pm_distKolm::setKolmRand Interface Reference

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

Detailed Description

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

See the documentation of pm_distKolm for more information on generating random numbers from the Kolmogorov distribution.

Parameters

[out]	rand	: The input/output 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). containing the Kolmogorov-distributed random value(s) in the range \([0, +\infty)\).
[in]	unif	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as the output rand, containing uniformly-distributed random value(s) in the range \([0, 1)\).

Possible calling interfaces ⛓

use pm_distKolm, only: setKolmRand
 
call setKolmRand(rand, unif)

Warning

The condition 0 <= unif < 1 must hold for the corresponding input arguments.
This condition is 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

getKolmRand

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_io, only: display_type
    use pm_distKolm, only: setKolmRand
    use pm_distUnif, only: getUnifRand
    use pm_arrayResize, only: setResized
 
    implicit none
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    block
        use pm_kind, only: TKG => RKS
        real(TKG), allocatable :: rand(:)
        call disp%skip()
        call disp%show("call setResized(rand, 3_IK)")
                        call setResized(rand, 3_IK)
        call disp%show("call setKolmRand(rand(1), getUnifRand(0._TKG, 1._TKG))")
                        call setKolmRand(rand(1), getUnifRand(0._TKG, 1._TKG))
        call disp%show("rand(1)")
        call disp%show( rand(1) )
        call disp%show("call setKolmRand(rand, getUnifRand(0._TKG, 1._TKG, 3_IK))")
                        call setKolmRand(rand, getUnifRand(0._TKG, 1._TKG, 3_IK))
        call disp%show("rand")
        call disp%show( rand )
        call disp%skip()
    end block
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        use pm_io, only: getErrTableWrite
        use pm_kind, only: TKG => RKH
        real(TKG) :: rand(1500)
        call setKolmRand(rand, getUnifRand(0._TKG, 1._TKG, size(rand, 1, IK)))
        if (0 /= getErrTableWrite(SK_"setKolmRand.RK.txt", rand, header = SK_"rand")) error stop "table output 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 ⛓

 
call setResized(rand, 3_IK)
call setKolmRand(rand(1), getUnifRand(0._TKG, 1._TKG))
rand(1)
+0.768051147
call setKolmRand(rand, getUnifRand(0._TKG, 1._TKG, 3_IK))
rand
+1.00601602, +0.880411625, +0.626510322
 
 

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" : "Random Value ( Real / Imaginary ))"
        , "IK" : "Random Value ( Integer )"
        , "RK" : "Random Value ( Real )"
        }
legends =   [ r"Kolmogorov Distribution"
            ]
 
for kind in ["IK", "CK", "RK"]:
 
    pattern = "*." + kind + ".txt"
    fileList = glob.glob(pattern)
    if len(fileList) == 1:
 
        df = pd.read_csv(fileList[0], delimiter = ",")
 
        fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
        ax = plt.subplot()
 
        if kind == "CK":
            ax.hist ( df.values[:, 0]
                    , bins = 30
                    , histtype = "stepfilled"
                    , density = True
                    , alpha = 0.7
                    )
            ax.hist ( df.values[:, 1]
                    , bins = 30
                    , histtype = "stepfilled"
                    , density = True
                    , alpha = 0.7
                    )
        else:
            ax.hist ( df.values[:,:]
                    , bins = 50
                    , histtype = "stepfilled"
                    , density = True
                    , alpha = 0.7
                    )
            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("Density", fontsize = 17)
        ax.set_title("Histogram of {} randomly generated values".format(len(df.values)), fontsize = fontsize)
        #ax.set_yscale("log")
        #ax.set_xscale("log")
 
        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")
        ax.set_axisbelow(True)
 
        plt.tight_layout()
        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_distKolm

Todo:

Critical Priority: This interface can be extended to support vector-like rand arguments other than the elemental approach.
Such an extension would be sensible only if the new interface improves the performance against the elemental approach.

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 1037 of file pm_distKolm.F90.

---

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

• src/fortran/main/pm_distKolm.F90