh"]}},function(e,t){e.exports={name:"sin",category:"Trigonometry",syntax:["sin(x)"],description:"Compute the sine of x in radians.",examples:["sin(2)","sin(pi / 4) ^ 2","sin(90 deg)","sin(30 deg)","sin(0.2)^2 + cos(0.2)^2"],seealso:["asin","cos","tan"]}},function(e,t){e.exports={name:"sinh",category:"Trigonometry",syntax:["sinh(x)"],description:"Compute the hyperbolic sine of x in radians.",examples:["sinh(0.5)"],seealso:["cosh","tanh"]}},function(e,t){e.exports={name:"tan",category:"Trigonometry",syntax:["tan(x)"],description:"Compute the tangent of x in radians.",examples:["tan(0.5)","sin(0.5) / cos(0.5)","tan(pi / 4)","tan(45 deg)"],seealso:["atan","sin","cos"]}},function(e,t){e.exports={name:"tanh",category:"Trigonometry",syntax:["tanh(x)"],description:"Compute the hyperbolic tangent of x in radians.",examples:["tanh(0.5)","sinh(0.5) / cosh(0.5)"],seealso:["sinh","cosh"]}},function(e,t){e.exports={name:"to",category:"Units",syntax:["x to unit","to(x, unit)"],description:"Change the unit of a value.",examples:["5 inch to cm","3.2kg to g","16 bytes in bits"],seealso:[]}},function(e,t){e.exports={name:"clone",category:"Utils",syntax:["clone(x)"],description:"Clone a variable. 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diff --git a/00_blog/00040_Haskell/00220_Neural-Networks/neuroticus.html b/00_blog/00040_Haskell/00220_Neural-Networks/neuroticus.html
new file mode 100644
index 0000000..e63196d
--- /dev/null
+++ b/00_blog/00040_Haskell/00220_Neural-Networks/neuroticus.html
@@ -0,0 +1,181 @@
+<!DOCTYPE html>
+<html lang="en">
+    <head>
+      	<meta charset="UTF-8" />
+          <script src="math.min.js" type="text/javascript"></script>
+    </head>
+    <body>
+        
+        <div style="margin:auto;width:320px;">
+        <h1> N e U r O t I c U s </h1>
+        <p>
+        A simple feedforward neural network running in Javascript. It was trained in Haskell on the MNIST Dataset. 
+        You can read more about this little project <a href="index.html">here</a>.
+        </p>
+        <p>Press <b>rand simpl.</b> to cycle randomly through 100 test samples, then press <b> ask neuro</b> to fire the neuro net</p>
+        </div>
+        <div style="margin:auto;width:280px;"> <!--<button onclick="cleanCanv()">Clean</button>--> <button onclick="askNet()">Ask Neuro</button> <button onclick="rndSmpl()">rand smpl.</button></div>
+        <canvas id="canvasInAPerfectWorld" width="280" height="280" style="display:block;margin:auto;border:3px solid black;"></canvas>
+        <div style="margin:auto;width:280px;"> <!--<button onclick="cleanCanv()">Clean</button>--> <button onclick="askNet()">Ask Neuro</button> <button onclick="rndSmpl()">rand smpl.</button></div>
+        <div id="outp" style="margin:auto;width:280px;"></div>
+        <div style="margin:auto;width:280px;margin-top:10px;"><hr />hacked together by <a href="https://www.idziorek.net">miguel</a> on 23rd Mar 2019.</div>
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+   ,[   3.0152536268987657,   -1.768819489748337,  2.6840470390474955, -0.6937304887273016,  -4.6997514308880355,   0.6564302564485156, -2.2370714302892587,   4.065890382036308, -3.7550850487507943,  -0.6927602223370888,    2.612377750170405,  0.3581326019355834,  -2.390724471032244,   2.0593091032509396,    -3.651832908730063,  0.4950643540939668,    -2.41901052068881,  -2.445594681511396, -2.6787899401309883,  3.2805394739444638,   1.4265608228224793,  -1.2422991451495746, -3.8166655673993075,  0.7551304974680245, -1.8397614654267695,  -1.8391046547865348,   -3.862649346993681,    0.5389653795520633,  -6.495370635982221,  0.4411849295737402 ]
+   ,[   0.8740335414751595,  -0.5747844418499032, 0.12347691053264598,   4.267889396736106,  -2.5916172747485335,    1.358861085121812,  -3.390680887353097, -3.8674324438433327,  0.4057762580221447,   -4.613039316341899, -0.31446725487779653,  -1.688945549148426,  -5.065571317899549,  -1.4989416137169185,    0.6777393821687536,  0.9930679303169044,  -0.9350483001152696,   -5.32758578006543, 0.12347310816819795,  0.7248904341859621,  -0.4153481357115005,     7.03449483430138,  3.1238154177673043, -1.9130637670757287,  3.7606015264975987, -0.19073679872715343,   1.1139014156144673,   0.39133353568162227, -3.8741491968104533,  -2.203636328215666 ]
+   ,[   2.6520105644300984,  0.38464033327928265, -0.6649550651263968,  1.9367366623291158,    5.364803872048157, -0.29854351240485266, -0.2632748704161152, -2.6033129882952943,  -1.845142264123316,    -0.65454724981816,   -5.459385057993004, -2.2309622850632174,  2.3040635204416198,  -1.9430136636616877,   -2.6067895513465618,  -0.357804476362298,    0.689880390529237, -1.2854996080383956, -2.8153824586316576,  2.5024530051872067,   -2.117525066879449,  -1.7245277462749329,  -5.722669200181782,   2.492839455538656,  0.7841565568203629,    1.318653447141769,  -1.9847108179117507,   -2.3065110441535674,   6.076938248551628,  2.8318046385014064 ]
+   ,[  -1.6709924284919644,  -0.9663630073418923,  0.5844135636968599, -1.1330995881446064,   2.8609177095645193,  -3.4256068964137585, -1.6942698875266295,  -4.113079754051621,  2.3011887917466223,   -2.708325670595643,   1.8798179711963379,  1.3927352783473963, -1.4826842333092483,  -0.6009145421358238,   -2.4804471993273505,  2.7832141135341963,   1.3632702166218051,  -3.593517041615111,   4.529859734335387, -1.2901412825065792,   -2.497831855755299,  -2.4493128493733485,  0.2245440514335598, -2.4138021523224493, -1.4707391795625582,  0.29367702102457666,  0.35696537669436845,     3.491034580592242,  2.8192214566331346,   -2.98595755311592 ]
+   ,[   1.5529804718531854, -0.24635985759786794,   0.678161102628826,   2.486198820195804,  0.15924074692018977,   4.3135137499114125,  -7.592139994625877,   5.086794383480168,   2.304956931869405,    1.533237178179708,  -0.3494033842487449,  2.8076797987223507,   3.934251567943248,   3.2064054962717874, 4.5020602390229175e-2,  0.6532935689583343,  -0.6353663667261286,  -6.761978210201565,   2.570064606051503, -0.6359106364046679, -0.32206614817735485,  0.12970497074616205,    4.43599201788948, -1.6143158409079594,  -3.734509094574477,   -1.285873687550009,   1.5776615138364067,   0.46034354697235624,  1.7346082695248215,  1.4421237144287347 ]
+   ,[   -2.445183776335705,   1.3534218400182683, -1.9521382505454812,  -2.106418426774921,  -3.6839709862586236,   3.9005512634032296, -3.4804595397202163, -3.4786070401545315,  -2.910358951325745, -0.27032745582197376,   1.5070735083509057, -2.9579280958966496, -2.6037841169870863, 7.434514216855644e-3,    -2.933547242400761,    5.84726991177822,  -1.4533441248625618, -3.1913369289740263,   3.055469713428449,  -2.760579667647416,   -2.634824331870147,   1.5435316228687375,  -2.970464493602326,  -4.500612661172782,  -4.914281876271146,   2.0241667181145657, -0.21746546954764992,  5.752456513860073e-2, -2.6272032781798913,   1.998850719789653 ]
+   ,[  0.35328267184306206,   1.2997752239604499, -0.7130470671124841,  -6.538209735654815,  -3.0464259012480506,   1.5957149950044396, -2.3918785161176914,  -5.690202833294665,  -4.362055515086487,    5.632842355862257,  -1.3996719228941163,  1.0444767595454572, -4.1700691122916895,   0.2555688014799678,   -0.7400251233847023,  -2.085464032654301,   1.2099805125704204,  -4.132206845762882,  -2.742560185537445,   1.865640165977124,   9.4423576662463e-2,     0.69558302021461,   3.449157684481115, -1.3225196176906227,   3.653058570674245,   1.6763527691049536,  -0.7603255290291382,   -0.7060331305130817, -0.7859244191924831,   2.976472400229503 ]];
+
+ b2=[-4.210458192745416,-0.3198620559445251,-2.268919221342209,-4.251761663692756,-4.39203765214934,-2.0417124706303276,-3.8262587025357746,-6.712722134146137,-4.53584022534966,-5.0421173349804125];
+
+            var mouseIsDown = false;
+            function getContext(){
+                return document.getElementById('canvasInAPerfectWorld').getContext("2d");
+            }
+
+            function getMousePos(canvas, evt) {
+                var rect = canvas.getBoundingClientRect();
+                return {
+                x: evt.clientX - rect.left,
+                y: evt.clientY - rect.top
+                };
+            }
+
+
+            function rndSmpl(){
+                cleanCanv();
+                ctx=getContext();
+                r=Math.floor((Math.random() * 100));
+                sam=samp[r];
+                p=0;
+                for(j=0;j<28;j++)
+                for(i=0;i<28;i++)
+                {
+                        c=sam[p];
+                        c*=255;
+                        c=255-c;
+                        c+=c*256+c*256*256;
+                        p++;
+                        
+                        ctx.fillStyle=('#' + c.toString(16).padStart(6, '0'));
+                        ctx.fillRect(10*i, 10*j, 10, 10); 
+                }
+            }
+
+
+            function cleanCanv(){
+                ctx=getContext();
+                for(i=0;i<28;i++)
+                    for(j=0;j<28;j++)
+                        {
+                            if((i+j)%2==0)ctx.fillStyle="#eeeeff";
+                            else ctx.fillStyle="#ccccff";
+                            ctx.fillRect(10*i, 10*j, 10, 10); 
+                        }
+            }
+
+            function askNet(){
+                ctx=getContext();
+                var arr=[];
+                var imgd = ctx.getImageData(0, 0, 280, 280);
+                var pix = imgd.data;
+                for(j=0;j<28;j++)
+                for(i=0;i<28;i++)
+                    {
+                        c=0;
+                        for(ii=0;ii<10;ii++)
+                            for(jj=0;jj<10;jj++)
+                                if(pix[((i*10+ii)*4+(j*10+jj)*280*4)]<200)c++;
+                       
+                        if(c<20)c=0;
+                        else c=100;
+                        arr.push(c/100);
+                        c=255-c*255/100;
+                        c+=256*c+256*256*c;
+                        ctx.fillStyle=('#' + c.toString(16).padStart(6, '0'));
+                        ctx.fillRect(10*i, 10*j, 10, 10); 
+                    }
+
+                inp=math.matrix(arr);
+                //alert (inp);
+
+                m1=math.matrix(w1);
+                v1=math.matrix(b1);
+                m2=math.matrix(w2);
+                v2=math.matrix(b2);
+
+                outp=math.multiply(m1,inp);
+                outp=math.add(outp,v1);
+                outp=outp.map(function (value,index,matrix){return 1/(1+math.exp(-value));});
+                outp=math.multiply(m2,outp);
+                outp=math.add(outp,v2);
+                outp=outp.map(function (value,index,matrix){return 1/(1+math.exp(-value));});
+                max=0;
+                ans=0;
+                for(i=0;i<10;i++)
+                {
+
+                    if(outp.valueOf()[i]>max){
+                        max=outp.valueOf()[i];
+                        ans=i;
+                    }
+                }
+
+                document.getElementById("outp").innerHTML = "<p>I think this is a <b>" + ans + "</b><br/><i>confid.:"+max+"</i></p>";
+            }
+
+            cnv=document.getElementById('canvasInAPerfectWorld');
+            cnv.onmousedown = function(e){mouseIsDown = true;}
+            cnv.onmouseup   = function(e){mouseIsDown = false;}
+            cnv.onmousemove=function(e){
+                    ctx=getContext();
+                    if(!mouseIsDown)return;
+                    ctx.fillStyle="#222222";
+                    pos=getMousePos(this,e)
+                //    ctx.fillRect(pos.x, pos.y, 25,25); 
+            }
+
+            rndSmpl();
+        </script>
+    </body>
+</html>