pm_distExpGamma::getExpGammaLogPDFNF Interface Reference

Generate and return the natural logarithm of the normalization factor of the Probability Density Function (PDF) of the ExpGamma distribution.
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Detailed Description

Generate and return the natural logarithm of the normalization factor of the Probability Density Function (PDF) of the ExpGamma distribution.

The normalization factor of the ExpGamma PDF is defined as \(\eta = 1 / \Gamma(\kappa)\) where \(\kappa\) is the shape parameter of the ExpGamma distribution.
For more information, see the documentation of pm_distExpGamma.

Parameters

[in]

kappa

: The input scalar or array of the same shape as other array-like arguments, containing the shape parameter ( \(\kappa\)) of the distribution.

Returns

logPDFNF : The output scalar or array of the same shape as array-like input arguments, of the same type, kind, and highest rank as the input arguments containing the natural logarithm of the normalization factor of the distribution.

Possible calling interfaces ⛓

use pm_distExpGamma, only: getExpGammaLogPDFNF
 
logPDFNF = getExpGammaLogPDFNF(kappa)

Warning

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.

These procedures are particularly useful and needed in computing the PDF of the distribution.
The logic behind pre-computing the normalization factor is to speed up the calculations since the normalization factor contains log() and log_gamma() computations which are computationally costly operations.
See the benchmark below for more details.

See also

setExpGammaLogPDF
setExpGammaLogPDF

Example usage ⛓

program example
 
    use pm_kind, only: IK
    use pm_kind, only: SK
    use pm_kind, only: RK => RKS ! all other real kinds are also supported.
    use pm_io, only: display_type
    use pm_arraySpace, only: getLinSpace
    use pm_arraySpace, only: setLinSpace
    use pm_distExpGamma, only: getExpGammaLogPDFNF
 
    implicit none
 
    integer(IK) , parameter :: NP = 1000_IK
    real(RK)    , allocatable :: logPDFNF(:), Kappa(:)
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    Kappa = getLinSpace(0.01_RK, 10._RK, count = NP)
    allocate(logPDFNF, mold = Kappa)
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the natural logarithm of the normalization factor of the ExpGamma distribution PDF.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the PDF at an input scalar real value.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("Kappa(1:NP:NP/5)")
    call disp%show( Kappa(1:NP:NP/5) )
    call disp%show("logPDFNF(1:NP:NP/5) = getExpGammaLogPDFNF(1._RK)")
                    logPDFNF(1:NP:NP/5) = getExpGammaLogPDFNF(1._RK)
    call disp%show("logPDFNF(1:NP:NP/5)")
    call disp%show( logPDFNF(1:NP:NP/5) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("Kappa(1)")
    call disp%show( Kappa(1) )
    call disp%show("logPDFNF(1) = getExpGammaLogPDFNF(kappa = Kappa(1))")
                    logPDFNF(1) = getExpGammaLogPDFNF(kappa = Kappa(1))
    call disp%show("logPDFNF(1)")
    call disp%show( logPDFNF(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("Kappa(1:NP:NP/5)")
    call disp%show( Kappa(1:NP:NP/5) )
    call disp%show("logPDFNF(1:NP:NP/5) = getExpGammaLogPDFNF(Kappa(1:NP:NP/5))")
                    logPDFNF(1:NP:NP/5) = getExpGammaLogPDFNF(Kappa(1:NP:NP/5))
    call disp%show("logPDFNF(1:NP:NP/5)")
    call disp%show( logPDFNF(1:NP:NP/5) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    logPDFNF = getExpGammaLogPDFNF(Kappa)
 
    block
 
        integer :: fileUnit, i
 
        open(newunit = fileUnit, file = "getExpGammaLogPDFNF.RK.txt")
        write(fileUnit,"(2(g0,:,' '))") (Kappa(i), exp(logPDFNF(i)), i = 1, size(logPDFNF))
        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 natural logarithm of the normalization factor of the ExpGamma distribution PDF.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the PDF at an input scalar real value.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
Kappa(1:NP:NP/5)
+0.999999978E-2, +2.00999999, +4.01000023, +6.01000023, +8.01000023
logPDFNF(1:NP:NP/5) = getExpGammaLogPDFNF(1._RK)
logPDFNF(1:NP:NP/5)
-0.00000000, -0.00000000, -0.00000000, -0.00000000, -0.00000000
 
 
Kappa(1)
+0.999999978E-2
logPDFNF(1) = getExpGammaLogPDFNF(kappa = Kappa(1))
logPDFNF(1)
-4.59948015
 
 
Kappa(1:NP:NP/5)
+0.999999978E-2, +2.00999999, +4.01000023, +6.01000023, +8.01000023
logPDFNF(1:NP:NP/5) = getExpGammaLogPDFNF(Kappa(1:NP:NP/5))
logPDFNF(1:NP:NP/5)
-4.59948015, -0.426001893E-2, -1.80433512, -4.80456209, -8.54532528
 
 

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
 
fontsize = 17
 
marker ={ "CK" : "-"
        , "IK" : "."
        , "RK" : "-"
        }
xlab =  { "CK" : r"shape parameter: $\kappa$ ( real/imaginary )"
        , "IK" : r"shape parameter: $\kappa$ ( integer-valued )"
        , "RK" : r"shape parameter: $\kappa$ ( real-valued )"
        }
 
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[:,2]
                    , marker[kind]
                    , color = "r"
                    )
            plt.plot( df.values[:,1]
                    , df.values[:,3]
                    , marker[kind]
                    , color = "blue"
                    )
        else:
            plt.plot( df.values[:, 0]
                    , df.values[:,1]
                    , marker[kind]
                    , color = "r"
                    )
 
        plt.xticks(fontsize = fontsize - 2)
        plt.yticks(fontsize = fontsize - 2)
        ax.set_xlabel(xlab[kind], fontsize = fontsize)
        ax.set_ylabel("Normalization Factor of the PDF", fontsize = fontsize)
 
        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_distExpGamma

Todo:

Normal 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.
   
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.
   

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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 198 of file pm_distExpGamma.F90.

---

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

• src/fortran/main/pm_distExpGamma.F90