pm_distBeta::setBetaRand Interface Reference

Return a scalar or array of arbitrary rank of Beta-distributed random values in range \([0, 1]\) (or \((0, 1)\), depending on the specific parameter values) with the specified two shape parameters \((\alpha, \beta)\) of the Beta distribution corresponding to the procedure arguments (alpha, beta). More...

Detailed Description

Return a scalar or array of arbitrary rank of Beta-distributed random values in range \([0, 1]\) (or \((0, 1)\), depending on the specific parameter values) with the specified two shape parameters \((\alpha, \beta)\) of the Beta distribution corresponding to the procedure arguments (alpha, beta).

See the documentation of pm_distBeta for more information on the Probability Density Function (PDF) of the Beta distribution and RNG.

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, or of, type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128). On output, it contains Beta-distributed random value(s).
[in]	alpha	: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as rand, containing the first shape parameter of the distribution.
[in]	beta	: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as rand, containing the second shape parameter of the distribution.

Possible calling interfaces ⛓

use pm_distBeta, only: setBetaRand
 
call setBetaRand(rand, alpha, beta)
call setBetaRand(rand(..), alpha, beta)
call setBetaRand(rng, rand, alpha, beta)
call setBetaRand(rng, rand(:), alpha, beta)

Warning

The conditions \(0. < \alpha\) and \(0. < \beta\) must hold for the input arguments (alpha, beta).
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.

The procedures under discussion are recursive.

Note

For repeated Beta RNG with fixed alpha, it is best to pass a vector of rand to be filled with random numbers rather than calling the procedures with scalar rand argument repeatedly.
In addition to avoiding procedure call overhead, vectorized RGN in this particular case also avoids an unnecessary division and square-root operation.

See also

getBetaLogPDF
setBetaLogPDF
getBetaCDF
setBetaCDF

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_distBeta, only: setBetaRand
    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
    real(RKG), dimension(NP) :: alpha, beta, rand
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call setLogSpace(alpha, logx1 = log(0.1_RKG), logx2 = log(10._RKG))
    call setLogSpace(beta, logx1 = log(0.1_RKG), logx2 = log(10._RKG))
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Generate random numbers from the Beta distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("alpha(1)")
    call disp%show( alpha(1) )
    call disp%show("beta(1)")
    call disp%show( beta(1) )
    call disp%show("call setBetaRand(rand(1), 1._RKG, beta = beta(1))")
                    call setBetaRand(rand(1), 1._RKG, beta = beta(1))
    call disp%show("rand(1)")
    call disp%show( rand(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("alpha(1)")
    call disp%show( alpha(1) )
    call disp%show("beta(1)")
    call disp%show( beta(1) )
    call disp%show("rng = xoshiro256ssw_type()")
                    rng = xoshiro256ssw_type()
    call disp%show("call setBetaRand(rng, rand(1:2), 1._RKG, beta = beta(1))")
                    call setBetaRand(rng, rand(1:2), 1._RKG, beta = beta(1))
    call disp%show("rand(1:2)")
    call disp%show( rand(1:2) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("alpha(1)")
    call disp%show( alpha(1) )
    call disp%show("beta(1)")
    call disp%show( beta(1) )
    call disp%show("call setBetaRand(rand(1:2), alpha(1), beta = beta(1))")
                    call setBetaRand(rand(1:2), alpha(1), beta = beta(1))
    call disp%show("rand(1:2)")
    call disp%show( rand(1:2) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("alpha(1:NP:NP/3)")
    call disp%show( alpha(1:NP:NP/3) )
    call disp%show("beta(1:NP:NP/3)")
    call disp%show( beta(1:NP:NP/3) )
    call disp%show("call setBetaRand(rand(1:NP:NP/3), alpha(1:NP:NP/3), beta = beta(1:NP:NP/3))")
                    call setBetaRand(rand(1:NP:NP/3), alpha(1:NP:NP/3), beta = beta(1:NP:NP/3))
    call disp%show("rand(1:NP:NP/3)")
    call disp%show( rand(1:NP:NP/3) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example rand array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        use pm_io, only: getErrTableWrite
        real(RKG) :: rand(5000, 4)
        call setBetaRand(rand(:, 1), alpha = 0.5_RKG, beta = 0.5_RKG)
        call setBetaRand(rand(:, 2), alpha = 2.0_RKG, beta = 2.0_RKG)
        call setBetaRand(rand(:, 3), alpha = 2.0_RKG, beta = 5.0_RKG)
        call setBetaRand(rand(:, 4), alpha = 5.0_RKG, beta = 2.0_RKG)
        if (0 /= getErrTableWrite(SK_"setBetaRand.RK.txt", rand)) error stop "Failed to write table."
    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 ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Generate random numbers from the Beta distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
alpha(1)
+0.999999940E-1
beta(1)
+0.999999940E-1
call setBetaRand(rand(1), 1._RKG, beta = beta(1))
rand(1)
+0.975416720
 
 
alpha(1)
+0.999999940E-1
beta(1)
+0.999999940E-1
rng = xoshiro256ssw_type()
call setBetaRand(rng, rand(1:2), 1._RKG, beta = beta(1))
rand(1:2)
+0.999997199, +0.600171797E-1
 
 
alpha(1)
+0.999999940E-1
beta(1)
+0.999999940E-1
call setBetaRand(rand(1:2), alpha(1), beta = beta(1))
rand(1:2)
+0.141968787, +0.999999702
 
 
alpha(1:NP:NP/3)
+0.999999940E-1, +0.464158833, +2.15443444, +10.0000010
beta(1:NP:NP/3)
+0.999999940E-1, +0.464158833, +2.15443444, +10.0000010
call setBetaRand(rand(1:NP:NP/3), alpha(1:NP:NP/3), beta = beta(1:NP:NP/3))
rand(1:NP:NP/3)
+0.662140606E-3, +0.850791335E-1, +0.814989626, +0.523548245
 
 

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" : "Beta Random Value ( real/imaginary components )"
        , "IK" : "Beta Random Value ( integer-valued )"
        , "RK" : "Beta Random Value ( real-valued )"
        }
legends =   [ r"$\alpha = 0.5, \beta = 0.5$"
            , r"$\alpha = 2.0, \beta = 2.0$"
            , r"$\alpha = 2.0, \beta = 5.0$"
            , r"$\alpha = 5.0, \beta = 2.0$"
            ]     
 
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 {} Beta 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_distBeta

Final Remarks ⛓

---

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 1039 of file pm_distBeta.F90.

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

• src/fortran/main/pm_distBeta.F90