# random_field

This function generates the random field using both Cholesky Decomposition method and Kriging. Details are explained by Yang et al. (2022).  

Yang, Y., Wang, P., and Brandenberg, S. J. (2022) "An algorithm for generating spatially correlated random fields using Cholesky decomposition and ordinary kriging." Computers and Geotechnics, 147. [[official version](https://doi.org/10.1016/j.compgeo.2022.104783)] [[open access](https://authors.elsevier.com/a/1f13c,63b%7EyYS2)]

## Installation
```bash
pip install ucla_geotech_tools.random_field
```

## Functions
```bash
sort_nodes(x,z): sort the nodes to better separate cholesky nodes from kriging nodes; return sorted node coordinates x and z
get_random_field(x,z,theta_z,mu,sigma): main function for generating the random field
get_chol_krig_nodes(x,z,Dhchol): group cholesky nodes and kriging nodes separately and return the index of cholesky and kriging nodes
get_COV(xvchol,zvchol,theta_z,model,sigma_chol): get covariance matrix
get_C_chol_krig(xvchol, zvchol, xvkrig, zvkrig, theta_z, model, sigma_chol, sigma_krig): get covariance matrix between cholesky nodes and kriging nodes
get_chol_field(COV, mu_chol): generate the random field for cholskey nodes
get_krig_field(COV, C_chol_krig, chol_field): generate the random field for kriging nodes
```

## Input Parameters for main function
```bash
x: x coordinates (list or array of x coordinates)
z: z coordinates (list or array of z coordinates)
mu: mean of random field
sigma: standard deviation of random field
theta_z: vertical scale of fluctuation
model: (optional) default is 0 for Guassian correlation matrix. Other intergers for Markovian correlation matrix
```

## Output Data
```bash
output : an array of values, and it has the same of order of the sorted nodes.
```

## Usage
```python
import ucla_geotech_tools.random_field as ugtrf
import numpy as np

x = np.linspace(0.0,40,641)
z = np.linspace(0.0,10,161)
x,z = np.meshgrid(x,z)
x = x.reshape(np.prod(x.shape),) # create a vector of X coordinates
z = z.reshape(np.prod(z.shape),) # create a vector of Y coordinates
x,z = ugtrf.sort_nodes(x,z)      # sort nodes

RF = ugtrf.get_random_field(x=x,z=z,mu=50,sigma=10,theta_z = 1.25)
```