@sakitam-gis/kriging
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kriging.js is a Javascript library providing spatial prediction and mapping capabilities via the ordinary kriging algorithm.
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kriging.js
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[](https://npmjs.org/package/@sakitam-gis/kriging)
[](https://www.npmjs.org/package/@sakitam-gis/kriging)
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## Dev
```bash
git clone https://github.com/sakitam-gis/kriging.js
npm install or yarn
npm run dev
npm run build
```
## Use
### CDN
```bash
https://unpkg.com/@sakitam-gis/kriging/dist/kriging.min.js
https://unpkg.com/@sakitam-gis/kriging/dist/kriging.js
```
### PACKAGES
```bash
npm i @sakitam-gis/kriging
# node
const kriging = require('@sakitam-gis/kriging');
# es
import kriging from '@sakitam-gis/kriging';
# or
import { train, grid } from '@sakitam-gis/kriging';
```
**kriging.js** is a Javascript library providing spatial prediction and mapping capabilities via the ordinary kriging algorithm.
Kriging is a type of gaussian process where 2-dimensional coordinates are mapped to some target variable using kernel regression. This algorithm has been specifically designed to accurately model smaller data sets by assigning a prior to the variogram parameters.
Fitting a Model
---------------
The first step is to link **kriging.js** to your html code and assign your coordinate and target variables to 3 separate arrays.
``` html
<script src="kriging.js" type="text/javascript"></script>
<script type="text/javascript">
var t = [ /* Target variable */ ];
var x = [ /* X-axis coordinates */ ];
var y = [ /* Y-axis coordinates */ ];
var model = "exponential";
var sigma2 = 0, alpha = 100;
var variogram = kriging.train(t, x, y, model, sigma2, alpha);
</script>
```
The train method in the kriging object fits your input to whatever variogram model you specify - gaussian, exponential or spherical - and returns a variogram object.
Error and Bayesian Prior
------------------------
Notice the σ<sup>2</sup> (sigma2) and α (alpha) variables, these correspond to the variance parameters of the gaussian process and the prior of the variogram model, respectively. A diffuse α prior is typically used; a formal mathematical definition of the model is provided below.
Predicting New Values
---------------------
Values can be predicted for new coordinate pairs by using the predict method in the kriging object.
``` javascript
var xnew, ynew /* Pair of new coordinates to predict */;
var tpredicted = kriging.predict(xnew, ynew, variogram);
```
Creating a Map
--------------
Variogram and Probability Model
-------------------------------
The various variogram models can be interpreted as kernel functions for 2-dimensional coordinates **a**, **b** and parameters nugget, range, sill and A. Reparameterized as a linear function, with w = [nugget, (sill-nugget)/range], this becomes:
- Gaussian: k(**a**,**b**) = w[0] + w[1] * ( 1 - exp{ -( ||**a**-**b**|| / range )<sup>2</sup> / A } )
- Exponential: k(**a**,**b**) = w[0] + w[1] * ( 1 - exp{ -( ||**a**-**b**|| / range ) / A } )
- Spherical: k(**a**,**b**) = w[0] + w[1] * ( 1.5 * ( ||**a**-**b**|| / range ) - 0.5 * ( ||**a**-**b**|| / range )<sup>3</sup> )
The variance parameter α of the prior distribution for w should be manually set, according to:
- w ~ N(w|**0**, α**I**)
Using the fitted kernel function hyperparameters and setting K as the Gram matrix, the prior and likelihood for the gaussian process become:
- **y** ~ N(**y**|**0**, **K**)
- **t**|**y** ~ N(**t**|**y**, σ<sup>2</sup>**I**)
The variance parameter σ<sup>2</sup> of the likelihood reflects the error in the gaussian process and should be manually set.