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Use function bignumber(x) to convert to BigNumber.");return new r(e)}},{from:"number",to:"Complex",convert:function(e){return n||f(e),new n(e,0)}},{from:"number",to:"string",convert:function(e){return e+""}},{from:"BigNumber",to:"Complex",convert:function(e){return n||f(e),new n(e.toNumber(),0)}},{from:"Fraction",to:"BigNumber",convert:function(){throw new TypeError("Cannot implicitly convert a Fraction to BigNumber or vice versa. Use function bignumber(x) to convert to BigNumber or fraction(x) to convert to Fraction.")}},{from:"Fraction",to:"Complex",convert:function(e){return n||f(e),new n(e.valueOf(),0)}},{from:"number",to:"Fraction",convert:function(e){i||l(e);var t=new i(e);if(t.valueOf()!==e)throw new TypeError("Cannot implicitly convert a number to a Fraction when there will be a loss of precision (value: "+e+"). Use function fraction(x) to convert to Fraction.");return t}},{from:"string",to:"number",convert:function(e){var t=Number(e);if(isNaN(t))throw new Error('Cannot convert "'+e+'" to a number');return t}},{from:"string",to:"BigNumber",convert:function(t){r||c(t);try{return new r(t)}catch(e){throw new Error('Cannot convert "'+t+'" to BigNumber')}}},{from:"string",to:"Fraction",convert:function(t){i||l(t);try{return new i(t)}catch(e){throw new Error('Cannot convert "'+t+'" to Fraction')}}},{from:"string",to:"Complex",convert:function(t){n||f(t);try{return new n(t)}catch(e){throw new Error('Cannot convert "'+t+'" to Complex')}}},{from:"boolean",to:"number",convert:function(e){return+e}},{from:"boolean",to:"BigNumber",convert:function(e){return r||c(e),new r(+e)}},{from:"boolean",to:"Fraction",convert:function(e){return i||l(e),new i(+e)}},{from:"boolean",to:"string",convert:function(e){return String(e)}},{from:"Array",to:"Matrix",convert:function(e){return t||function(){throw new Error("Cannot convert array into a Matrix: no class 'DenseMatrix' provided")}(),new t(e)}},{from:"Matrix",to:"Array",convert:function(e){return e.valueOf()}}],a});function c(e){throw new Error("Cannot convert value ".concat(e," into a BigNumber: no class 'BigNumber' provided"))}function f(e){throw new Error("Cannot convert value ".concat(e," into a Complex number: no class 'Complex' provided"))}function l(e){throw new Error("Cannot convert value ".concat(e," into a Fraction, no class 'Fraction' provided."))}var p=[],m=Object(s.a)("ResultSet",p,function(){function t(e){if(!(this instanceof t))throw new SyntaxError("Constructor must be called with the new operator");this.entries=e||[]}return t.prototype.type="ResultSet",t.prototype.isResultSet=!0,t.prototype.valueOf=function(){return this.entries},t.prototype.toString=function(){return"["+this.entries.join(", ")+"]"},t.prototype.toJSON=function(){return{mathjs:"ResultSet",entries:this.entries}},t.fromJSON=function(e){return new t(e.entries)},t},{isClass:!0}),h=r(15),d=r.n(h),y=["?on","config"],g=Object(s.a)("BigNumber",y,function(e){var t=e.on,r=e.config,n=d.a.clone({precision:r.precision});return n.prototype.type="BigNumber",n.prototype.isBigNumber=!0,n.prototype.toJSON=function(){return{mathjs:"BigNumber",value:this.toString()}},n.fromJSON=function(e){return new n(e.value)},t&&t("config",function(e,t){e.precision!==t.precision&&n.config({precision:e.precision})}),n},{isClass:!0}),b=r(8),v=r.n(b);function x(e){return(x="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator?function(e){return typeof e}:function(e){return e&&"function"==typeof Symbol&&e.constructor===Symbol&&e!==Symbol.prototype?"symbol":typeof e})(e)}var w=[],N=Object(s.a)("Complex",w,function(){return v.a.prototype.type="Complex",v.a.prototype.isComplex=!0,v.a.prototype.toJSON=function(){return{mathjs:"Complex",re:this.re,im:this.im}},v.a.prototype.toPolar=function(){return{r:this.abs(),phi:this.arg()}},v.a.prototype.format=function(e){var t,r=this.im,n=this.re,i=Object(E.h)(this.re,e),a=Object(E.h)(this.im,e),o=Object(ie.y)(e)?e:e?e.precision:null;return null!==o&&(t=Math.pow(10,-o),Math.abs(n/r)<t&&(n=0),Math.abs(r/n)<t&&(r=0)),0===r?i:0===n?1===r?"i":-1===r?"-i":a+"i":r<0?-1===r?i+" - i":i+" - "+a.substring(1)+"i":1===r?i+" + i":i+" + "+a+"i"},v.a.fromPolar=function(e){switch(arguments.length){case 1:var t=e;if("object"===x(t))return v()(t);throw new TypeError("Input has to be an object with r and phi keys.");case 2:var r=e,n=arguments[1];if(Object(ie.y)(r)){if(Object(ie.L)(n)&&n.hasBase("ANGLE")&&(n=n.toNumber("rad")),Object(ie.y)(n))return new v.a({r:r,phi:n});throw new TypeError("Phi is not a number nor an angle unit.")}throw new TypeError("Radius r is not a number.");default:throw new SyntaxError("Wrong number of arguments in function fromPolar")}},v.a.prototype.valueOf=v.a.prototype.toString,v.a.fromJSON=function(e){return new v.a(e)},v.a.compare=function(e,t){return e.re>t.re?1:e.re<t.re?-1:e.im>t.im?1:e.im<t.im?-1:0},v.a},{isClass:!0}),O=r(10),M=r.n(O),j=[],S=Object(s.a)("Fraction",j,function(){return M.a.prototype.type="Fraction",M.a.prototype.isFraction=!0,M.a.prototype.toJSON=function(){return{mathjs:"Fraction",n:this.s*this.n,d:this.d}},M.a.fromJSON=function(e){return new M.a(e)},M.a},{isClass:!0}),A=[],C=Object(s.a)("Range",A,function(){function o(e,t,r){if(!(this instanceof o))throw new SyntaxError("Constructor must be called with the new operator");var n=null!=e,i=null!=t,a=null!=r;if(n)if(Object(ie.e)(e))e=e.toNumber();else if("number"!=typeof e)throw new TypeError("Parameter start must be a number");if(i)if(Object(ie.e)(t))t=t.toNumber();else if("number"!=typeof t)throw new TypeError("Parameter end must be a 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0<e?0<this.step?this.start+(e-1)*this.step:this.start:void 0},o.prototype.forEach=function(e){var t=this.start,r=this.step,n=this.end,i=0;if(0<r)for(;t<n;)e(t,[i],this),t+=r,i++;else if(r<0)for(;n<t;)e(t,[i],this),t+=r,i++},o.prototype.map=function(n){var i=[];return this.forEach(function(e,t,r){i[t[0]]=n(e,t,r)}),i},o.prototype.toArray=function(){var r=[];return this.forEach(function(e,t){r[t[0]]=e}),r},o.prototype.valueOf=function(){return this.toArray()},o.prototype.format=function(e){var t=Object(E.h)(this.start,e);return 1!==this.step&&(t+=":"+Object(E.h)(this.step,e)),t+=":"+Object(E.h)(this.end,e)},o.prototype.toString=function(){return this.format()},o.prototype.toJSON=function(){return{mathjs:"Range",start:this.start,end:this.end,step:this.step}},o.fromJSON=function(e){return new o(e.start,e.end,e.step)},o},{isClass:!0}),T=[],_=Object(s.a)("Matrix",T,function(){function e(){if(!(this instanceof e))throw new SyntaxError("Constructor must be called with the new operator")}return e.prototype.type="Matrix",e.prototype.isMatrix=!0,e.prototype.storage=function(){throw new Error("Cannot invoke storage on a Matrix interface")},e.prototype.datatype=function(){throw new Error("Cannot invoke datatype on a Matrix interface")},e.prototype.create=function(e,t){throw new Error("Cannot invoke create on a Matrix interface")},e.prototype.subset=function(e,t,r){throw new Error("Cannot invoke subset on a Matrix interface")},e.prototype.get=function(e){throw new Error("Cannot invoke get on a Matrix interface")},e.prototype.set=function(e,t,r){throw new Error("Cannot invoke set on a Matrix interface")},e.prototype.resize=function(e,t){throw new Error("Cannot invoke resize on a Matrix interface")},e.prototype.reshape=function(e,t){throw new Error("Cannot invoke reshape on a Matrix interface")},e.prototype.clone=function(){throw new Error("Cannot invoke clone on a Matrix interface")},e.prototype.size=function(){throw new Error("Cannot invoke size on a Matrix interface")},e.prototype.map=function(e,t){throw new Error("Cannot invoke map on a Matrix interface")},e.prototype.forEach=function(e){throw new Error("Cannot invoke forEach on a Matrix interface")},e.prototype.toArray=function(){throw new Error("Cannot invoke toArray on a Matrix interface")},e.prototype.valueOf=function(){throw new Error("Cannot invoke valueOf on a Matrix interface")},e.prototype.format=function(e){throw new Error("Cannot invoke format on a Matrix interface")},e.prototype.toString=function(){throw new Error("Cannot invoke toString on a Matrix interface")},e},{isClass:!0}),q=r(2),V=r(5),ae=r(3),z=r(6),I=["Matrix"],k=Object(s.a)("DenseMatrix",I,function(e){var t=e.Matrix;function m(e,t){if(!(this instanceof m))throw new SyntaxError("Constructor must be called with the new operator");if(t&&!Object(ie.I)(t))throw new Error("Invalid datatype: "+t);if(Object(ie.v)(e))"DenseMatrix"===e.type?(this._data=Object(ae.a)(e._data),this._size=Object(ae.a)(e._size)):(this._data=e.toArray(),this._size=e.size()),this._datatype=t||e._datatype;else if(e&&Object(ie.b)(e.data)&&Object(ie.b)(e.size))this._data=e.data,this._size=e.size,Object(q.p)(this._data,this._size),this._datatype=t||e.datatype;else if(Object(ie.b)(e))this._data=function e(t){for(var r=0,n=t.length;r<n;r++){var i=t[r];Object(ie.b)(i)?t[r]=e(i):i&&!0===i.isMatrix&&(t[r]=e(i.valueOf()))}return t}(e),this._size=Object(q.a)(this._data),Object(q.p)(this._data,this._size),this._datatype=t;else{if(e)throw new TypeError("Unsupported type of data ("+Object(ie.M)(e)+")");this._data=[],this._size=[0],this._datatype=t}}function s(e,t,r){if(0!==t.length)return e._size=t.slice(0),e._data=Object(q.m)(e._data,e._size,r),e;for(var n=e._data;Object(ie.b)(n);)n=n[0];return n}function l(e,t,r){for(var n=e._size.slice(0),i=!1;n.length<t.length;)n.push(0),i=!0;for(var a=0,o=t.length;a<o;a++)t[a]>n[a]&&(n[a]=t[a],i=!0);i&&s(e,n,r)}return(m.prototype=new t).createDenseMatrix=function(e,t){return new m(e,t)},m.prototype.type="DenseMatrix",m.prototype.isDenseMatrix=!0,m.prototype.getDataType=function(){return Object(q.h)(this._data,ie.M)},m.prototype.storage=function(){return"dense"},m.prototype.datatype=function(){return this._datatype},m.prototype.create=function(e,t){return new m(e,t)},m.prototype.subset=function(e,t,r){switch(arguments.length){case 1:return function(e,t){if(!Object(ie.t)(t))throw new TypeError("Invalid index");{if(t.isScalar())return e.get(t.min());var r=t.size();if(r.length!==e._size.length)throw new z.a(r.length,e._size.length);for(var n=t.min(),i=t.max(),a=0,o=e._size.length;a<o;a++)Object(q.q)(n[a],e._size[a]),Object(q.q)(i[a],e._size[a]);return new m(function r(n,i,a,o){var e=o===a-1;var t=i.dimension(o);return e?t.map(function(e){return Object(q.q)(e,n.length),n[e]}).valueOf():t.map(function(e){Object(q.q)(e,n.length);var 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TypeError("Array expected");if(e.length!==this._size.length)throw new z.a(e.length,this._size.length);for(var t=0;t<e.length;t++)Object(q.q)(e[t],this._size[t]);for(var r=this._data,n=0,i=e.length;n<i;n++){var a=e[n];Object(q.q)(a,r.length),r=r[a]}return r},m.prototype.set=function(e,t,r){if(!Object(ie.b)(e))throw new TypeError("Array expected");if(e.length<this._size.length)throw new z.a(e.length,this._size.length,"<");var n;l(this,e.map(function(e){return e+1}),r);for(var i=this._data,a=0,o=e.length-1;a<o;a++)n=e[a],Object(q.q)(n,i.length),i=i[n];return n=e[e.length-1],Object(q.q)(n,i.length),i[n]=t,this},m.prototype.resize=function(e,t,r){if(!Object(ie.i)(e))throw new TypeError("Array or Matrix expected");var n=e.valueOf().map(function(e){return Array.isArray(e)&&1===e.length?e[0]:e});return s(r?this.clone():this,n,t)},m.prototype.reshape=function(e,t){var r=t?this.clone():this;return r._data=Object(q.l)(r._data,e),r._size=e.slice(0),r},m.prototype.clone=function(){return new m({data:Object(ae.a)(this._data),size:Object(ae.a)(this._size),datatype:this._datatype})},m.prototype.size=function(){return this._size.slice(0)},m.prototype.map=function(t){var i=this,e=function r(e,n){return Object(ie.b)(e)?e.map(function(e,t){return r(e,n.concat(t))}):t(e,n,i)}(this._data,[]);return new m(e,void 0!==this._datatype?Object(q.h)(e,ie.M):void 0)},m.prototype.forEach=function(t){var i=this;!function r(e,n){Object(ie.b)(e)?e.forEach(function(e,t){r(e,n.concat(t))}):t(e,n,i)}(this._data,[])},m.prototype.toArray=function(){return Object(ae.a)(this._data)},m.prototype.valueOf=function(){return this._data},m.prototype.format=function(e){return Object(V.d)(this._data,e)},m.prototype.toString=function(){return Object(V.d)(this._data)},m.prototype.toJSON=function(){return{mathjs:"DenseMatrix",data:this._data,size:this._size,datatype:this._datatype}},m.prototype.diagonal=function(e){if(e){if(Object(ie.e)(e)&&(e=e.toNumber()),!Object(ie.y)(e)||!Object(E.i)(e))throw new TypeError("The parameter k must be an integer number")}else e=0;for(var t=0<e?e:0,r=e<0?-e:0,n=this._size[0],i=this._size[1],a=Math.min(n-r,i-t),o=[],s=0;s<a;s++)o[s]=this._data[s+r][s+t];return new m({data:o,size:[a],datatype:this._datatype})},m.diagonal=function(e,t,r,n){if(!Object(ie.b)(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(Object(ie.e)(e)&&(e=e.toNumber()),!Object(ie.y)(e)||!Object(E.i)(e)||e<1)throw new Error("Size values must be positive integers");return e}),r){if(Object(ie.e)(r)&&(r=r.toNumber()),!Object(ie.y)(r)||!Object(E.i)(r))throw new TypeError("The parameter k must be an integer number")}else r=0;var i,a=0<r?r:0,o=r<0?-r:0,s=e[0],u=e[1],c=Math.min(s-o,u-a);if(Object(ie.b)(t)){if(t.length!==c)throw new Error("Invalid value array length");i=function(e){return t[e]}}else if(Object(ie.v)(t)){var f=t.size();if(1!==f.length||f[0]!==c)throw new Error("Invalid 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o=this._ptr[a],s=this._ptr[a+1],u=o;u<s;u++){var c=this._index[u];i+="\n    ("+Object(V.d)(c,e)+", "+Object(V.d)(a,e)+") ==> "+(this._values?Object(V.d)(this._values[u],e):"X")}return i},j.prototype.toString=function(){return Object(V.d)(this.toArray())},j.prototype.toJSON=function(){return{mathjs:"SparseMatrix",values:this._values,index:this._index,ptr:this._ptr,size:this._size,datatype:this._datatype}},j.prototype.diagonal=function(e){if(e){if(Object(ie.e)(e)&&(e=e.toNumber()),!Object(ie.y)(e)||!Object(E.i)(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],a=Math.min(n-r,i-t),o=[],s=[],u=[];u[0]=0;for(var c=t;c<i&&o.length<a;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){o.push(this._values[p]),s[o.length-1]=m-r;break}}return u.push(o.length),new j({values:o,index:s,ptr:u,size:[a,1]})},j.fromJSON=function(e){return new 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Matrix A ("+a+") must match Matrix B ("+f+")");if(!s)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var p,m=a[0],h=a[1],d=A,y=0,g=r;"string"==typeof o&&o===l&&(p=o,d=S.find(A,[p,p]),y=S.convert(0,p),g=S.find(r,[p,p]));for(var b=[],v=[],x=[],w=0;w<h;w++){x[w]=v.length;for(var N=c[w],O=c[w+1],M=N;M<O;M++){var j=u[M],E=n?g(s[M],i[j][w]):g(i[j][w],s[M]);d(E,y)||(v.push(j),b.push(E))}}return x[h]=v.length,t.createSparseMatrix({values:b,index:v,ptr:x,size:[m,h],datatype:p})}}),rr=["typed","equalScalar"],nr=Object(s.a)("algorithm06",rr,function(e){var S=e.typed,A=e.equalScalar;return function(e,t,r){var n=e._values,i=e._size,a=e._datatype,o=t._values,s=t._size,u=t._datatype;if(i.length!==s.length)throw new z.a(i.length,s.length);if(i[0]!==s[0]||i[1]!==s[1])throw new RangeError("Dimension mismatch. Matrix A ("+i+") must match Matrix B ("+s+")");var c,f=i[0],l=i[1],p=A,m=0,h=r;"string"==typeof a&&a===u&&(c=a,p=S.find(A,[c,c]),m=S.convert(0,c),h=S.find(r,[c,c]));for(var d=n&&o?[]:void 0,y=[],g=[],b=d?[]:void 0,v=[],x=[],w=0;w<l;w++){g[w]=y.length;var N=w+1;if(H(e,w,v,b,x,N,y,h),H(t,w,v,b,x,N,y,h),b)for(var O=g[w];O<y.length;){var M,j=y[O];x[j]!==N||p(M=b[j],m)?y.splice(O,1):(d.push(M),O++)}else for(var E=g[w];E<y.length;){x[y[E]]!==N?y.splice(E,1):E++}}return g[l]=y.length,e.createSparseMatrix({values:d,index:y,ptr:g,size:[f,l],datatype:c})}}),ir=["typed","equalScalar"],ar=Object(s.a)("algorithm11",ir,function(e){var M=e.typed,j=e.equalScalar;return function(e,t,r,n){var i=e._values,a=e._index,o=e._ptr,s=e._size,u=e._datatype;if(!i)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var c,f=s[0],l=s[1],p=j,m=0,h=r;"string"==typeof u&&(c=u,p=M.find(j,[c,c]),m=M.convert(0,c),t=M.convert(t,c),h=M.find(r,[c,c]));for(var d=[],y=[],g=[],b=0;b<l;b++){g[b]=y.length;for(var v=o[b],x=o[b+1],w=v;w<x;w++){var N=a[w],O=n?h(t,i[w]):h(i[w],t);p(O,m)||(y.push(N),d.push(O))}}return g[l]=y.length,e.createSparseMatrix({values:d,index:y,ptr:g,size:[f,l],datatype:c})}}),or=["typed","matrix","equalScalar"],sr=Object(s.a)("lcm",or,function(e){var t=e.typed,r=e.matrix,n=e.equalScalar,i=tr({typed:t,equalScalar:n}),a=nr({typed:t,equalScalar:n}),o=ar({typed:t,equalScalar:n}),s=Wt({typed:t}),u=Xt({typed:t});return t("lcm",{"number, number":nt,"BigNumber, BigNumber":function(e,t){if(!e.isInt()||!t.isInt())throw new Error("Parameters in function lcm must be integer numbers");if(e.isZero())return e;if(t.isZero())return t;var r=e.times(t);for(;!t.isZero();){var n=t;t=e.mod(n),e=n}return r.div(e).abs()},"Fraction, Fraction":function(e,t){return e.lcm(t)},"SparseMatrix, SparseMatrix":function(e,t){return a(e,t,this)},"SparseMatrix, DenseMatrix":function(e,t){return i(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return i(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return s(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, number | BigNumber":function(e,t){return o(e,t,this,!1)},"DenseMatrix, number | BigNumber":function(e,t){return u(e,t,this,!1)},"number | BigNumber, SparseMatrix":function(e,t){return o(t,e,this,!0)},"number | BigNumber, DenseMatrix":function(e,t){return u(t,e,this,!0)},"Array, number | BigNumber":function(e,t){return u(r(e),t,this,!1).valueOf()},"number | BigNumber, Array":function(e,t){return u(r(t),e,this,!0).valueOf()},"Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber":function(e,t,r){for(var n=this(e,t),i=0;i<r.length;i++)n=this(n,r[i]);return n}})}),ur=["typed","config","Complex"],cr=Object(s.a)("log10",ur,function(e){var t=e.typed,r=e.config,n=e.Complex;return t("log10",{number:function(e){return 0<=e||r.predictable?at(e):new n(e,0).log().div(Math.LN10)},Complex:function(e){return new n(e).log().div(Math.LN10)},BigNumber:function(e){return!e.isNegative()||r.predictable?e.log():new n(e.toNumber(),0).log().div(Math.LN10)},"Array | Matrix":function(e){return oe(e,this)}})}),fr=["typed","config","Complex"],lr=Object(s.a)("log2",fr,function(e){var t=e.typed,r=e.config,n=e.Complex;return t("log2",{number:function(e){return 0<=e||r.predictable?ot(e):i(new n(e,0))},Complex:i,BigNumber:function(e){return!e.isNegative()||r.predictable?e.log(2):i(new n(e.toNumber(),0))},"Array | Matrix":function(e){return oe(e,this)}});function i(e){var t=Math.sqrt(e.re*e.re+e.im*e.im);return new n(Math.log2?Math.log2(t):Math.log(t)/Math.LN2,Math.atan2(e.im,e.re)/Math.LN2)}}),pr=["typed"],mr=Object(s.a)("algorithm03",pr,function(e){var A=e.typed;return function(e,t,r,n){var i=e._data,a=e._size,o=e._datatype,s=t._values,u=t._index,c=t._ptr,f=t._size,l=t._datatype;if(a.length!==f.length)throw new z.a(a.length,f.length);if(a[0]!==f[0]||a[1]!==f[1])throw new RangeError("Dimension mismatch. Matrix A ("+a+") must match Matrix B ("+f+")");if(!s)throw new Error("Cannot perform operation on Dense Matrix and Pattern Sparse Matrix");var p,m=a[0],h=a[1],d=0,y=r;"string"==typeof o&&o===l&&(p=o,d=A.convert(0,p),y=A.find(r,[p,p]));for(var g=[],b=0;b<m;b++)g[b]=[];for(var v=[],x=[],w=0;w<h;w++){for(var N=w+1,O=c[w],M=c[w+1],j=O;j<M;j++){var E=u[j];v[E]=n?y(s[j],i[E][w]):y(i[E][w],s[j]),x[E]=N}for(var S=0;S<m;S++)x[S]===N?g[S][w]=v[S]:g[S][w]=n?y(d,i[S][w]):y(i[S][w],d)}return e.createDenseMatrix({data:g,size:[m,h],datatype:p})}}),hr=["typed","equalScalar"],dr=Object(s.a)("algorithm05",hr,function(e){var k=e.typed,B=e.equalScalar;return function(e,t,r){var n=e._values,i=e._index,a=e._ptr,o=e._size,s=e._datatype,u=t._values,c=t._index,f=t._ptr,l=t._size,p=t._datatype;if(o.length!==l.length)throw new z.a(o.length,l.length);if(o[0]!==l[0]||o[1]!==l[1])throw new RangeError("Dimension mismatch. Matrix A ("+o+") must match Matrix B ("+l+")");var m,h=o[0],d=o[1],y=B,g=0,b=r;"string"==typeof s&&s===p&&(m=s,y=k.find(B,[m,m]),g=k.convert(0,m),b=k.find(r,[m,m]));for(var v,x=n&&u?[]:void 0,w=[],N=[],O=x?[]:void 0,M=x?[]:void 0,j=[],E=[],S=0;S<d;S++){N[S]=w.length;for(var A=S+1,C=a[S],T=a[S+1];C<T;C++)v=i[C],w.push(v),j[v]=A,O&&(O[v]=n[C]);for(C=f[S],T=f[S+1];C<T;C++)j[v=c[C]]!==A&&w.push(v),E[v]=A,M&&(M[v]=u[C]);if(x)for(C=N[S];C<w.length;){var _,q=j[v=w[C]],I=E[v];q!==A&&I!==A||(y(_=b(q===A?O[v]:g,I===A?M[v]:g),g)?w.splice(C,1):(x.push(_),C++))}}return N[d]=w.length,e.createSparseMatrix({values:x,index:w,ptr:N,size:[h,d],datatype:m})}}),yr=["typed","DenseMatrix"],gr=Object(s.a)("algorithm12",yr,function(e){var O=e.typed,M=e.DenseMatrix;return function(e,t,r,n){var i=e._values,a=e._index,o=e._ptr,s=e._size,u=e._datatype;if(!i)throw new Error("Cannot perform operation on Pattern Sparse Matrix and Scalar value");var c,f=s[0],l=s[1],p=r;"string"==typeof u&&(c=u,t=O.convert(t,c),p=O.find(r,[c,c]));for(var m=[],h=[],d=[],y=0;y<l;y++){for(var g=y+1,b=o[y],v=o[y+1],x=b;x<v;x++){var w=a[x];h[w]=i[x],d[w]=g}for(var N=0;N<f;N++)0===y&&(m[N]=[]),d[N]===g?m[N][y]=n?p(t,h[N]):p(h[N],t):m[N][y]=n?p(t,0):p(0,t)}return new M({data:m,size:[f,l],datatype:c})}}),br=["typed","matrix","equalScalar","DenseMatrix"],vr=Object(s.a)("mod",br,function(e){var t=e.typed,r=e.matrix,n=e.equalScalar,i=e.DenseMatrix,a=tr({typed:t,equalScalar:n}),o=mr({typed:t}),s=dr({typed:t,equalScalar:n}),u=ar({typed:t,equalScalar:n}),c=gr({typed:t,DenseMatrix:i}),f=Wt({typed:t}),l=Xt({typed:t});return t("mod",{"number, number":st,"BigNumber, BigNumber":function(e,t){return t.isZero()?e:e.mod(t)},"Fraction, Fraction":function(e,t){return e.mod(t)},"SparseMatrix, SparseMatrix":function(e,t){return s(e,t,this,!1)},"SparseMatrix, DenseMatrix":function(e,t){return a(t,e,this,!0)},"DenseMatrix, SparseMatrix":function(e,t){return o(e,t,this,!1)},"DenseMatrix, DenseMatrix":function(e,t){return f(e,t,this)},"Array, Array":function(e,t){return this(r(e),r(t)).valueOf()},"Array, Matrix":function(e,t){return this(r(e),t)},"Matrix, Array":function(e,t){return this(e,r(t))},"SparseMatrix, any":function(e,t){return u(e,t,this,!1)},"DenseMatrix, any":function(e,t){return l(e,t,this,!1)},"any, SparseMatrix":function(e,t){return c(t,e,this,!0)},"any, DenseMatrix":function(e,t){return l(t,e,this,!0)},"Array, any":function(e,t){return l(r(e),t,this,!1).valueOf()},"any, Array":function(e,t){return l(r(t),e,this,!0).valueOf()}})}),xr=["typed"],wr=Object(s.a)("multiplyScalar",xr,function(e){return(0,e.typed)("multiplyScalar",{"number, number":Je,"Complex, Complex":function(e,t){return e.mul(t)},"BigNumber, BigNumber":function(e,t){return e.times(t)},"Fraction, Fraction":function(e,t){return e.mul(t)},"number | Fraction | BigNumber | Complex, Unit":function(e,t){var r=t.clone();return r.value=null===r.value?r._normalize(e):this(r.value,e),r},"Unit, number | Fraction | BigNumber | Complex":function(e,t){var r=e.clone();return r.value=null===r.value?r._normalize(t):this(r.value,t),r},"Unit, Unit":function(e,t){return e.multiply(t)}})}),Nr="multiply",Or=["typed","matrix","addScalar","multiplyScalar","equalScalar","dot"],Mr=Object(s.a)(Nr,Or,function(e){var z=e.typed,n=e.matrix,D=e.addScalar,R=e.multiplyScalar,k=e.equalScalar,i=e.dot,r=ar({typed:z,equalScalar:k}),a=Xt({typed:z});function o(e,t){switch(e.length){case 1:switch(t.length){case 1:if(e[0]!==t[0])throw new RangeError("Dimension mismatch in multiplication. 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Matrix A columns ("+e[1]+") must match Matrix B rows ("+t[0]+")");break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix B has "+t.length+" dimensions)")}break;default:throw new Error("Can only multiply a 1 or 2 dimensional matrix (Matrix A has "+e.length+" dimensions)")}}function s(e,t){if("dense"!==t.storage())throw new Error("Support for SparseMatrix not implemented");return function(e,t){var r,n=e._data,i=e._size,a=e._datatype,o=t._data,s=t._size,u=t._datatype,c=i[0],f=s[1],l=D,p=R;a&&u&&a===u&&"string"==typeof a&&(r=a,l=z.find(D,[r,r]),p=z.find(R,[r,r]));for(var m=[],h=0;h<f;h++){for(var d=p(n[0],o[0][h]),y=1;y<c;y++)d=l(d,p(n[y],o[y][h]));m[h]=d}return e.createDenseMatrix({data:m,size:[f],datatype:r})}(e,t)}var u=z("_multiplyMatrixVector",{"DenseMatrix, any":function(e,t){var r,n=e._data,i=e._size,a=e._datatype,o=t._data,s=t._datatype,u=i[0],c=i[1],f=D,l=R;a&&s&&a===s&&"string"==typeof a&&(r=a,f=z.find(D,[r,r]),l=z.find(R,[r,r]));for(var 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o=a._index,s=a._ptr,u=0,c=0;c<r;c++){var f=s[c];if(s[c]=u,!(s[c+1]-f>i))for(var l=s[c+1];f<l;f++)o[u++]=o[f]}return s[r]=u,t=te(a),ee(a,t)}(e,t,n,i,o=Math.min(i-2,o));!function(e,t,r){for(var n=e._values,i=e._index,a=e._ptr,o=e._size[1],s=0,u=0;u<o;u++){var c=a[u];for(a[u]=s;c<a[u+1];c++)t(i[c],u,n?n[c]:1,r)&&(i[s]=i[c],n&&(n[s]=n[c]),s++)}a[o]=s,i.splice(s,i.length-s),n&&n.splice(s,n.length-s)}(s,ne,null);for(var u,c,f,l,p,m,h,d,y,g,b,v,x=s._index,w=s._ptr,N=w[i],O=[],M=[],j=i+1,E=2*(i+1),S=3*(i+1),A=4*(i+1),C=5*(i+1),T=6*(i+1),_=7*(i+1),q=O,I=function(e,t,r,n,i,a,o,s,u,c,f,l){for(var p=0;p<e;p++)r[n+p]=t[p+1]-t[p];for(var m=r[n+e]=0;m<=e;m++)r[i+m]=-1,a[m]=-1,r[o+m]=-1,r[s+m]=-1,r[u+m]=1,r[c+m]=1,r[f+m]=0,r[l+m]=r[n+m];var h=re(0,0,r,c,e);return r[f+e]=-2,t[e]=-1,r[c+e]=0,h}(i,w,M,0,S,q,E,_,j,T,A,C),k=function(e,t,r,n,i,a,o,s,u,c,f){for(var l=0,p=0;p<e;p++){var 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Q=M[0+X]===p&&M[A+X]===d;for(F=w[X]+1;Q&&F<=w[X]+p-1;F++)M[T+x[F]]!==I&&(Q=0);Q?(w[X]=-u-2,M[j+u]+=M[j+X],M[j+X]=0,M[A+X]=-1,X=M[E+X],M[E+Y]=X):X=M[E+(Y=X)]}}for(h=F=L;h<H;h++)(m=-M[j+(u=x[h])])<=0||(M[j+u]=m,v=M[C+u]+R-m,-1!==M[S+(v=Math.min(v,i-k-m))]&&(q[M[S+v]]=u),M[E+u]=M[S+v],q[u]=-1,M[S+v]=u,B=Math.min(B,v),M[C+u]=v,x[F++]=u);M[j+c]=D,0==(M[0+c]=F-L)&&(w[c]=-1,M[T+c]=0),0!==z&&(N=F)}for(u=0;u<i;u++)w[u]=-w[u]-2;for(X=0;X<=i;X++)M[S+X]=-1;for(X=i;0<=X;X--)0<M[j+X]||(M[E+X]=M[S+w[X]],M[S+w[X]]=X);for(U=i;0<=U;U--)M[j+U]<=0||-1!==w[U]&&(M[E+U]=M[S+w[U]],M[S+w[U]]=U);for(u=c=0;u<=i;u++)-1===w[u]&&(c=el(u,c,M,S,E,O,T));return O.splice(O.length-1,1),O};function re(e,t,r,n,i){if(e<2||e+t<0){for(var a=0;a<i;a++)0!==r[n+a]&&(r[n+a]=1);e=2}return e}function ne(e,t){return e!==t}});var nl=["transpose"],il=Object(s.a)("csCounts",nl,function(e){var E=e.transpose;return function(e,t,r,n){if(!e||!t||!r)return null;for(var i,a,o,s,u,c,f=e._size,l=f[0],p=f[1],m=4*p+(n?p+l+1:0),h=[],d=p,y=2*p,g=3*p,b=4*p,v=5*p+1,x=0;x<m;x++)h[x]=-1;var w=[],N=E(e),O=N._index,M=N._ptr;for(x=0;x<p;x++)for(w[a=r[x]]=-1===h[g+a]?1:0;-1!==a&&-1===h[g+a];a=t[a])h[g+a]=x;if(n){for(x=0;x<p;x++)h[r[x]]=x;for(i=0;i<l;i++){for(x=p,u=M[i],c=M[i+1],s=u;s<c;s++)x=Math.min(x,h[O[s]]);h[v+i]=h[b+x],h[b+x]=i}}for(i=0;i<p;i++)h[0+i]=i;for(x=0;x<p;x++){for(-1!==t[a=r[x]]&&w[t[a]]--,o=n?h[b+x]:a;-1!==o;o=n?h[v+o]:-1)for(s=M[o];s<M[o+1];s++){var j=function(e,t,r,n,i,a,o){var s,u,c,f=0;if(e<=t||r[n+t]<=r[i+e])return-1;r[i+e]=r[n+t];var l=r[a+e];if(r[a+e]=t,-1===l)f=1,c=e;else{for(f=2,c=l;c!==r[o+c];c=r[o+c]);for(s=l;s!==c;s=u)u=r[o+s],r[o+s]=c}return{jleaf:f,q:c}}(i=O[s],a,h,g,d,y,0);1<=j.jleaf&&w[a]++,2===j.jleaf&&w[j.q]--}-1!==t[a]&&(h[0+a]=t[a])}for(a=0;a<p;a++)-1!==t[a]&&(w[t[a]]+=w[a]);return w}}),al=["add","multiply","transpose"],ol=Object(s.a)("csSqr",al,function(e){var t=e.add,r=e.multiply,n=e.transpose,c=rl({add:t,multiply:r,transpose:n}),f=il({transpose:n});return function(e,t,r){var n,i=t._ptr,a=t._size[1],o={};if(o.q=c(e,t),e&&!o.q)return null;if(r){var s=e?function(e,t,r,n){for(var i=e._values,a=e._index,o=e._ptr,s=e._size,u=e._datatype,c=s[0],f=s[1],l=n&&e._values?[]:null,p=[],m=[],h=0,d=0;d<f;d++){m[d]=h;for(var y=r?r[d]:d,g=o[y],b=o[y+1],v=g;v<b;v++){var x=t?t[a[v]]:a[v];p[h]=x,l&&(l[h]=i[v]),h++}}return m[f]=h,e.createSparseMatrix({values:l,index:p,ptr:m,size:[c,f],datatype:u})}(t,null,o.q,0):t;o.parent=function(e,t){if(!e)return null;var r,n=e._index,i=e._ptr,a=e._size,o=a[0],s=a[1],u=[],c=[],f=s;if(t)for(y=0;y<o;y++)c[f+y]=-1;for(var l=0;l<s;l++){u[l]=-1,c[0+l]=-1;for(var p=i[l],m=i[l+1],h=p;h<m;h++){for(var d=n[h],y=t?c[f+d]:d;-1!==y&&y<l;y=r)r=c[0+y],c[0+y]=l,-1===r&&(u[y]=l);t&&(c[f+d]=l)}}return u}(s,1);var u=function(e,t){if(!e)return null;for(var r=0,n=[],i=[],a=t,o=2*t,s=0;s<t;s++)i[0+s]=-1;for(s=t-1;0<=s;s--)-1!==e[s]&&(i[a+s]=i[0+e[s]],i[0+e[s]]=s);for(s=0;s<t;s++)-1===e[s]&&(r=el(s,r,i,0,a,n,o));return n}(o.parent,a);if(o.cp=f(s,o.parent,u,1),s&&o.parent&&o.cp&&function(e,t){var r=e._ptr,n=e._index,i=e._size,a=i[0],o=i[1];t.pinv=[],t.leftmost=[];var s,u,c,f,l,p=t.parent,m=t.pinv,h=t.leftmost,d=[],y=a,g=a+o,b=a+2*o;for(u=0;u<o;u++)d[y+u]=-1,d[g+u]=-1,d[b+u]=0;for(s=0;s<a;s++)h[s]=-1;for(u=o-1;0<=u;u--)for(f=r[u],l=r[u+1],c=f;c<l;c++)h[n[c]]=u;for(s=a-1;0<=s;s--)(m[s]=-1)!==(u=h[s])&&(0==d[b+u]++&&(d[g+u]=s),d[0+s]=d[y+u],d[y+u]=s);for(t.lnz=0,t.m2=a,u=0;u<o;u++){var v;s=d[y+u],t.lnz++,s<0&&(s=t.m2++),m[s]=u,--b[u]<=0||(t.lnz+=d[b+u],-1!==(v=p[u])&&(0===d[b+v]&&(d[g+v]=d[g+u]),d[0+d[g+u]]=d[y+v],d[y+v]=d[0+s],d[b+v]+=d[b+u]))}for(s=0;s<a;s++)m[s]<0&&(m[s]=u++);return!0}(s,o))for(n=o.unz=0;n<a;n++)o.unz+=o.cp[n]}else o.unz=4*i[a]+a,o.lnz=o.unz;return o}});function sl(e,t){e[t]=-e[t]-2}function ul(e){return e<0?-e-2:e}function 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g}}),pl=["abs","divideScalar","multiply","subtract","larger","largerEq","SparseMatrix"],ml=Object(s.a)("csLu",pl,function(e){var S=e.abs,A=e.divideScalar,C=e.multiply,t=e.subtract,T=e.larger,_=e.largerEq,q=e.SparseMatrix,I=ll({divideScalar:A,multiply:C,subtract:t});return function(e,t,r){if(!e)return null;var n,i=e._size[1],a=100,o=100;t&&(n=t.q,a=t.lnz||a,o=t.unz||o);var s=[],u=[],c=[],f=new q({values:s,index:u,ptr:c,size:[i,i]}),l=[],p=[],m=[],h=new q({values:l,index:p,ptr:m,size:[i,i]}),d=[],y=[],g=[];for(x=0;x<i;x++)y[x]=0,d[x]=-1,c[x+1]=0;for(var b=o=a=0;b<i;b++){c[b]=a,m[b]=o;for(var v,x,w=n?n[b]:b,N=I(f,e,w,g,y,d,1),O=-1,M=-1,j=N;j<i;j++){d[x=g[j]]<0?(v=S(y[x]),T(v,M)&&(M=v,O=x)):(p[o]=d[x],l[o++]=y[x])}if(-1===O||M<=0)return null;d[w]<0&&_(S(y[w]),C(M,r))&&(O=w);var E=y[O];for(p[o]=b,l[o++]=E,d[O]=b,u[a]=O,s[a++]=1,j=N;j<i;j++)d[x=g[j]]<0&&(u[a]=x,s[a++]=A(y[x],E)),y[x]=0}for(c[i]=a,m[i]=o,j=0;j<a;j++)u[j]=d[u[j]];return 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vacuum",examples:["speedOfLight"]},gravitationConstant:{description:"Newtonian constant of gravitation",examples:["gravitationConstant"]},planckConstant:{description:"Planck constant",examples:["planckConstant"]},reducedPlanckConstant:{description:"Reduced Planck constant",examples:["reducedPlanckConstant"]},magneticConstant:{description:"Magnetic constant (vacuum permeability)",examples:["magneticConstant"]},electricConstant:{description:"Electric constant (vacuum permeability)",examples:["electricConstant"]},vacuumImpedance:{description:"Characteristic impedance of vacuum",examples:["vacuumImpedance"]},coulomb:{description:"Coulomb's constant",examples:["coulomb"]},elementaryCharge:{description:"Elementary charge",examples:["elementaryCharge"]},bohrMagneton:{description:"Borh magneton",examples:["bohrMagneton"]},conductanceQuantum:{description:"Conductance quantum",examples:["conductanceQuantum"]},inverseConductanceQuantum:{description:"Inverse conductance quantum",examples:["inverseConductanceQuantum"]},magneticFluxQuantum:{description:"Magnetic flux quantum",examples:["magneticFluxQuantum"]},nuclearMagneton:{description:"Nuclear magneton",examples:["nuclearMagneton"]},klitzing:{description:"Von Klitzing constant",examples:["klitzing"]},bohrRadius:{description:"Borh radius",examples:["bohrRadius"]},classicalElectronRadius:{description:"Classical electron radius",examples:["classicalElectronRadius"]},electronMass:{description:"Electron mass",examples:["electronMass"]},fermiCoupling:{description:"Fermi coupling constant",examples:["fermiCoupling"]},fineStructure:{description:"Fine-structure constant",examples:["fineStructure"]},hartreeEnergy:{description:"Hartree energy",examples:["hartreeEnergy"]},protonMass:{description:"Proton mass",examples:["protonMass"]},deuteronMass:{description:"Deuteron Mass",examples:["deuteronMass"]},neutronMass:{description:"Neutron mass",examples:["neutronMass"]},quantumOfCirculation:{description:"Quantum of circulation",examples:["quantumOfCirculation"]},rydberg:{description:"Rydberg constant",examples:["rydberg"]},thomsonCrossSection:{description:"Thomson cross section",examples:["thomsonCrossSection"]},weakMixingAngle:{description:"Weak mixing angle",examples:["weakMixingAngle"]},efimovFactor:{description:"Efimov factor",examples:["efimovFactor"]},atomicMass:{description:"Atomic mass constant",examples:["atomicMass"]},avogadro:{description:"Avogadro's number",examples:["avogadro"]},boltzmann:{description:"Boltzmann constant",examples:["boltzmann"]},faraday:{description:"Faraday constant",examples:["faraday"]},firstRadiation:{description:"First radiation constant",examples:["firstRadiation"]},loschmidt:{description:"Loschmidt constant at T=273.15 K and p=101.325 kPa",examples:["loschmidt"]},gasConstant:{description:"Gas constant",examples:["gasConstant"]},molarPlanckConstant:{description:"Molar Planck constant",examples:["molarPlanckConstant"]},molarVolume:{description:"Molar volume of an ideal gas at T=273.15 K and p=101.325 kPa",examples:["molarVolume"]},sackurTetrode:{description:"Sackur-Tetrode constant at T=1 K and p=101.325 kPa",examples:["sackurTetrode"]},secondRadiation:{description:"Second radiation constant",examples:["secondRadiation"]},stefanBoltzmann:{description:"Stefan-Boltzmann constant",examples:["stefanBoltzmann"]},wienDisplacement:{description:"Wien displacement law constant",examples:["wienDisplacement"]},molarMass:{description:"Molar mass constant",examples:["molarMass"]},molarMassC12:{description:"Molar mass constant of carbon-12",examples:["molarMassC12"]},gravity:{description:"Standard acceleration of gravity (standard acceleration of free-fall on Earth)",examples:["gravity"]},planckLength:{description:"Planck length",examples:["planckLength"]},planckMass:{description:"Planck mass",examples:["planckMass"]},planckTime:{description:"Planck time",examples:["planckTime"]},planckCharge:{description:"Planck charge",examples:["planckCharge"]},planckTemperature:{description:"Planck temperature",examples:["planckTemperature"]},derivative:{name:"derivative",category:"Algebra",syntax:["derivative(expr, variable)","derivative(expr, variable, {simplify: boolean})"],description:"Takes the derivative of an expression expressed in parser Nodes. The derivative will be taken over the supplied variable in the second parameter. If there are multiple variables in the expression, it will return a partial derivative.",examples:['derivative("2x^3", "x")','derivative("2x^3", "x", {simplify: false})','derivative("2x^2 + 3x + 4", "x")','derivative("sin(2x)", "x")','f = parse("x^2 + x")','x = parse("x")',"df = derivative(f, x)","df.evaluate({x: 3})"],seealso:["simplify","parse","evaluate"]},lsolve:{name:"lsolve",category:"Algebra",syntax:["x=lsolve(L, b)"],description:"Solves the linear system L * x = b where L is an [n x n] lower triangular matrix and b is a [n] column vector.",examples:["a = [-2, 3; 2, 1]","b = [11, 9]","x = lsolve(a, b)"],seealso:["lup","lusolve","usolve","matrix","sparse"]},lup:{name:"lup",category:"Algebra",syntax:["lup(m)"],description:"Calculate the Matrix LU decomposition with partial pivoting. 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"]},lusolve:{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"]},simplify:{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.evaluate({x: 2})"],seealso:["derivative","parse","evaluate"]},rationalize:{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"]},slu:{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"]},usolve:{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"]},qr:{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"]},abs:{name:"abs",category:"Arithmetic",syntax:["abs(x)"],description:"Compute the absolute value.",examples:["abs(3.5)","abs(-4.2)"],seealso:["sign"]},add:{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"]},cbrt:{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"]},ceil:{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"]},cube:{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"]},divide:{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"]},dotDivide:{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"]},dotMultiply:{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"]},dotPow:{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"]},exp:{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"]},expm:{name:"expm",category:"Arithmetic",syntax:["exp(x)"],description:"Compute the matrix exponential, expm(A) = e^A. The matrix must be square. Not to be confused with exp(a), which performs element-wise exponentiation.",examples:["expm([[0,2],[0,0]])"],seealso:["exp"]},expm1:{name:"expm1",category:"Arithmetic",syntax:["expm1(x)"],description:"Calculate the value of subtracting 1 from the exponential value.",examples:["expm1(2)","pow(e, 2) - 1","log(expm1(2) + 1)"],seealso:["exp","pow","log"]},fix:{name:"fix",category:"Arithmetic",syntax:["fix(x)"],description:"Round a value towards zero. If x is complex, both real and imaginary part are rounded towards zero.",examples:["fix(3.2)","fix(3.8)","fix(-4.2)","fix(-4.8)"],seealso:["ceil","floor","round"]},floor:{name:"floor",category:"Arithmetic",syntax:["floor(x)"],description:"Round a value towards minus infinity.If x is complex, both real and imaginary part are rounded towards minus infinity.",examples:["floor(3.2)","floor(3.8)","floor(-4.2)"],seealso:["ceil","fix","round"]},gcd:{name:"gcd",category:"Arithmetic",syntax:["gcd(a, b)","gcd(a, b, c, ...)"],description:"Compute the greatest common divisor.",examples:["gcd(8, 12)","gcd(-4, 6)","gcd(25, 15, -10)"],seealso:["lcm","xgcd"]},hypot:{name:"hypot",category:"Arithmetic",syntax:["hypot(a, b, c, ...)","hypot([a, b, c, ...])"],description:"Calculate the hypotenusa of a list with values. ",examples:["hypot(3, 4)","sqrt(3^2 + 4^2)","hypot(-2)","hypot([3, 4, 5])"],seealso:["abs","norm"]},lcm:{name:"lcm",category:"Arithmetic",syntax:["lcm(x, y)"],description:"Compute the least common multiple.",examples:["lcm(4, 6)","lcm(6, 21)","lcm(6, 21, 5)"],seealso:["gcd"]},log:{name:"log",category:"Arithmetic",syntax:["log(x)","log(x, base)"],description:"Compute the logarithm of a value. If no base is provided, the natural logarithm of x is calculated. If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).",examples:["log(3.5)","a = log(2.4)","exp(a)","10 ^ 4","log(10000, 10)","log(10000) / log(10)","b = log(1024, 2)","2 ^ b"],seealso:["exp","log1p","log2","log10"]},log2:{name:"log2",category:"Arithmetic",syntax:["log2(x)"],description:"Calculate the 2-base of a value. 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"]},log1p:{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"]},log10:{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"]},mod:{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"]},multiply:{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"]},norm:{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")']},nthRoot:{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"]},nthRoots:{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"]},pow:{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"]},round:{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"]},sign:{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"]},sqrt:{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"]},sqrtm:{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"]},square:{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"]},subtract:{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"]},unaryMinus:{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"]},unaryPlus:{name:"unaryPlus",category:"Operators",syntax:["+x","unaryPlus(x)"],description:"Converts booleans and strings to numbers.",examples:["+true",'+"2"'],seealso:["add","subtract","unaryMinus"]},xgcd:{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"]},bitAnd:{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"]},bitNot:{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"]},bitOr:{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"]},bitXor:{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"]},leftShift:{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"]},rightArithShift:{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"]},rightLogShift:{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"]},bellNumbers:{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"]},catalan:{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"]},composition:{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"]},stirlingS2:{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"]},config:{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:[]},import:{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:[]},typed:{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:[]},arg:{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"]},conj:{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"]},re:{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"]},im:{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"]},evaluate:{name:"evaluate",category:"Expression",syntax:["evaluate(expression)","evaluate([expr1, expr2, expr3, ...])"],description:"Evaluate an expression or an array with expressions.",examples:['evaluate("2 + 3")','evaluate("sqrt(" + 4 + ")")'],seealso:[]},help:{name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]},distance:{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:[]},intersect:{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:[]},and:{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"]},not:{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"]},or:{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"]},xor:{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"]},concat:{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"]},cross:{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"]},column:{name:"column",category:"Matrix",syntax:["column(x, index)"],description:"Return a column from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","column(A, 1)","column(A, 2)"],seealso:["row"]},ctranspose:{name:"ctranspose",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"]},det:{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"]},diag:{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"]},diff:{name:"diff",category:"Matrix",syntax:["diff(arr)","diff(arr, dim)"],description:["Create a new matrix or array with the difference of the passed matrix or array.","Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference","If no dimension parameter is passed it is assumed as dimension 0","Dimension is zero-based in javascript and one-based in the parser","Arrays must be 'rectangular' meaning arrays like [1, 2]","If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays"],examples:["diff([1, 2, 4, 7, 0])","diff([1, 2, 4, 7, 0], 0)","diff(matrix([1, 2, 4, 7, 0]))","diff([[1, 2], [3, 4]])","diff([[1, 2], [3, 4]], 0)","diff([[1, 2], [3, 4]], 1)","diff([[1, 2], [3, 4]], bignumber(1))","diff(matrix([[1, 2], [3, 4]]), 1)","diff([[1, 2], matrix([3, 4])], 1)"],seealso:["subtract","partitionSelect"]},dot:{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"]},getMatrixDataType:{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"]},identity:{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"]},filter:{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"]},flatten:{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"]},forEach:{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"]},inv:{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"]},eigs:{name:"eigs",category:"Matrix",syntax:["eigs(x)"],description:"Calculate the eigenvalues and eigenvectors of a real symmetric matrix",examples:["eigs([[5, 2.3], [2.3, 1]])"],seealso:["inv"]},kron:{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"]},map:{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"]},ones:{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"]},partitionSelect:{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"]},range:{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"]},resize:{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"]},reshape:{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"]},row:{name:"row",category:"Matrix",syntax:["row(x, index)"],description:"Return a row from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","row(A, 1)","row(A, 2)"],seealso:["column"]},size:{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"]},sort:{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"]},squeeze:{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"]},subset:{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"]},trace:{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"]},transpose:{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"]},zeros:{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"]},combinations:{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:["combinationsWithRep","permutations","factorial"]},combinationsWithRep:{name:"combinationsWithRep",category:"Probability",syntax:["combinationsWithRep(n, k)"],description:"Compute the number of combinations of n items taken k at a time with replacements.",examples:["combinationsWithRep(7, 5)"],seealso:["combinations","permutations","factorial"]},factorial:{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","combinationsWithRep","permutations","gamma"]},gamma:{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"]},kldivergence:{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:[]},multinomial:{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"]},permutations:{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","combinationsWithRep","factorial"]},pickRandom:{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"]},random:{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"]},randomInt:{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"]},compare:{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"]},compareNatural:{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"]},compareText:{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"]},deepEqual:{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"]},equal:{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"]},equalText:{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"]},larger:{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"]},largerEq:{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"]},smaller:{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"]},smallerEq:{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"]},unequal:{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"]},setCartesian:{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"]},setDifference:{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"]},setDistinct:{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"]},setIntersect:{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"]},setIsSubset:{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"]},setMultiplicity:{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"]},setPowerset:{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"]},setSize:{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"]},setSymDifference:{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"]},setUnion:{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"]},erf:{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:[]},mad:{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"]},max:{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","variance"]},mean:{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","variance"]},median:{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","variance","quantileSeq"]},min:{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","variance"]},mode:{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","variance"]},prod:{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","variance"]},quantileSeq:{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","variance"]},std:{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(variance(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","prod","sum","variance"]},sum:{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","variance"]},variance:{name:"variance",category:"Statistics",syntax:["variance(a, b, c, ...)","variance(A)","variance(A, normalization)"],description:'Compute the variance of all values. Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["variance(2, 4, 6)","variance([2, 4, 6, 8])",'variance([2, 4, 6, 8], "uncorrected")','variance([2, 4, 6, 8], "biased")',"variance([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","min","prod","std","sum"]},acos:{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"]},acosh:{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"]},acot:{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"]},acoth:{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"]},acsc:{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"]},acsch:{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"]},asec:{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"]},asech:{name:"asech",category:"Trigonometry",syntax:["asech(x)"],description:"Calculate the inverse secant of a value.",examples:["asech(0.5)"],seealso:["acsch","acoth"]},asin:{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"]},asinh:{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"]},atan:{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"]},atanh:{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"]},atan2:{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"]},cos:{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"]},cosh:{name:"cosh",category:"Trigonometry",syntax:["cosh(x)"],description:"Compute the hyperbolic cosine of x in radians.",examples:["cosh(0.5)"],seealso:["sinh","tanh","coth"]},cot:{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"]},coth:{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"]},csc:{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"]},csch:{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"]},sec:{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"]},sech:{name:"sech",category:"Trigonometry",syntax:["sech(x)"],description:"Compute the hyperbolic secant of x in radians. 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		<input type="radio" onclick="setUnit(this.id)" name="unit" id="Mas">质量&nbsp;&nbsp;
		<input type="radio" onclick="setUnit(this.id)" name="unit" id="Tim">时间&nbsp;&nbsp;
		<input type="radio" onclick="setUnit(this.id)" name="unit" id="Eng">能量&nbsp;&nbsp;
		<input type="radio" onclick="setUnit(this.id)" name="unit" id="Frc">力  &nbsp;&nbsp;
		<input type="radio" onclick="setUnit(this.id)" name="unit" id="Prs">压强&nbsp;&nbsp;
		<input type="radio" onclick="setUnit(this.id)" name="unit" id="Con">浓度&nbsp;&nbsp;
		<input type="radio" onclick="setUnit(this.id)" name="unit" id="Rho">密度&nbsp;&nbsp;
		<input type="radio" onclick="setUnit(this.id)" name="unit" id="VDW">VDW参数<br>
		<span style='font: .6em Consolas;'>
		<ol><li>支持js函数: <code>**</code> <code>pow</code> <code>sqrt</code> <code>exp</code> <code>log</code>; <code>abs</code> <code>ceil</code> <code>floor</code>; <code>min</code> <code>max</code> <code>round</code> <code>random</code>; <code>sin</code> <code>cos</code> <code>tan</code>; <code>asin</code> <code>acos</code> <code>atan</code> <code>atan2</code></li><li>
		支持常量符号:<code>pi</code>; <code>c</code>:真空光速; <code>Na</code>:阿伏加德罗常数; <code>qe</code>:基元电荷; <code>ang</code>:埃; <code>nm</code>nm: 纳米; <code>h</code>:普朗克常数; <code>hbar</code>:h/2pi; <code>amu</code>:原子质量单位; <code>ha</code>:原子能量单位; <code>bohr</code>:原子长度单位; <code>kb</code>:玻尔兹曼常数; <code>mu0</code>:介磁常数; <code>eps0</code>:介电常数; <code>me</code>:电子质量; <code>mp</code>:质子质量; <code>g</code>:标准重力加速度; <code>G</code>:万有引力常数; <code>atm</code>:标准大气压; <code>P0</code>:标准压力; <code>T0</code>:标准温度; <code>R</code>:摩尔气体常数; <code>c2j</code>:卡焦互换; <code>j2c</code>:焦卡互换; <code>debye</code>:偶极矩单位德拜</li>
		</ol><strong id='inputValue'></strong> </span>
		<table id="TabLen" style="display: none;">
		<tbody><tr><td>
			<input type="box" name="Length" oninput="setVal(this.name,this.id)" id="L_m"> 米(m)<br>
			<input type="box" name="Length" oninput="setVal(this.name,this.id)" id="L_km"> 千米(km)<br>
			<input type="box" name="Length" oninput="setVal(this.name,this.id)" id="L_cm"> 厘米(cm)<br>
			<input type="box" name="Length" oninput="setVal(this.name,this.id)" id="L_mm"> 毫米(mm)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Length" onInput="setVal(this.name,this.id)" id="L_um"> 微米(&mu;m)<br>
			<input type="box" name="Length" onInput="setVal(this.name,this.id)" id="L_nm"> 纳米(nm)<br>
			<input type="box" name="Length" onInput="setVal(this.name,this.id)" id="L_pm"> 皮米(pm)<br>
			<input type="box" name="Length" onInput="setVal(this.name,this.id)" id="L_fm"> 飞米(fm)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Length" onInput="setVal(this.name,this.id)" id="L_bohr"> 玻尔(Bohr)<br>
			<input type="box" name="Length" onInput="setVal(this.name,this.id)" id="L_ang"> 埃(&#197;)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Length" onInput="setVal(this.name,this.id)" id="L_pnt"> 点(point)<br>
			<input type="box" name="Length" onInput="setVal(this.name,this.id)" id="L_inch"> 英寸(inch)<br>
			<input type="box" name="Length" onInput="setVal(this.name,this.id)" id="L_foot"> 英尺(foot)<br>
			<input type="box" name="Length" onInput="setVal(this.name,this.id)" id="L_yard"> 码(yard)<br>
			<input type="box" name="Length" onInput="setVal(this.name,this.id)" id="L_mile"> 英里(mile)<br>
		</td></tr>
		</table>

		<table id="TabMas">
		<tr><td>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_kg"> 千克(kg)<br>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_g"> 克(g)<br>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_mg"> 毫克(mg)<br>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_ug"> 微克(&mu;g)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_amu"> 原子质量(amu/Dalton)<br>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_emas"> 电子质量(me)<br>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_pmas"> 质子质量(mp)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_eV"> 电子伏(eV)<br>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_MeV"> 兆电子伏(MeV)<br>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_GeV"> 吉电子伏(GeV)<br>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_TeV"> 太电子伏(TeV)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_ton"> 吨(ton)<br>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_pd"> 磅(pound)<br>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_car"> 克拉(carat宝石)<br>
			<input type="box" name="Mass" onInput="setVal(this.name,this.id)" id="M_onc"> 盎司(ounce)<br>
		</td></tr>
		</table>

		<table id="TabTim">
		<tr><td>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_s"> 秒(s)<br>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_minu"> 分(min)<br>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_h"> 时(h)<br>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_d"> 日(d)<br>
		</td></tr>

		<tr><td>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_ms"> 毫秒(ms)<br>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_us"> 微秒(&mu;s)<br>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_ns"> 纳秒(ns)<br>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_ps"> 皮秒(ps)<br>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_fs"> 飞秒(fs)<br>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_as"> 阿秒(as)<br>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_au"> 原子时间单位(au)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_m"> 月(m, 30 d)<br>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_a"> 年(a, 365 d)<br>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_am"> 平均月(29.53 d)<br>
			<input type="box" name="Time" onInput="setVal(this.name,this.id)" id="T_aa"> 平均年(365.2422 d)<br>
		</td></tr>
		</table>

		<table id="TabEng" style="display:block">
		<tr><td>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="J"> 焦耳(J)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="cal"> 卡(cal)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="erg"> 尔格(erg)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="kJ_mol"> 千焦/摩尔(kJ/mol)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="kcal_mol"> 千卡/摩尔(kcal/mol)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="MJ_mol"> 兆焦/摩尔(MJ/mol)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Mcal_mol"> 兆卡/摩尔(Mcal/mol)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Hatr"> 哈垂(Hartree)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Ry"> 里德伯(Rydberg)<br>

		</td></tr>
		<tr><td>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Ee2bohr"> 静电势能(e<sup>2</sup>/Bohr)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Ee2nm"> 静电势能(e<sup>2</sup>/nm)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Ee2A"> 静电势能(e<sup>2</sup>/&#197;)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Emd"> MD常用单位(amu-&#197;<sup>2</sup>/fs<sup>2</sup>)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Emd2"> MD常用单位(amu-nm<sup>2</sup>/ps<sup>2</sup>)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="K"> 热力学温度(K)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="kg"> 质量(kg)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="amu"> 原子质量(amu)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="eV"> 电子伏(eV)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="MeV"> 兆电子伏(MeV)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="GeV"> 吉电子伏(GeV)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="TeV"> 太电子伏(TeV)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="PeV"> 拍电子伏(PeV)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Em"> 米(m)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Ecm"> 厘米(cm)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Emm"> 毫米(mm)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Eum"> 微米(&mu;m)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Enm"> 纳米(nm)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Eang"> 埃(&#197;)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="invm"> 波数(m<sup>-1</sup>)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="invcm"> 厘米波数(cm<sup>-1</sup>)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="Hz"> 赫兹(Hz)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="MHz"> 兆赫兹(MHz)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="GHz"> 吉赫兹(GHz)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="THz"> 太赫兹(THz)<br>
			<input type="box" name="Energy" onInput="setVal(this.name, this.id)" id="PHz"> 拍赫兹(PHz)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Energy" onInput="setVal(this.name,this.id)" id="Es">周期   秒(s)<br>
			<input type="box" name="Energy" onInput="setVal(this.name,this.id)" id="Ems">周期 毫秒(ms)<br>
			<input type="box" name="Energy" onInput="setVal(this.name,this.id)" id="Eus">周期 微秒(&mu;s)<br>
			<input type="box" name="Energy" onInput="setVal(this.name,this.id)" id="Ens">周期 纳秒(ns)<br>
			<input type="box" name="Energy" onInput="setVal(this.name,this.id)" id="Eps">周期 皮秒(ps)<br>
			<input type="box" name="Energy" onInput="setVal(this.name,this.id)" id="Efs">周期 飞秒(fs)<br>
			<input type="box" name="Energy" onInput="setVal(this.name,this.id)" id="Eas">周期 阿秒(as)<br>
		</td></tr>
		</table>

		<table id="TabFrc">
		<tr><td>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_N"> 牛顿(N)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_dyn"> 达因(dyn)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_mN"> 毫牛(mN)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_uN"> 微牛(&mu;N)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_nN"> 纳牛(nN)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_pN"> 皮牛(pN)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_au"> 原子单位(Hartree/Bohr)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_auA"> 原子埃单位(Hartree/&#197;)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_e2A"> 静电埃(e<sup>2</sup>/&#197;<sup>2</sup>)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_e2nm"> 静电纳米(e<sup>2</sup>/nm<sup>2</sup>)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_mpc"> MOPAC单位(kcal/mol-&#197;)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_md"> MD常见单位(kJ/mol-&#197;)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_gmx"> GROMACS单位(kJ/mol-nm)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_amu1"> MD常用单位(amu-&#197;/fs<sup>2</sup>)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_amu2"> MD常用单位(amu-nm/ps<sup>2</sup>)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_Pam"> 压强面积单位(Pa-m<sup>2</sup>)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_MPaA"> 压强面积单位(MPa-&#197;<sup>2</sup>)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_MPanm"> 压强面积单位(MPa-nm<sup>2</sup>)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_GPaA"> 压强面积单位(GPa-&#197;<sup>2</sup>)<br>
			<input type="box" name="Force" onInput="setVal(this.name,this.id)" id="F_GPanm"> 压强面积单位(GPa-nm<sup>2</sup>)<br>
		</td></tr>
		</table>

		<table id="TabPrs">
		<tr><td>
			<input type="box" name="Press" onInput="setVal(this.name,this.id)" id="P_Pa"> 帕斯卡(Pa)<br>
			<input type="box" name="Press" onInput="setVal(this.name,this.id)" id="P_kPa"> 千帕(kPa)<br>
			<input type="box" name="Press" onInput="setVal(this.name,this.id)" id="P_MPa"> 兆帕(Mpa)<br>
			<input type="box" name="Press" onInput="setVal(this.name,this.id)" id="P_GPa"> 吉帕(Gpa)<br>
			<input type="box" name="Press" onInput="setVal(this.name,this.id)" id="P_dyncm"> 达因/厘米<sup>2</sup>(dyn/cm<sup>2</sup>)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Press" onInput="setVal(this.name,this.id)" id="P_bar"> 巴(bar, 标准压力)<br>
			<input type="box" name="Press" onInput="setVal(this.name,this.id)" id="P_atm"> 标准大气压(atm)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Press" onInput="setVal(this.name,this.id)" id="P_mmH2O"> 毫米水柱(mmH2O)<br>
			<input type="box" name="Press" onInput="setVal(this.name,this.id)" id="P_mmHg"> 毫米汞柱(mmHg)<br>
			<input type="box" name="Press" onInput="setVal(this.name,this.id)" id="P_Torr"> 托(Torr)<br>
		</td></tr>
		</table>

		<table id="TabCon">
		<tr><td>
			<input type="box" name="Conc" onInput="setVal(this.name,this.id)" id="C_M"> M(mol/L)<br>
			<input type="box" name="Conc" onInput="setVal(this.name,this.id)" id="C_mM"> mM(mmol/L)<br>
			<input type="box" name="Conc" onInput="setVal(this.name,this.id)" id="C_uM"> &mu;M(&mu;mol/L)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Conc" onInput="setVal(this.name,this.id)" id="C_cm3"> molec/cm<sup>3</sup><br>
			<input type="box" name="Conc" onInput="setVal(this.name,this.id)" id="C_nm3"> molec/nm<sup>3</sup><br>
			<input type="box" name="Conc" onInput="setVal(this.name,this.id)" id="C_A3"> molec/&#197;<sup>3</sup><br>
		</td></tr>
		<tr><td>
			<input type="checkbox" name="TP" onClick="setTP(this.name,this.id)" id="chk_TP" > 使用温度/压强计算(理想气体)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Conc" onInput="setTP(this.name,this.id)" id="C_K" value="298.15"> 温度(K)&nbsp;
			<input type="radio" name="TP" id="rdo_K" checked> 固定<br>
			<input type="box" name="Conc" onInput="setTP(this.name,this.id)" id="C_Pa" value="101325"> 压强(Pa)
			<input type="radio" name="TP" id="rdo_Pa"> 固定<br>
		</td></tr>
		</table>

		<table id="TabRho">
		<tr><td>
			<input type="box" name="Rho" onInput="setVal(this.name,this.id)" id="R_gmL"> g/mL(g/cm<sup>3</sup>, kg/L)<br>
			<input type="box" name="Rho" onInput="setVal(this.name,this.id)" id="R_gL"> g/L(kg/m<sup>3</sup>)<br>
			<input type="box" name="Rho" onInput="setVal(this.name,this.id)" id="R_amuA3"> amu/&#197;<sup>3</sup><br>
		</td></tr>
		<tr><td>
			<input type="checkbox" name="MC" onClick="setMC(this.name,this.id)" id="chk_MC"> 使用分子量/摩尔浓度计算(纯物质)<br>
		</td></tr>
		<tr><td>
			<input type="box" name="Rho" onInput="setMC(this.name,this.id)" id="R_amu" value="18"> 分子量(amu, g/mol)
			<input type="radio" name="MC" id="rdo_amu" checked> 固定<br>
			<input type="box" name="Rho" onInput="setMC(this.name,this.id)" id="R_M" value="55.5"> 摩尔浓度(M, mol/L)
			<input type="radio" name="MC" id="rdo_M"> 固定<br>
		</td></tr>
		</table>

		<table id="TabVDW">
		<tr align="center">
		<td colspan="5">
		<img src="Ulj.png" width="50%"><br>
		$U_{LJ}(r) = {C_{12} \over r^{12}} - {C_6 \over r^6} ={A \over r^{12}} - {C \over r^6}
		=4ε\left[\left( {σ\over r}\right)^{12}-\left({σ\over r}\right)^6\right] \\
		=ε\left[\left( {R_{min}\over r}\right)^{12}-2\left({R_{min}\over r}\right)^6\right]
		=ε\left[\left( {R_e\over r}\right)^{12}-2\left({R_e\over r}\right)^6\right]
		=D_0\left[\left( {R_0\over r}\right)^{12}-2\left({R_0\over r}\right)^6\right]$
		</td>
		</tr>
		<tr>
		<td>原子 1</td><td>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_sgm1" value='1'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_eps1" value='1'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_re1" value='1.122462048'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_C61" value='4'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_C121" value='4'><br>
		</td><td>
			&sigma;=(C<sub>12</sub>/C<sub>6</sub>)<sup>1/6</sup>(硬球半径)<br>
			&epsilon;=C<sub>6</sub><sup>2</sup>/(4*C<sub>12</sub>)(势阱深度)<br>
			R<sub>min</sub>=2<sup>1/6</sup>&sigma;(平衡距离)<br>
			C<sub>6</sub>=4&epsilon;&sigma;<sup>6</sup><br>
			C<sub>12</sub>=4&epsilon;&sigma;<sup>12</sup><br>
		</td>
		<td>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_sgm2" value='1'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_eps2" value='0.25'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_re2" value='1.122462048'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_C62" value='1'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_C122" value='1'><br>
		</td>
		<td>原子 2</td>
		</tr>
		<tr><td>LB组合规则<br>(Lorentz-Berthelot)<br>AMBER CHARMM</td>
		<td>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_sgmLB" value='1'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_epsLB" value='0.5'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_reLB" value='1.122462048'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_C6LB" value='2'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_C12LB" value='2'><br>
		</td><td>
			&sigma;=(&sigma;<sub>1</sub>+&sigma;<sub>2</sub>)/2 (算术均值)<br>
			&epsilon;=sqrt(&epsilon;<sub>1</sub>*&epsilon;<sub>2</sub>) (几何均值)<br>
			R<sub>min</sub>=2<sup>1/6</sup>&sigma;<br>
			C<sub>6</sub>=4&epsilon;&sigma;<sup>6</sup><br>
			C<sub>12</sub>=4&epsilon;&sigma;<sup>12</sup><br>
		</td>
		</tr>
		<tr><td>OPLS-AA组合规则<br>(几何平均值)<br><br><br>C6/C12组合规则<br>(C系数几何平均值)</td><td>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_sgmg" value='1'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_epsg" value='0.5'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_reg" value='1.122462048'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_C6g" value='2'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_C12g" value='2'><br>
		</td><td>
			&sigma;=sqrt(&sigma;<sub>1</sub>*&sigma;<sub>2</sub>)=(C<sub>12</sub>/C<sub>6</sub>)<sup>1/6</sup> (几何均值)<br>
			&epsilon;=sqrt(&epsilon;<sub>1</sub>*&epsilon;<sub>2</sub>)=C<sub>6</sub><sup>2</sup>/(4*C<sub>12</sub>) (几何均值)<br>
			R<sub>min</sub>=2<sup>1/6</sup>&sigma;<br>
			C<sub>6</sub>=4&epsilon;&sigma;<sup>6</sup>=sqrt(C<sub>6</sub><sup>(1)</sup>*C<sub>6</sub><sup>(2)</sup>)<br>
			C<sub>12</sub>=4&epsilon;&sigma;<sup>12</sup>=sqrt(C<sub>12</sub><sup>(1)</sup>*C<sub>12</sub><sup>(2)</sup>)<br>
		</td>
		</tr>
		<tr><td>算术平均规则<br>(算术平均值)</td><td>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_sgma" value='1'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_epsa" value='0.5'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_rea" value='1.122462048'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_C6a" value='2'><br>
			<input type="box" name="VDW" onInput="setVDW(this.name,this.id)" id="V_C12a" value='2'><br>
		</td><td>
			&sigma;=(&sigma;<sub>1</sub>+&sigma;<sub>2</sub>)/2 (算术均值)<br>
			&epsilon;=(&epsilon;<sub>1</sub>+&epsilon;<sub>2</sub>)/2 (算术均值)<br>
			R<sub>min</sub>=2<sup>1/6</sup>&sigma;<br>
			C<sub>6</sub>=4&epsilon;&sigma;<sup>6</sup><br>
			C<sub>12</sub>=4&epsilon;&sigma;<sup>12</sup><br>
		</td>
		</tr>
		</table>
	</div>

	<input type="radio" name="tab-radio" class="tab-radio" id="tab-radio-3">
	<label for="tab-radio-3" class="tab-handler">统计</label>
	<div class="tab-content tab-content-3">
		<table style="display: block;">
		<tr><th>A数据集</th><th>B数据集</th></tr>
		<tr><td><textarea id="datA" style="width: 200px; height: 300px; margin: 0px;"></textarea></td>
			<td><textarea id="datB" style="width: 200px; height: 300px; margin: 0px;"></textarea></td></tr>
		</tbody></table>

		<br><input type="button" value="统计" onclick="getRMSE()" style="width:100px; height:30px">
		数值换算因子<input type="box" id="fac" value="1" style="width:300px; height:30px">
		输出格式<input type="box" id="fmt" value="9.3" style="width:100px; height:30px"><br>
		数据个数: <span id="datNum"></span> 数据维数: <span id="datDim"></span><br><br>

		<table style="display: block;overflow:auto">
			<tbody><tr><th>数据点</th><th>加和<br>$$\text{SUM}=\Sum_{j=1}^{N_{dim} } a_{i,j}$$</th><th>平均值<br>$$\text{AVG}={\text{SUM} \over N_{dim} }$$</th><th>平方和<br>$\text{SSQ}=\Sum_{j=1}^{N_{dim} } a_{i,j}^2$</th><th>长度<br>$$\text{LEN}=\sqrt{\text{SSQ} }$$</th><th>方差<br>$$\text{VAR}=\s^2={\text{SSQ} \over N_{dim} }-\text{AVG}^2$$</th><th>总体标准偏差<br>$$\text{RMSD}=\s=\sqrt{\text{VAR} }$$</th><th>样本标准偏差<br>$$\text{RMSE}=s={\sqrt{N_{dim} } \over \sqrt{N_{dim}-1 } }\text{RMSD}$$</th></tr>

			<tr><td>A</td><td id="sumA"></td><td id="avgA"></td><td id="ssqA"></td><td id="magA"></td><td id="varA"></td><td id="rmsdA"></td><td id="rmseA"></td></tr>
			<!--tr><td>A长度</td><td id="summagA"></td><td id="avgmagA"></td><td id="magmagA"></td><td id="ssqmagA"></td><td id="varmagA"></td><td id="rmsdmagA"></td></tr-->

			<tr><td>B</td><td id="sumB"></td><td id="avgB"></td><td id="ssqB"></td><td id="magB"></td><td id="varB"></td><td id="rmsdB"></td><td id="rmseB"></td></tr>
			<!--tr><td>B长度</td><td id="summagB"></td><td id="avgmagB"></td><td id="magmagB"></td><td id="ssqmagB"></td><td id="varmagB"></td><td id="rmsdmagB"></td></tr-->

			<!--tr><th>数据</th><th>加和<br>$$\text{SUM}=\Sum_{j=1}^{N_{dim} }(a_{i,j}-b_{i,j})$$</th><th>平均值<br>$$\text{AVG}={\text{SUM} \over N_{dim} }$$</th><th>平方和<br>$\text{SSQ}=\Sum_{j=1}^{N_{dim} } (a_{i,j}-b_{i,j})^2$</th><th>长度<br>$$\text{LEN}=\sqrt{\text{SSQ} }$$</th><th>方差<br>$$\text{VAR}={\text{SSQ} \over N_{dim} }$$</th><th>标准偏差<br>$$\text{RMSD}=\sqrt{\text{VAR} \over N_{dim} -1}$$</th><th>标准误差<br>$$\text{RMSD}=\sqrt{\text{VAR} \over N_{dim} }$$</th></tr-->

			<tr><td>A-B</td><td id="sumC"></td><td id="avgC"></td><td id="ssqC"></td><td id="magC"></td><td id="varC"></td><td id="rmsdC"></td><td id="rmseC"></td></tr>
			<!--tr><td>A-B长度</td><td id="summagC"></td><td id="avgmagC"></td><td id="ssqmagC"></td><td id="magmagC"></td><td id="varmagC"></td><td id="rmsemagC"></td></tr-->

		</table>
	</div>

	<input type="radio" name="tab-radio" class="tab-radio" id="tab-radio-4">
	<label for="tab-radio-4" class="tab-handler">回归</label>
	<div class="tab-content tab-content-4" style="height:600;">
		<div style="height:100%;width:100%;display:flex;justify-content:space-between;">
			<div style="flex:0 0 40%;overflow:scroll;">
				数据
				<textarea id="data" style="width: 90%; height:60%; margin: 0px;">
1 1 2
2 1 3
1 2 3
				</textarea><br>
				<input type="checkbox" id="Yconst">包含常数项<br>
				<input type="checkbox" id="Y1st">第一列为Y<br>
				<input type="button" value="线性回归" onClick="reg()" style="width:100px; height:30px"><br>
				<span id='Yreg' style='font: .6em Consolas;'></span>
			</div>

			<div id='right' style="height:100%;flex:1;overflow:scroll">
				<canvas id="myChart" style="width:90%; height:90%;"></canvas>
			</div>
		</div>
	</div>

	<input type="radio" name="tab-radio" class="tab-radio" id="tab-radio-5">
	<label for="tab-radio-5" class="tab-handler">拟合</label>
	<div class="tab-content tab-content-5" >

<table style="display: block; width:100%; height:600; border-collapse: collapse;">

<tr>
<td rowspan='2' style="width:80%;height:100%;"><canvas id="datChart"></canvas></td>

<td>拟合数据(第一行给出每列名称, 应与拟合方程一致)<br><textarea id='xy' style="width:100%; height:80%;" onChange='init()'>
 # x        y
-5.000 14.268071
-4.950 14.423786
-4.900 14.223596
-4.850 13.989981
-4.800 14.338510
-4.750 13.849040
-4.700 13.465171
-4.650 13.641030
-4.600 13.636354
-4.550 13.486437
-4.500 13.965506
-4.450 13.397157
-4.400 13.684428
-4.350 13.329412
-4.300 13.070533
-4.250 12.908668
-4.200 12.985545
-4.150 12.106797
-4.100 12.333003
-4.050 12.465366
-4.000 11.655077
-3.950 11.087115
-3.900 11.182680
-3.850 10.577002
-3.800 10.169610
-3.750 10.436797
-3.700 10.165538
-3.650  9.401062
-3.600  8.788209
-3.550  8.660851
-3.500  8.457529
-3.450  7.433727
-3.400  7.758740
-3.350  7.499469
-3.300  6.555065
-3.250  5.990471
-3.200  5.508866
-3.150  5.280279
-3.100  5.272088
-3.050  4.394562
-3.000  3.639678
-2.950  4.133405
-2.900  3.432616
-2.850  2.464773
-2.800  2.689545
-2.750  2.665073
-2.700  1.937793
-2.650  1.847824
-2.600  1.316487
-2.550  0.655342
-2.500  1.207846
-2.450 -0.023536
-2.400 -0.240676
-2.350  0.096509
-2.300 -0.648143
-2.250 -0.049333
-2.200 -0.819018
-2.150 -0.579105
-2.100 -0.198047
-2.050 -0.562822
-2.000 -1.228407
-1.950 -0.919969
-1.900 -0.436566
-1.850 -0.238462
-1.800 -0.705457
-1.750 -0.268166
-1.700 -0.321615
-1.650 -0.273104
-1.600  0.095263
-1.550  0.168069
-1.500 -0.022335
-1.450  0.335233
-1.400  0.460525
-1.350  0.771372
-1.300  0.704674
-1.250  1.509236
-1.200  1.615110
-1.150  1.729355
-1.100  2.134087
-1.050  2.116924
-1.000  2.573202
-0.950  2.452794
-0.900  2.879854
-0.850  3.086274
-0.800  3.523536
-0.750  3.645728
-0.700  4.189110
-0.650  4.163559
-0.600  4.420417
-0.550  4.257384
-0.500  5.152350
-0.450  4.916877
-0.400  4.977034
-0.350  5.109310
-0.300  5.425246
-0.250  4.915457
-0.200  5.313216
-0.150  5.335836
-0.100  5.753816
-0.050  5.625750
-0.000  5.096752
 0.050  5.902090
 0.100  5.322333
 0.150  5.457066
 0.200  5.135733
 0.250  5.371180
 0.300  4.702331
 0.350  4.562546
 0.400  5.029012
 0.450  4.780856
 0.500  3.971323
 0.550  4.455629
 0.600  3.662749
 0.650  3.959948
 0.700  3.391426
 0.750  3.237756
 0.800  3.053220
 0.850  1.866086
 0.900  1.890811
 0.950  1.249901
 1.000  1.279436
 1.050  1.558698
 1.100  0.474996
 1.150  0.258619
 1.200  0.023783
 1.250  0.234939
 1.300 -0.389851
 1.350 -1.133469
 1.400 -1.455334
 1.450 -1.648919
 1.500 -1.432953
 1.550 -1.302325
 1.600 -2.257790
 1.650 -1.772068
 1.700 -2.308125
 1.750 -2.950250
 1.800 -2.653814
 1.850 -3.303896
 1.900 -3.421123
 1.950 -2.871874
 2.000 -2.845264
 2.050 -2.724668
 2.100 -2.840239
 2.150 -3.319548
 2.200 -3.317007
 2.250 -2.898392
 2.300 -3.204079
 2.350 -3.164109
 2.400 -2.457605
 2.450 -2.683270
 2.500 -2.438133
 2.550 -2.780601
 2.600 -1.635540
 2.650 -2.083215
 2.700 -1.958221
 2.750 -1.040967
 2.800 -0.893060
 2.850 -0.880647
 2.900 -0.874101
 2.950  0.033159
 3.000  0.135663
 3.050  0.153694
 3.100  0.489535
 3.150  0.514524
 3.200  0.562089
 3.250  1.003905
 3.300  1.664742
 3.350  1.659570
 3.400  1.934570
 3.450  2.042136
 3.500  2.873422
 3.550  3.464070
 3.600  3.530585
 3.650  3.677281
 3.700  4.080500
 3.750  4.260203
 3.800  4.177858
 3.850  4.114284
 3.900  4.047129
 3.950  4.165538
 4.000  4.744170
 4.050  4.070192
 4.100  4.516457
 4.150  4.711072
 4.200  4.178957
 4.250  4.825447
 4.300  5.048423
 4.350  4.773474
 4.400  4.264367
 4.450  4.302545
 4.500  4.435278
 4.550  4.015977
 4.600  4.039300
 4.650  3.959156
 4.700  3.076028
 4.750  3.402972
 4.800  3.197145
 4.850  3.159013
 4.900  2.165810
 4.950  1.995178
 5.000  1.626322
</textarea></td>
</tr>

<tr><td style="height:20%;max-height:20%;">
拟合方程<br>
<input class='box' style="width:100%; height: 2em; font-weight: bold; font-family: Consolas, 'Courier New', Courier, monospace" id='y'  onChange='init()' value='y=exp(-a*x)+b*cos(c*x)'><br><br>
拟合参数<br>
<input class='box' style="width:100%; height: 2em; font-weight: bold; font-family: Consolas, 'Courier New', Courier, monospace" id='py' value='a b c'>
</td></tr>

<tr>
<td rowspan='2' style="width:80%;height:100%;"><canvas id="fitChart"></canvas></td>
<td id='optParam' style="height:25%;max-height:25%;"><input type='button' class='box' value='设定初值' onClick='init(); setParam();'>
</td>
</tr>

<tr><td>
最大迭代次数 <input class='box' style='width:6em' id='maxIter' value='20'><br>
初始阻尼因子 <input class='box' style='width:6em' id='tau' value='1E-3'><br>
最大梯度值   <input class='box' style='width:6em' id='tolg' value='1E-4'><br>
步长百分比   <input class='box' style='width:6em' id='tolx' value='1E-8'><br>

<input type='button' class='box' value='单纯形优化' onClick='nmOpt()'><br>
<input type='button' class='box' value='LM优化' onClick='lmOpt()'>

</td></tr>

</table>
	</div>

</div>

<script>
var $=function(id){return document.getElementById(id)}

c=299792458           // exact 真空光速
Navg=6.02214076E23    // exact 阿付加德罗常数
echg=1.602176634E-19  // exact 基元电荷
ang=1.E-10            // exact 埃
nm=1.E-9              // exact 纳米
h=6.62607015E-34      // exact 普朗克常数
kb=1.380649E-23       // exact 玻尔兹曼常数
g=9.80665             // exact 标准重力加速度
atm=101325            // exact 标准大气压
P0=100000             // exact 标准压力
T0=298.15             // exact 标准压力
R=8.314462618         // exact 摩尔气体常数
c2j=4.184             // exact 卡焦互换
debye=1.E-21/c        // exact Debye

hbar=.5*h/Math.PI     // 原子作用单位
Na=Navg
qe=echg
pi=Math.PI
j2cal=1./c2j

amu=1.66053906660E-27    // 原子质量单位
ha=4.3597447222071E-18   // 原子能量单位
bohr=5.29177210903E-11   // 原子长度单位

eps0=8.8541878128E-12    // 介电常数
mu0 = 1.25663706212E-6   // 介磁常数
me=9.1093837015E-31      // 电子质量
mp=1.67262192369E-27     // 质子质量

G=6.67430E-11            // 万有引力常数

emas     = 9.1093837015e-31
pmas     = 1.67262192369e-27

aut      = 2.4188843265857e-17
auf      = 8.2387234983e-8

Rinf     = 2.1798723611035e-18    //  0.000 000 000 0042 e-18  J

amu2eV    =    9.3149410242e8      //  0.0000000028e8eV
amu2Hatr  =    3.4231776874e7      //  0.0000000010e7E_h
amu2Hz    =    2.25234271871e23    //  0.00000000068e23Hz
amu2invm  =    7.5130066104e14     //  0.0000000023e14m^-1
amu2J     =    1.49241808560e-10   //  0.00000000045e-10J
amu2K     =    1.08095401916e13    //  0.00000000033e13K
amu2kg    =    1.66053906660e-27   //  0.00000000050e-27kg
eV2amu    =    1.07354410233e-9    //  0.00000000032e-9u
eV2Hatr   =    3.6749322175655e-2  //  0.0000000000071e-2E_h
eV2Hz     =    2.417989242e14      //  (exact)Hz
eV2invm   =    8.065543937e5       //  (exact)m^-1
eV2J      =    1.602176634e-19     //  (exact)J
eV2K      =    1.160451812e4       //  (exact)K
eV2kg     =    1.782661921e-36     //  (exact)kg
Hatr2amu  =    2.92126232205e-8    //  0.00000000088e-8u
Hatr2eV   =   27.211386245988      //  0.000000000053eV
Hatr2Hz   =    6.579683920502e15   //  0.000000000013e15Hz
Hatr2invm =    2.1947463136320e7   //  0.0000000000043e7m^-1
Hatr2J    =    4.3597447222071e-18 //  0.0000000000085e-18J
Hatr2K    =    3.1577502480407e5   //  0.0000000000061e5K
Hatr2kg   =    4.8508702095432e-35 //  0.0000000000094e-35kg
Hz2amu    =    4.4398216652e-24    //  0.0000000013e-24u
Hz2eV     =    4.135667696e-15     //  (exact)eV
Hz2Hatr   =    1.5198298460570e-16 //  0.0000000000029e-16E_h
Hz2invm   =    3.335640951e-9      //  (exact)m^-1
Hz2J      =    6.62607015e-34      //  (exact)J
Hz2K      =    4.799243073e-11     //  (exact)K
Hz2kg     =    7.372497323e-51     //  (exact)kg
invm2amu  =    1.33102505010e-15   //  0.00000000040e-15u
invm2eV   =    1.239841984e-6      //  (exact)eV
invm2Hatr =    4.5563352529120e-8  //  0.0000000000088e-8E_h
invm2Hz   =      299792458         //  (exact)Hz
invm2J    =    1.986445857e-25     //  (exact)J
invm2K    =    1.438776877e-2      //  (exact)K
invm2kg   =    2.210219094e-42     //  (exact)kg
J2amu     =    6.7005352565e9      //  0.0000000020e9u
J2eV      =    6.241509074e18      //  (exact)eV
J2Hatr    =    2.2937122783963e17  //  0.0000000000045e17E_h
J2Hz      =    1.509190179e33      //  (exact)Hz
J2invm    =    5.034116567e24      //  (exact)m^-1
J2K       =    7.242970516e22      //  (exact)K
J2kg      =    1.112650056e-17     //  (exact)kg
K2amu     =    9.2510873014e-14    //  0.0000000028e-14u
K2eV      =    8.617333262e-5      //  (exact)eV
K2Hatr    =    3.1668115634556e-6  //  0.0000000000061e-6E_h
K2Hz      =    2.083661912e10      //  (exact)Hz
K2invm    =   69.50348004          //  (exact)m^-1
K2J       =    1.380649e-23        //  (exact)J
K2kg      =    1.536179187e-40     //  (exact)kg
kg2amu    =    6.0221407621e26     //  0.0000000018e26u
kg2eV     =    5.609588603e35      //  (exact)eV
kg2Hatr   =    2.0614857887409e34  //  0.0000000000040e34E_h
kg2Hz     =    1.356392489e50      //  (exact)Hz
kg2invm   =    4.524438335e41      //  (exact)m^-1
kg2J      =    8.987551787e16      //  (exact)J
kg2K      =    6.509657260e39      //  (exact)K

L_m    =1.0;   L_km =1.E3;  L_cm =1.E-2;  L_mm =1.E-3;
L_um   =1.E-6; L_nm =1.E-9; L_pm =1.E-12; L_fm =1.E-15
L_bohr  =bohr;   L_ang =1.E-10
L_pnt  =.0254/72.; L_inch =.0254; L_foot =.3048
L_yard =.9144; L_mile =1609.344

M_kg=1.0; M_g=1E-3; M_mg=1E-6; M_ug=1E-9
M_emas=emas; M_pmas=pmas; M_amu=amu2kg
M_eV=eV2kg; M_MeV=eV2kg*1E6; M_GeV=eV2kg*1E9; M_TeV=eV2kg*1E12
M_ton=1E3; M_car=2E-4; M_onc=.028352; M_pd=.453632

T_s=1.; T_minu=60; T_h=3600; T_d=86400
T_ms=1E-3; T_us=1E-6; T_ns=1E-9; T_ps=1E-12; T_fs=1E-15; T_as=1E-18
T_au=aut; T_m=30*T_d; T_a=365*T_d; T_am=29.53*T_d; T_aa=365.2422*T_d

cal=4.184
J2cal      = 1./cal
J2erg      = 1./1.E-7
J2kJ_mol   = Navg/1000.
J2kcal_mol = Navg/1000.*J2cal
J2MJ_mol   = Navg/1.E6
J2Mcal_mol = Navg/1.E6*J2cal
J2Emd      = 1./(amu*(ang/T_fs)**2)
J2Emd2     = 1./(amu*(nm /T_ps)**2)
J2Ry       = 1./Rinf
invm2invcm=1.E-2
Hatr2Ee2bohr=1.
Hatr2Ee2A=ang/bohr
Hatr2Ee2nm=nm/bohr

m2Em=1; m2Ecm=1E2;  m2Emm=1E3;     m2Eum=1.E6;   m2Enm=1.E9; m2Eang=1.E10
eV2MeV=1.E-6; eV2GeV=1.E-9; eV2TeV=1.E-12; eV2PeV=1.E-15
Hz2MHz=1.E-6; Hz2GHz=1.E-9; Hz2THz=1.E-12; Hz2PHz=1.E-15
Hz2Es=T_s; Hz2Ems=T_ms; Hz2Eus=T_us; Hz2Ens=T_ns; Hz2Eps=T_ps; Hz2Efs=T_fs; Hz2Eas=T_as

F_N=1.0; F_dyn=1E-5; F_mN=1E-3; F_uN=1E-6; F_nN=1E-9; F_pN=1E-12
F_au=auf; F_auA=Hatr2J/L_ang
F_e2A=auf*bohr*bohr/(ang*ang); F_e2nm=auf*bohr*bohr/(nm*nm);
F_mpc=1/J2kcal_mol/L_ang; F_gmx=1/J2kJ_mol/L_nm
F_md=1/J2kJ_mol/L_ang
F_amu1=amu2kg*ang/T_fs**2;
F_amu2=amu2kg*nm/T_ps**2;

P_Pa=1.; P_kPa=1E3; P_MPa=1E6; P_GPa=1E9
P_dyncm=1E-1; P_bar=1E5; P_atm=101325
P_mmH2O=1.004514556*g; P_mmHg=13.5951*g; P_Torr=P_mmHg

F_Pam=1.0
F_MPaA=P_MPa*ang**2; F_MPanm=P_MPa*nm**2
F_GPaA=P_GPa*ang**2; F_GPanm=P_GPa*nm**2

C_M=1.; C_mM=1E-3; C_uM=1E-6; C_A3=1/Navg*1E27; C_cm3=1/Navg*1E3; C_nm3=1/Navg*1E24

R_gmL=1.; R_gL=1.E-3; R_amuA3=amu2kg*1E30*1E-3

function setUnit(id) {
	unit=document.getElementsByTagName('table')
	for(i=0; i<unit.length; i++) unit[i].style.display='none'
	$('Tab'+id).style.display='block'
}

$('V_sgmg').disabled=true; $('V_sgma').disabled=true
$('V_epsg').disabled=true; $('V_epsa').disabled=true
$('V_reg' ).disabled=true; $('V_rea' ).disabled=true
$('V_C6g' ).disabled=true; $('V_C6a' ).disabled=true
$('V_C12g').disabled=true; $('V_C12a').disabled=true

$('V_sgmLB').disabled=true
$('V_epsLB').disabled=true
$('V_reLB' ).disabled=true
$('V_C6LB' ).disabled=true
$('V_C12LB').disabled=true

function mathEval(str) {
	var fun="abs acos asin atan atan2 ceil cos exp floor log max min pow random round sin sqrt tan toSource valueOf"
	fun=fun.split(/\s+/)
	for(var i=0, n=fun.length; i<n; i++)
		str=str.replace(new RegExp(fun[i]+'\\(','g'), 'Math.'+fun[i]+'\(')
	return eval(str)
}

function setVDW(name, id) {
	var f=Math.pow(2, 1./6.)
	val=mathEval($(id).value)

	$('inputValue').innerHTML='输入框: '+$(id).value+' = '+mathEval($(id).value)

	if(id=='V_sgm1' || id=='V_re1' || id=='V_eps1') {
		if(id=='V_sgm1') { V_sgm1=val; V_re1=f*V_sgm1; V_eps1=mathEval($('V_eps1').value) }
		if(id=='V_re1')  { V_re1=val;  V_sgm1=val/f;   V_eps1=mathEval($('V_eps1').value) }
		if(id=='V_eps1') { V_eps1=val; V_sgm1=mathEval($('V_sgm1').value); V_re1=f*V_sgm1 }

		V_C61=4*V_eps1*Math.pow(V_sgm1, 6)
		V_C121=4*V_eps1*Math.pow(V_sgm1, 12)
	} else if(id=='V_C61' || id=='V_C121') {
		if(id=='V_C61')  { V_C61=val;  V_C121=mathEval($('V_C121').value) }
		if(id=='V_C121') { V_C121=val; V_C61=mathEval($('V_C61').value) }

		V_sgm1=Math.pow(V_C121/V_C61, 1./6.)
		V_eps1=0.25*V_C61*V_C61/V_C121
		V_re1=f*V_sgm1
	}

	if(id=='V_sgm2' || id=='V_re2' || id=='V_eps2') {
		if(id=='V_sgm2') { V_sgm2=val; V_re2=f*V_sgm2; V_eps2=mathEval($('V_eps2').value) }
		if(id=='V_re2')  { V_re2=val;  V_sgm2=val/f;   V_eps2=mathEval($('V_eps2').value) }
		if(id=='V_eps2') { V_eps2=val; V_sgm2=mathEval($('V_sgm2').value); V_re2=f*V_sgm2 }

		V_C62=4*V_eps2*Math.pow(V_sgm2, 6)
		V_C122=4*V_eps2*Math.pow(V_sgm2, 12)
	} else if(id=='V_C62' || id=='V_C122') {
		if(id=='V_C62')  { V_C62=val;  V_C122=mathEval($('V_C122').value) }
		if(id=='V_C122') { V_C122=val; V_C62=mathEval($('V_C62').value) }

		V_sgm2=Math.pow(V_C122/V_C62, 1./6.)
		V_eps2=0.25*V_C62*V_C62/V_C122
		V_re2=f*V_sgm2
	}

	if(id.slice(-1)=='2') {
		V_sgm1=mathEval($('V_sgm1').value)
		V_eps1=mathEval($('V_eps1').value)
		V_C61=mathEval($('V_C61').value)
		V_C121=mathEval($('V_C121').value)
		V_re1=f*V_sgm1
	}
	if(id.slice(-1)=='1') {
		V_sgm2=mathEval($('V_sgm2').value)
		V_eps2=mathEval($('V_eps2').value)
		V_C62 =mathEval($('V_C62').value)
		V_C122=mathEval($('V_C122').value)
		V_re2=f*V_sgm2
	}

	V_sgmg=Math.sqrt(V_sgm1*V_sgm2); V_sgma=0.5*(V_sgm1+V_sgm2)
	V_epsg=Math.sqrt(V_eps1*V_eps2); V_epsa=0.5*(V_eps1+V_eps2)
	V_reg =Math.sqrt(V_re1*V_re2)  ; V_rea =0.5*(V_re1+V_re2)
	V_C6g =Math.sqrt(V_C61*V_C62)  ; V_C6a =0.5*(V_C61+V_C62)
	V_C12g=Math.sqrt(V_C121*V_C122); V_C12a=0.5*(V_C121+V_C122)

	V_sgmLB=0.5*(V_sgm1+V_sgm2)
	V_epsLB=Math.sqrt(V_eps1*V_eps2)
	V_reLB =f*V_sgmLB
	V_C6LB =4*V_epsLB*Math.pow(V_sgmLB, 6)
	V_C12LB=4*V_epsLB*Math.pow(V_sgmLB, 12)

	unit=document.getElementsByName(name)
	for(i=0; i<unit.length; i++) {
		if(unit[i].id!=id) unit[i].value=fmt(mathEval(unit[i].id))
	}
}

function setTP(name, id) {
	if(id=='chk_TP') {
		$('C_M').disabled=$(id).checked
		$('C_mM').disabled=$(id).checked
		$('C_uM').disabled=$(id).checked
		$('C_A3').disabled=$(id).checked
		$('C_cm3').disabled=$(id).checked
		$('C_nm3').disabled=$(id).checked
		$('rdo_K').disabled=$(id).checked
		$('rdo_Pa').disabled=$(id).checked
		$('C_K').value=298.15
		$('C_Pa').value=101325
	}
	var Temp=mathEval($('C_K').value), Pres=mathEval($('C_Pa').value)
	$('C_M').value=fmt(Pres*1E-3/(R*Temp))
	setVal('Conc', 'C_M')
}

function setMC(name, id) {
	if(id=='chk_MC') {
		$('R_gmL').disabled=$(id).checked
		$('R_gL').disabled=$(id).checked
		$('R_amuA3').disabled=$(id).checked
		$('rdo_amu').disabled=$(id).checked
		$('rdo_M').disabled=$(id).checked
		$('R_amu').value=18
		$('R_M').value=55.56
	}
	var C=mathEval($('R_M').value), M=mathEval($('R_amu').value)
	$('R_gmL').value=fmt(M*C*1E-3)
	setVal('Rho', 'R_gmL')
}

function setVal(name, id) {
	var i, j, tmp, id2, txt, val

	var drvUnit={ 'Emd':'J', 'Emd2':'J', 'invcm':'invm',
		'cal':'J', 'erg':'J', 'Ry':'J',
		'kcal_mol':'J', 'kJ_mol':'J',
		'Mcal_mol':'J', 'MJ_mol':'J',
		'MeV':'eV', 'GeV':'eV', 'TeV':'eV', 'PeV':'eV',
		'MHz':'Hz', 'GHz':'Hz', 'PHz':'Hz', 'THz':'Hz',
		'Em':'Rinvm', 'Ecm':'Rinvm', 'Emm':'Rinvm',
		'Eum':'Rinvm', 'Enm':'Rinvm', 'Eang':'Rinvm',
		'Ee2bohr':'Hatr', 'Ee2A':'Hatr', 'Ee2nm':'Hatr',
		'Es': 'RinvHz', 'Ems': 'RinvHz', 'Eus': 'RinvHz',
		'Ens': 'RinvHz', 'Eps': 'RinvHz', 'Efs': 'RinvHz',
		'Eas': 'RinvHz'}

	unit=document.getElementsByName(name)

	$('inputValue').innerHTML='输入表达式: '+$(id).value+' = '+mathEval($(id).value)
	if(name!='Energy') {
		val=mathEval($(id).value+'*'+id); // 转换为基本单位
		for(i=0; i<unit.length; i++) {
			if(unit[i].id!=id) {
				if(unit[i].id!='C_K' && unit[i].id!='C_Pa'
					&& unit[i].id!='R_amu' && unit[i].id!='R_M') {
					unit[i].value=fmt(mathEval(val+'/'+unit[i].id)) // 反转换
				} else {
					if(!$('chk_TP').checked) {
						if(unit[i].id=='C_K'  && !$('rdo_K').checked)  $('C_K').value=fmt(mathEval($('C_Pa').value)*1E-3/(val*R))
						if(unit[i].id=='C_Pa' && !$('rdo_Pa').checked) $('C_Pa').value=fmt(val*R*mathEval($('C_K').value)*1E3)
					}
					if(!$('chk_MC').checked) {
						if(unit[i].id=='R_amu' && !$('rdo_amu').checked) $('R_amu').value=fmt(val/mathEval($('R_M').value))
						if(unit[i].id=='R_M'   && !$('rdo_M').checked) $('R_M').value=fmt(val*1E3/mathEval($('R_amu').value))
					}
				}
			}
		}
	} else {
		val=mathEval($(id).value)
		txt=drvUnit[id]
		if(txt) {
			if(txt=='Rinvm') { val=mathEval(1/val+'*m2'+id); txt='invm' }
			else if(txt=='RinvHz') { val=mathEval(1/val+'/Hz2'+id); txt='Hz' }
			else val=mathEval(val+'/'+txt+'2'+id)

			$(txt).value=fmt(val)
			id2=id
			id=txt
		}

		for(i=0; i<unit.length; i++) {
			tmp=id+'2'+unit[i].id
			if(window[tmp] != undefined && unit[i].id!=id2) {
				unit[i].value=fmt(mathEval(val+'*'+tmp))
			}
		}

		for(i=0; i<unit.length; i++) {
			tmp=unit[i].id
			txt=drvUnit[tmp]
			if(txt) {
				if(txt=='Rinvm') {
					val=1/$('invm').value
					if(unit[i].id!=id2) unit[i].value=fmt(mathEval(val+'*m2'+tmp))
				}
				else if(txt=='RinvHz') {
					val=1/$('Hz').value
					if(unit[i].id!=id2) unit[i].value=fmt(mathEval(val+'/Hz2'+tmp))
				} else {
					val=$(txt).value
					if(unit[i].id!=id2) unit[i].value=fmt(mathEval(val+'*'+txt+'2'+tmp))
				}
			}
		}
	}
}

function fmt(txt) {
	txt=txt.toPrecision(15).replace(/0+e/,'e').replace(/\.0+$/,'.')
	if(txt.indexOf('e')==-1 && txt.indexOf('.')!=-1) txt=txt.replace(/0+$/, '')
	return txt
}

function printf() {
	var map = {
		s: function(str, fmt) { var n=str.length; return n>fmt ? str : str+Array(fmt-n+1).join(' ')},
		f: function(str, fmt) { fmt=fmt.split('.'); str=parseFloat(str).toFixed(fmt[1]);
			var m=fmt[0], n=str.length; return n>m ? str : Array(m-n+1).join('&nbsp;')+str
		}
	}
	var args = Array.prototype.slice.call(arguments).slice();
	return args.shift().toString().replace(/%(-*\d*\.*\d*)([sf])/g, function(_, fmt, type){
		if(!args.length) throw new Error('Too few elements')
		return map[type](args.shift().toString(), fmt);
	});
}

Array.prototype.sum = function () {
	for(var t=0,i=this.length; i--; t+=parseFloat(this[i])); return t;
}
Array.prototype.ssq = function () {
	for(var t=0,i=this.length; i--; t+=parseFloat(this[i])*parseFloat(this[i])); return t;
}
Array.prototype.avg  = function () { return this.sum()/this.length }
Array.prototype.mag  = function () { return Math.sqrt(this.ssq())  }
Array.prototype.var  = function () { return this.ssq()/this.length - Math.pow(this.avg(), 2)  }
Array.prototype.rmsd = function () { return Math.sqrt(this.var()) }
Array.prototype.rmse = function () { return Math.sqrt(this.var()*this.length/(this.length-1)) }

function getRMSE() {
	var i, j, tmp, txt, Ndat=0, Ndim=0, NdatA, NdimA=0, NdatB, NdimB=0,
		datA=[], sumA=[], avgA=[], magA=[], ssqA=[], varA=[], rmsdA=[],
		datB=[], sumB=[], avgB=[], magB=[], ssqB=[], varB=[], rmsdB=[],
		datC=[], sumC=[], avgC=[], magC=[], ssqC=[], varC=[], rmseC=[],
		factor=parseFloat(mathEval($('fac').value)), digit='%'+$('fmt').value+'f'

	txt=$('datA').value.replace(/^\s*\n*/,"").replace(/\s*\n*$/,"").replace(/\s+[\n|$]/g,"\n")
	if(txt.length>0) { txt=txt.split('\n'); NdimA=txt[0].split(/\s+/).length }

	NdatA=txt.length
	for(i=0; i<NdatA; i++) {
		datA[i]=txt[i].replace(/^\s+/,"").split(/\s+/)
		j=datA[i].length; while(j--) datA[i][j] *= factor
		sumA[i] = datA[i].sum()
		avgA[i] = datA[i].avg()
		magA[i] = datA[i].mag()
		ssqA[i] = datA[i].ssq()
		varA[i] = datA[i].var()
		rmsdA[i] = datA[i].rmsd()
		rmseA[i] = datA[i].rmse()
	}
	txt='<details>'; for(i=0;i<NdatA;i++) txt+=printf(digit,sumA[i])+'<br>'; $('sumA').innerHTML=txt+'</details>总计: '+printf(digit,sumA.sum())+'<br>平均: '+printf(digit,sumA.sum()/NdatA)
	txt='<details>'; for(i=0;i<NdatA;i++) txt+=printf(digit,avgA[i])+'<br>'; $('avgA').innerHTML=txt+'</details>总计: '+printf(digit,avgA.sum())+'<br>平均: '+printf(digit,avgA.sum()/NdatA)
	txt='<details>'; for(i=0;i<NdatA;i++) txt+=printf(digit,magA[i])+'<br>'; $('magA').innerHTML=txt+'</details>总计: '+printf(digit,magA.sum())+'<br>平均: '+printf(digit,magA.sum()/NdatA)
	txt='<details>'; for(i=0;i<NdatA;i++) txt+=printf(digit,ssqA[i])+'<br>'; $('ssqA').innerHTML=txt+'</details>总计: '+printf(digit,ssqA.sum())+'<br>平均: '+printf(digit,ssqA.sum()/NdatA)
	txt='<details>'; for(i=0;i<NdatA;i++) txt+=printf(digit,varA[i])+'<br>'; $('varA').innerHTML=txt +'<br><br>'
	txt='<details>'; for(i=0;i<NdatA;i++) txt+=printf(digit,rmsdA[i])+'<br>';$('rmsdA').innerHTML=txt+'<br><br>'
	txt='<details>'; for(i=0;i<NdatA;i++) txt+=printf(digit,rmseA[i])+'<br>';$('rmseA').innerHTML=txt+'<br><br>'

	//$('summagA').innerHTML='' ; $('summagB').innerHTML='' ; $('summagC').innerHTML=''
	//$('avgmagA').innerHTML='' ; $('avgmagB').innerHTML='' ; $('avgmagC').innerHTML=''
	//$('magmagA').innerHTML='' ; $('magmagB').innerHTML='' ; $('magmagC').innerHTML=''
	//$('ssqmagA').innerHTML='' ; $('ssqmagB').innerHTML='' ; $('ssqmagC').innerHTML=''
	//$('varmagA').innerHTML='' ; $('varmagB').innerHTML='' ; $('varmagC').innerHTML=''
	//$('rmsdmagA').innerHTML=''; $('rmsdmagB').innerHTML=''; $('rmsemagC').innerHTML=''
	//if(NdatA>0) {
	//	NdimA=datA[0].length
	//	$('summagA').innerHTML=printf(digit, magA.sum())
	//	$('avgmagA').innerHTML=printf(digit, magA.avg())
	//	$('magmagA').innerHTML=printf(digit, magA.mag())
	//	$('ssqmagA').innerHTML=printf(digit, magA.ssq())
	//	$('varmagA').innerHTML=printf(digit, magA.var())
	//	$('rmsdmagA').innerHTML=printf(digit, magA.rmsd())
	//}

	txt=$('datB').value.replace(/^\s*\n*/,"").replace(/\s*\n*$/,"").replace(/\s+[\n|$]/g,"\n")
	if(txt.length>0) { txt=txt.split('\n'); NdimB=txt[0].split(/\s+/).length }

	NdatB=txt.length
	for(i=0; i<NdatB; i++) {
		datB[i]=txt[i].replace(/^\s+/,"").split(/\s+/)
		j=datB[i].length; while(j--) datB[i][j] *= factor
		sumB[i] = datB[i].sum()
		avgB[i] = datB[i].avg()
		magB[i] = datB[i].mag()
		ssqB[i] = datB[i].ssq()
		varB[i] = datB[i].var()
		rmsdB[i] = datB[i].rmsd()
		rmseB[i] = datB[i].rmse()
	}
	txt='<details>'; for(i=0;i<NdatB;i++) txt+=printf(digit,sumB[i])+'<br>'; $('sumB').innerHTML=txt+'</details>总计: '+printf(digit,sumB.sum())+'<br>平均: '+printf(digit,sumB.sum()/NdatB)
	txt='<details>'; for(i=0;i<NdatB;i++) txt+=printf(digit,avgB[i])+'<br>'; $('avgB').innerHTML=txt+'</details>总计: '+printf(digit,avgB.sum())+'<br>平均: '+printf(digit,avgB.sum()/NdatB)
	txt='<details>'; for(i=0;i<NdatB;i++) txt+=printf(digit,magB[i])+'<br>'; $('magB').innerHTML=txt+'</details>总计: '+printf(digit,magB.sum())+'<br>平均: '+printf(digit,magB.sum()/NdatB)
	txt='<details>'; for(i=0;i<NdatB;i++) txt+=printf(digit,ssqB[i])+'<br>'; $('ssqB').innerHTML=txt+'</details>总计: '+printf(digit,ssqB.sum())+'<br>平均: '+printf(digit,ssqB.sum()/NdatB)
	txt='<details>'; for(i=0;i<NdatB;i++) txt+=printf(digit,varB[i])+'<br>'; $('varB').innerHTML=txt +'<br><br>'
	txt='<details>'; for(i=0;i<NdatB;i++) txt+=printf(digit,rmsdB[i])+'<br>';$('rmsdB').innerHTML=txt+'<br><br>'
	txt='<details>'; for(i=0;i<NdatB;i++) txt+=printf(digit,rmseB[i])+'<br>';$('rmseB').innerHTML=txt+'<br><br>'

	//if(NdatB>0) {
	//	NdimB=datB[0].length
	//	$('summagB').innerHTML=printf(digit, magB.sum())
	//	$('avgmagB').innerHTML=printf(digit, magB.avg())
	//	$('magmagB').innerHTML=printf(digit, magB.mag())
	//	$('ssqmagB').innerHTML=printf(digit, magB.ssq())
	//	$('varmagB').innerHTML=printf(digit, magB.var())
	//	$('rmsdmagB').innerHTML=printf(digit, magB.rmsd())
	//}

	Ndat=Math.min(NdatA, NdatB); $('datNum').innerHTML='A: '+NdatA+' B: '+NdatB+' A-B: '+Ndat
	Ndim=Math.min(NdimA, NdimB); $('datDim').innerHTML='A: '+NdimA+' B: '+NdimB+' A-B: '+Ndim

	for(i=0; i<Ndat; i++) {
		datC[i]=[]
		for(j=0; j<Ndim; j++) datC[i][j]=parseFloat(datA[i][j])-parseFloat(datB[i][j])
		sumC[i] = datC[i].sum()
		avgC[i] = datC[i].avg()
		magC[i] = datC[i].mag()
		ssqC[i] = datC[i].ssq()
		varC[i] = datC[i].var()
		rmsdC[i] = datC[i].rmsd()
		rmseC[i] = datC[i].rmse()
	}

	txt='<details>'; for(i=0;i<Ndat;i++) txt+=printf(digit,sumC[i])+'<br>'; $('sumC').innerHTML=txt+'</details>总计: '+printf(digit,sumC.sum())+'<br>平均: '+printf(digit,sumC.sum()/Ndat)
	txt='<details>'; for(i=0;i<Ndat;i++) txt+=printf(digit,avgC[i])+'<br>'; $('avgC').innerHTML=txt+'</details>总计: '+printf(digit,avgC.sum())+'<br>平均: '+printf(digit,avgC.sum()/Ndat)
	txt='<details>'; for(i=0;i<Ndat;i++) txt+=printf(digit,magC[i])+'<br>'; $('magC').innerHTML=txt+'</details>总计: '+printf(digit,magC.sum())+'<br>平均: '+printf(digit,magC.sum()/Ndat)
	txt='<details>'; for(i=0;i<Ndat;i++) txt+=printf(digit,ssqC[i])+'<br>'; $('ssqC').innerHTML=txt+'</details>总计: '+printf(digit,ssqC.sum())+'<br>平均: '+printf(digit,ssqC.sum()/Ndat)
	txt='<details>'; for(i=0;i<Ndat;i++) txt+=printf(digit,varC[i])+'<br>'; $('varC').innerHTML=txt +'<br><br>'
	txt='<details>'; for(i=0;i<Ndat;i++) txt+=printf(digit,rmseC[i])+'<br>';$('rmsdC').innerHTML=txt+'<br><br>'
	txt='<details>'; for(i=0;i<Ndat;i++) txt+=printf(digit,rmseC[i])+'<br>';$('rmseC').innerHTML=txt+'<br><br>'

	//if(Ndat>0) {
	//	$('summagC').innerHTML=printf(digit, magC.sum())
	//	$('avgmagC').innerHTML=printf(digit, magC.avg())
	//	$('magmagC').innerHTML=printf(digit, magC.mag())
	//	$('ssqmagC').innerHTML=printf(digit, magC.ssq())
	//	$('varmagC').innerHTML=printf(digit, magC.var())
	//	$('rmsemagC').innerHTML=printf(digit, magC.rmse())
	//}
}

var trim=function(s){return s.replace(/^\s*\n*/,"").replace(/\s*\n*$/,"").replace(/\s+[\n|$]/g,"\n")}
function reg() {
	let i, row, col

	txt=trim($('data').value).split(/\n/)
	row=txt.length

	let A=[], b=[]
	for(i=0; i<row; i++) {
		A[i]=trim(txt[i]).split(/\s+/)
		col=A[i].length
		if($('Y1st').checked) {
			b[i]=parseFloat(A[i][0])
			for(j=0; j<col-1; j++) A[i][j]=parseFloat(A[i][j+1])
		} else {
			b[i]=parseFloat(A[i][col-1])
			for(j=0; j<col-1; j++) A[i][j]=parseFloat(A[i][j])
		}
		if($('Yconst').checked) A[i][col-1]=1
		else { col--; A[i].splice(col,1) }
	}

	let { u, v, q } = SVDJS.SVD(A)

	x=[], xt=[]
	for(i=0; i<col; i++) {
		xt[i]=0
		for(j=0; j<row; j++) xt[i] += u[j][i]*b[j]
		xt[i] /= q[i]
	}

	str='Y = '
	for(i=0; i<col; i++) {
		x[i]=0
		for(j=0; j<col; j++)  x[i] += v[i][j]*xt[j]
		if(i==col-1) {
			if($('Yconst').checked) str += printf('%.9f', x[i])
			else str += printf('%.9f * X%0f', x[i], i+1)
		} else   str += printf('%.9f * X%0f + ', x[i], i+1)
	}
	$('Yreg').innerHTML=str

	var myChart = new Chart($("myChart").getContext('2d'), {
		type: 'scatter',
		options: {
			responsive: false,
			scales: {
				xAxes: [{
					type: 'linear',
					position: 'bottom'
				}],
				yAxes: [{
					display: true,
					ticks: {
					//	beginAtZero: true,
					//	steps: 10,
					//	stepValue: .1,
					//	max: 10
					}
				}]
			},
		}
		})

	myChart.data.datasets=[]

	data=[]
	data[0]=[]; data[1]=[]

	for(i=0; i<row; i++) {
		data[0][i]={x:i+1, y:b[i]}
		let y=0
		for(j=0; j<col; j++) y += A[i][j]*x[j]
		data[1][i]={x:i+1, y:y}
	}
	addData(myChart, data[0], "原始值", "red",3);
	addData(myChart, data[1], "回归值 "+str, "blue",3);
}

var $=function(id){return document.getElementById(id)}
function trim(s){return s.replace(/^(\s|\u00A0)+/,'').replace(/(\s|\u00A0)+$/,'')}
function norm(s){return s.replace(/^(\s|\u00A0)*\n*/,'').replace(/(\s|\u00A0)*\n*$/,'').replace(/(\s|\u00A0)+[\n|$]/g,'\n')}
function normtrim(s){return norm(trim(s))}

var datChart = new Chart($("datChart").getContext('2d'), {
	type: 'line',
	options: {
		responsive: true,
		scales: {
			xAxes: [{
				type: 'linear',
				position: 'bottom'
			}],
			yAxes: [{
				display: true,
				ticks: {
				//	beginAtZero: true,
				//	steps: 10,
				//	stepValue: .1,
				//	max: 10
				}
			}]
		},
	}
})

var fitChart = new Chart($("fitChart").getContext('2d'), {
	type: 'line',
	options: {
		responsive: true,
		scales: {
			xAxes: [{
				type: 'linear',
				position: 'bottom'
			}],
			yAxes: [{
				display: true,
				ticks: {
				//	beginAtZero: true,
				//	steps: 10,
				//	stepValue: .1,
				//	max: 10
				}
			}]
		},
	}
})

var f, dy=[], py, np, pxy=[], npxy, xy={}, ix=0, iy, ndat,
	yfit=[], res=[], data=[[], [], []], scope={}

datChart.data.datasets=[]
datChart.options.animation.duration = 0;
addData(datChart, data[0], "参考值", "black", 3, false);
addData(datChart, data[1], "拟合值 ", "red",  0, true);

fitChart.data.datasets=[]
fitChart.options.animation.duration = 0;
addData(fitChart, data[2], "残差平方和", "red",  0, true);

function init() {
	var i, j, k

	var txt=normtrim($('xy').value).split('\n')

	pxy=trim(txt[0].replace(/^.*#/, '')).split(/\s+/)
	npxy=pxy.length

	for(i=0; i<npxy; i++) xy[pxy[i]]=[]

	txt=txt.slice(1)
	ndat=txt.length
	for(i=0; i<ndat; i++) {
		str=trim(txt[i]).split(/\s+/)
		for(j=0; j<str.length; j++) xy[pxy[j]][i]=parseFloat(str[j])
	}

	ix=0
	iy=pxy.indexOf(trim($('y').value.replace(/=.*/,'')))
	for(i=0; i<ndat; i++) data[0][i]={x:xy[pxy[ix]][i], y:xy[pxy[iy]][i]}

	updData(datChart, 0, data[0]);
}

function setParam() {
	py=trim($('py').value.replace(/[,;|]/g,' ')).split(/\s+/)
	np=py.length

	$('optParam').innerHTML='参数 拟合值<br>'
	for(let i=0; i<np; i++) $('optParam').innerHTML += py[i]
		+" <input class='box' value='1' id='pf__"+i+"'><br>"
	showFit()
}

function showFit() {
	var i, j

	y=trim($('y').value.replace(/^.*=/,''))
	for(i=0; i<np; i++) dy[i]=math.derivative(y, py[i]).compile()

	y=math.compile(y)

	for(i=0; i<np;   i++) scope[py[i]]=parseFloat($('pf__'+i).value)
	for(i=0; i<ndat; i++) {
		for(j=0; j<npxy; j++) if(!j==iy) scope[pxy[j]]=xy[pxy[j]][i]
		yfit[i]=y.evaluate(scope)
		res[i]=yfit[i]-xy[pxy[iy]][i]
		data[1][i]={x:xy[pxy[ix]][i], y:yfit[i]}
	}
	updData(datChart, 1, data[1]);
}

function dot(a, b) {
    var ret = 0;
    for (var i = 0; i < a.length; ++i) {
        ret += a[i] * b[i];
    }
    return ret;
}

function norm2(a)  {
    return Math.sqrt(dot(a, a));
}

function weightedSum(ret, w1, v1, w2, v2) {
    for (var j = 0; j < ret.length; ++j) {
        ret[j] = w1 * v1[j] + w2 * v2[j];
    }
}

function addData(chart, data, label, color, size, line) {
	chart.data.datasets.push({
		data: data,
		label: label,
		fill: false, //
		fillColor : "#888",
		borderColor: color,//曲线边框色,
		backgroundColor: color,//填充色
		//pointBackgroundColor: 'purple',//数据点的填充色
		//pointBorderColor: 'blue',//数据点边框颜色
		borderWidth: 4,//曲线的宽度
		//borderDash: [2, 3],
		pointBorderWidth: 4,//数据点边框的宽度
		pointRadius: size, //数据点的大小
		pointStyle:'circle',//'cross''crossRot''dash''line''rect''rectRounded''rectRot''star''triangle'
		showLine: line, //如果为false,两数据点之间的线不会渲染
		spanGaps: true, //如果为false,NaN data会在折线上有断点
		steppedLine: false,//可选值[false, true, 'before', 'after'],为true,折线图的曲线会成直角，
	});
	chart.update();
}

function updData(chart, idx, data) {
	chart.data.datasets[idx].data = data
	chart.options.animation.duration = 0;
	chart.update();
}

</script>