Cesium-Examples/examples/cesiumEx/kriging(es6).js

// Extend the Array class
Array.prototype.max = function() {
    return Math.max.apply(null, this);
};
Array.prototype.min = function() {
    return Math.min.apply(null, this);
};
Array.prototype.mean = function() {
    let 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) {
    let 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;
};

let kriging = {};

// Matrix algebra
var kriging_matrix_diag = function(c, n) {
    let i, Z = [0].rep(n*n);
    for(i=0;i<n;i++) Z[i*n+i] = c;
    return Z;
};
var kriging_matrix_transpose = function(X, n, m) {
    let 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;
};
var kriging_matrix_scale = function(X, c, n, m) {
    let i, j;
    for(i=0;i<n;i++)
        for(j=0;j<m;j++)
            X[i*m+j] *= c;
};
var kriging_matrix_add = function(X, Y, n, m) {
    let 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;
};
// Naive matrix multiplication
var kriging_matrix_multiply = function(X, Y, n, m, p) {
    let 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;
};
// Cholesky decomposition
var kriging_matrix_chol = function(X, n) {
    let 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;
};
// Inversion of cholesky decomposition
var kriging_matrix_chol2inv = function(X, n) {
    let 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];

};
// Inversion via gauss-jordan elimination
var kriging_matrix_solve = function(X, n) {
    let m = n;
    let b = Array(n*n);
    let indxc = Array(n);
    let indxr = Array(n);
    let ipiv = Array(n);
    let i, icol, irow, j, k, l, ll;
    let 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; // Singular

        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;
}

// Variogram models
var 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)) );
};
var kriging_variogram_exponential = function(h, nugget, range, sill, A) {
    return nugget + ((sill-nugget)/range)*
        ( 1.0 - Math.exp(-(1.0/A) * (h/range)) );
};
var 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) );
};

// Train using gaussian processes with bayesian priors
kriging.train = function(t, x, y, model, sigma2, alpha) {
    let 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;
    };

    // Lag distance/semivariance
    let i, j, k, l, n = t.length;
    let 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];

    // Bin lag distance
    let lags = ((n*n-n)/2)>30?30:(n*n-n)/2;
    let tolerance = variogram.range/lags;
    let lag = [0].rep(lags);
    let 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; // Error: Not enough points
    }

    // Feature transformation
    n = l;
    variogram.range = lag[n-1]-lag[0];
    let X = [1].rep(2*n);
    let Y = Array(n);
    let 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];
    }

    // Least squares
    let Xt = kriging_matrix_transpose(X, n, 2);
    let Z = kriging_matrix_multiply(Xt, X, 2, n, 2);
    Z = kriging_matrix_add(Z, kriging_matrix_diag(1/alpha, 2), 2, 2);
    let cloneZ = Z.slice(0);
    if(kriging_matrix_chol(Z, 2))
        kriging_matrix_chol2inv(Z, 2);
    else {
        kriging_matrix_solve(cloneZ, 2);
        Z = cloneZ;
    }
    let W = kriging_matrix_multiply(kriging_matrix_multiply(Z, Xt, 2, 2, n), Y, 2, n, 1);

    // Variogram parameters
    variogram.nugget = W[0];
    variogram.sill = W[1]*variogram.range+variogram.nugget;
    variogram.n = x.length;

    // Gram matrix with prior
    n = x.length;
    let 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);
    }

    // Inverse penalized Gram matrix projected to target vector
    let C = kriging_matrix_add(K, kriging_matrix_diag(sigma2, n), n, n);
    let cloneC = C.slice(0);
    if(kriging_matrix_chol(C, n))
        kriging_matrix_chol2inv(C, n);
    else {
        kriging_matrix_solve(cloneC, n);
        C = cloneC;
    }

    // Copy unprojected inverted matrix as K
    var K_C = C.slice(0);
    let M = kriging_matrix_multiply(C, t, n, n, 1);
    variogram.K = K_C;
    variogram.M = M;

    return variogram;
};

// Model prediction
kriging.predict = function(x, y, variogram) {
    let 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) {
    let 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];
};

// Gridded matrices or contour paths
//OpenLayers的polygon：ol.geom.Polygon(coordinates, opt_layout)
kriging.grid = function(polygons, variogram, width) {
    let i, j, k, n = polygons.length;
    if(n==0) return;

    // Boundaries of polygons space
    let xlim = [polygons[0][0][0], polygons[0][0][0]];
    let ylim = [polygons[0][0][1], polygons[0][0][1]];
    for(i=0;i<n;i++) // Polygons
        for(j=0;j<polygons[i].length;j++) { // Vertices
            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];
        }
    // Alloc for O(n^2) space
    let xtarget, ytarget;
    let a = Array(2), b = Array(2);
    let lxlim = Array(2); // Local dimensions
    let lylim = Array(2); // Local dimensions
    let x = Math.ceil((xlim[1]-xlim[0])/width);//x方向上的格子数
    let y = Math.ceil((ylim[1]-ylim[0])/width);//y方向上的格子数

    let A = Array(x+1);
    for(i=0;i<=x;i++) A[i] = Array(y+1);//A是一个二维矩阵
    for(i=0;i<n;i++) {
        // Range for polygons[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++) { // Vertices
            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];
        }

        // Loop through polygon subspace
        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) {
    return null;
};

// Plotting on the DOM
kriging.plot = function(canvas, grid, xlim, ylim, colors) {
    // Clear screen
    let ctx = canvas.getContext("2d");
    ctx.clearRect(0, 0, canvas.width, canvas.height);

    // Starting boundaries
    let range = [xlim[1]-xlim[0], ylim[1]-ylim[0], grid.zlim[1]-grid.zlim[0]];
    let i, j, x, y, z;
    let n = grid.length;
    let m = grid[0].length;
    let wx = Math.ceil(grid.width*canvas.width/(xlim[1]-xlim[0]));
    let 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);
        }
};

kriging.plot_rainbow = function(canvas, grid, xlim, ylim, rainbow) {
    // Clear screen
    let ctx = canvas.getContext("2d");
    ctx.clearRect(0, 0, canvas.width, canvas.height);

    // Starting boundaries
    let range = [xlim[1]-xlim[0], ylim[1]-ylim[0], grid.zlim[1]-grid.zlim[0]];
    let i, j, x, y, z;
    let n = grid.length;
    let m = grid[0].length;
    let wx = Math.ceil(grid.width*canvas.width/(xlim[1]-xlim[0]));
    let 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 ='#'+ rainbow.colourAt(z);
            ctx.fillRect(Math.round(x-wx/2), Math.round(y-wy/2), wx, wy);
        }
};

export default kriging;

/*
eg.
 var variogram = K.kriging.train(values, lngs, lats, model, sigma2, alpha);
 var grid = K.kriging.grid(_polygons, variogram, width);
 K.kriging.plot(this.canvas, grid, [extent.xmin, extent.xmax], [extent.ymin, extent.ymax], colors);
*/