science.v1.min.js

(function(exports){(function(exports){science={version:"1.9.3"};science.ascending=function(a,b){return a-b};science.EULER=.5772156649015329;science.expm1=function(x){return x<1e-5&&x>-1e-5?x+.5*x*x:Math.exp(x)-1};science.functor=function(v){return typeof v==="function"?v:function(){return v}};science.hypot=function(x,y){x=Math.abs(x);y=Math.abs(y);var max,min;if(x>y){max=x;min=y}else{max=y;min=x}var r=min/max;return max*Math.sqrt(1+r*r)};science.quadratic=function(){var complex=false;function quadratic(a,b,c){var d=b*b-4*a*c;if(d>0){d=Math.sqrt(d)/(2*a);return complex?[{r:-b-d,i:0},{r:-b+d,i:0}]:[-b-d,-b+d]}else if(d===0){d=-b/(2*a);return complex?[{r:d,i:0}]:[d]}else{if(complex){d=Math.sqrt(-d)/(2*a);return[{r:-b,i:-d},{r:-b,i:d}]}return[]}}quadratic.complex=function(x){if(!arguments.length)return complex;complex=x;return quadratic};return quadratic};science.zeroes=function(n){var i=-1,a=[];if(arguments.length===1)while(++i<n)a[i]=0;else while(++i<n)a[i]=science.zeroes.apply(this,Array.prototype.slice.call(arguments,1));return a}})(this);(function(exports){science.lin={};science.lin.decompose=function(){function decompose(A){var n=A.length,V=[],d=[],e=[];for(var i=0;i<n;i++){V[i]=[];d[i]=[];e[i]=[]}var symmetric=true;for(var j=0;j<n;j++){for(var i=0;i<n;i++){if(A[i][j]!==A[j][i]){symmetric=false;break}}}if(symmetric){for(var i=0;i<n;i++)V[i]=A[i].slice();science_lin_decomposeTred2(d,e,V);science_lin_decomposeTql2(d,e,V)}else{var H=[];for(var i=0;i<n;i++)H[i]=A[i].slice();science_lin_decomposeOrthes(H,V);science_lin_decomposeHqr2(d,e,H,V)}var D=[];for(var i=0;i<n;i++){var row=D[i]=[];for(var j=0;j<n;j++)row[j]=i===j?d[i]:0;D[i][e[i]>0?i+1:i-1]=e[i]}return{D:D,V:V}}return decompose};function science_lin_decomposeTred2(d,e,V){var n=V.length;for(var j=0;j<n;j++)d[j]=V[n-1][j];for(var i=n-1;i>0;i--){var scale=0,h=0;for(var k=0;k<i;k++)scale+=Math.abs(d[k]);if(scale===0){e[i]=d[i-1];for(var j=0;j<i;j++){d[j]=V[i-1][j];V[i][j]=0;V[j][i]=0}}else{for(var k=0;k<i;k++){d[k]/=scale;h+=d[k]*d[k]}var f=d[i-1];var g=Math.sqrt(h);if(f>0)g=-g;e[i]=scale*g;h=h-f*g;d[i-1]=f-g;for(var j=0;j<i;j++)e[j]=0;for(var j=0;j<i;j++){f=d[j];V[j][i]=f;g=e[j]+V[j][j]*f;for(var k=j+1;k<=i-1;k++){g+=V[k][j]*d[k];e[k]+=V[k][j]*f}e[j]=g}f=0;for(var j=0;j<i;j++){e[j]/=h;f+=e[j]*d[j]}var hh=f/(h+h);for(var j=0;j<i;j++)e[j]-=hh*d[j];for(var j=0;j<i;j++){f=d[j];g=e[j];for(var k=j;k<=i-1;k++)V[k][j]-=f*e[k]+g*d[k];d[j]=V[i-1][j];V[i][j]=0}}d[i]=h}for(var i=0;i<n-1;i++){V[n-1][i]=V[i][i];V[i][i]=1;var h=d[i+1];if(h!=0){for(var k=0;k<=i;k++)d[k]=V[k][i+1]/h;for(var j=0;j<=i;j++){var g=0;for(var k=0;k<=i;k++)g+=V[k][i+1]*V[k][j];for(var k=0;k<=i;k++)V[k][j]-=g*d[k]}}for(var k=0;k<=i;k++)V[k][i+1]=0}for(var j=0;j<n;j++){d[j]=V[n-1][j];V[n-1][j]=0}V[n-1][n-1]=1;e[0]=0}function science_lin_decomposeTql2(d,e,V){var n=V.length;for(var i=1;i<n;i++)e[i-1]=e[i];e[n-1]=0;var f=0;var tst1=0;var eps=1e-12;for(var l=0;l<n;l++){tst1=Math.max(tst1,Math.abs(d[l])+Math.abs(e[l]));var m=l;while(m<n){if(Math.abs(e[m])<=eps*tst1){break}m++}if(m>l){var iter=0;do{iter++;var g=d[l];var p=(d[l+1]-g)/(2*e[l]);var r=science.hypot(p,1);if(p<0)r=-r;d[l]=e[l]/(p+r);d[l+1]=e[l]*(p+r);var dl1=d[l+1];var h=g-d[l];for(var i=l+2;i<n;i++)d[i]-=h;f+=h;p=d[m];var c=1;var c2=c;var c3=c;var el1=e[l+1];var s=0;var s2=0;for(var i=m-1;i>=l;i--){c3=c2;c2=c;s2=s;g=c*e[i];h=c*p;r=science.hypot(p,e[i]);e[i+1]=s*r;s=e[i]/r;c=p/r;p=c*d[i]-s*g;d[i+1]=h+s*(c*g+s*d[i]);for(var k=0;k<n;k++){h=V[k][i+1];V[k][i+1]=s*V[k][i]+c*h;V[k][i]=c*V[k][i]-s*h}}p=-s*s2*c3*el1*e[l]/dl1;e[l]=s*p;d[l]=c*p}while(Math.abs(e[l])>eps*tst1)}d[l]=d[l]+f;e[l]=0}for(var i=0;i<n-1;i++){var k=i;var p=d[i];for(var j=i+1;j<n;j++){if(d[j]<p){k=j;p=d[j]}}if(k!=i){d[k]=d[i];d[i]=p;for(var j=0;j<n;j++){p=V[j][i];V[j][i]=V[j][k];V[j][k]=p}}}}function science_lin_decomposeOrthes(H,V){var n=H.length;var ort=[];var low=0;var high=n-1;for(var m=low+1;m<high;m++){var scale=0;for(var i=m;i<=high;i++)scale+=Math.abs(H[i][m-1]);if(scale!==0){var h=0;for(var i=high;i>=m;i--){ort[i]=H[i][m-1]/scale;h+=ort[i]*ort[i]}var g=Math.sqrt(h);if(ort[m]>0)g=-g;h=h-ort[m]*g;ort[m]=ort[m]-g;for(var j=m;j<n;j++){var f=0;for(var i=high;i>=m;i--)f+=ort[i]*H[i][j];f/=h;for(var i=m;i<=high;i++)H[i][j]-=f*ort[i]}for(var i=0;i<=high;i++){var f=0;for(var j=high;j>=m;j--)f+=ort[j]*H[i][j];f/=h;for(var j=m;j<=high;j++)H[i][j]-=f*ort[j]}ort[m]=scale*ort[m];H[m][m-1]=scale*g}}for(var i=0;i<n;i++){for(var j=0;j<n;j++)V[i][j]=i===j?1:0}for(var m=high-1;m>=low+1;m--){if(H[m][m-1]!==0){for(var i=m+1;i<=high;i++)ort[i]=H[i][m-1];for(var j=m;j<=high;j++){var g=0;for(var i=m;i<=high;i++)g+=ort[i]*V[i][j];g=g/ort[m]/H[m][m-1];for(var i=m;i<=high;i++)V[i][j]+=g*ort[i]}}}}function science_lin_decomposeHqr2(d,e,H,V){var nn=H.length,n=nn-1,low=0,high=nn-1,eps=1e-12,exshift=0,p=0,q=0,r=0,s=0,z=0,t,w,x,y;var norm=0;for(var i=0;i<nn;i++){if(i<low||i>high){d[i]=H[i][i];e[i]=0}for(var j=Math.max(i-1,0);j<nn;j++)norm+=Math.abs(H[i][j])}var iter=0;while(n>=low){var l=n;while(l>low){s=Math.abs(H[l-1][l-1])+Math.abs(H[l][l]);if(s===0)s=norm;if(Math.abs(H[l][l-1])<eps*s)break;l--}if(l===n){H[n][n]=H[n][n]+exshift;d[n]=H[n][n];e[n]=0;n--;iter=0}else if(l===n-1){w=H[n][n-1]*H[n-1][n];p=(H[n-1][n-1]-H[n][n])/2;q=p*p+w;z=Math.sqrt(Math.abs(q));H[n][n]=H[n][n]+exshift;H[n-1][n-1]=H[n-1][n-1]+exshift;x=H[n][n];if(q>=0){z=p+(p>=0?z:-z);d[n-1]=x+z;d[n]=d[n-1];if(z!==0)d[n]=x-w/z;e[n-1]=0;e[n]=0;x=H[n][n-1];s=Math.abs(x)+Math.abs(z);p=x/s;q=z/s;r=Math.sqrt(p*p+q*q);p/=r;q/=r;for(var j=n-1;j<nn;j++){z=H[n-1][j];H[n-1][j]=q*z+p*H[n][j];H[n][j]=q*H[n][j]-p*z}for(var i=0;i<=n;i++){z=H[i][n-1];H[i][n-1]=q*z+p*H[i][n];H[i][n]=q*H[i][n]-p*z}for(var i=low;i<=high;i++){z=V[i][n-1];V[i][n-1]=q*z+p*V[i][n];V[i][n]=q*V[i][n]-p*z}}else{d[n-1]=x+p;d[n]=x+p;e[n-1]=z;e[n]=-z}n=n-2;iter=0}else{x=H[n][n];y=0;w=0;if(l<n){y=H[n-1][n-1];w=H[n][n-1]*H[n-1][n]}if(iter==10){exshift+=x;for(var i=low;i<=n;i++){H[i][i]-=x}s=Math.abs(H[n][n-1])+Math.abs(H[n-1][n-2]);x=y=.75*s;w=-.4375*s*s}if(iter==30){s=(y-x)/2;s=s*s+w;if(s>0){s=Math.sqrt(s);if(y<x){s=-s}s=x-w/((y-x)/2+s);for(var i=low;i<=n;i++){H[i][i]-=s}exshift+=s;x=y=w=.964}}iter++;var m=n-2;while(m>=l){z=H[m][m];r=x-z;s=y-z;p=(r*s-w)/H[m+1][m]+H[m][m+1];q=H[m+1][m+1]-z-r-s;r=H[m+2][m+1];s=Math.abs(p)+Math.abs(q)+Math.abs(r);p=p/s;q=q/s;r=r/s;if(m==l)break;if(Math.abs(H[m][m-1])*(Math.abs(q)+Math.abs(r))<eps*(Math.abs(p)*(Math.abs(H[m-1][m-1])+Math.abs(z)+Math.abs(H[m+1][m+1])))){break}m--}for(var i=m+2;i<=n;i++){H[i][i-2]=0;if(i>m+2)H[i][i-3]=0}for(var k=m;k<=n-1;k++){var notlast=k!=n-1;if(k!=m){p=H[k][k-1];q=H[k+1][k-1];r=notlast?H[k+2][k-1]:0;x=Math.abs(p)+Math.abs(q)+Math.abs(r);if(x!=0){p/=x;q/=x;r/=x}}if(x==0)break;s=Math.sqrt(p*p+q*q+r*r);if(p<0){s=-s}if(s!=0){if(k!=m)H[k][k-1]=-s*x;else if(l!=m)H[k][k-1]=-H[k][k-1];p+=s;x=p/s;y=q/s;z=r/s;q/=p;r/=p;for(var j=k;j<nn;j++){p=H[k][j]+q*H[k+1][j];if(notlast){p=p+r*H[k+2][j];H[k+2][j]=H[k+2][j]-p*z}H[k][j]=H[k][j]-p*x;H[k+1][j]=H[k+1][j]-p*y}for(var i=0;i<=Math.min(n,k+3);i++){p=x*H[i][k]+y*H[i][k+1];if(notlast){p+=z*H[i][k+2];H[i][k+2]=H[i][k+2]-p*r}H[i][k]=H[i][k]-p;H[i][k+1]=H[i][k+1]-p*q}for(var i=low;i<=high;i++){p=x*V[i][k]+y*V[i][k+1];if(notlast){p=p+z*V[i][k+2];V[i][k+2]=V[i][k+2]-p*r}V[i][k]=V[i][k]-p;V[i][k+1]=V[i][k+1]-p*q}}}}}if(norm==0){return}for(n=nn-1;n>=0;n--){p=d[n];q=e[n];if(q==0){var l=n;H[n][n]=1;for(var i=n-1;i>=0;i--){w=H[i][i]-p;r=0;for(var j=l;j<=n;j++){r=r+H[i][j]*H[j][n]}if(e[i]<0){z=w;s=r}else{l=i;if(e[i]===0){H[i][n]=-r/(w!==0?w:eps*norm)}else{x=H[i][i+1];y=H[i+1][i];q=(d[i]-p)*(d[i]-p)+e[i]*e[i];t=(x*s-z*r)/q;H[i][n]=t;if(Math.abs(x)>Math.abs(z)){H[i+1][n]=(-r-w*t)/x}else{H[i+1][n]=(-s-y*t)/z}}t=Math.abs(H[i][n]);if(eps*t*t>1){for(var j=i;j<=n;j++)H[j][n]=H[j][n]/t}}}}else if(q<0){var l=n-1;if(Math.abs(H[n][n-1])>Math.abs(H[n-1][n])){H[n-1][n-1]=q/H[n][n-1];H[n-1][n]=-(H[n][n]-p)/H[n][n-1]}else{var zz=science_lin_decomposeCdiv(0,-H[n-1][n],H[n-1][n-1]-p,q);H[n-1][n-1]=zz[0];H[n-1][n]=zz[1]}H[n][n-1]=0;H[n][n]=1;for(var i=n-2;i>=0;i--){var ra=0,sa=0,vr,vi;for(var j=l;j<=n;j++){ra=ra+H[i][j]*H[j][n-1];sa=sa+H[i][j]*H[j][n]}w=H[i][i]-p;if(e[i]<0){z=w;r=ra;s=sa}else{l=i;if(e[i]==0){var zz=science_lin_decomposeCdiv(-ra,-sa,w,q);H[i][n-1]=zz[0];H[i][n]=zz[1]}else{x=H[i][i+1];y=H[i+1][i];vr=(d[i]-p)*(d[i]-p)+e[i]*e[i]-q*q;vi=(d[i]-p)*2*q;if(vr==0&vi==0){vr=eps*norm*(Math.abs(w)+Math.abs(q)+Math.abs(x)+Math.abs(y)+Math.abs(z))}var zz=science_lin_decomposeCdiv(x*r-z*ra+q*sa,x*s-z*sa-q*ra,vr,vi);H[i][n-1]=zz[0];H[i][n]=zz[1];if(Math.abs(x)>Math.abs(z)+Math.abs(q)){H[i+1][n-1]=(-ra-w*H[i][n-1]+q*H[i][n])/x;H[i+1][n]=(-sa-w*H[i][n]-q*H[i][n-1])/x}else{var zz=science_lin_decomposeCdiv(-r-y*H[i][n-1],-s-y*H[i][n],z,q);H[i+1][n-1]=zz[0];H[i+1][n]=zz[1]}}t=Math.max(Math.abs(H[i][n-1]),Math.abs(H[i][n]));if(eps*t*t>1){for(var j=i;j<=n;j++){H[j][n-1]=H[j][n-1]/t;H[j][n]=H[j][n]/t}}}}}}for(var i=0;i<nn;i++){if(i<low||i>high){for(var j=i;j<nn;j++)V[i][j]=H[i][j]}}for(var j=nn-1;j>=low;j--){for(var i=low;i<=high;i++){z=0;for(var k=low;k<=Math.min(j,high);k++)z+=V[i][k]*H[k][j];V[i][j]=z}}}function science_lin_decomposeCdiv(xr,xi,yr,yi){if(Math.abs(yr)>Math.abs(yi)){var r=yi/yr,d=yr+r*yi;return[(xr+r*xi)/d,(xi-r*xr)/d]}else{var r=yr/yi,d=yi+r*yr;return[(r*xr+xi)/d,(r*xi-xr)/d]}}science.lin.cross=function(a,b){return[a[1]*b[2]-a[2]*b[1],a[2]*b[0]-a[0]*b[2],a[0]*b[1]-a[1]*b[0]]};science.lin.dot=function(a,b){var s=0,i=-1,n=Math.min(a.length,b.length);while(++i<n)s+=a[i]*b[i];return s};science.lin.length=function(p){return Math.sqrt(science.lin.dot(p,p))};science.lin.normalize=function(p){var length=science.lin.length(p);return p.map(function(d){return d/length})};science.lin.determinant=function(matrix){var m=matrix[0].concat(matrix[1]).concat(matrix[2]).concat(matrix[3]);return m[12]*m[9]*m[6]*m[3]-m[8]*m[13]*m[6]*m[3]-m[12]*m[5]*m[10]*m[3]+m[4]*m[13]*m[10]*m[3]+m[8]*m[5]*m[14]*m[3]-m[4]*m[9]*m[14]*m[3]-m[12]*m[9]*m[2]*m[7]+m[8]*m[13]*m[2]*m[7]+m[12]*m[1]*m[10]*m[7]-m[0]*m[13]*m[10]*m[7]-m[8]*m[1]*m[14]*m[7]+m[0]*m[9]*m[14]*m[7]+m[12]*m[5]*m[2]*m[11]-m[4]*m[13]*m[2]*m[11]-m[12]*m[1]*m[6]*m[11]+m[0]*m[13]*m[6]*m[11]+m[4]*m[1]*m[14]*m[11]-m[0]*m[5]*m[14]*m[11]-m[8]*m[5]*m[2]*m[15]+m[4]*m[9]*m[2]*m[15]+m[8]*m[1]*m[6]*m[15]-m[0]*m[9]*m[6]*m[15]-m[4]*m[1]*m[10]*m[15]+m[0]*m[5]*m[10]*m[15]};science.lin.gaussjordan=function(m,eps){if(!eps)eps=1e-10;var h=m.length,w=m[0].length,y=-1,y2,x;while(++y<h){var maxrow=y;y2=y;while(++y2<h){if(Math.abs(m[y2][y])>Math.abs(m[maxrow][y]))maxrow=y2}var tmp=m[y];m[y]=m[maxrow];m[maxrow]=tmp;if(Math.abs(m[y][y])<=eps)return false;y2=y;while(++y2<h){var c=m[y2][y]/m[y][y];x=y-1;while(++x<w){m[y2][x]-=m[y][x]*c}}}y=h;while(--y>=0){var c=m[y][y];y2=-1;while(++y2<y){x=w;while(--x>=y){m[y2][x]-=m[y][x]*m[y2][y]/c}}m[y][y]/=c;x=h-1;while(++x<w){m[y][x]/=c}}return true};science.lin.inverse=function(m){var n=m.length,i=-1;if(n!==m[0].length)return;m=m.map(function(row,i){var identity=new Array(n),j=-1;while(++j<n)identity[j]=i===j?1:0;return row.concat(identity)});science.lin.gaussjordan(m);while(++i<n){m[i]=m[i].slice(n)}return m};science.lin.multiply=function(a,b){var m=a.length,n=b[0].length,p=b.length,i=-1,j,k;if(p!==a[0].length)throw{error:"columns(a) != rows(b); "+a[0].length+" != "+p};var ab=new Array(m);while(++i<m){ab[i]=new Array(n);j=-1;while(++j<n){var s=0;k=-1;while(++k<p)s+=a[i][k]*b[k][j];ab[i][j]=s}}return ab};science.lin.transpose=function(a){var m=a.length,n=a[0].length,i=-1,j,b=new Array(n);while(++i<n){b[i]=new Array(m);j=-1;while(++j<m)b[i][j]=a[j][i]}return b};science.lin.tridag=function(a,b,c,d,x,n){var i,m;for(i=1;i<n;i++){m=a[i]/b[i-1];b[i]-=m*c[i-1];d[i]-=m*d[i-1]}x[n-1]=d[n-1]/b[n-1];for(i=n-2;i>=0;i--){x[i]=(d[i]-c[i]*x[i+1])/b[i]}}})(this);(function(exports){science.stats={};science.stats.bandwidth={nrd0:function(x){var hi=Math.sqrt(science.stats.variance(x));if(!(lo=Math.min(hi,science.stats.iqr(x)/1.34)))(lo=hi)||(lo=Math.abs(x[1]))||(lo=1);return.9*lo*Math.pow(x.length,-.2)},nrd:function(x){var h=science.stats.iqr(x)/1.34;return 1.06*Math.min(Math.sqrt(science.stats.variance(x)),h)*Math.pow(x.length,-1/5)}};science.stats.distance={euclidean:function(a,b){var n=a.length,i=-1,s=0,x;while(++i<n){x=a[i]-b[i];s+=x*x}return Math.sqrt(s)},manhattan:function(a,b){var n=a.length,i=-1,s=0;while(++i<n)s+=Math.abs(a[i]-b[i]);return s},minkowski:function(p){return function(a,b){var n=a.length,i=-1,s=0;while(++i<n)s+=Math.pow(Math.abs(a[i]-b[i]),p);return Math.pow(s,1/p)}},chebyshev:function(a,b){var n=a.length,i=-1,max=0,x;while(++i<n){x=Math.abs(a[i]-b[i]);if(x>max)max=x}return max},hamming:function(a,b){var n=a.length,i=-1,d=0;while(++i<n)if(a[i]!==b[i])d++;return d},jaccard:function(a,b){var n=a.length,i=-1,s=0;while(++i<n)if(a[i]===b[i])s++;return s/n},braycurtis:function(a,b){var n=a.length,i=-1,s0=0,s1=0,ai,bi;while(++i<n){ai=a[i];bi=b[i];s0+=Math.abs(ai-bi);s1+=Math.abs(ai+bi)}return s0/s1}};science.stats.erf=function(x){var a1=.254829592,a2=-.284496736,a3=1.421413741,a4=-1.453152027,a5=1.061405429,p=.3275911;var sign=x<0?-1:1;if(x<0){sign=-1;x=-x}var t=1/(1+p*x);return sign*(1-((((a5*t+a4)*t+a3)*t+a2)*t+a1)*t*Math.exp(-x*x))};science.stats.phi=function(x){return.5*(1+science.stats.erf(x/Math.SQRT2))};science.stats.kernel={uniform:function(u){if(u<=1&&u>=-1)return.5;return 0},triangular:function(u){if(u<=1&&u>=-1)return 1-Math.abs(u);return 0},epanechnikov:function(u){if(u<=1&&u>=-1)return.75*(1-u*u);return 0},quartic:function(u){if(u<=1&&u>=-1){var tmp=1-u*u;return 15/16*tmp*tmp}return 0},triweight:function(u){if(u<=1&&u>=-1){var tmp=1-u*u;return 35/32*tmp*tmp*tmp}return 0},gaussian:function(u){return 1/Math.sqrt(2*Math.PI)*Math.exp(-.5*u*u)},cosine:function(u){if(u<=1&&u>=-1)return Math.PI/4*Math.cos(Math.PI/2*u);return 0}};science.stats.kde=function(){var kernel=science.stats.kernel.gaussian,sample=[],bandwidth=science.stats.bandwidth.nrd;function kde(points,i){var bw=bandwidth.call(this,sample);return points.map(function(x){var i=-1,y=0,n=sample.length;while(++i<n){y+=kernel((x-sample[i])/bw)}return[x,y/bw/n]})}kde.kernel=function(x){if(!arguments.length)return kernel;kernel=x;return kde};kde.sample=function(x){if(!arguments.length)return sample;sample=x;return kde};kde.bandwidth=function(x){if(!arguments.length)return bandwidth;bandwidth=science.functor(x);return kde};return kde};science.stats.kmeans=function(){var distance=science.stats.distance.euclidean,maxIterations=1e3,k=1;function kmeans(vectors){var n=vectors.length,assignments=[],clusterSizes=[],repeat=1,iterations=0,centroids=science_stats_kmeansRandom(k,vectors),newCentroids,i,j,x,d,min,best;while(repeat&&iterations<maxIterations){j=-1;while(++j<k){clusterSizes[j]=0}i=-1;while(++i<n){x=vectors[i];min=Infinity;j=-1;while(++j<k){d=distance.call(this,centroids[j],x);if(d<min){min=d;best=j}}clusterSizes[assignments[i]=best]++}newCentroids=[];i=-1;while(++i<n){x=assignments[i];d=newCentroids[x];if(d==null)newCentroids[x]=vectors[i].slice();else{j=-1;while(++j<d.length){d[j]+=vectors[i][j]}}}j=-1;while(++j<k){x=newCentroids[j];d=1/clusterSizes[j];i=-1;while(++i<x.length)x[i]*=d}repeat=0;j=-1;while(++j<k){if(!science_stats_kmeansCompare(newCentroids[j],centroids[j])){repeat=1;break}}centroids=newCentroids;iterations++}return{assignments:assignments,centroids:centroids}}kmeans.k=function(x){if(!arguments.length)return k;k=x;return kmeans};kmeans.distance=function(x){if(!arguments.length)return distance;distance=x;return kmeans};return kmeans};function science_stats_kmeansCompare(a,b){if(!a||!b||a.length!==b.length)return false;var n=a.length,i=-1;while(++i<n)if(a[i]!==b[i])return false;return true}function science_stats_kmeansRandom(k,vectors){var n=vectors.length;if(k>n)return null;var selected_vectors=[];var selected_indices=[];var tested_indices={};var tested=0;var selected=0;var i,vector,select;while(selected<k){if(tested===n)return null;var random_index=Math.floor(Math.random()*n);if(random_index in tested_indices)continue;tested_indices[random_index]=1;tested++;vector=vectors[random_index];select=true;for(i=0;i<selected;i++){if(science_stats_kmeansCompare(vector,selected_vectors[i])){select=false;break}}if(select){selected_vectors[selected]=vector;selected_indices[selected]=random_index;selected++}}return selected_vectors}science.stats.hcluster=function(){var distance=science.stats.distance.euclidean,linkage="single";function hcluster(vectors){var n=vectors.length,dMin=[],cSize=[],distMatrix=[],clusters=[],c1,c2,c1Cluster,c2Cluster,p,root,i,j;i=-1;while(++i<n){dMin[i]=0;distMatrix[i]=[];j=-1;while(++j<n){distMatrix[i][j]=i===j?Infinity:distance(vectors[i],vectors[j]);if(distMatrix[i][dMin[i]]>distMatrix[i][j])dMin[i]=j}}i=-1;while(++i<n){clusters[i]=[];clusters[i][0]={left:null,right:null,dist:0,centroid:vectors[i],size:1,depth:0};cSize[i]=1}for(p=0;p<n-1;p++){c1=0;for(i=0;i<n;i++){if(distMatrix[i][dMin[i]]<distMatrix[c1][dMin[c1]])c1=i}c2=dMin[c1];c1Cluster=clusters[c1][0];c2Cluster=clusters[c2][0];var newCluster={left:c1Cluster,right:c2Cluster,dist:distMatrix[c1][c2],centroid:calculateCentroid(c1Cluster.size,c1Cluster.centroid,c2Cluster.size,c2Cluster.centroid),size:c1Cluster.size+c2Cluster.size,depth:1+Math.max(c1Cluster.depth,c2Cluster.depth)};clusters[c1].splice(0,0,newCluster);cSize[c1]+=cSize[c2];for(j=0;j<n;j++){switch(linkage){case"single":if(distMatrix[c1][j]>distMatrix[c2][j])distMatrix[j][c1]=distMatrix[c1][j]=distMatrix[c2][j];break;case"complete":if(distMatrix[c1][j]<distMatrix[c2][j])distMatrix[j][c1]=distMatrix[c1][j]=distMatrix[c2][j];break;case"average":distMatrix[j][c1]=distMatrix[c1][j]=(cSize[c1]*distMatrix[c1][j]+cSize[c2]*distMatrix[c2][j])/(cSize[c1]+cSize[j]);break}}distMatrix[c1][c1]=Infinity;for(i=0;i<n;i++)distMatrix[i][c2]=distMatrix[c2][i]=Infinity;for(j=0;j<n;j++){if(dMin[j]==c2)dMin[j]=c1;if(distMatrix[c1][j]<distMatrix[c1][dMin[c1]])dMin[c1]=j}root=newCluster}return root}hcluster.distance=function(x){if(!arguments.length)return distance;distance=x;return hcluster};return hcluster};function calculateCentroid(c1Size,c1Centroid,c2Size,c2Centroid){var newCentroid=[],newSize=c1Size+c2Size,n=c1Centroid.length,i=-1;while(++i<n){newCentroid[i]=(c1Size*c1Centroid[i]+c2Size*c2Centroid[i])/newSize}return newCentroid}science.stats.iqr=function(x){var quartiles=science.stats.quantiles(x,[.25,.75]);return quartiles[1]-quartiles[0]};science.stats.loess=function(){var bandwidth=.3,robustnessIters=2,accuracy=1e-12;function smooth(xval,yval,weights){var n=xval.length,i;if(n!==yval.length)throw{error:"Mismatched array lengths"};if(n==0)throw{error:"At least one point required."};if(arguments.length<3){weights=[];i=-1;while(++i<n)weights[i]=1}science_stats_loessFiniteReal(xval);science_stats_loessFiniteReal(yval);science_stats_loessFiniteReal(weights);science_stats_loessStrictlyIncreasing(xval);if(n==1)return[yval[0]];if(n==2)return[yval[0],yval[1]];var bandwidthInPoints=Math.floor(bandwidth*n);if(bandwidthInPoints<2)throw{error:"Bandwidth too small."};var res=[],residuals=[],robustnessWeights=[];i=-1;while(++i<n){res[i]=0;residuals[i]=0;robustnessWeights[i]=1}var iter=-1;while(++iter<=robustnessIters){var bandwidthInterval=[0,bandwidthInPoints-1];var x;i=-1;while(++i<n){x=xval[i];if(i>0){science_stats_loessUpdateBandwidthInterval(xval,weights,i,bandwidthInterval)}var ileft=bandwidthInterval[0],iright=bandwidthInterval[1];var edge=xval[i]-xval[ileft]>xval[iright]-xval[i]?ileft:iright;var sumWeights=0,sumX=0,sumXSquared=0,sumY=0,sumXY=0,denom=Math.abs(1/(xval[edge]-x));for(var k=ileft;k<=iright;++k){var xk=xval[k],yk=yval[k],dist=k<i?x-xk:xk-x,w=science_stats_loessTricube(dist*denom)*robustnessWeights[k]*weights[k],xkw=xk*w;sumWeights+=w;sumX+=xkw;sumXSquared+=xk*xkw;sumY+=yk*w;sumXY+=yk*xkw}var meanX=sumX/sumWeights,meanY=sumY/sumWeights,meanXY=sumXY/sumWeights,meanXSquared=sumXSquared/sumWeights;var beta=Math.sqrt(Math.abs(meanXSquared-meanX*meanX))<accuracy?0:(meanXY-meanX*meanY)/(meanXSquared-meanX*meanX);var alpha=meanY-beta*meanX;res[i]=beta*x+alpha;residuals[i]=Math.abs(yval[i]-res[i])}if(iter===robustnessIters){break}var medianResidual=science.stats.median(residuals);if(Math.abs(medianResidual)<accuracy)break;var arg,w;i=-1;while(++i<n){arg=residuals[i]/(6*medianResidual);robustnessWeights[i]=arg>=1?0:(w=1-arg*arg)*w}}return res}smooth.bandwidth=function(x){if(!arguments.length)return x;bandwidth=x;return smooth};smooth.robustnessIterations=function(x){if(!arguments.length)return x;robustnessIters=x;return smooth};smooth.accuracy=function(x){if(!arguments.length)return x;accuracy=x;return smooth};return smooth};function science_stats_loessFiniteReal(values){var n=values.length,i=-1;while(++i<n)if(!isFinite(values[i]))return false;return true}function science_stats_loessStrictlyIncreasing(xval){var n=xval.length,i=0;while(++i<n)if(xval[i-1]>=xval[i])return false;return true}function science_stats_loessTricube(x){return(x=1-x*x*x)*x*x}function science_stats_loessUpdateBandwidthInterval(xval,weights,i,bandwidthInterval){var left=bandwidthInterval[0],right=bandwidthInterval[1];var nextRight=science_stats_loessNextNonzero(weights,right);if(nextRight<xval.length&&xval[nextRight]-xval[i]<xval[i]-xval[left]){var nextLeft=science_stats_loessNextNonzero(weights,left);bandwidthInterval[0]=nextLeft;bandwidthInterval[1]=nextRight}}function science_stats_loessNextNonzero(weights,i){var j=i+1;while(j<weights.length&&weights[j]===0)j++;return j}science.stats.mean=function(x){var n=x.length;if(n===0)return NaN;var m=0,i=-1;while(++i<n)m+=(x[i]-m)/(i+1);return m};science.stats.median=function(x){return science.stats.quantiles(x,[.5])[0]};science.stats.mode=function(x){var counts={},mode=[],max=0,n=x.length,i=-1,d,k;while(++i<n){k=counts.hasOwnProperty(d=x[i])?++counts[d]:counts[d]=1;if(k===max)mode.push(d);else if(k>max){max=k;mode=[d]}}if(mode.length===1)return mode[0]};science.stats.quantiles=function(d,quantiles){d=d.slice().sort(science.ascending);var n_1=d.length-1;return quantiles.map(function(q){if(q===0)return d[0];else if(q===1)return d[n_1];var index=1+q*n_1,lo=Math.floor(index),h=index-lo,a=d[lo-1];return h===0?a:a+h*(d[lo]-a)})};science.stats.variance=function(x){var n=x.length;if(n<1)return NaN;if(n===1)return 0;var mean=science.stats.mean(x),i=-1,s=0;while(++i<n){var v=x[i]-mean;s+=v*v}return s/(n-1)};science.stats.distribution={};science.stats.distribution.gaussian=function(){var random=Math.random,mean=0,sigma=1,variance=1;function gaussian(){var x1,x2,rad,y1;do{x1=2*random()-1;x2=2*random()-1;rad=x1*x1+x2*x2}while(rad>=1||rad===0);return mean+sigma*x1*Math.sqrt(-2*Math.log(rad)/rad)}gaussian.pdf=function(x){x=(x-mean)/sigma;return science_stats_distribution_gaussianConstant*Math.exp(-.5*x*x)/sigma};gaussian.cdf=function(x){x=(x-mean)/sigma;return.5*(1+science.stats.erf(x/Math.SQRT2))};gaussian.mean=function(x){if(!arguments.length)return mean;mean=+x;return gaussian};gaussian.variance=function(x){if(!arguments.length)return variance;sigma=Math.sqrt(variance=+x);return gaussian};gaussian.random=function(x){if(!arguments.length)return random;random=x;return gaussian};return gaussian};science_stats_distribution_gaussianConstant=1/Math.sqrt(2*Math.PI)})(this)})(this);