LHS

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LHS#

Function for Latin Hypercube Sampling

This module was written by Matthias Cuntz while at Department of Computational Hydrosystems, Helmholtz Centre for Environmental Research - UFZ, Leipzig, Germany, and continued while at Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Nancy, France.

copyright:

Copyright 2012-2025 Matthias Cuntz, see AUTHORS.rst for details.

license:

MIT License, see LICENSE for details.

The following functions are provided

lhs(dist, param, nsample)

Latin Hypercube Sampling of any distribution after Stein (1987)
History

  • Written May 2012 by Matthias Cuntz making a combination of a Matlab routine of Budiman (2003) and a Python routine of Flavio Codeco Coelho (2008)

  • Ported to Python 3, Feb 2013, Matthias Cuntz

  • Preserve shape of dist parameter, Nov 2016, Matthias Cuntz

  • Code refactoring, Sep 2021, Matthias Cuntz

  • Porting into pyjams, Oct 2025, Matthias Cuntz

lhs(dist, param, nsample)[source]#

Latin Hypercube Sampling of any distribution after Stein (1987)

There can be no correlation between parameters.

Parameters:

  • dist (instance or list of scipy.stats distributions) – Instance(s) of random number generator from scipy.stats such as scipy.stats.norm, scipy.stats.beta, etc.

  • param (tuple or list of tuple) – Tuple of parameters as required for dist

  • nsample (int) – Number of samples per parameter, i.e. per dist

Returns:

Latin Hypercube Samples of dist

Return type:

[len(dist), nsample] ndarray

Notes

Stein, M. 1987. Large Sample Properties of Simulations Using

Latin Hypercube Sampling. Technometrics 29:143-151

Examples

>>> import numpy as np
>>> import scipy.stats as stats
>>> # seed for reproducible results in doctest
>>> np.random.seed(1)

>>> dist = [stats.norm, stats.uniform] # for uniform (min, max-min)
>>> pars = [(50, 2), (1, 5)]
>>> c = lhs(dist, pars, 20)
>>> print(c[0:2, 0:4])
[[52.8216393  51.95643181 46.71040364 50.58536004]
 [ 4.95018614  2.49206539  2.07835604  4.67308065]]

>>> np.random.seed(1)
>>> dist = [stats.norm]
>>> pars = [(50,2)]
>>> c = lhs(dist, pars, 20)
>>> print(c.shape)
(1, 20)

>>> print(c[0, 0:4])
[51.17074344 48.56164788 51.68328332 50.58536004]

>>> np.random.seed(1)
>>> dist = stats.norm
>>> pars = (50,2)
>>> c = lhs(dist, pars, 20)

>>> print(c.shape)
(20,)

>>> print(c[0:4])
[51.17074344 48.56164788 51.68328332 50.58536004]
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