ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
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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

logPDFNF = getExpGammaLogPDFNF(kappa)
Generate and return the natural logarithm of the normalization factor of the Probability Density Func...
This module contains classes and procedures for computing various statistical quantities related to t...
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

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
10
11 implicit none
12
13 integer(IK) , parameter :: NP = 1000_IK
14 real(RK) , allocatable :: 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 allocate(logPDFNF, mold = Kappa)
21
22 call disp%skip()
23 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
24 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
25 call disp%show("! Compute the natural logarithm of the normalization factor of the ExpGamma distribution PDF.")
26 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
27 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
28 call disp%skip()
29
30 call disp%skip()
31 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
32 call disp%show("! Compute the PDF at an input scalar real value.")
33 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
34 call disp%skip()
35
36 call disp%skip()
37 call disp%show("Kappa(1:NP:NP/5)")
38 call disp%show( Kappa(1:NP:NP/5) )
39 call disp%show("logPDFNF(1:NP:NP/5) = getExpGammaLogPDFNF(1._RK)")
40 logPDFNF(1:NP:NP/5) = getExpGammaLogPDFNF(1._RK)
41 call disp%show("logPDFNF(1:NP:NP/5)")
42 call disp%show( logPDFNF(1:NP:NP/5) )
43 call disp%skip()
44
45 call disp%skip()
46 call disp%show("Kappa(1)")
47 call disp%show( Kappa(1) )
48 call disp%show("logPDFNF(1) = getExpGammaLogPDFNF(kappa = Kappa(1))")
49 logPDFNF(1) = getExpGammaLogPDFNF(kappa = Kappa(1))
50 call disp%show("logPDFNF(1)")
51 call disp%show( logPDFNF(1) )
52 call disp%skip()
53
54 call disp%skip()
55 call disp%show("Kappa(1:NP:NP/5)")
56 call disp%show( Kappa(1:NP:NP/5) )
57 call disp%show("logPDFNF(1:NP:NP/5) = getExpGammaLogPDFNF(Kappa(1:NP:NP/5))")
58 logPDFNF(1:NP:NP/5) = getExpGammaLogPDFNF(Kappa(1:NP:NP/5))
59 call disp%show("logPDFNF(1:NP:NP/5)")
60 call disp%show( logPDFNF(1:NP:NP/5) )
61 call disp%skip()
62
63 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
64 ! Output an example array for visualization.
65 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
66
67 logPDFNF = getExpGammaLogPDFNF(Kappa)
68
69 block
70
71 integer :: fileUnit, i
72
73 open(newunit = fileUnit, file = "getExpGammaLogPDFNF.RK.txt")
74 write(fileUnit,"(2(g0,:,' '))") (Kappa(i), exp(logPDFNF(i)), i = 1, size(logPDFNF))
75 close(fileUnit)
76
77 end block
78
79end program example
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
Return the linSpace output argument with size(linSpace) elements of evenly-spaced values over the int...
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
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
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
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
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
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 ExpGamma distribution PDF.
5!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7
8
9!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
10! Compute the PDF at an input scalar real value.
11!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
12
13
14Kappa(1:NP:NP/5)
15+0.999999978E-2, +2.00999999, +4.01000023, +6.01000023, +8.01000023
16logPDFNF(1:NP:NP/5) = getExpGammaLogPDFNF(1._RK)
17logPDFNF(1:NP:NP/5)
18-0.00000000, -0.00000000, -0.00000000, -0.00000000, -0.00000000
19
20
21Kappa(1)
22+0.999999978E-2
23logPDFNF(1) = getExpGammaLogPDFNF(kappa = Kappa(1))
24logPDFNF(1)
25-4.59948015
26
27
28Kappa(1:NP:NP/5)
29+0.999999978E-2, +2.00999999, +4.01000023, +6.01000023, +8.01000023
30logPDFNF(1:NP:NP/5) = getExpGammaLogPDFNF(Kappa(1:NP:NP/5))
31logPDFNF(1:NP:NP/5)
32-4.59948015, -0.426001893E-2, -1.80433512, -4.80456209, -8.54532528
33
34

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
Test:
test_pm_distExpGamma
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.

  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.

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: