/**
* jStat - JavaScript Statistical Library
* Copyright (c) 2011
* This document is licensed as free software under the terms of the
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f=0,g=(d-c)/2,h=[],i=[],j=[],k,l,m,n,o,p;while(f<e/2){o=a(c);for(m=c,n=0;m<=d;m+=g,n++)h[n]=m;k=h.length;for(m=1;m<k-1;m++)o+=(m%2!==0?4:2)*a(h[m]);o=g/3*(o+a(d)),j[f]=o,g/=2,f++}l=j.length,k=1;while(l!==1){for(m=0;m<l-1;m++)i[m]=(b.pow(4,k)*j[m+1]-j[m])/(b.pow(4,k)-1);l=i.length,j=i,i=[],k++}return j},richardson:function(a,c,d,e){function f(a,b){var c=0,d=a.length,e;for(;c<d;c++)a[c]===b&&(e=c);return e}var g=a.length,h=b.abs(d-a[f(a,d)+1]),i=0,j=[],k=[],l,m,n,o,p;while(e>=h)l=f(a,d+e),m=f(a,d),j[i]=(c[l]-2*c[m]+c[2*m-l])/(e*e),e/=2,i++;o=j.length,n=1;while(o!=1){for(p=0;p<o-1;p++)k[p]=(b.pow(4,n)*j[p+1]-j[p])/(b.pow(4,n)-1);o=k.length,j=k,k=[],n++}return j},simpson:function(a,b,c,d){var e=(c-b)/d,f=a(b),g=[],h=b,i=0,j=1,k;for(;h<=c;h+=e,i++)g[i]=h;k=g.length;for(;j<k-1;j++)f+=(j%2!==0?4:2)*a(g[j]);return e/3*(f+a(c))},hermite:function(a,b,c,d){var e=a.length,f=0,g=0,h=[],i=[],j=[],k=[],l;for(;g<e;g++){h[g]=1;for(l=0;l<e;l++)g!=l&&(h[g]*=(d-a[l])/(a[g]-a[l]));i[g]=0;for(l=0;l<e;l++)g!=l&&(i[g]+=1/(a[g]-a[l]));j[g]=(1-2*(d-a[g])*i[g])*h[g]*h[g],k[g]=(d-a[g])*h[g]*h[g],f+=j[g]*b[g]+k[g]*c[g]}return f},lagrange:function(a,b,c){var d=0,e=0,f,g,h=a.length;for(;e<h;e++){g=b[e];for(f=0;f<h;f++)e!=f&&(g*=(c-a[f])/(a[e]-a[f]));d+=g}return d},cubic_spline:function(b,c,d){var e=b.length,f=0,g,h=[],i=[],j=[],k=[],l=[],m=[],n=[];for(;f<e-1;f++)l[f]=b[f+1]-b[f];j[0]=0;for(f=1;f<e-1;f++)j[f]=3/l[f]*(c[f+1]-c[f])-3/l[f-1]*(c[f]-c[f-1]);for(f=1;f<e-1;f++)h[f]=[],i[f]=[],h[f][f-1]=l[f-1],h[f][f]=2*(l[f-1]+l[f]),h[f][f+1]=l[f],i[f][0]=j[f];k=a.multiply(a.inv(h),i);for(g=0;g<e-1;g++)m[g]=(c[g+1]-c[g])/l[g]-l[g]*(k[g+1][0]+2*k[g][0])/3,n[g]=(k[g+1][0]-k[g][0])/(3*l[g]);for(g=0;g<e;g++)if(b[g]>d)break;return g-=1,c[g]+(d-b[g])*m[g]+a.sq(d-b[g])*k[g]+(d-b[g])*a.sq(d-b[g])*n[g]},gauss_quadrature:function(){},PCA:function(b){var c=b.length,d=b[0].length,e=!1,f=0,g,h,i=[],j=[],k=[],l=[],m=[],n=[],o=[],p=[],q=[],r=[];for(f=0;f<c;f++)i[f]=a.sum(b[f])/d;for(f=0;f<d;f++){o[f]=[];for(g=0;g<c;g++)o[f][g]=b[g][f]-i[g]}o=a.transpose(o);for(f=0;f<c;f++){p[f]=[];for(g=0;g<c;g++)p[f][g]=a.dot([o[f]],[o[g]])/(d-1)}k=a.jacobi(p),q=k[0],j=k[1],r=a.transpose(q);for(f=0;f<j.length;f++)for(g=f;g<j.length;g++)j[f]<j[g]&&(h=j[f],j[f]=j[g],j[g]=h,l=r[f],r[f]=r[g],r[g]=l);n=a.transpose(o);for(f=0;f<c;f++){m[f]=[];for(g=0;g<n.length;g++)m[f][g]=a.dot([r[f]],[n[g]])}return[b,j,r,m]}}),function(b){for(var c=0;c<b.length;c++)(function(b){a.fn[b]=function(c,d){var e=this;return d?(setTimeout(function(){d.call(e,a.fn[b].call(e,c))},15),this):a(a[b](this,c))}})(b[c])}("add divide multiply subtract dot pow abs norm angle".split(" "))}(this.jStat,Math),function(a,b){var c=[].slice,d=a.utils.isNumber;a.extend({zscore:function(){var b=c.call(arguments);return d(b[1])?(b[0]-b[1])/b[2]:(b[0]-a.mean(b[1]))/a.stdev(b[1],b[2])},ztest:function(){var e=c.call(arguments);if(e.length===4){if(d(e[1])){var f=a.zscore(e[0],e[1],e[2]);return e[3]===1?a.normal.cdf(-b.abs(f),0,1):a.normal.cdf(-b.abs(f),0,1)*2}var f=e[0];return e[2]===1?a.normal.cdf(-b.abs(f),0,1):a.normal.cdf(-b.abs(f),0,1)*2}var f=a.zscore(e[0],e[1],e[3]);return e[1]===1?a.normal.cdf(-b.abs(f),0,1):a.normal.cdf(-b.abs(f),0,1)*2}}),a.extend(a.fn,{zscore:function(a,b){return(a-this.mean())/this.stdev(b)},ztest:function(c,d,e){var f=b.abs(this.zscore(c,e));return d===1?a.normal.cdf(-f,0,1):a.normal.cdf(-f,0,1)*2}}),a.extend({tscore:function(){var d=c.call(arguments);return d.length===4?(d[0]-d[1])/(d[2]/b.sqrt(d[3])):(d[0]-a.mean(d[1]))/(a.stdev(d[1],!0)/b.sqrt(d[1].length))},ttest:function(){var e=c.call(arguments),f;return e.length===5?(f=b.abs(a.tscore(e[0],e[1],e[2],e[3])),e[4]===1?a.studentt.cdf(-f,e[3]-1):a.studentt.cdf(-f,e[3]-1)*2):d(e[1])?(f=b.abs(e[0]),e[2]==1?a.studentt.cdf(-f,e[1]-1):a.studentt.cdf(-f,e[1]-1)*2):(f=b.abs(a.tscore(e[0],e[1])),e[2]==1?a.studentt.cdf(-f,e[1].length-1):a.studentt.cdf(-f,e[1].length-1)*2)}}),a.extend(a.fn,{tscore:function(a){return(a-this.mean())/(this.stdev(!0)/b.sqrt(this.cols()))},ttest:function(c,d){return d===1?1-a.studentt.cdf(b.abs(this.tscore(c)),this.cols()-1):a.studentt.cdf(-b.abs(this.tscore(c)),this.cols()-1)*2}}),a.extend({anovafscore:function(){var d=c.call(arguments),e,f,g,h,i,j,k,l;if(d.length===1){i=new Array(d[0].length);for(k=0;k<d[0].length;k++)i[k]=d[0][k];d=i}if(d.length===2)return a.variance(d[0])/a.variance(d[1]);f=new Array;for(k=0;k<d.length;k++)f=f.concat(d[k]);g=a.mean(f),e=0;for(k=0;k<d.length;k++)e+=d[k].length*b.pow(a.mean(d[k])-g,2);e/=d.length-1,j=0;for(k=0;k<d.length;k++){h=a.mean(d[k]);for(l=0;l<d[k].length;l++)j+=b.pow(d[k][l]-h,2)}return j/=f.length-d.length,e/j},anovaftest:function(){var b=c.call(arguments),e,f,g,h;if(d(b[0]))return 1-a.centralF.cdf(b[0],b[1],b[2]);anovafscore=a.anovafscore(b),e=b.length-1,g=0;for(h=0;h<b.length;h++)g+=b[h].length;return f=g-e-1,1-a.centralF.cdf(anovafscore,e,f)},ftest:function(b,c,d){return 1-a.centralF.cdf(b,c,d)}}),a.extend(a.fn,{anovafscore:function(){return a.anovafscore(this.toArray())},anovaftest:function(){var b=0,c;for(c=0;c<this.length;c++)b+=this[c].length;return a.ftest(this.anovafscore(),this.length-1,b-this.length)}}),a.extend({normalci:function(){var d=c.call(arguments),e=new Array(2),f;return d.length===4?f=b.abs(a.normal.inv(d[1]/2,0,1)*d[2]/b.sqrt(d[3])):f=b.abs(a.normal.inv(d[1]/2,0,1)*a.stdev(d[2])/b.sqrt(d[2].length)),e[0]=d[0]-f,e[1]=d[0]+f,e},tci:function(){var d=c.call(arguments),e=new Array(2),f;return d.length===4?f=b.abs(a.studentt.inv(d[1]/2,d[3]-1)*d[2]/b.sqrt(d[3])):f=b.abs(a.studentt.inv(d[1]/2,d[2].length)*a.stdev(d[2],!0)/b.sqrt(d[2].length)),e[0]=d[0]-f,e[1]=d[0]+f,e},significant:function(a,b){return a<b}}),a.extend(a.fn,{normalci:function(b,c){return a.normalci(b,c,this.toArray())},tci:function(b,c){return a.tci(b,c,this.toArray())}})}(this.jStat,Math);
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