Generate and return the natural logarithm of the Probability Density Function (PDF) of the Exponential distribution for an input x within the support of the distribution $[\mu, +\infty)$. More...

Detailed Description

Generate and return the natural logarithm of the Probability Density Function (PDF) of the Exponential distribution for an input x within the support of the distribution $[\mu, +\infty)$.

Parameters

[in]	x	: 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 values at which the PDF must be computed.
[in]	mu	: The input scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as `x` containing the location parameter of the distribution. (optional, default = `0`)
[in]	invSigma	: The input scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as `x` containing the inverse scale (i.e., the rate or the inverse mean) parameter of the distribution. (optional, default = `1.`)

Returns: logPDF : The output scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as x, containing the natural logarithm of the PDF of the distribution at the specified point.

Possible calling interfaces ⛓

: use pm_distExp, only: getExpLogPDF

logPDF = getExpLogPDF(x, mu = mu, invSigma = invSigma)

pm_distExp::getExpLogPDF
Generate and return the natural logarithm of the Probability Density Function (PDF) of the Exponentia...
Definition: pm_distExp.F90:221

pm_distExp
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distExp.F90:112

Warning: The condition mu <= x must hold for the corresponding input arguments.
The condition 0 < invSigma 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: setExpLogPDF

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK

4 use pm_io, only: display_type

5 use pm_distExp, only: getExpLogPDF

6

7 implicit none

8

9 real :: logPDF(3)

10 type(display_type) :: disp

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

12

13 call disp%skip()

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

15 call disp%show("! Compute the Probability Density Function (PDF) of Exponential distribution at the specified values.")

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

17 call disp%skip()

18

19 call disp%skip()

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

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

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

23 call disp%skip()

24

25 call disp%skip()

26 call disp%show("logPDF(1) = getExpLogPDF(x = +.5)")

27 logPDF(1) = getExpLogPDF(x = +.5)

28 call disp%show("logPDF(1)")

29 call disp%show( logPDF(1) )

30 call disp%skip()

31

32 call disp%skip()

33 call disp%show("logPDF(1) = getExpLogPDF(x = +.5, mu = 0.)")

34 logPDF(1) = getExpLogPDF(x = +.5, mu = 0.)

35 call disp%show("logPDF(1)")

36 call disp%show( logPDF(1) )

37 call disp%skip()

38

39 call disp%skip()

40 call disp%show("logPDF(1) = getExpLogPDF(x = +.5, invSigma = 1.)")

41 logPDF(1) = getExpLogPDF(x = +.5, invSigma = 1.)

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

43 call disp%show( logPDF(1) )

44 call disp%skip()

45

46 call disp%skip()

47 call disp%show("logPDF(1) = getExpLogPDF(x = +.5, mu = 0., invSigma = 1.)")

48 logPDF(1) = getExpLogPDF(x = +.5, mu = 0., invSigma = 1.)

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

50 call disp%show( logPDF(1) )

51 call disp%skip()

52

53 call disp%skip()

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

55 call disp%show("! Compute the PDF at an input vector real value with different parameter values.")

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

57 call disp%skip()

58

59 call disp%skip()

60 call disp%show("logPDF(1:3) = getExpLogPDF(x = +[.5, 1., 2.])")

61 logPDF(1:3) = getExpLogPDF(x = +[.5, 1., 2.])

62 call disp%show("logPDF(1:3)")

63 call disp%show( logPDF(1:3) )

64 call disp%skip()

65

66 call disp%skip()

67 call disp%show("logPDF(1:3) = getExpLogPDF(x = +[.5, 1., 2.], mu = 0.)")

68 logPDF(1:3) = getExpLogPDF(x = +[.5, 1., 2.], mu = 0.)

69 call disp%show("logPDF(1:3)")

70 call disp%show( logPDF(1:3) )

71 call disp%skip()

72

73 call disp%skip()

74 call disp%show("logPDF(1:3) = getExpLogPDF(x = +[.5, 1., 2.], invSigma = [2., 1., .5])")

75 logPDF(1:3) = getExpLogPDF(x = +[.5, 1., 2.], invSigma = [2., 1., .5])

76 call disp%show("logPDF(1:3)")

77 call disp%show( logPDF(1:3) )

78 call disp%skip()

79

80 call disp%skip()

81 call disp%show("logPDF(1:3) = getExpLogPDF(x = +[.5, 1., 2.], mu = [-1., 0., +1.], invSigma = 1.)")

82 logPDF(1:3) = getExpLogPDF(x = +[.5, 1., 2.], mu = [-1., 0., +1.], invSigma = 1.)

83 call disp%show("logPDF(1:3)")

84 call disp%show( logPDF(1:3) )

85 call disp%skip()

86

87 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

88 ! Output an example array for visualization.

89 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

90

91 block

92 use pm_arraySpace, only: getLinSpace

93 real, parameter :: invSigma(3) = [2., 1., .5]

94 real, parameter :: mu(3) = [-2., 0., 2.]

95 real :: Point(1000)

96 integer :: fileUnit, i, j

97 Point = getLinSpace(-4., +8., size(Point,1,IK))

98 open(newunit = fileUnit, file = "getExpLogPDF.RK.txt")

99 do i = 1, size(Point)

100 do j = 1, size(logPDF)

101 logPDF(j) = -huge(0.)

102 if (mu(j) <= Point(i)) logPDF(j) = getExpLogPDF(Point(i), mu(j), invSigma(j))

103 end do

104 write(fileUnit,"(*(g0,:,', '))") Point(i), exp(logPDF)

105 end do

106 close(fileUnit)

107 end block

108

109end 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_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::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_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! Compute the Probability Density Function (PDF) of Exponential distribution at the specified values.

4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

5

6

7!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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

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

10

11

12logPDF(1) = getExpLogPDF(x = +.5)

13logPDF(1)

14-0.500000000

15

16

17logPDF(1) = getExpLogPDF(x = +.5, mu = 0.)

18logPDF(1)

19-0.500000000

20

21

22logPDF(1) = getExpLogPDF(x = +.5, invSigma = 1.)

23logPDF(1)

24-0.500000000

25

26

27logPDF(1) = getExpLogPDF(x = +.5, mu = 0., invSigma = 1.)

28logPDF(1)

29-0.500000000

30

31

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

33! Compute the PDF at an input vector real value with different parameter values.

34!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

35

36

37logPDF(1:3) = getExpLogPDF(x = +[.5, 1., 2.])

38logPDF(1:3)

39-0.500000000, -1.00000000, -2.00000000

40

41

42logPDF(1:3) = getExpLogPDF(x = +[.5, 1., 2.], mu = 0.)

43logPDF(1:3)

44-0.500000000, -1.00000000, -2.00000000

45

46

47logPDF(1:3) = getExpLogPDF(x = +[.5, 1., 2.], invSigma = [2., 1., .5])

48logPDF(1:3)

49-0.306852818, -1.00000000, -1.69314718

50

51

52logPDF(1:3) = getExpLogPDF(x = +[.5, 1., 2.], mu = [-1., 0., +1.], invSigma = 1.)

53logPDF(1:3)

54-1.50000000, -1.00000000, -1.00000000

55

56

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" : "X ( real/imaginary components )"

16 , "IK" : "X ( integer-valued )"

17 , "RK" : "X ( real-valued )"

18 }

19legends = [ r"$\mu = -2., invSigma = +2.$"

20 , r"$\mu = +0., invSigma = +1.$"

21 , r"$\mu = +2., invSigma = +.5$"

22 ]

23

24for kind in ["IK", "CK", "RK"]:

25

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

27 fileList = glob.glob(pattern)

28 if len(fileList) == 1:

29

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

31

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

33 ax = plt.subplot()

34

35 if kind == "CK":

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

37 , df.values[:,2]

38 , marker[kind]

39 , color = "r"

40 )

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

42 , df.values[:,3]

43 , marker[kind]

44 , color = "blue"

45 )

46 ax.legend ( ["real", "imaginary"]

47 , fontsize = fontsize

48 )

49 else:

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

51 , df.values[:,1:4]

52 , marker[kind]

53 )

54 ax.legend ( legends

55 , fontsize = fontsize - 5

56 )

57

58 plt.xticks(fontsize = fontsize - 2)

59 plt.yticks(fontsize = fontsize - 2)

60 ax.set_xlabel(xlab[kind], fontsize = 17)

61 ax.set_ylabel("Probability Density Function (PDF)", fontsize = 17)

62

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

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

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

66

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

68

69 elif len(fileList) > 1:

70

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

Visualization of the example output ⛓

Test:: test_pm_distExp

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 221 of file pm_distExp.F90.

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

src/fortran/main/pm_distExp.F90