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

The normalization factor of the GenExpGamma PDF is defined as $\eta = 1 / (\omega \Gamma(\kappa))$ where $(\omega, \kappa)$ are the scale and shape parameters of the GenExpGamma distribution, respectively.
For more information, see the documentation of pm_distGenExpGamma.

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.
[in]	invOmega	: The input scalar or array of the same shape as other array-like arguments, containing the inverse of the scale parameter ( $\omega$) of the distribution. (optional, default = `1.`)

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_distGenExpGamma, only: getGenExpGammaLogPDFNF

logPDFNF = getGenExpGammaLogPDFNF(kappa)

logPDFNF = getGenExpGammaLogPDFNF(kappa, invOmega)

pm_distGenExpGamma::getGenExpGammaLogPDFNF
Generate and return the natural logarithm of the normalization factor of the Probability Density Func...
Definition: pm_distGenExpGamma.F90:270

pm_distGenExpGamma
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distGenExpGamma.F90:133

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: setGenExpGammaLogPDF
setGenExpGammaLogPDF

Example usage ⛓

: 1program example

2

3 use pm_kind, only: IK

4 use pm_kind, only: SK

5 use pm_kind, only: RK => RKS ! all other real kinds are also supported.

6 use pm_io, only: display_type

7 use pm_arraySpace, only: getLinSpace

8 use pm_arraySpace, only: setLinSpace

9 use pm_distGenExpGamma, only: getGenExpGammaLogPDFNF

10

11 implicit none

12

13 integer(IK) , parameter :: NP = 1000_IK

14 real(RK) , allocatable :: invOmega(:), logPDFNF(:), Kappa(:)

15

16 type(display_type) :: disp

17 disp = display_type(file = "main.out.F90")

18

19 Kappa = getLinSpace(0.01_RK, 10._RK, count = NP)

20 invOmega = getLinSpace(0.1_RK, 10._RK, count = NP)

21 allocate(logPDFNF, mold = Kappa)

22

23 call disp%skip()

24 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

25 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

26 call disp%show("! Compute the natural logarithm of the normalization factor of the GenExpGamma distribution PDF.")

27 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

28 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

29 call disp%skip()

30

31 call disp%skip()

32 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

33 call disp%show("! Compute the PDF at an input scalar real value.")

34 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

35 call disp%skip()

36

37 call disp%skip()

38 call disp%show("Kappa(1)")

39 call disp%show( Kappa(1) )

40 call disp%show("logPDFNF(1) = getGenExpGammaLogPDFNF(kappa = Kappa(1))")

41 logPDFNF(1) = getGenExpGammaLogPDFNF(kappa = Kappa(1))

42 call disp%show("logPDFNF(1)")

43 call disp%show( logPDFNF(1) )

44 call disp%skip()

45

46 call disp%skip()

47 call disp%show("Kappa(1)")

48 call disp%show( Kappa(1) )

49 call disp%show("invOmega(1)")

50 call disp%show( invOmega(1) )

51 call disp%show("logPDFNF(1) = getGenExpGammaLogPDFNF(Kappa(1), invOmega(1))")

52 logPDFNF(1) = getGenExpGammaLogPDFNF(Kappa(1), invOmega(1))

53 call disp%show("logPDFNF(1)")

54 call disp%show( logPDFNF(1) )

55 call disp%skip()

56

57 call disp%skip()

58 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

59 call disp%show("! Compute the PDF at at a mix of scalar and vector input values.")

60 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

61 call disp%skip()

62

63 call disp%skip()

64 call disp%show("Kappa(1:NP:NP/5)")

65 call disp%show( Kappa(1:NP:NP/5) )

66 call disp%show("logPDFNF(1:NP:NP/5) = getGenExpGammaLogPDFNF(Kappa(1:NP:NP/5))")

67 logPDFNF(1:NP:NP/5) = getGenExpGammaLogPDFNF(Kappa(1:NP:NP/5))

68 call disp%show("logPDFNF(1:NP:NP/5)")

69 call disp%show( logPDFNF(1:NP:NP/5) )

70 call disp%skip()

71

72 call disp%skip()

73 call disp%show("Kappa(1:NP:NP/5)")

74 call disp%show( Kappa(1:NP:NP/5) )

75 call disp%show("logPDFNF(1:NP:NP/5) = getGenExpGammaLogPDFNF(Kappa(1:NP:NP/5), 1._RK)")

76 logPDFNF(1:NP:NP/5) = getGenExpGammaLogPDFNF(Kappa(1:NP:NP/5), 1._RK)

77 call disp%show("logPDFNF(1:NP:NP/5)")

78 call disp%show( logPDFNF(1:NP:NP/5) )

79 call disp%skip()

80

81 call disp%skip()

82 call disp%show("Kappa(1:NP:NP/5)")

83 call disp%show( Kappa(1:NP:NP/5) )

84 call disp%show("invOmega(1:NP:NP/5)")

85 call disp%show( invOmega(1:NP:NP/5) )

86 call disp%show("logPDFNF(1:NP:NP/5) = getGenExpGammaLogPDFNF(1._RK, invOmega(1:NP:NP/5))")

87 logPDFNF(1:NP:NP/5) = getGenExpGammaLogPDFNF(1._RK, invOmega(1:NP:NP/5))

88 call disp%show("logPDFNF(1:NP:NP/5)")

89 call disp%show( logPDFNF(1:NP:NP/5) )

90 call disp%skip()

91

92 call disp%skip()

93 call disp%show("Kappa(1:NP:NP/5)")

94 call disp%show( Kappa(1:NP:NP/5) )

95 call disp%show("invOmega(1:NP:NP/5)")

96 call disp%show( invOmega(1:NP:NP/5) )

97 call disp%show("logPDFNF(1:NP:NP/5) = getGenExpGammaLogPDFNF(Kappa(1:NP:NP/5), invOmega(1:NP:NP/5))")

98 logPDFNF(1:NP:NP/5) = getGenExpGammaLogPDFNF(Kappa(1:NP:NP/5), invOmega(1:NP:NP/5))

99 call disp%show("logPDFNF(1:NP:NP/5)")

100 call disp%show( logPDFNF(1:NP:NP/5) )

101 call disp%skip()

102

103 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

104 ! Output an example array for visualization.

105 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

106

107 block

108 integer :: fileUnit, i

109 logPDFNF = getGenExpGammaLogPDFNF(Kappa)

110 open(newunit = fileUnit, file = "getGenExpGammaLogPDFNF.RK.txt")

111 write(fileUnit,"(2(g0,:,' '))") (Kappa(i), exp(logPDFNF(i)), i = 1, size(logPDFNF))

112 close(fileUnit)

113 end block

114

115end program example

pm_arraySpace::getLinSpace
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
Definition: pm_arraySpace.F90:108

pm_arraySpace::setLinSpace
Return the linSpace output argument with size(linSpace) elements of evenly-spaced values over the int...
Definition: pm_arraySpace.F90:324

pm_io::show
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508

pm_arraySpace
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
Definition: pm_arraySpace.F90:33

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268

pm_kind::RK
integer, parameter RK
The default real kind in the ParaMonte library: real64 in Fortran, c_double in C-Fortran Interoperati...
Definition: pm_kind.F90:543

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539

pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example output ⛓
1

2!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

3!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

4! Compute the natural logarithm of the normalization factor of the GenExpGamma distribution PDF.

5!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

6!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

7

8

9!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

10! Compute the PDF at an input scalar real value.

11!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

12

13

14Kappa(1)

15+0.999999978E-2

16logPDFNF(1) = getGenExpGammaLogPDFNF(kappa = Kappa(1))

17logPDFNF(1)

18-4.59948015

19

20

21Kappa(1)

22+0.999999978E-2

23invOmega(1)

24+0.100000001

25logPDFNF(1) = getGenExpGammaLogPDFNF(Kappa(1), invOmega(1))

26logPDFNF(1)

27-6.90206528

28

29

30!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

31! Compute the PDF at at a mix of scalar and vector input values.

32!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

33

34

35Kappa(1:NP:NP/5)

36+0.999999978E-2, +2.00999999, +4.01000023, +6.01000023, +8.01000023

37logPDFNF(1:NP:NP/5) = getGenExpGammaLogPDFNF(Kappa(1:NP:NP/5))

38logPDFNF(1:NP:NP/5)

39-4.59948015, -0.426001893E-2, -1.80433512, -4.80456209, -8.54532528

40

41

42Kappa(1:NP:NP/5)

43+0.999999978E-2, +2.00999999, +4.01000023, +6.01000023, +8.01000023

44logPDFNF(1:NP:NP/5) = getGenExpGammaLogPDFNF(Kappa(1:NP:NP/5), 1._RK)

45logPDFNF(1:NP:NP/5)

46-4.59948015, -0.426001893E-2, -1.80433512, -4.80456209, -8.54532528

47

48

49Kappa(1:NP:NP/5)

50+0.999999978E-2, +2.00999999, +4.01000023, +6.01000023, +8.01000023

51invOmega(1:NP:NP/5)

52+0.100000001, +2.08198190, +4.06396389, +6.04594564, +8.02792740

53logPDFNF(1:NP:NP/5) = getGenExpGammaLogPDFNF(1._RK, invOmega(1:NP:NP/5))

54logPDFNF(1:NP:NP/5)

55-2.30258512, +0.733320296, +1.40215886, +1.79938793, +2.08292627

56

57

58Kappa(1:NP:NP/5)

59+0.999999978E-2, +2.00999999, +4.01000023, +6.01000023, +8.01000023

60invOmega(1:NP:NP/5)

61+0.100000001, +2.08198190, +4.06396389, +6.04594564, +8.02792740

62logPDFNF(1:NP:NP/5) = getGenExpGammaLogPDFNF(Kappa(1:NP:NP/5), invOmega(1:NP:NP/5))

63logPDFNF(1:NP:NP/5)

64-6.90206528, +0.729060292, -0.402176261, -3.00517416, -6.46239901

65

66

Postprocessing of the example output ⛓
1#!/usr/bin/env python

2

3import matplotlib.pyplot as plt

4import pandas as pd

5import numpy as np

6import glob

7import sys

8

9fontsize = 17

10

11marker ={ "CK" : "-"

12 , "IK" : "."

13 , "RK" : "-"

14 }

15xlab = { "CK" : r"shape parameter: $\kappa$ ( real/imaginary )"

16 , "IK" : r"shape parameter: $\kappa$ ( integer-valued )"

17 , "RK" : r"shape parameter: $\kappa$ ( real-valued )"

18 }

19

20for kind in ["IK", "CK", "RK"]:

21

22 pattern = "*." + kind + ".txt"

23 fileList = glob.glob(pattern)

24 if len(fileList) == 1:

25

26 df = pd.read_csv(fileList[0], delimiter = " ")

27

28 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)

29 ax = plt.subplot()

30

31 if kind == "CK":

32 plt.plot( df.values[:, 0]

33 , df.values[:,2]

34 , marker[kind]

35 , color = "r"

36 )

37 plt.plot( df.values[:, 1]

38 , df.values[:,3]

39 , marker[kind]

40 , color = "blue"

41 )

42 else:

43 plt.plot( df.values[:, 0]

44 , df.values[:, 1]

45 , marker[kind]

46 , color = "r"

47 )

48

49 plt.xticks(fontsize = fontsize - 2)

50 plt.yticks(fontsize = fontsize - 2)

51 ax.set_xlabel(xlab[kind], fontsize = fontsize)

52 ax.set_ylabel("Normalization Factor of the PDF", fontsize = fontsize)

53

54 plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")

55 ax.tick_params(axis = "y", which = "minor")

56 ax.tick_params(axis = "x", which = "minor")

57

58 plt.savefig(fileList[0].replace(".txt",".png"))

59

60 elif len(fileList) > 1:

61

62 sys.exit("Ambiguous file list exists.")

Visualization of the example output ⛓

Benchmarks:

Benchmark :: The runtime performance of setGenExpGammaLogPDF with and without scale ⛓

program benchmark
 
    use iso_fortran_env, only: error_unit
    use pm_bench, only: bench_type
    use pm_kind, only: IK, RK, SK
 
    implicit none
 
    integer(IK)                         :: i
    integer(IK)                         :: isize
    integer(IK)                         :: fileUnit
    integer(IK)     , parameter         :: NSIZE = 15_IK
    integer(IK)     , parameter         :: NBENCH = 3_IK
    integer(IK)                         :: arraySize(NSIZE)
    real(RK)        , allocatable       :: InvScale(:)
    real(RK)        , allocatable       :: shape(:)
    real(RK)                            :: dummy = 0._RK
    type(bench_type)                    :: Bench(NBENCH)
 
    Bench(1) = bench_type(name = SK_"scalarAddition", exec = scalarAddition, overhead = setOverhead)
    Bench(2) = bench_type(name = SK_"logPDFNFWithShape", exec = logPDFNFWithShape, overhead = setOverhead)
    Bench(3) = bench_type(name = SK_"logPDFNFWithShapeScale", exec = logPDFNFWithShapeScale, overhead = setOverhead)
 
    arraySize = [( 2**isize, isize = 1, NSIZE )]
 
    write(*,"(*(g0,:,' '))")
    write(*,"(*(g0,:,' vs. '))") (Bench(i)%name, i = 1, NBENCH)
    write(*,"(*(g0,:,' '))")
 
    open(newunit = fileUnit, file = "main.out", status = "replace")
 
        write(fileUnit, "(*(g0,:,','))") "arraySize", (Bench(i)%name, i = 1, NBENCH)
 
        loopOverArraySize: do isize = 1, NSIZE
 
            write(*,"(*(g0,:,' '))") "Benchmarking with rank", arraySize(isize)
 
            allocate(shape(arraySize(isize)), InvScale(arraySize(isize)))
            do i = 1, NBENCH
                Bench(i)%timing = Bench(i)%getTiming(minsec = 0.05_RK)
            end do
            deallocate(shape, InvScale)
 
            write(fileUnit,"(*(g0,:,','))") arraySize(isize), (Bench(i)%timing%mean, i = 1, NBENCH)
 
        end do loopOverArraySize
 
        write(*,"(*(g0,:,' '))") dummy
        write(*,"(*(g0,:,' '))")
 
    close(fileUnit)
 
contains
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! procedure wrappers.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    subroutine setOverhead()
        call initialize()
    end subroutine
 
    subroutine initialize()
        call random_number(shape)
        shape = shape + epsilon(0._RK)
        InvScale = shape + 1._RK
    end subroutine
 
    subroutine scalarAddition()
        call initialize()
        dummy = dummy + sum(scalarAdditionCallee(shape,InvScale))
    end subroutine
 
    impure elemental function scalarAdditionCallee(shape, invScale) result(summation)
        real(RK), intent(in) :: shape, invScale
        real(RK) :: summation
        summation = shape + invScale
    end function
 
    subroutine logPDFNFWithShape()
        use pm_distGenExpGamma, only: getGenExpGammaLogPDFNF
        call initialize()
        dummy = dummy + sum(getGenExpGammaLogPDFNF(shape))
    end subroutine
 
    subroutine logPDFNFWithShapeScale()
        use pm_distGenExpGamma, only: getGenExpGammaLogPDFNF
        call initialize()
        dummy = dummy + sum(getGenExpGammaLogPDFNF(shape, InvScale))
    end subroutine
 
end program benchmark

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

Postprocessing of the benchmark output ⛓

#!/usr/bin/env python
 
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
 
import os
dirname = os.path.basename(os.getcwd()) 
 
fontsize = 14
 
df = pd.read_csv("main.out", delimiter = ",")
colnames = list(df.columns.values)
 
 
 
ax = plt.figure(figsize = 1.25 * np.array([6.4,4.6]), dpi = 200)
ax = plt.subplot()
 
for colname in colnames[1:]:
    plt.plot( df[colnames[0]].values
            , df[colname].values
            , linewidth = 2
            )
 
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
ax.set_xlabel(colnames[0], fontsize = fontsize)
ax.set_ylabel("Runtime [ seconds ]", fontsize = fontsize)
ax.set_title(" vs. ".join(colnames[1:])+"\nLower is better.", fontsize = fontsize)
ax.set_xscale("log")
ax.set_yscale("log")
plt.minorticks_on()
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")
ax.legend   ( colnames[1:]
           #, loc='center left'
           #, bbox_to_anchor=(1, 0.5)
            , fontsize = fontsize
            )
 
plt.tight_layout()
plt.savefig("benchmark." + dirname + ".runtime.png")
 
 
 
ax = plt.figure(figsize = 1.25 * np.array([6.4,4.6]), dpi = 200)
ax = plt.subplot()
 
plt.plot( df[colnames[0]].values
        , np.ones(len(df[colnames[0]].values))
        , linestyle = "--"
       #, color = "black"
        , linewidth = 2
        )
for colname in colnames[2:]:
    plt.plot( df[colnames[0]].values
            , df[colname].values / df[colnames[1]].values
            , linewidth = 2
            )
 
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
ax.set_xlabel(colnames[0], fontsize = fontsize)
ax.set_ylabel("Runtime compared to {}".format(colnames[1]), fontsize = fontsize)
ax.set_title("Runtime Ratio Comparison. Lower means faster.\nLower than 1 means faster than {}().".format(colnames[1]), fontsize = fontsize)
ax.set_xscale("log")
#ax.set_yscale("log")
plt.minorticks_on()
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")
ax.legend   ( colnames[1:]
           #, bbox_to_anchor = (1, 0.5)
           #, loc = "center left"
            , fontsize = fontsize
            )
 
plt.tight_layout()
plt.savefig("benchmark." + dirname + ".runtime.ratio.png")

Visualization of the benchmark output ⛓

Benchmark moral ⛓

The procedures under the generic interface getGenExpGammaLogPDFNF aim to precompute the natural logarithm of the normalization factor of the GenExpGamma PDF.
Based on the results of this benchmark, passing this precomputed normalization factor to getGenExpGammaLogPDF or setGenExpGammaLogPDF appears to lead to significant performance improvement (20-30 times) when the GenExpGamma PDF procedures are to called repeatedly with the same set of input distribution parameters (kappa, sigma).
This speedup is entirely due to avoiding the redundant repeated computations of log_gamma() and log() terms in getGenExpGammaLogPDFNF.
The initial closing in the performance gap for small array sizes (of $\sim4$ or less elements) is likely artificial and due to extremely small cost of simpleAddition procedure which is likely less than the time resolution of the processor ( $\sim10ns$ as of V2 of ParaMonte library).

Test:: test_pm_distGenExpGamma

Todo:: Normal Priority: This generic interface can be extended to complex arguments.

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
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.

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.
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 270 of file pm_distGenExpGamma.F90.

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

src/fortran/main/pm_distGenExpGamma.F90