pm_distPois::setPoisRand Interface Reference

Return a scalar (or array of arbitrary rank of) random value(s) from the Poisson distribution.
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Detailed Description

Return a scalar (or array of arbitrary rank of) random value(s) from the Poisson distribution.

See the documentation of pm_distPois for more details.

Parameters

[in,out]	rng	: The input/output scalar that can be an object of, type rngf_type, implying the use of intrinsic Fortran uniform RNG. type xoshiro256ssw_type, implying the use of xoshiro256** uniform RNG. (optional, default = rngf_type, implying the use of the intrinsic Fortran URNG.)
[out]	rand	: The output scalar or array of rank 1, or array of arbitrary rank if the rng argument is missing or set to rngf_type, of type integer of default kind IK, containing the Poisson-distributed random value(s).
[in]	lambda	: The input scalar (or array of the same rank, shape, and size as other array-like arguments), of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), representing the parameter(s) of the distribution(s). (optional. It must be present if and only if LAMBDA_LIMIT \(\leq \lambda\))
[in]	logLambda	: The input scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as lambda, representing log(lambda). This argument is required to ensure fast computation of many random values from the same distribution. (optional. It must be present if and only if LAMBDA_LIMIT \(\leq \lambda\))
[in]	sqrtLambda	: The input scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as lambda, representing sqrt(lambda). This argument is required to ensure fast computation of many random values from the same distribution. (optional. It must be present if and only if LAMBDA_LIMIT \(\leq \lambda\))
[in]	expNegLambda	: The input scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as lambda, representing exp(-lambda). (optional. It must be present if and only if \(0 < \lambda <\) LAMBDA_LIMIT)

Possible calling interfaces ⛓

use pm_distPois, only: setPoisRand
 
! when `LAMBDA_LIMIT <= lambda`
 
call setPoisRand(rand, lambda, logLambda, sqrtLambda)
call setPoisRand(rand(..), lambda, logLambda, sqrtLambda)
call setPoisRand(rng, rand, lambda, logLambda, sqrtLambda)
call setPoisRand(rng, rand(:), lambda, logLambda, sqrtLambda)
 
! when `0. < lambda < LAMBDA_LIMIT`
 
call setPoisRand(rand, expNegLambda)
call setPoisRand(rand(..), expNegLambda)
call setPoisRand(rng, rand, expNegLambda)
call setPoisRand(rng, rand(:), expNegLambda)

Warning

The condition expNegLambda < 1. must hold for the corresponding input arguments.
The condition exp(-LAMBDA_LIMIT) < expNegLambda must hold for the corresponding input arguments.
The condition logLambda == log(lambda) must hold for the corresponding input arguments.
The condition sqrtLambda == sqrt(lambda) must hold for the corresponding input arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.

Remarks

The procedures under discussion are elemental.

See also

getPoisRand

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK
    use pm_kind, only: RKG => RKS ! all real kinds are supported.
    use pm_distUnif, only: xoshiro256ssw_type
    use pm_distPois, only: setPoisRand
    use pm_arraySpace, only: setLinSpace
    use pm_arraySpace, only: setLogSpace
    use pm_io, only: display_type
 
    implicit none
 
    type(xoshiro256ssw_type) :: rng
    integer(IK), parameter  :: NP = 1000_IK
    integer(IK) :: rand(NP)
    real(RKG) :: lambda(NP)
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call setLinSpace(lambda, x1 = 0.1_RKG, x2 = 100._RKG)
 
    call disp%skip()
    call disp%show("lambda(1)")
    call disp%show( lambda(1) )
    call disp%show("call setPoisRand(rand(1), exp(-lambda(1)))")
                    call setPoisRand(rand(1), exp(-lambda(1)))
    call disp%show("rand(1)")
    call disp%show( rand(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("lambda(1)")
    call disp%show( lambda(1) )
    call disp%show("rng = xoshiro256ssw_type()")
                    rng = xoshiro256ssw_type()
    call disp%show("call setPoisRand(rng, rand(1:2), exp(-lambda(1)))")
                    call setPoisRand(rng, rand(1:2), exp(-lambda(1)))
    call disp%show("rand(1:2)")
    call disp%show( rand(1:2) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("lambda(1)")
    call disp%show( lambda(1) )
    call disp%show("call setPoisRand(rand(1:2), exp(-lambda(1)))")
                    call setPoisRand(rand(1:2), exp(-lambda(1)))
    call disp%show("rand(1:2)")
    call disp%show( rand(1:2) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("lambda(NP-2:NP)")
    call disp%show( lambda(NP-2:NP) )
    call disp%show("call setPoisRand(rand(NP-2:NP), lambda(NP-2:NP), log(lambda(NP-2:NP)), sqrt(lambda(NP-2:NP)))")
                    call setPoisRand(rand(NP-2:NP), lambda(NP-2:NP), log(lambda(NP-2:NP)), sqrt(lambda(NP-2:NP)))
    call disp%show("rand(NP-2:NP)")
    call disp%show( rand(NP-2:NP) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example rand array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        use pm_io, only: getErrTableWrite
        integer(IK) :: rand(500, 4)
        real(RKG), parameter :: lambda(4) = [.1_RKG, 1._RKG, 4._RKG, 11._RKG]
        call setPoisRand(rand(:, 1), exp(-lambda(1)))
        call setPoisRand(rand(:, 2), exp(-lambda(2)))
        call setPoisRand(rand(:, 3), exp(-lambda(3)))
        call setPoisRand(rand(:, 4), lambda(4), log(lambda(4)), sqrt(lambda(4)))
        if (0 /= getErrTableWrite(SK_"setPoisRand.IK.txt", rand)) error stop "Table writing failed."
    end block
 
end program example

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example output ⛓

 
lambda(1)
+0.100000001
call setPoisRand(rand(1), exp(-lambda(1)))
rand(1)
+0
 
 
lambda(1)
+0.100000001
rng = xoshiro256ssw_type()
call setPoisRand(rng, rand(1:2), exp(-lambda(1)))
rand(1:2)
+0, +0
 
 
lambda(1)
+0.100000001
call setPoisRand(rand(1:2), exp(-lambda(1)))
rand(1:2)
+0, +0
 
 
lambda(NP-2:NP)
+99.8000031, +99.9000015, +100.000000
call setPoisRand(rand(NP-2:NP), lambda(NP-2:NP), log(lambda(NP-2:NP)), sqrt(lambda(NP-2:NP)))
rand(NP-2:NP)
+106, +84, +103
 
 

Postprocessing of the example output ⛓

#!/usr/bin/env python
 
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import glob
import sys
 
linewidth = 2
fontsize = 17
 
marker ={ "CK" : "-"
        , "IK" : "."
        , "RK" : "-"
        }
xlab =  { "CK" : "Poisson Random Value ( real/imaginary components )"
        , "IK" : "Poisson Random Value ( integer-valued )"
        , "RK" : "Poisson Random Value ( real-valued )"
        }
legends =   [ r"$\lambda = 0.1$"
            , r"$\lambda = 1.0$"
            , r"$\lambda = 4.0$"
            , r"$\lambda = 11.$"
            ]     
 
for kind in ["IK", "CK", "RK"]:
 
    pattern = "*." + kind + ".txt"
    fileList = glob.glob(pattern)
    if len(fileList) == 1:
 
        df = pd.read_csv(fileList[0], delimiter = ",", header = None)
 
        fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
        ax = plt.subplot()
 
        for j in range(len(df.values[0,:])):
            if kind == "CK":
                plt.hist( df.values[:,j]
                        , histtype = "stepfilled"
                        , alpha = 0.5
                        , bins = 75
                        )
            else:
                plt.hist( df.values[:,j]
                        , histtype = "stepfilled"
                        , alpha = 0.5
                        , bins = 75
                        )
                ax.legend   ( legends
                            , fontsize = fontsize
                            )
        plt.xticks(fontsize = fontsize - 2)
        plt.yticks(fontsize = fontsize - 2)
        ax.set_xlabel(xlab[kind], fontsize = 17)
        ax.set_ylabel("Count", fontsize = 17)
        ax.set_title("Histograms of {} Poisson random values".format(len(df.values[:, 0])), fontsize = 17)
 
        plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
        ax.tick_params(axis = "y", which = "minor")
        ax.tick_params(axis = "x", which = "minor")
 
        plt.savefig(fileList[0].replace(".txt",".png"))
 
    elif len(fileList) > 1:
 
        sys.exit("Ambiguous file list exists.")

Visualization of the example output ⛓

Test:

test_pm_distPois

Final Remarks ⛓

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If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
   
2. If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.
   

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, Oct 16, 2009, 11:14 AM, Michigan

Definition at line 976 of file pm_distPois.F90.

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The documentation for this interface was generated from the following file:

• src/fortran/main/pm_distPois.F90