pm_distLogUnif::getLogUnifPDF Interface Reference

Generate and return the Probability Density Function (PDF) of the LogUniform distribution for an input x within the support of the distribution \(x \in [0 < x_\mathrm{min}, x_\mathrm{max} < +\infty]\).
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Detailed Description

Generate and return the Probability Density Function (PDF) of the LogUniform distribution for an input x within the support of the distribution \(x \in [0 < x_\mathrm{min}, x_\mathrm{max} < +\infty]\).

See the documentation of pm_distLogUnif for more information on the LogUniform 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 PDF must be computed.
[in]	minx	: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as x, containing the first scale parameter of the distribution, representing the minimum of the support of the distribution.
[in]	maxx	: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as x, containing the second scale parameter of the distribution, representing the maximum of the support of the distribution.

Returns

pdf : 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 PDF of the distribution.

Possible calling interfaces ⛓

use pm_distLogUnif, only: getLogUnifPDF
 
pdf = getLogUnifPDF(x, minx, maxx)

Warning

The condition 0. < minx must hold for the corresponding input arguments.
The condition minx <= x must hold for the corresponding input arguments.
The condition x <= maxx 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

setLogUnifPDF

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_io, only: display_type
    use pm_distLogUnif, only: getLogUnifPDF
 
    implicit none
 
    real :: PDF(3)
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the Probability Density Function (PDF) of the LogUniform distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("PDF(1) = getLogUnifPDF(x = 3., minx = 2., maxx = 5.)")
                    PDF(1) = getLogUnifPDF(x = 3., minx = 2., maxx = 5.)
    call disp%show("PDF(1)")
    call disp%show( PDF(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("PDF(1:3) = getLogUnifPDF(x = [3., 4., 2.5], minx = 2., maxx = 5.)")
                    PDF(1:3) = getLogUnifPDF(x = [3., 4., 2.5], minx = 2., maxx = 5.)
    call disp%show("PDF(1:3)")
    call disp%show( PDF(1:3) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        use pm_arraySpace, only: setLogSpace
        real :: MinX(2), MaxX(2), PDF(2), X(2000)
        integer(IK) :: fileUnit, i
        call setLogSpace(X, logx1 = log(0.1), logx2 = log(13.))
        MinX = [3., 2.0]
        MaxX = [7., 10.]
        open(newunit = fileUnit, file = "getLogUnifPDF.RK.txt")
        do i = 1, size(X)
            PDF = 0.
            if (MinX(1) <= X(i) .and. X(i) <= MaxX(1)) PDF(1) = getLogUnifPDF(X(i), MinX(1), MaxX(1))
            if (MinX(2) <= X(i) .and. X(i) <= MaxX(2)) PDF(2) = getLogUnifPDF(X(i), MinX(2), MaxX(2))
            write(fileUnit, "(*(g0,:,', '))") X(i), PDF
        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 ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the Probability Density Function (PDF) of the LogUniform distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
PDF(1) = getLogUnifPDF(x = 3., minx = 2., maxx = 5.)
PDF(1)
+0.363785535
 
 
PDF(1:3) = getLogUnifPDF(x = [3., 4., 2.5], minx = 2., maxx = 5.)
PDF(1:3)
+0.363785535, +0.272839159, +0.436542660
 
 

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"$x_{min} = +3., x_{max} = +7.$"
            , r"$x_{min} = +2., x_{max} = +10.$"
            ]
 
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[:,1:5]
                    , marker[kind]
                    , linewidth = linewidth
                   #, color = "r"
                    )
            plt.plot( df.values[:, 1]
                    , df.values[:,1:5]
                    , 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 - 5
                        )
 
        plt.xticks(fontsize = fontsize - 2)
        plt.yticks(fontsize = fontsize - 2)
        ax.set_xlabel(xlab[kind], fontsize = 17)
        ax.set_ylabel("Probability Density Function (PDF)", fontsize = 17)
        #ax.set_xscale("log")
        #ax.set_yscale("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")
 
        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_distLogUnif

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.
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Copyright

Computational Data Science Lab

Author:

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

Definition at line 357 of file pm_distLogUnif.F90.

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

• src/fortran/main/pm_distLogUnif.F90