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Cesium-Examples/examples/cesiumEx/kriging.js
jiawanlong bba0680b03 refactor: 求个star
2025-03-11 17:51:04 +08:00

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/*!
* author: [object Object]
* @sakitam-gis/kriging v0.1.0
* build-time: 2019-7-6 20:41
* LICENSE: MIT
* (c) 2019-2019 https://github.com/sakitam-gis/kriging.js
*/
(function (global, factory) {
typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) :
typeof define === 'function' && define.amd ? define(['exports'], factory) :
(global = global || self, factory(global.kriging = {}));
}(this, function (exports) { 'use strict';
function max(source) {
return Math.max.apply(null, source);
}
function min(source) {
return Math.min.apply(null, source);
}
function rep(source, n) {
var array = [];
for (var i = 0; i < n; i++) {
array.push(source);
}
return array;
}
function pip(source, x, y) {
var i = 0;
var j = source.length - 1;
var c = false;
var length = source.length;
for (; i < length; j = i++) {
if (((source[i][1] > y) !== (source[j][1] > y))
&& (x < (source[j][0] - source[i][0]) * (y - source[i][1]) / (source[j][1] - source[i][1]) + source[i][0])) {
c = !c;
}
}
return c;
}
function matrixDiag(c, n) {
var i = 0;
var Z = rep(0, n * n);
for (; i < n; i++) {
Z[i * n + i] = c;
}
return Z;
}
function matrixTranspose(X, n, m) {
var i = 0;
var j;
var Z = Array(m * n);
for (; i < n; i++) {
j = 0;
for (; j < m; j++) {
Z[j * n + i] = X[i * m + j];
}
}
return Z;
}
function matrixAdd(X, Y, n, m) {
var i = 0;
var j;
var Z = Array(n * m);
for (; i < n; i++) {
j = 0;
for (; j < m; j++) {
Z[i * m + j] = X[i * m + j] + Y[i * m + j];
}
}
return Z;
}
function matrixMultiply(X, Y, n, m, p) {
var i = 0;
var j;
var k;
var Z = Array(n * p);
for (; i < n; i++) {
j = 0;
for (; j < p; j++) {
Z[i * p + j] = 0;
k = 0;
for (; k < m; k++) {
Z[i * p + j] += X[i * m + k] * Y[k * p + j];
}
}
}
return Z;
}
function matrixChol(X, n) {
var i;
var j;
var k;
var 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;
}
function matrixChol2inv(X, n) {
var i;
var j;
var k;
var 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];
}
function matrixSolve(X, n) {
var m = n;
var b = Array(n * n);
var indxc = Array(n);
var indxr = Array(n);
var ipiv = Array(n);
var i;
var icol = 0;
var irow = 0;
var j;
var k;
var l;
var ll;
var big;
var dum;
var pivinv;
var 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;
}
function variogramGaussian(h, nugget, range, sill, A) {
return nugget + ((sill - nugget) / range)
* (1.0 - Math.exp(-(1.0 / A) * Math.pow(h / range, 2)));
}
function variogramExponential(h, nugget, range, sill, A) {
return nugget + ((sill - nugget) / range)
* (1.0 - Math.exp(-(1.0 / A) * (h / range)));
}
function variogramSpherical(h, nugget, range, sill) {
if (h > range)
return nugget + (sill - nugget) / range;
return nugget + ((sill - nugget) / range)
* (1.5 * (h / range) - 0.5 * Math.pow(h / range, 3));
}
function train(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,
model: variogramExponential,
K: [],
M: [],
};
switch (model) {
case 'gaussian':
variogram.model = variogramGaussian;
break;
case 'exponential':
variogram.model = variogramExponential;
break;
case 'spherical':
variogram.model = variogramSpherical;
break;
default:
variogram.model = variogramExponential;
}
var i;
var j;
var k;
var l;
var 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 = rep(0, lags);
var semi = rep(0, 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 = rep(1, 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 = matrixTranspose(X, n, 2);
var Z = matrixMultiply(Xt, X, 2, n, 2);
Z = matrixAdd(Z, matrixDiag(1 / alpha, 2), 2, 2);
var cloneZ = Z.slice(0);
if (matrixChol(Z, 2)) {
matrixChol2inv(Z, 2);
}
else {
matrixSolve(cloneZ, 2);
Z = cloneZ;
}
var W = matrixMultiply(matrixMultiply(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 = matrixAdd(K, matrixDiag(sigma2, n), n, n);
var cloneC = C.slice(0);
if (matrixChol(C, n)) {
matrixChol2inv(C, n);
}
else {
matrixSolve(cloneC, n);
C = cloneC;
}
var K1 = C.slice(0);
var M = matrixMultiply(C, t, n, n, 1);
variogram.K = K1;
variogram.M = M;
return variogram;
}
function predict(x, y, variogram) {
var i;
var 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 matrixMultiply(k, variogram.M, 1, variogram.n, 1)[0];
}
function variance(x, y, variogram) {
var i;
var 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);
}
var val = matrixMultiply(matrixMultiply(k, variogram.K, 1, variogram.n, variogram.n), k, 1, variogram.n, 1)[0];
return variogram.model(0, variogram.nugget, variogram.range, variogram.sill, variogram.A) + val;
}
function grid(polygons, variogram, width) {
var i;
var j;
var k;
var 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;
var ytarget;
var a = Array(2);
var 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 (pip(polygons[i], xtarget, ytarget)) {
A[j][k] = predict(xtarget, ytarget, variogram);
}
}
}
}
return {
xlim: xlim,
ylim: ylim,
width: width,
data: A,
zlim: [min(variogram.t), max(variogram.t)],
};
}
function plot(canvas, grid, xlim, ylim, colors) {
var ctx = canvas.getContext('2d');
var data = grid.data, zlim = grid.zlim, width = grid.width;
if (ctx) {
ctx.clearRect(0, 0, canvas.width, canvas.height);
var range = [xlim[1] - xlim[0], ylim[1] - ylim[0], zlim[1] - zlim[0]];
var i = void 0;
var j = void 0;
var x = void 0;
var y = void 0;
var z = void 0;
var n = data.length;
var m = data[0].length;
var wx = Math.ceil(width * canvas.width / (xlim[1] - xlim[0]));
var wy = Math.ceil(width * canvas.height / (ylim[1] - ylim[0]));
for (i = 0; i < n; i++) {
for (j = 0; j < m; j++) {
if (data[i][j] === undefined)
continue;
x = canvas.width * (i * width + grid.xlim[0] - xlim[0]) / range[0];
y = canvas.height * (1 - (j * width + grid.ylim[0] - ylim[0]) / range[1]);
z = (data[i][j] - 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);
}
}
}
}
var index = {
train: train,
predict: predict,
variance: variance,
grid: grid,
plot: plot,
max: max,
min: min,
pip: pip,
rep: rep,
matrixDiag: matrixDiag,
matrixTranspose: matrixTranspose,
matrixAdd: matrixAdd,
matrixMultiply: matrixMultiply,
matrixChol: matrixChol,
matrixChol2inv: matrixChol2inv,
matrixSolve: matrixSolve,
variogramGaussian: variogramGaussian,
variogramExponential: variogramExponential,
variogramSpherical: variogramSpherical,
};
exports.default = index;
exports.grid = grid;
exports.matrixAdd = matrixAdd;
exports.matrixChol = matrixChol;
exports.matrixChol2inv = matrixChol2inv;
exports.matrixDiag = matrixDiag;
exports.matrixMultiply = matrixMultiply;
exports.matrixSolve = matrixSolve;
exports.matrixTranspose = matrixTranspose;
exports.max = max;
exports.min = min;
exports.pip = pip;
exports.plot = plot;
exports.predict = predict;
exports.rep = rep;
exports.train = train;
exports.variance = variance;
exports.variogramExponential = variogramExponential;
exports.variogramGaussian = variogramGaussian;
exports.variogramSpherical = variogramSpherical;
Object.defineProperty(exports, '__esModule', { value: true });
}));
//# sourceMappingURL=kriging.js.map
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