uc-sgsim 1.2.4

Random Field Generation

Python Sonar Cloud state

C Sonar Cloud state

Warning This project is still in the pre-dev stage, the API usuage may be subject to change

UnConditional Sequential Gaussian SIMulation (UCSGSIM)

An unconditional random field generation tools that are easy to use.

Introduction of UCSGSIM

Sequential Gaussian Simulation is a random field generation method which was based on the kriging interporlation method.

Unconditonal simulation don't follow the patterns of "data", but follow the users's settings like mean and variance.

The core ideas of UCSGSIM are:

1. Create the grid (no any data value exist now).

$$ \Omega\to R $$

2. Visit random point of the model (draw one random value of the x_grid)

$$ X = RandomValue(\Omega), X:\Omega\to R $$

3. Select the theoritical covariance model to use, and set the sill and range properly.

$$ Gaussian = (C_{0} - s)(1 - e^{-h^{2}/r^{2}a})$$

$$ Spherical = (C_{0} - s)(3h/2r - h^3/2r^3)$$

$$ Exponential = (C_{0} - s)(1 - e^{-h/ra})$$

4. If there have more than 1 data value closed to the visted point (depend on the range of covariance model), then go next step. Else draw the random value from normal distribution as the simulation results of this iteration.

$$ Z_{k}({X_{simulation}}) = RandomNormal(m = 0 ,\sigma^2 = Sill)$$

5. Calculate weights from the data covaraince and distance coavariance

$$ \sum_{j=1}^{n}\omega_{j} = C(X_{data}^{i},X_{data}^{i})C^{-1}(X_i,X_i), i=1...N $$

6. Calculate the kriging estimate from the weight and data value

$$ Z_{k}(X_{estimate}) = \sum_{i=1}^{n} \omega_{i} Z(X_{data}) + (1- \sum_{i=1}^{n} \omega_{i} m_{g}) $$

7. Calculate the kriging error (kriging variance) from weights and data covariance

$$ \sigma_{krige}^{2} = \sum_{i=1}^{n}\omega_{i}C(X_{data}^{i},X_{data}^{i}) $$

8. Draw the random value from the normal distribution and add to the kriging estimate.

$$ Z(X_{simulation}) = Z(X_{estimate}) + RandomNormal(m = 0, \sigma^2 = \sigma_{krige}^{2}) $$

9. Repeat 2 ~ 8 until the whole model are simulated.

10. Repeat 1 ~ 9 with different randomseed number to produceed mutiple realizations.

Installation

pip install uc-sgsim

Features

• One dimensional unconditional randomfield generation with sequential gaussian simulation algorithm
• Muti-cores simulation (mutiprocessing)
• Run C to generate randomfield in python via ctype interface, or just generate randomfield in python with numpy and scipy library.

Example

import matplotlib.pyplot as plt
import uc_sgsim as uc
from uc_sgsim.cov_model import Gaussian

if __name__ == '__main__':
    x = 151  # Model grid, only 1D case is support now

    bw_s = 1  # lag step
    bw_l = 35  # lag range
    randomseed = 151  # randomseed for simulation
    k_range = 17.32  # effective range of covariance model
    sill = 1  # sill of covariance model

    nR = 10  # numbers of realizations in each CPU cores,
    # if nR = 1 n_process = 8
    # than you will compute total 8 realizations

    # Create Covariance model first
    cov_model = Gaussian(bw_l, bw_s, k_range, sill)

    # Create simulation and input the Cov model
    sgsim_py = uc.UCSgsim(x, nR, cov_model) # run sgsim with python
    sgsim_c = uc.UCSgsimDLL(x, nR, cov_model) # run sgsim with c

    # Start compute with n CPUs
    sgsim_c.compute(n_process=2, randomseed=randomseed)
    sgsim_py.compute(n_process=2, randomseed=987654)

    sgsim_c.mean_plot('ALL')  # Plot mean
    sgsim_c.variance_plot()  # Plot variance
    sgsim_c.cdf_plot(x_location=10)  # CDF
    sgsim_c.hist_plot(x_location=10)  # Hist
    sgsim_c.variogram_compute(n_process=2)  # Compute variogram before plotting
    # Plot variogram and mean variogram for validation
    sgsim.variogram_plot()
    # Save random_field and variogram
    sgsim_c.save_random_field('randomfields.csv', save_single=True)
    sgsim_c.save_variogram('variograms.csv', save_single=True)

    # show figure
    plt.show()

Future plans

• 2D unconditional randomfield generation
• GUI (pyhton)
• More covariance models
• More kriging methods (etc. Oridinary Kriging)
• Performance enhancement
• More completely documents and easy to use designs.

Performance

Parameters:

model len = 150

number of realizations = 1000

Range scale = 17.32

Variogram model = Gaussian model

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Testing platform:

CPU: AMD Ryzen 9 4900 hs

RAM: DDR4 - 3200 40GB (Dual channel 16GB)

Disk: WD SN530