// 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() {
|
var i, sum
|
for (i = 0, sum = 0; i < this.length; i++) { sum += this[i] }
|
return sum / this.length
|
}
|
Array.prototype.pip = function(x, y) {
|
var i; var j; var 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 = {}
|
|
function createArrayWithValues(value, n) {
|
var array = []
|
for (var i = 0; i < n; i++) {
|
array.push(value)
|
}
|
return array
|
}
|
|
// Matrix algebra
|
function kriging_matrix_diag(c, n) {
|
var Z = createArrayWithValues(0, n * n)
|
for (let i = 0; i < n; i++) Z[i * n + i] = c
|
return Z
|
}
|
function kriging_matrix_transpose(X, n, m) {
|
var i; var j; var 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
|
}
|
function kriging_matrix_scale(X, c, n, m) {
|
var i, j
|
for (i = 0; i < n; i++) {
|
for (j = 0; j < m; j++) { X[i * m + j] *= c }
|
}
|
}
|
function kriging_matrix_add(X, Y, n, m) {
|
var i; var j; var 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
|
function kriging_matrix_multiply(X, Y, n, m, p) {
|
var i; var j; var k; var 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
|
function kriging_matrix_chol(X, n) {
|
var i; var j; var k; var sum; 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
|
}
|
// Inversion of cholesky decomposition
|
function kriging_matrix_chol2inv(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] }
|
}
|
}
|
// Inversion via gauss-jordan elimination
|
function kriging_matrix_solve(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 // 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
|
function kriging_variogram_gaussian(h, nugget, range, sill, A) {
|
return nugget + ((sill - nugget) / range) *
|
(1.0 - Math.exp(-(1.0 / A) * Math.pow(h / range, 2)))
|
}
|
function kriging_variogram_exponential(h, nugget, range, sill, A) {
|
return nugget + ((sill - nugget) / range) *
|
(1.0 - Math.exp(-(1.0 / A) * (h / range)))
|
}
|
function kriging_variogram_spherical(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) {
|
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
|
}
|
|
// Lag distance/semivariance
|
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]
|
|
// Bin lag distance
|
var lags = ((n * n - n) / 2) > 30 ? 30 : (n * n - n) / 2
|
var tolerance = variogram.range / lags
|
var lag = createArrayWithValues(0, lags)
|
var semi = createArrayWithValues(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 // Error: Not enough points
|
}
|
|
// Feature transformation
|
n = l
|
variogram.range = lag[n - 1] - lag[0]
|
var X = createArrayWithValues(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]
|
}
|
|
// Least squares
|
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 parameters
|
variogram.nugget = W[0]
|
variogram.sill = W[1] * variogram.range + variogram.nugget
|
variogram.n = x.length
|
|
// Gram matrix with prior
|
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)
|
}
|
|
// Inverse penalized Gram matrix projected to target vector
|
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
|
}
|
|
// Copy unprojected inverted matrix as K
|
var K = C.slice(0)
|
var M = kriging_matrix_multiply(C, t, n, n, 1)
|
variogram.K = K
|
variogram.M = M
|
|
return variogram
|
}
|
|
// Model prediction
|
kriging.predict = function(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 kriging_matrix_multiply(k, variogram.M, 1, variogram.n, 1)[0]
|
}
|
kriging.variance = function(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 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
|
kriging.grid = function(polygons, variogram, width) {
|
var i; var j; var k; var n = polygons.length
|
if (n == 0) return
|
|
// Boundaries of polygons space
|
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++) // 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
|
var xtarget, ytarget
|
var a = Array(2); var b = Array(2)
|
var lxlim = Array(2) // Local dimensions
|
var lylim = Array(2) // Local dimensions
|
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++) {
|
// 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) {
|
|
}
|
|
// Plotting on the DOM
|
kriging.plot = function(canvas, grid, xlim, ylim, colors) {
|
// Clear screen
|
var ctx = canvas.getContext('2d')
|
ctx.clearRect(0, 0, canvas.width, canvas.height)
|
|
// Starting boundaries
|
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
|
}())
|
export { kriging }
|
// if (module && module.exports) {
|
// module.exports = kriging
|
// }
|
