Generate and return the regularized Lower Incomplete Gamma function for the specified shape parameter ( $\kappa$) and upper limit of the integral x. More...

Detailed Description

Generate and return the regularized Lower Incomplete Gamma function for the specified shape parameter ( $\kappa$) and upper limit of the integral x.

The regularized Lower Incomplete Gamma function is defined as,

\begin{equation} \large P(\kappa, x) = \frac{1}{\Gamma(\kappa)} \int_0^{x}~t^{\kappa-1}{\mathrm e}^{-t} ~ dt ~, \end{equation}

where $(\kappa > 0, x > 0)$ should hold, with $\kappa$ representing the shape parameter of the Gamma function (or distribution) and $x$ representing the upper limit in the integral of the Lower Incomplete Gamma function.
Note that this integral is bounded between zero and one ( $[0,1]$).
The regularized Lower Incomplete Gamma function also represents the complement of the Cumulative Distribution Function (CDF) of the univariate Gamma distribution with the specified shape parameter and standardized x (with the scale parameter of unity).

Parameters

[in]	x	: The input scalar of type `real` of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), representing the upper limit in the integral of the Lower Incomplete Gamma function $P(\kappa,x)$.
[in]	kappa	: The input scalar of the same type and kind as `x`, representing the shape parameter ( $\kappa$) of the Lower Incomplete Gamma function $P(\kappa,x)$.

Returns: gammaIncLow : The output scalar of the same type and kind as the output argument x representing the Lower Incomplete Gamma function for the specified kappa and upper limit.
Note that gammaIncLow is, by definition, always positive in the range $[0, 1]$.
Note that the procedure will abruptly end the program by calling error stop if the computation of the Incomplete Gamma function fails to converge**.

Possible calling interfaces ⛓

: use pm_mathGammaGil, only: getGammaIncLowGil

gammaIncLow = getGammaIncLowGil(x, kappa)

pm_mathGammaGil::getGammaIncLowGil
Generate and return the regularized Lower Incomplete Gamma function for the specified shape parameter...
Definition: pm_mathGammaGil.F90:137

pm_mathGammaGil
This module contains procedures and generic interfaces for the Lower and Upper Incomplete Gamma funct...
Definition: pm_mathGammaGil.F90:57

Warning: The condition 0 < x must hold for the corresponding input arguments.
The condition 0 < kappa must hold for the corresponding input arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

Remarks: The procedures under discussion are impure.; The procedures under discussion are elemental.

See also: getGammaIncLowGil
setGammaIncGil

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_kind, only: RKS, RKD, RKH

5 use pm_mathGammaGil, only: getGammaIncLowGil

6 use pm_io, only: display_type

7

8 implicit none

9

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("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

16 call disp%show("! Compute the regularized Lower Incomplete Gamma Function using its series representation.")

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

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

19 call disp%skip()

20

21 call disp%skip()

22 call disp%show("getGammaIncLowGil(x = 1.5_RKS, kappa = 2._RKS)")

23 call disp%show( getGammaIncLowGil(x = 1.5_RKS, kappa = 2._RKS) )

24 call disp%skip()

25

26 call disp%skip()

27 call disp%show("getGammaIncLowGil(x = 1.5_RKD, kappa = 2._RKD)")

28 call disp%show( getGammaIncLowGil(x = 1.5_RKD, kappa = 2._RKD) )

29 call disp%skip()

30

31 call disp%skip()

32 call disp%show("getGammaIncLowGil(x = 1.5_RKH, kappa = 2._RKH)")

33 call disp%show( getGammaIncLowGil(x = 1.5_RKH, kappa = 2._RKH) )

34 call disp%skip()

35

36 call disp%skip()

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

38 call disp%show("! Compute the regularized Lower Incomplete Gamma Function for a vector of points.")

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

40 call disp%skip()

41

42 call disp%skip()

43 call disp%show("getGammaIncLowGil(x = [0._RKS, 1._RKS, 10._RKS], kappa = 2._RKS)")

44 call disp%show( getGammaIncLowGil(x = [0._RKS, 1._RKS, 10._RKS], kappa = 2._RKS) )

45 call disp%skip()

46

47 call disp%skip()

48 call disp%show("getGammaIncLowGil(x = [0._RKD, 1._RKD, 10._RKD], kappa = 2._RKD)")

49 call disp%show( getGammaIncLowGil(x = [0._RKD, 1._RKD, 10._RKD], kappa = 2._RKD) )

50 call disp%skip()

51

52 call disp%skip()

53 call disp%show("getGammaIncLowGil(x = [0._RKH, 1._RKH, 10._RKH], kappa = 2._RKH)")

54 call disp%show( getGammaIncLowGil(x = [0._RKH, 1._RKH, 10._RKH], kappa = 2._RKH) )

55 call disp%skip()

56

57 call disp%skip()

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

59 call disp%show("! Compute the regularized Lower Incomplete Gamma Function for a vector of shape parameters.")

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

61 call disp%skip()

62

63 call disp%skip()

64 call disp%show("getGammaIncLowGil(x = 1._RKS, kappa = [0.1_RKS, 1._RKS, 10._RKS])")

65 call disp%show( getGammaIncLowGil(x = 1._RKS, kappa = [0.1_RKS, 1._RKS, 10._RKS]) )

66 call disp%skip()

67

68 call disp%skip()

69 call disp%show("getGammaIncLowGil(x = 1._RKD, kappa = [0.1_RKD, 1._RKD, 10._RKD])")

70 call disp%show( getGammaIncLowGil(x = 1._RKD, kappa = [0.1_RKD, 1._RKD, 10._RKD]) )

71 call disp%skip()

72

73 call disp%skip()

74 call disp%show("getGammaIncLowGil(x = 1._RKH, kappa = [0.1_RKH, 1._RKH, 10._RKH])")

75 call disp%show( getGammaIncLowGil(x = 1._RKH, kappa = [0.1_RKH, 1._RKH, 10._RKH]) )

76 call disp%skip()

77

78 call disp%skip()

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

80 call disp%show("! Compute the regularized Lower Incomplete Gamma Function for a vector of points and shape parameters.")

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

82 call disp%skip()

83

84 block

85 use pm_kind, only: RKG => RKS

86 integer(IK) :: i, rprecision

87 integer(IK), allocatable :: exprange(:), info(:)

88 real(RKG), allocatable :: gamIncLow(:)

89 call disp%skip()

90 call disp%show("rprecision = precision(0._RKG) * 2")

91 rprecision = precision(0._RKG) * 2

92 call disp%show("rprecision")

93 call disp%show( rprecision )

94 call disp%show("exprange = [(i, i = -rprecision, rprecision)]")

95 exprange = [(i, i = -rprecision, rprecision)]

96 call disp%show("exprange")

97 call disp%show( exprange )

98 call disp%show("allocate(gamIncLow(size(exprange)), info(size(exprange)))")

99 allocate(gamIncLow(size(exprange)), info(size(exprange)))

100 call disp%show("gamIncLow = getGammaIncLowGil(x = 10._RKG**exprange, kappa = 10._RKG**exprange)")

101 gamIncLow = getGammaIncLowGil(x = 10._RKG**exprange, kappa = 10._RKG**exprange)

102 call disp%show("reshape([10._RKG**exprange, gamIncLow], shape = [size(info), 2])")

103 call disp%show( reshape([10._RKG**exprange, gamIncLow], shape = [size(info), 2]) )

104 call disp%skip()

105 end block

106

107 block

108 use pm_kind, only: RKG => RKD

109 integer(IK) :: i, rprecision

110 integer(IK), allocatable :: exprange(:), info(:)

111 real(RKG), allocatable :: gamIncLow(:)

112 call disp%skip()

113 call disp%show("rprecision = precision(0._RKG) * 2")

114 rprecision = precision(0._RKG) * 2

115 call disp%show("rprecision")

116 call disp%show( rprecision )

117 call disp%show("exprange = [(i, i = -rprecision, rprecision)]")

118 exprange = [(i, i = -rprecision, rprecision)]

119 call disp%show("exprange")

120 call disp%show( exprange )

121 call disp%show("allocate(gamIncLow(size(exprange)), info(size(exprange)))")

122 allocate(gamIncLow(size(exprange)), info(size(exprange)))

123 call disp%show("gamIncLow = getGammaIncLowGil(x = 10._RKG**exprange, kappa = 10._RKG**exprange)")

124 gamIncLow = getGammaIncLowGil(x = 10._RKG**exprange, kappa = 10._RKG**exprange)

125 call disp%show("reshape([10._RKG**exprange, gamIncLow], shape = [size(info), 2])")

126 call disp%show( reshape([10._RKG**exprange, gamIncLow], shape = [size(info), 2]) )

127 call disp%skip()

128 end block

129

130 block

131 use pm_kind, only: RKG => RKH

132 integer(IK) :: i, rprecision

133 integer(IK), allocatable :: exprange(:), info(:)

134 real(RKG), allocatable :: gamIncLow(:)

135 call disp%skip()

136 call disp%show("rprecision = precision(0._RKG) * 2")

137 rprecision = precision(0._RKG) * 2

138 call disp%show("rprecision")

139 call disp%show( rprecision )

140 call disp%show("exprange = [(i, i = -rprecision, rprecision)]")

141 exprange = [(i, i = -rprecision, rprecision)]

142 call disp%show("exprange")

143 call disp%show( exprange )

144 call disp%show("allocate(gamIncLow(size(exprange)), info(size(exprange)))")

145 allocate(gamIncLow(size(exprange)), info(size(exprange)))

146 call disp%show("gamIncLow = getGammaIncLowGil(x = 10._RKG**exprange, kappa = 10._RKG**exprange)")

147 gamIncLow = getGammaIncLowGil(x = 10._RKG**exprange, kappa = 10._RKG**exprange)

148 call disp%show("reshape([10._RKG**exprange, gamIncLow], shape = [size(info), 2])")

149 call disp%show( reshape([10._RKG**exprange, gamIncLow], shape = [size(info), 2]) )

150 call disp%skip()

151 end block

152

153 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

154 ! Output an example array of the regularized Lower Incomplete Gamma function for visualization.

155 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

156

157 block

158

159 use pm_arraySpace, only: setLinSpace

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

161 real(RKS) :: x_RKS(NP)

162 integer :: fileUnit, i

163

164 call setLinSpace(x_RKS, 0._RKS, 10._RKS)

165 open(newunit = fileUnit, file = "getGammaIncLowGil.RK.txt")

166 do i = 1, NP

167 write(fileUnit, "(*(g0,:,' '))") x_RKS(i), getGammaIncLowGil(x_RKS(i), kappa = [1.0_RKS, 2.5_RKS, 5.0_RKS])

168 end do

169 close(fileUnit)

170

171 end block

172

173end program example

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::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541

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::RKD
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:568

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::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
Definition: pm_kind.F90:858

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 regularized Lower Incomplete Gamma Function using its series representation.

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

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

7

8

9getGammaIncLowGil(x = 1.5_RKS, kappa = 2._RKS)

10+0.442174435

11

12

13getGammaIncLowGil(x = 1.5_RKD, kappa = 2._RKD)

14+0.44217459962892536

15

16

17getGammaIncLowGil(x = 1.5_RKH, kappa = 2._RKH)

18+0.442174599628925427666798823089968559

19

20

21!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

22! Compute the regularized Lower Incomplete Gamma Function for a vector of points.

23!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

24

25

26getGammaIncLowGil(x = [0._RKS, 1._RKS, 10._RKS], kappa = 2._RKS)

27+0.00000000, +0.264241129, +0.999500573

28

29

30getGammaIncLowGil(x = [0._RKD, 1._RKD, 10._RKD], kappa = 2._RKD)

31+0.0000000000000000, +0.26424111765711528, +0.99950060077261271

32

33

34getGammaIncLowGil(x = [0._RKH, 1._RKH, 10._RKH], kappa = 2._RKH)

35+0.00000000000000000000000000000000000, +0.264241117657115356808952459677078110, +0.999500600772612666633108493328833987

36

37

38!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

39! Compute the regularized Lower Incomplete Gamma Function for a vector of shape parameters.

40!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

41

42

43getGammaIncLowGil(x = 1._RKS, kappa = [0.1_RKS, 1._RKS, 10._RKS])

44+0.975872695, +0.632120550, +0.111424356E-6

45

46

47getGammaIncLowGil(x = 1._RKD, kappa = [0.1_RKD, 1._RKD, 10._RKD])

48+0.97587265627367237, +0.63212055882855767, +0.11142547833872021E-6

49

50

51getGammaIncLowGil(x = 1._RKH, kappa = [0.1_RKH, 1._RKH, 10._RKH])

52+0.975872656273672222617030564366645365, +0.632120558828557678404476229838539127, +0.111425478338720677353048198587738909E-6

53

54

55!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

56! Compute the regularized Lower Incomplete Gamma Function for a vector of points and shape parameters.

57!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

58

59

60rprecision = precision(0._RKG) * 2

61rprecision

62+12

63exprange = [(i, i = -rprecision, rprecision)]

64exprange

65-12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, +0, +1, +2, +3, +4, +5, +6, +7, +8, +9, +10, +11, +12

66allocate(gamIncLow(size(exprange)), info(size(exprange)))

67gamIncLow = getGammaIncLowGil(x = 10._RKG**exprange, kappa = 10._RKG**exprange)

68reshape([10._RKG**exprange, gamIncLow], shape = [size(info), 2])

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93+0.999999996E+12, +0.500000119

94

95

96rprecision = precision(0._RKG) * 2

97rprecision

98+30

99exprange = [(i, i = -rprecision, rprecision)]

100exprange

101-30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, +0, +1, +2, +3, +4, +5, +6, +7, +8, +9, +10, +11, +12, +13, +14, +15, +16, +17, +18, +19, +20, +21, +22, +23, +24, +25, +26, +27, +28, +29, +30

102allocate(gamIncLow(size(exprange)), info(size(exprange)))

103gamIncLow = getGammaIncLowGil(x = 10._RKG**exprange, kappa = 10._RKG**exprange)

104reshape([10._RKG**exprange, gamIncLow], shape = [size(info), 2])

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166

167

168rprecision = precision(0._RKG) * 2

169rprecision

170+66

171exprange = [(i, i = -rprecision, rprecision)]

172exprange

173-66, -65, -64, -63, -62, -61, -60, -59, -58, -57, -56, -55, -54, -53, -52, -51, -50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, +0, +1, +2, +3, +4, +5, +6, +7, +8, +9, +10, +11, +12, +13, +14, +15, +16, +17, +18, +19, +20, +21, +22, +23, +24, +25, +26, +27, +28, +29, +30, +31, +32, +33, +34, +35, +36, +37, +38, +39, +40, +41, +42, +43, +44, +45, +46, +47, +48, +49, +50, +51, +52, +53, +54, +55, +56, +57, +58, +59, +60, +61, +62, +63, +64, +65, +66

174allocate(gamIncLow(size(exprange)), info(size(exprange)))

175gamIncLow = getGammaIncLowGil(x = 10._RKG**exprange, kappa = 10._RKG**exprange)

176reshape([10._RKG**exprange, gamIncLow], shape = [size(info), 2])

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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

11kind = "RK"

12label = [ r"shape: $\kappa = 1.0$"

13 , r"shape: $\kappa = 2.5$"

14 , r"shape: $\kappa = 5.0$"

15 ]

16

17pattern = "*." + kind + ".txt"

18fileList = glob.glob(pattern)

19if len(fileList) == 1:

20

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

22

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

24 ax = plt.subplot()

25

26 for i in range(1,len(df.values[0,:]+1)):

27

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

29 , df.values[:,i]

30 , linewidth = 2

31 )

32

33 plt.xticks(fontsize = fontsize - 2)

34 plt.yticks(fontsize = fontsize - 2)

35 ax.set_xlabel("x", fontsize = fontsize)

36 ax.set_ylabel("Regularized Lower\nIncomplete Gamma Function", fontsize = fontsize)

37

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

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

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

41

42 ax.legend ( label

43 , fontsize = fontsize

44 #, loc = "center left"

45 #, bbox_to_anchor = (1, 0.5)

46 )

47

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

49

50else:

51

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

Visualization of the example output ⛓

Test:: test_pm_mathGammaGil

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:: Fatemeh Bagheri, Monday 12:36 pm, August 16, 2021, Dallas TX

Definition at line 137 of file pm_mathGammaGil.F90.

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

src/fortran/main/pm_mathGammaGil.F90