pm_distPois::getPoisRand Interface Reference

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

Generate and 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]

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 location/scale parameter of the distribution.

Returns

rand : The output positive scalar (or array of the same rank, shape, and size as other array-like arguments), of type integer of default kind IK, containing random value(s) from the distribution.

Possible calling interfaces ⛓

use pm_distPois, only: getPoisRand
use pm_kind, only: IK
integer(IK) :: rand
 
rand = getPoisRand(lambda)

Warning

The condition 0 < 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.

Remarks

The procedures under discussion are impure.

The procedures under discussion are elemental.

See also

setPoisRand

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK
    use pm_kind, only: RKG => RKS ! all real kinds are supported.
    use pm_distPois, only: getPoisRand
    use pm_arraySpace, only: setLinSpace
    use pm_arraySpace, only: setLogSpace
    use pm_io, only: display_type
 
    implicit none
 
    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("rand(1) = getPoisRand(lambda(1))")
                    rand(1) = getPoisRand(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("rand(1:2) = getPoisRand(lambda(1))")
                    rand(1:2) = getPoisRand(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("rand(1:2) = getPoisRand(lambda(1))")
                    rand(1:2) = getPoisRand(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("rand(NP-2:NP) = getPoisRand(lambda(NP-2:NP))")
                    rand(NP-2:NP) = getPoisRand(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
        integer(IK) :: fileUnit, i
        integer(IK) , parameter :: NP = 5000_IK
        real(RKG)   , parameter :: lambda(4) = [.1_RKG, 1._RKG, 4._RKG, 11._RKG]
        open(newunit = fileUnit, file = "getPoisRand.IK.txt")
        do i = 1, NP
            write(fileUnit,"(*(g0,:,' '))") getPoisRand(lambda)
        end do
        close(fileUnit)
    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
rand(1) = getPoisRand(lambda(1))
rand(1)
+0
 
 
lambda(1)
+0.100000001
rand(1:2) = getPoisRand(lambda(1))
rand(1:2)
+0, +0
 
 
lambda(1)
+0.100000001
rand(1:2) = getPoisRand(lambda(1))
rand(1:2)
+0, +0
 
 
lambda(NP-2:NP)
+99.8000031, +99.9000015, +100.000000
rand(NP-2:NP) = getPoisRand(lambda(NP-2:NP))
rand(NP-2:NP)
+123, +105, +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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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.
   
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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 821 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