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RandomPointConfiguration
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RandomPointConfiguration

[Experimental]

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generates a pseudorandom spatial point configuration from the spatial point process pproc in the observation region reg.

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RandomPointConfiguration[pproc,reg, n]

generates an ensemble of n spatial point configurations.

Details and Options

  • RandomPointConfiguration takes a point process pproc and generates a point configuration as a SpatialPointData object.
  •     
  • RandomPointConfiguration gives a different realization of pseudorandom point configurations whenever you run the Wolfram Language. You can start with a particular seed using SeedRandom.
  • The same process can generate an ensemble consisting of different realizations.
  •     
  • The observation region reg needs to be a parameter-free region, as well as SpatialObservationRegionQ.
  • The following options can be given:
  • Method Automaticwhat method to use
    WorkingPrecision MachinePrecisionprecision used in internal computations
  • With the setting WorkingPrecisionp, random numbers of precision p will be generated.
  • Special settings for Method are documented under the individual point process reference pages.
  • Typical Method settings include:
  • "MCMC"Markov chain Monte Carlo birth and death
    "Thinning"random thinning
    "Exact"coupling from the past

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

Sample from a Poisson point process:

In[1]:=1
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https://wolfram.com/xid/0j0dlyb2oij39e-nn7onq
Out[1]=1
In[3]:=3
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https://wolfram.com/xid/0j0dlyb2oij39e-d381by
Out[3]=3

Sample 5 realizations from a binomial point process:

In[1]:=1
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https://wolfram.com/xid/0j0dlyb2oij39e-cfx34l
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0j0dlyb2oij39e-fp19j3
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0j0dlyb2oij39e-ilo8fq
Out[3]=3

Scope  (5)Survey of the scope of standard use cases

RandomPointConfiguration returns a SpatialPointData object:

In[1]:=1
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https://wolfram.com/xid/0j0dlyb2oij39e-b9hhl
Out[1]=1

Obtain a list of locations of the points:

In[2]:=2
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https://wolfram.com/xid/0j0dlyb2oij39e-h9a13
Out[2]=2

Simulate a Strauss point process in a rectangle:

In[1]:=1
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https://wolfram.com/xid/0j0dlyb2oij39e-11u5ba
Out[1]=1

Retrieve points that lie within a unit disk centered at {2,3}:

In[2]:=2
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https://wolfram.com/xid/0j0dlyb2oij39e-s9xzvw
Out[2]=2

Visualize points on the plane:

In[3]:=3
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https://wolfram.com/xid/0j0dlyb2oij39e-z8uyu0
Out[3]=3

Estimate the parameters for a point process using a simulated point configuration:

In[1]:=1
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https://wolfram.com/xid/0j0dlyb2oij39e-evf2j1
In[2]:=2
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https://wolfram.com/xid/0j0dlyb2oij39e-btg93s
Out[2]=2

Simulate from a Cauchy point process:

In[1]:=1
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https://wolfram.com/xid/0j0dlyb2oij39e-pc2ht7
In[2]:=2
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https://wolfram.com/xid/0j0dlyb2oij39e-zhyjp7
Out[2]=2

Estimate Ripley's function from the sampled point configuration and compare it with the theoretical function:

In[3]:=3
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https://wolfram.com/xid/0j0dlyb2oij39e-183br5
In[4]:=4
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https://wolfram.com/xid/0j0dlyb2oij39e-i25jxi
Out[4]=4

Simulate an ensemble of 5 realizations over the same region:

In[1]:=1
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https://wolfram.com/xid/0j0dlyb2oij39e-gkfq3s

Number of points in each realization:

In[2]:=2
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https://wolfram.com/xid/0j0dlyb2oij39e-ggja2m
Out[2]=2

Visualize the distribution of points in different realizations:

In[3]:=3
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https://wolfram.com/xid/0j0dlyb2oij39e-cb443p
Out[3]=3

Options  (3)Common values & functionality for each option

Method  (2)

Sample from an InhomogeneousPoissonPointProcess using the different methods:

In[3]:=3
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https://wolfram.com/xid/0j0dlyb2oij39e-8j1bt
In[2]:=2
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https://wolfram.com/xid/0j0dlyb2oij39e-8lje4s

Use the method "Thinning":

In[4]:=4
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https://wolfram.com/xid/0j0dlyb2oij39e-8i748x
Out[4]=4

Use the Markov chain Monte Carlo method "MCMC":

In[5]:=5
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https://wolfram.com/xid/0j0dlyb2oij39e-r8z4hx
Out[5]=5

Visualize samples over the region:

In[10]:=10
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https://wolfram.com/xid/0j0dlyb2oij39e-mhakyk
Out[10]=10

Sample from a Gibbs point process using the Markov chain Monte Carlo method "MCMC" with the number of iterations equal to 30000:

In[1]:=1
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https://wolfram.com/xid/0j0dlyb2oij39e-usnk9
In[2]:=2
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https://wolfram.com/xid/0j0dlyb2oij39e-jjyqjn
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0j0dlyb2oij39e-lavt93
Out[3]=3

WorkingPrecision  (1)

Generate a sample point configuration with default machine precision:

In[1]:=1
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https://wolfram.com/xid/0j0dlyb2oij39e-t52tzx
Out[1]=1

Use WorkingPrecision to generate a sample point configuration with higher precision:

In[2]:=2
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https://wolfram.com/xid/0j0dlyb2oij39e-c4j61e
Out[2]=2

Applications  (2)Sample problems that can be solved with this function

Estimate the density of a PoissonPointProcess from a sample:

In[1]:=1
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https://wolfram.com/xid/0j0dlyb2oij39e-cnq0d4
Out[2]=2

The intensity estimate:

In[3]:=3
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https://wolfram.com/xid/0j0dlyb2oij39e-dopmb
Out[3]=3

Compare the expected point counts and the average of number of points for an inhomogeneous Poisson point process:

In[1]:=1
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https://wolfram.com/xid/0j0dlyb2oij39e-14dn2
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0j0dlyb2oij39e-hkyt6c
Out[2]=2
Wolfram Research (2020), RandomPointConfiguration, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomPointConfiguration.html.
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Wolfram Research (2020), RandomPointConfiguration, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomPointConfiguration.html.

Text

Wolfram Research (2020), RandomPointConfiguration, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomPointConfiguration.html.

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Wolfram Research (2020), RandomPointConfiguration, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomPointConfiguration.html.

CMS

Wolfram Language. 2020. "RandomPointConfiguration." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RandomPointConfiguration.html.

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Wolfram Language. 2020. "RandomPointConfiguration." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RandomPointConfiguration.html.

APA

Wolfram Language. (2020). RandomPointConfiguration. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RandomPointConfiguration.html

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Wolfram Language. (2020). RandomPointConfiguration. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RandomPointConfiguration.html

BibTeX

@misc{reference.wolfram_2025_randompointconfiguration, author="Wolfram Research", title="{RandomPointConfiguration}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/RandomPointConfiguration.html}", note=[Accessed: 27-March-2025 ]}

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@misc{reference.wolfram_2025_randompointconfiguration, author="Wolfram Research", title="{RandomPointConfiguration}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/RandomPointConfiguration.html}", note=[Accessed: 27-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_randompointconfiguration, organization={Wolfram Research}, title={RandomPointConfiguration}, year={2020}, url={https://reference.wolfram.com/language/ref/RandomPointConfiguration.html}, note=[Accessed: 27-March-2025 ]}

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@online{reference.wolfram_2025_randompointconfiguration, organization={Wolfram Research}, title={RandomPointConfiguration}, year={2020}, url={https://reference.wolfram.com/language/ref/RandomPointConfiguration.html}, note=[Accessed: 27-March-2025 ]}