cLHS: Conditioned Latin Hypercube Sampling¶
About conditioned Latin Hypercube Sampling (cLHS) in Python¶
This code is based on the cLHS method of Minasny & McBratney (2006). It follows some of the code from the R package clhs of Roudier et al.
For cLHS the problem is: given \(N\) sites with ancillary variables (\(X\)), select \(x\) a sub-sample of size \(n \ll N\) in order that \(x\) forms a Latin hypercube, or the multivariate distribution of \(X\) is maximally stratified.
In short, this code attempts to create a Latin Hypercube sample by selecting only from input data. It uses simulated annealing to force the sampling to converge more rapidly, and also allows for setting a stopping criterion on the objective function described in Minasny & McBratney (2006).
Credits: Erika Wagoner (wagoner47) and Zhonghua Zheng (zzheng93)
Installation instructions¶
Install on local machine with pip¶
$ pip install clhs
Install on local machine from source¶
The get the latest verson that is not uploaded to PyPI yet:
Clone the github repository
$ git clone https://github.com/wagoner47/clhs_py.git
Or using SSH clone
$ git clone git@github.com:wagoner47/clhs_py.git
Move into the new directory
$ cd clhs_pyRun the setup script
$ python setup.py install
You may also supply the –user option to install for a single user (which is helpful if you don’t have admin/root privledges, for instance)
$ python setup.py install --user
Other options are also available for the setup script. To see all of them with documentation, use
$ python setup.py install --help
Licensing¶
clhs_py is licensed with the MIT License.
Copyright (c) 2019 Erika Wagoner and contributors.
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Quickstart¶
[1]:
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import xarray as xr
import clhs as cl
Create a Dataset¶
[2]:
ds = xr.tutorial.open_dataset('air_temperature') # use xr.tutorial.load_dataset() for xarray<v0.11.0
df=ds["air"][0,:,:].to_dataframe().reset_index()[["lat","lon","air"]]
# set temperature and relative humidity, relative humidty is normal distribution
df["temp"] = df["air"]-273.15
df["rh"] = np.random.normal(50, 12, 1325)
df.shape[0]
[2]:
1325
Implement cLHS¶
[3]:
# set sample number
num_sample=15
# cLHS
sampled=cl.clhs(df[["temp","rh"]], num_sample, max_iterations=1000)
clhs_sample=df.iloc[sampled["sample_indices"]]
# random sample, as a comparison
random_sample=df.sample(num_sample)
cLHS:100%|██████████|1000/1000 [Elapsed time: 6.365708112716675, ETA: 0.0, 157.09it/s]
Visualization and Comparison¶
[4]:
fig, [ax1,ax2] = plt.subplots(1,2, figsize=(18,8))
ax1.scatter(df["lon"],df["lat"],label="All",c=df["temp"],marker="s",s=300)
ax1.scatter(random_sample["lon"],random_sample["lat"],label="Random sampling",c="blue")
ax1.scatter(clhs_sample["lon"],
clhs_sample["lat"],
label="cLHS sampling",c="red")
ax1.legend()
ax1.set_title("Temperature",fontsize=20)
ax2.scatter(df["lon"],df["lat"],label="All",c=df["rh"],marker="s",s=300)
ax2.scatter(random_sample["lon"],random_sample["lat"],label="Random sampling",c="blue")
ax2.scatter(clhs_sample["lon"],
clhs_sample["lat"],
label="cLHS sampling",c="red")
ax2.legend()
ax2.set_title("Relative Humidity",fontsize=20)
plt.show()
fig, [ax1, ax2, ax3] = plt.subplots(1,3, figsize=(18,8))
df[["temp","rh"]].boxplot(ax=ax1)
random_sample[["temp","rh"]].boxplot(ax=ax2)
clhs_sample[["temp","rh"]].boxplot(ax=ax3)
ax1.set_ylim([-60,100])
ax1.set_title("All",fontsize=20)
ax2.set_ylim([-60,100])
ax2.set_title("Random sampling",fontsize=20)
ax3.set_ylim([-60,100])
ax3.set_title("cLHS sampling",fontsize=20)
matplotlib.rc('xtick', labelsize=20)
matplotlib.rc('ytick', labelsize=20)
plt.show()
print("Overall")
print(df[["temp","rh"]].describe())
print("\n")
print("Random sampling")
print(random_sample[["temp","rh"]].describe())
print("\n")
print("cLHS sampling")
print(clhs_sample[["temp","rh"]].describe())
print("\n")
Overall
temp rh
count 1325.000000 1325.000000
mean 1.016275 49.783078
std 19.110956 11.866438
min -46.149994 14.095438
25% -14.859985 41.674848
50% 4.350006 49.635435
75% 18.250000 57.099548
max 29.450012 93.291254
Random sampling
temp rh
count 15.000000 15.000000
mean 0.866668 47.374234
std 17.082689 16.324525
min -27.949997 22.440250
25% -11.355003 39.034426
50% 5.350006 43.010765
75% 14.399994 57.418314
max 23.640015 84.635052
cLHS sampling
temp rh
count 15.000000 15.000000
mean 1.048006 49.060304
std 24.219866 11.522810
min -39.949997 26.673582
25% -21.555000 42.597241
50% 8.850006 50.116637
75% 21.640015 57.448803
max 24.950012 67.569718
clhs¶
get_strata |
|
get_correlation_matrix |
|
get_strata |
|
get_correlation_matrix |
|
get_random_samples |
|
counts_matrix |
|
continuous_objective_func |
|
categorical_objective_func |
|
correlation_objective_func |
|
clhs_objective_func |
|
resample_random |
|
resample_worst |
|
resample |
|
clhs |