| 1 |
- ;Array.prototype.max=function(){return Math.max.apply(null,this)};Array.prototype.min=function(){return Math.min.apply(null,this)};Array.prototype.mean=function(){var i,sum;for(i=0,sum=0;i<this.length;i++)sum+=this[i];return sum/this.length};Array.prototype.rep=function(n){return Array.apply(null,new Array(n)).map(Number.prototype.valueOf,this[0])};Array.prototype.pip=function(x,y){var i,j,c=false;for(i=0,j=this.length-1;i<this.length;j=i++){if(((this[i][1]>y)!=(this[j][1]>y))&&(x<(this[j][0]-this[i][0])*(y-this[i][1])/(this[j][1]-this[i][1])+this[i][0])){c=!c}}return c};var kriging=function(){var kriging={};kriging_matrix_diag=function(c,n){var i,Z=[0].rep(n*n);for(i=0;i<n;i++)Z[i*n+i]=c;return Z};kriging_matrix_transpose=function(X,n,m){var i,j,Z=Array(m*n);for(i=0;i<n;i++)for(j=0;j<m;j++)Z[j*n+i]=X[i*m+j];return Z};kriging_matrix_scale=function(X,c,n,m){var i,j;for(i=0;i<n;i++)for(j=0;j<m;j++)X[i*m+j]*=c};kriging_matrix_add=function(X,Y,n,m){var i,j,Z=Array(n*m);for(i=0;i<n;i++)for(j=0;j<m;j++)Z[i*m+j]=X[i*m+j]+Y[i*m+j];return Z};kriging_matrix_multiply=function(X,Y,n,m,p){var i,j,k,Z=Array(n*p);for(i=0;i<n;i++){for(j=0;j<p;j++){Z[i*p+j]=0;for(k=0;k<m;k++)Z[i*p+j]+=X[i*m+k]*Y[k*p+j]}}return Z};kriging_matrix_chol=function(X,n){var i,j,k,sum,p=Array(n);for(i=0;i<n;i++)p[i]=X[i*n+i];for(i=0;i<n;i++){for(j=0;j<i;j++)p[i]-=X[i*n+j]*X[i*n+j];if(p[i]<=0)return false;p[i]=Math.sqrt(p[i]);for(j=i+1;j<n;j++){for(k=0;k<i;k++)X[j*n+i]-=X[j*n+k]*X[i*n+k];X[j*n+i]/=p[i]}}for(i=0;i<n;i++)X[i*n+i]=p[i];return true};kriging_matrix_chol2inv=function(X,n){var i,j,k,sum;for(i=0;i<n;i++){X[i*n+i]=1/X[i*n+i];for(j=i+1;j<n;j++){sum=0;for(k=i;k<j;k++)sum-=X[j*n+k]*X[k*n+i];X[j*n+i]=sum/X[j*n+j]}}for(i=0;i<n;i++)for(j=i+1;j<n;j++)X[i*n+j]=0;for(i=0;i<n;i++){X[i*n+i]*=X[i*n+i];for(k=i+1;k<n;k++)X[i*n+i]+=X[k*n+i]*X[k*n+i];for(j=i+1;j<n;j++)for(k=j;k<n;k++)X[i*n+j]+=X[k*n+i]*X[k*n+j]}for(i=0;i<n;i++)for(j=0;j<i;j++)X[i*n+j]=X[j*n+i]};kriging_matrix_solve=function(X,n){var m=n;var b=Array(n*n);var indxc=Array(n);var indxr=Array(n);var ipiv=Array(n);var i,icol,irow,j,k,l,ll;var big,dum,pivinv,temp;for(i=0;i<n;i++)for(j=0;j<n;j++){if(i==j)b[i*n+j]=1;else b[i*n+j]=0}for(j=0;j<n;j++)ipiv[j]=0;for(i=0;i<n;i++){big=0;for(j=0;j<n;j++){if(ipiv[j]!=1){for(k=0;k<n;k++){if(ipiv[k]==0){if(Math.abs(X[j*n+k])>=big){big=Math.abs(X[j*n+k]);irow=j;icol=k}}}}}++(ipiv[icol]);if(irow!=icol){for(l=0;l<n;l++){temp=X[irow*n+l];X[irow*n+l]=X[icol*n+l];X[icol*n+l]=temp}for(l=0;l<m;l++){temp=b[irow*n+l];b[irow*n+l]=b[icol*n+l];b[icol*n+l]=temp}}indxr[i]=irow;indxc[i]=icol;if(X[icol*n+icol]==0)return false;pivinv=1/X[icol*n+icol];X[icol*n+icol]=1;for(l=0;l<n;l++)X[icol*n+l]*=pivinv;for(l=0;l<m;l++)b[icol*n+l]*=pivinv;for(ll=0;ll<n;ll++){if(ll!=icol){dum=X[ll*n+icol];X[ll*n+icol]=0;for(l=0;l<n;l++)X[ll*n+l]-=X[icol*n+l]*dum;for(l=0;l<m;l++)b[ll*n+l]-=b[icol*n+l]*dum}}}for(l=(n-1);l>=0;l--)if(indxr[l]!=indxc[l]){for(k=0;k<n;k++){temp=X[k*n+indxr[l]];X[k*n+indxr[l]]=X[k*n+indxc[l]];X[k*n+indxc[l]]=temp}}return true};kriging_variogram_gaussian=function(h,nugget,range,sill,A){return nugget+((sill-nugget)/range)*(1.0-Math.exp(-(1.0/A)*Math.pow(h/range,2)))};kriging_variogram_exponential=function(h,nugget,range,sill,A){return nugget+((sill-nugget)/range)*(1.0-Math.exp(-(1.0/A)*(h/range)))};kriging_variogram_spherical=function(h,nugget,range,sill,A){if(h>range)return nugget+(sill-nugget)/range;return nugget+((sill-nugget)/range)*(1.5*(h/range)-0.5*Math.pow(h/range,3))};kriging.train=function(t,x,y,model,sigma2,alpha){var variogram={t:t,x:x,y:y,nugget:0.0,range:0.0,sill:0.0,A:1/3,n:0};switch(model){case"gaussian":variogram.model=kriging_variogram_gaussian;break;case"exponential":variogram.model=kriging_variogram_exponential;break;case"spherical":variogram.model=kriging_variogram_spherical;break};var i,j,k,l,n=t.length;var distance=Array((n*n-n)/2);for(i=0,k=0;i<n;i++)for(j=0;j<i;j++,k++){distance[k]=Array(2);distance[k][0]=Math.pow(Math.pow(x[i]-x[j],2)+Math.pow(y[i]-y[j],2),0.5);distance[k][1]=Math.abs(t[i]-t[j])}distance.sort(function(a,b){return a[0]-b[0]});variogram.range=distance[(n*n-n)/2-1][0];var lags=((n*n-n)/2)>30?30:(n*n-n)/2;var tolerance=variogram.range/lags;var lag=[0].rep(lags);var semi=[0].rep(lags);if(lags<30){for(l=0;l<lags;l++){lag[l]=distance[l][0];semi[l]=distance[l][1]}}else{for(i=0,j=0,k=0,l=0;i<lags&&j<((n*n-n)/2);i++,k=0){while(distance[j][0]<=((i+1)*tolerance)){lag[l]+=distance[j][0];semi[l]+=distance[j][1];j++;k++;if(j>=((n*n-n)/2))break}if(k>0){lag[l]/=k;semi[l]/=k;l++}}if(l<2)return variogram}n=l;variogram.range=lag[n-1]-lag[0];var X=[1].rep(2*n);var Y=Array(n);var A=variogram.A;for(i=0;i<n;i++){switch(model){case"gaussian":X[i*2+1]=1.0-Math.exp(-(1.0/A)*Math.pow(lag[i]/variogram.range,2));break;case"exponential":X[i*2+1]=1.0-Math.exp(-(1.0/A)*lag[i]/variogram.range);break;case"spherical":X[i*2+1]=1.5*(lag[i]/variogram.range)-0.5*Math.pow(lag[i]/variogram.range,3);break};Y[i]=semi[i]}var Xt=kriging_matrix_transpose(X,n,2);var Z=kriging_matrix_multiply(Xt,X,2,n,2);Z=kriging_matrix_add(Z,kriging_matrix_diag(1/alpha,2),2,2);var cloneZ=Z.slice(0);if(kriging_matrix_chol(Z,2))kriging_matrix_chol2inv(Z,2);else{kriging_matrix_solve(cloneZ,2);Z=cloneZ}var W=kriging_matrix_multiply(kriging_matrix_multiply(Z,Xt,2,2,n),Y,2,n,1);variogram.nugget=W[0];variogram.sill=W[1]*variogram.range+variogram.nugget;variogram.n=x.length;n=x.length;var K=Array(n*n);for(i=0;i<n;i++){for(j=0;j<i;j++){K[i*n+j]=variogram.model(Math.pow(Math.pow(x[i]-x[j],2)+Math.pow(y[i]-y[j],2),0.5),variogram.nugget,variogram.range,variogram.sill,variogram.A);K[j*n+i]=K[i*n+j]}K[i*n+i]=variogram.model(0,variogram.nugget,variogram.range,variogram.sill,variogram.A)}var C=kriging_matrix_add(K,kriging_matrix_diag(sigma2,n),n,n);var cloneC=C.slice(0);if(kriging_matrix_chol(C,n))kriging_matrix_chol2inv(C,n);else{kriging_matrix_solve(cloneC,n);C=cloneC}var K=C.slice(0);var M=kriging_matrix_multiply(C,t,n,n,1);variogram.K=K;variogram.M=M;return variogram};kriging.predict=function(x,y,variogram){var i,k=Array(variogram.n);for(i=0;i<variogram.n;i++)k[i]=variogram.model(Math.pow(Math.pow(x-variogram.x[i],2)+Math.pow(y-variogram.y[i],2),0.5),variogram.nugget,variogram.range,variogram.sill,variogram.A);return kriging_matrix_multiply(k,variogram.M,1,variogram.n,1)[0]};kriging.variance=function(x,y,variogram){var i,k=Array(variogram.n);for(i=0;i<variogram.n;i++)k[i]=variogram.model(Math.pow(Math.pow(x-variogram.x[i],2)+Math.pow(y-variogram.y[i],2),0.5),variogram.nugget,variogram.range,variogram.sill,variogram.A);return variogram.model(0,variogram.nugget,variogram.range,variogram.sill,variogram.A)+kriging_matrix_multiply(kriging_matrix_multiply(k,variogram.K,1,variogram.n,variogram.n),k,1,variogram.n,1)[0]};kriging.grid=function(polygons,variogram,width){var i,j,k,n=polygons.length;if(n==0)return;var xlim=[polygons[0][0][0],polygons[0][0][0]];var ylim=[polygons[0][0][1],polygons[0][0][1]];for(i=0;i<n;i++)for(j=0;j<polygons[i].length;j++){if(polygons[i][j][0]<xlim[0])xlim[0]=polygons[i][j][0];if(polygons[i][j][0]>xlim[1])xlim[1]=polygons[i][j][0];if(polygons[i][j][1]<ylim[0])ylim[0]=polygons[i][j][1];if(polygons[i][j][1]>ylim[1])ylim[1]=polygons[i][j][1]}var xtarget,ytarget;var a=Array(2),b=Array(2);var lxlim=Array(2);var lylim=Array(2);var x=Math.ceil((xlim[1]-xlim[0])/width);var y=Math.ceil((ylim[1]-ylim[0])/width);var A=Array(x+1);for(i=0;i<=x;i++)A[i]=Array(y+1);for(i=0;i<n;i++){lxlim[0]=polygons[i][0][0];lxlim[1]=lxlim[0];lylim[0]=polygons[i][0][1];lylim[1]=lylim[0];for(j=1;j<polygons[i].length;j++){if(polygons[i][j][0]<lxlim[0])lxlim[0]=polygons[i][j][0];if(polygons[i][j][0]>lxlim[1])lxlim[1]=polygons[i][j][0];if(polygons[i][j][1]<lylim[0])lylim[0]=polygons[i][j][1];if(polygons[i][j][1]>lylim[1])lylim[1]=polygons[i][j][1]}a[0]=Math.floor(((lxlim[0]-((lxlim[0]-xlim[0])%width))-xlim[0])/width);a[1]=Math.ceil(((lxlim[1]-((lxlim[1]-xlim[1])%width))-xlim[0])/width);b[0]=Math.floor(((lylim[0]-((lylim[0]-ylim[0])%width))-ylim[0])/width);b[1]=Math.ceil(((lylim[1]-((lylim[1]-ylim[1])%width))-ylim[0])/width);for(j=a[0];j<=a[1];j++)for(k=b[0];k<=b[1];k++){xtarget=xlim[0]+j*width;ytarget=ylim[0]+k*width;if(polygons[i].pip(xtarget,ytarget))A[j][k]=kriging.predict(xtarget,ytarget,variogram)}}A.xlim=xlim;A.ylim=ylim;A.zlim=[variogram.t.min(),variogram.t.max()];A.width=width;return A};kriging.contour=function(value,polygons,variogram){};kriging.plot=function(canvas,grid,xlim,ylim,colors){var ctx=canvas.getContext("2d");ctx.clearRect(0,0,canvas.width,canvas.height);var range=[xlim[1]-xlim[0],ylim[1]-ylim[0],grid.zlim[1]-grid.zlim[0]];var i,j,x,y,z;var n=grid.length;var m=grid[0].length;var wx=Math.ceil(grid.width*canvas.width/(xlim[1]-xlim[0]));var wy=Math.ceil(grid.width*canvas.height/(ylim[1]-ylim[0]));for(i=0;i<n;i++)for(j=0;j<m;j++){if(grid[i][j]==undefined)continue;x=canvas.width*(i*grid.width+grid.xlim[0]-xlim[0])/range[0];y=canvas.height*(1-(j*grid.width+grid.ylim[0]-ylim[0])/range[1]);z=(grid[i][j]-grid.zlim[0])/range[2];if(z<0.0)z=0.0;if(z>1.0)z=1.0;ctx.fillStyle=colors[Math.floor((colors.length-1)*z)];ctx.fillRect(Math.round(x-wx/2),Math.round(y-wy/2),wx,wy)}};return kriging}();;
|
