pm_distKolm::getKolmCDF Interface Reference

Generate and return the Cumulative Distribution Function (CDF) of the Kolmogorov distribution for an input x within the support of the distribution \(X \in [0, +\infty)\). More...

Detailed Description

Generate and return the Cumulative Distribution Function (CDF) of the Kolmogorov distribution for an input x within the support of the distribution \(X \in [0, +\infty)\).

See the documentation of pm_distKolm for more information on the Kolmogorov distribution.

Parameters

[in]

x

: The input scalar or array of the same shape as other array like arguments, of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the value at which the CDF must be computed.

Returns

cdf : The output scalar or array of the same shape as any input array-like argument, of the same type and kind the input argument x, containing the CDF of the distribution.

Possible calling interfaces ⛓

use pm_distKolm, only: getKolmCDF
 
cdf = getKolmCDF(x)

Warning

The condition 0. <= x 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

setKolmCDF

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK
    use pm_distKolm, only: getKolmCDF
    use pm_arraySpace, only: getLinSpace
    use pm_arraySpace, only: getLogSpace
    use pm_io, only: display_type
 
    implicit none
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    block
        use pm_kind, only: TKG => RKS
        real(TKG), allocatable :: x(:), cdf(:)
        call disp%skip()
        call disp%show("x = [0._TKG, epsilon(0._TKG), 1._TKG, 2._TKG, 5._TKG]")
                        x = [0._TKG, epsilon(0._TKG), 1._TKG, 2._TKG, 5._TKG]
        call disp%show("x")
        call disp%show( x )
        call disp%show("cdf = getKolmCDF(x)")
                        cdf = getKolmCDF(x)
        call disp%show("cdf")
        call disp%show( cdf )
        call disp%skip()
    end block
 
    block
        use pm_kind, only: TKG => RKH
        real(TKG), allocatable :: x(:), cdf(:)
        call disp%skip()
        call disp%show("x = [0._TKG, epsilon(0._TKG), 1._TKG, 2._TKG, 5._TKG]")
                        x = [0._TKG, epsilon(0._TKG), 1._TKG, 2._TKG, 5._TKG]
        call disp%show("x")
        call disp%show( x )
        call disp%show("cdf = getKolmCDF(x)")
                        cdf = getKolmCDF(x)
        call disp%show("cdf")
        call disp%show( cdf )
        call disp%skip()
    end block
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example cdf array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        use pm_io, only: getErrTableWrite
        use pm_kind, only: TKG => RKH
        real(TKG) :: xcdf(1000, 2)
        xcdf(:, 1) = getLinSpace(0._TKG, +3._TKG, size(xcdf, 1, IK))
        xcdf(:, 2) = getKolmCDF(xcdf(:, 1))
        if (0 /= getErrTableWrite(SK_"getKolmCDF.RK.txt", xcdf, header = SK_"x,cdf")) 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 ⛓

 
x = [0._TKG, epsilon(0._TKG), 1._TKG, 2._TKG, 5._TKG]
x
+0.00000000, +0.119209290E-6, +1.00000000, +2.00000000, +5.00000000
cdf = getKolmCDF(x)
cdf
+0.00000000, +0.00000000, +0.730000257, +0.999329090, +1.00000000
 
 
x = [0._TKG, epsilon(0._TKG), 1._TKG, 2._TKG, 5._TKG]
x
+0.00000000000000000000000000000000000, +0.192592994438723585305597794258492732E-33, +1.00000000000000000000000000000000000, +2.00000000000000000000000000000000000, +5.00000000000000000000000000000000000
cdf = getKolmCDF(x)
cdf
+0.00000000000000000000000000000000000, +0.00000000000000000000000000000000000, +0.730000328322645478795099354415295337, +0.999329074744220304653455410099776938, +0.999999999999999999999614250030407219
 
 

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" : "X ( real/imaginary components )"
        , "IK" : "X ( integer-valued )"
        , "RK" : "X ( real-valued )"
        }
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":
            plt.plot( df.values[:, 0]
                    , df.values[:,1:]
                    , marker[kind]
                    , linewidth = linewidth
                   #, color = "r"
                    )
            plt.plot( df.values[:, 1]
                    , df.values[:,1:]
                    , marker[kind]
                    , linewidth = linewidth
                   #, color = "blue"
                    )
        else:
            plt.plot( df.values[:, 0]
                    , df.values[:,1:]
                    , marker[kind]
                    , linewidth = linewidth
                   #, color = "r"
                    )
            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("Cumulative Distribution Function (CDF)", 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_distKolm

Todo:

Very Low Priority: This generic interface can be extended to complex arguments.

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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Copyright

Computational Data Science Lab

Author:

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

Definition at line 432 of file pm_distKolm.F90.

---

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

• src/fortran/main/pm_distKolm.F90