pm_distPower::setPowerLogQuan Interface Reference

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

Detailed Description

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

See the documentation of pm_distPower for more information on the quantile of the (Truncated) Power 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 alpha, containing the natural logarithm of the quantile corresponding to the input logCDF. By definition, the condition logMinX <= logx <= logMaxX holds.
[in]	logCDF	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha, containing the natural logarithm of the desired CDF value of the distribution corresponding to the output quantile.
[in]	alpha	: 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 shape parameter ( \(\alpha\)) of the distribution.
[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 alpha, containing the natural logarithm of the first scale parameter of the distribution, representing the minimum of the support of the distribution. (optional, default = 0. It can be present if and only if logCDFNF is also present.)
[in]	logCDFNF	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha, containing the natural logarithm of the normalization factor of the CDF of the (Truncated) Power distribution. Specifying this argument when calling this procedure repeatedly with fixed \((\alpha, x_\mathrm{min}, x_\mathrm{max})\) parameters will significantly improve the runtime performance. This argument can be readily obtained by calling getPowerLogCDFNF(alpha, logMinX, logMaxX).

Possible calling interfaces ⛓

use pm_distPower, only: setPowerLogQuan
 
call setPowerLogQuan(logx, logCDF, alpha, logCDFNF) ! Power distributed.
call setPowerLogQuan(logx, logCDF, alpha, logMinX, logCDFNF) ! Truncated Power distributed.
!

Warning

The condition alpha > 0 must hold for the corresponding input arguments.
The condition logCDF < 0 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

getPowerLogQuan

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_distPower, only: getPowerLogCDFNF
    use pm_distPower, only: setPowerLogQuan
    use pm_io, only: display_type
 
    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 Quantile Function of the Power distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setPowerLogQuan(logx(1), logCDF = -3., alpha = +2., logCDFNF = getPowerLogCDFNF(alpha = +2., logMaxX = -2.)) ! Power distribution.")
                    call setPowerLogQuan(logx(1), logCDF = -3., alpha = +2., logCDFNF = getPowerLogCDFNF(alpha = +2., logMaxX = -2.)) ! Power distribution.
    call disp%show("logx(1)")
    call disp%show( logx(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setPowerLogQuan(logx(1:3), logCDF = -[3., 4., 5.], alpha = +[+2., +3., +4.], logCDFNF = getPowerLogCDFNF(alpha = +2., logMaxX = -2.)) ! Power distribution.")
                    call setPowerLogQuan(logx(1:3), logCDF = -[3., 4., 5.], alpha = +[+2., +3., +4.], logCDFNF = getPowerLogCDFNF(alpha = +2., logMaxX = -2.)) ! Power distribution.
    call disp%show("logx(1:3)")
    call disp%show( logx(1:3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the Quantile Function of the Truncated Power distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setPowerLogQuan(logx(1), logCDF = -3., alpha = +2., logMinX = -2., logCDFNF = getPowerLogCDFNF(alpha = +2., logMinX = -2., logMaxX = 5.)) ! Truncated Power distribution.")
                    call setPowerLogQuan(logx(1), logCDF = -3., alpha = +2., logMinX = -2., logCDFNF = getPowerLogCDFNF(alpha = +2., logMinX = -2., logMaxX = 5.)) ! Truncated Power distribution.
    call disp%show("logx(1)")
    call disp%show( logx(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setPowerLogQuan(logx(1:3), logCDF = -[3., 4., 5.], alpha = +[+2., +3., +4.], logMinX = -2., logCDFNF = getPowerLogCDFNF(alpha = +[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Power distribution.")
                    call setPowerLogQuan(logx(1:3), logCDF = -[3., 4., 5.], alpha = +[+2., +3., +4.], logMinX = -2., logCDFNF = getPowerLogCDFNF(alpha = +[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Power distribution.
    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
        integer(IK) :: fileUnit, i
        real :: alpha(2), logMinX, logMaxX, logx(4), logCDF(2000)
        call setLinSpace(logCDF, x1 = log(0.001), x2 = log(.999))
        alpha = [+0.5, +2.0]
        logMinX = log(3.)
        logMaxX = log(8.)
        open(newunit = fileUnit, file = "setPowerLogQuan.RK.txt")
        do i = 1, size(logCDF, 1, IK)
            call setPowerLogQuan(logx(1:2), logCDF(i), alpha, getPowerLogCDFNF(alpha, logMaxX))
            call setPowerLogQuan(logx(3:4), logCDF(i), alpha, logMinX, getPowerLogCDFNF(alpha, logMinX, logMaxX))
            write(fileUnit, "(*(g0,:,', '))") exp(logCDF(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 Quantile Function of the Power distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
call setPowerLogQuan(logx(1), logCDF = -3., alpha = +2., logCDFNF = getPowerLogCDFNF(alpha = +2., logMaxX = -2.)) ! Power distribution.
logx(1)
-3.50000000
 
 
call setPowerLogQuan(logx(1:3), logCDF = -[3., 4., 5.], alpha = +[+2., +3., +4.], logCDFNF = getPowerLogCDFNF(alpha = +2., logMaxX = -2.)) ! Power distribution.
logx(1:3)
-3.50000000, -2.66666675, -2.25000000
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the Quantile Function of the Truncated Power distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
call setPowerLogQuan(logx(1), logCDF = -3., alpha = +2., logMinX = -2., logCDFNF = getPowerLogCDFNF(alpha = +2., logMinX = -2., logMaxX = 5.)) ! Truncated Power distribution.
logx(1)
+3.50000763
 
 
call setPowerLogQuan(logx(1:3), logCDF = -[3., 4., 5.], alpha = +[+2., +3., +4.], logMinX = -2., logCDFNF = getPowerLogCDFNF(alpha = +[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Power distribution.
logx(1:3)
+3.50000763, +3.66666651, +3.75000000
 
 

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"$\alpha = -.5, x_{min} = 0, x_{max} = +8$"
            , r"$\alpha = -2., x_{min} = 0, x_{max} = +8$"
            , r"$\alpha = -.5, x_{min} = +3., x_{max} = +8$"
            , r"$\alpha = -2., x_{min} = +3., x_{max} = +8$"
            ]
 
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")
        #ax.set_ylim([3, 10])
 
        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_distPower

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.
   
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 1539 of file pm_distPower.F90.

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

• src/fortran/main/pm_distPower.F90