pm_distLogUnif::setLogUnifLogQuan Interface Reference

Return a scalar (or array of arbitrary rank) of the natural logarithm(s) of quantile corresponding to the specified CDF of LogUniform distribution with parameters \((x_\mathrm{min}, x_\mathrm{max})\). More...

Detailed Description

Return a scalar (or array of arbitrary rank) of the natural logarithm(s) of quantile corresponding to the specified CDF of LogUniform distribution with parameters \((x_\mathrm{min}, x_\mathrm{max})\).

See the documentation of pm_distLogUnif for more information on the quantile of the LogUniform distribution.

Parameters

[out]	logx	: The output scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as cdf, containing the natural logarithm of the quantile corresponding to the input cdf. By definition, the condition logMinX <= logx <= logMaxX holds.
[in]	cdf	: 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), containing the natural logarithm of the desired CDF value of the distribution corresponding to the output quantile.
[in]	logMinX	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as cdf, containing the natural logarithm of the first scale parameter of the distribution, representing the minimum of the support of the distribution.
[in]	pdfnf	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as cdf, containing the natural logarithm of the normalization factor of the PDF of the LogUniform distribution. Specifying this argument when calling this procedure repeatedly with fixed \((x_\mathrm{min}, x_\mathrm{max})\) parameters will significantly improve the runtime performance. This argument can be readily obtained by calling getLogUnifPDFNF(logMinX, logMaxX).

Possible calling interfaces ⛓

use pm_distLogUnif, only: setLogUnifLogQuan
 
call setLogUnifLogQuan(logx, cdf, logMinX, pdfnf)

Warning

The condition 0 <= cdf <= 1 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

getLogUnifLogQuan

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_io, only: display_type
    use pm_distLogUnif, only: getLogUnifPDFNF
    use pm_distLogUnif, only: setLogUnifLogQuan
 
    implicit none
 
    real :: logx(3)
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the Inverse CDF (Quantile) Function of the LogUniform distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setLogUnifLogQuan(logx(1), cdf = 0.5, logMinX = log(2.), pdfnf = getLogUnifPDFNF(logMinX = log(2.), logMaxX = log(5.)))")
                    call setLogUnifLogQuan(logx(1), cdf = 0.5, logMinX = log(2.), pdfnf = getLogUnifPDFNF(logMinX = log(2.), logMaxX = log(5.)))
    call disp%show("logx(1)")
    call disp%show( logx(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setLogUnifLogQuan(logx(1:3), cdf = [.3, .4, .25], logMinX = log(2.), pdfnf = getLogUnifPDFNF(logMinX = log(2.), logMaxX = log(5.)))")
                    call setLogUnifLogQuan(logx(1:3), cdf = [.3, .4, .25], logMinX = log(2.), pdfnf = getLogUnifPDFNF(logMinX = log(2.), logMaxX = log(5.)))
    call disp%show("logx(1:3)")
    call disp%show( logx(1:3) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        use pm_arraySpace, only: setLinSpace
        real :: logMinX(2), logMaxX(2), logx(2), CDF(2000)
        integer(IK) :: fileUnit, i
        call setLinSpace(CDF, x1 = 0., x2 = 1.)
        logMinX = log([3., 2.0])
        logMaxX = log([7., 10.])
        open(newunit = fileUnit, file = "setLogUnifLogQuan.RK.txt")
        do i = 1, size(CDF)
            call setLogUnifLogQuan(logx, CDF(i), logMinX, getLogUnifPDFNF(logMinX, logMaxX))
            write(fileUnit, "(*(g0,:,', '))") CDF(i), exp(logx)
        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 Inverse CDF (Quantile) Function of the LogUniform distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
call setLogUnifLogQuan(logx(1), cdf = 0.5, logMinX = log(2.), pdfnf = getLogUnifPDFNF(logMinX = log(2.), logMaxX = log(5.)))
logx(1)
+1.15129256
 
 
call setLogUnifLogQuan(logx(1:3), cdf = [.3, .4, .25], logMinX = log(2.), pdfnf = getLogUnifPDFNF(logMinX = log(2.), logMaxX = log(5.)))
logx(1:3)
+0.968034387, +1.05966353, +0.922219872
 
 

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" : "CDF ( real/imaginary components )"
        , "IK" : "CDF ( integer-valued )"
        , "RK" : "CDF ( 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("Quantile Function", 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

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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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 982 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