Return the regularized Incomplete Beta Function $I_x(\alpha, \beta)$ as defined in the details section of pm_mathBeta. More...

Detailed Description

Return the regularized Incomplete Beta Function $I_x(\alpha, \beta)$ as defined in the details section of pm_mathBeta.

Parameters

[in]	betaInc	: The output scalar (or array of the same shape as other array-like arguments) of the same type and kind as the input argument `x` containing the regularized Incomplete Beta Function.
[in]	x	: The input scalar (or array of the same shape as other array-like arguments) of, type `real` of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the value at which the function must be computed.
[in]	alpha	: The input scalar (or array of the same shape as other array-like arguments) of the same type and kind as `x`.
[in]	beta	: The input scalar (or array of the same shape as other array-like arguments) of the same type and kind as `x`.
[in]	logFuncBeta	: The input scalar (or array of the same shape as other array-like arguments) of the same type and kind as `x`, representing the natural logarithm of the Beta Function as returned by getLogBeta(alpha, beta). Providing this argument can lead to significant runtime performance gains when the interface is called repeatedly for different `x` values but with identical `alpha` and `beta`.
[in]	signed	: The input scalar (or array of the same shape as other array-like arguments) of type `logical` of default kind LK. If `signed = .false.`, the input `x` must be in range `0 <= x <= 1` and the output `betaInc` will be the expected incomplete Beta function in range `0 <= betaInc <= 1`. If `signed = .true.`, then the following rules hold: If the condition `x < 0` holds, then the value `x = 1 - x < 0` will be used instead of `x`. If the output `betaInc` is near `1`, the output will be returned as `betaInc = betaInc - 1 < 0` instead of `betaInc`. Therefore, the user is expected to be aware of the convention and apply the necessary correction (addition by `1`) before using the output value. Specifying `signed = .true.` can lead to considerably more accurate calculations (by orders of magnitudes) for values of `x` and `betaInc` that are near `1`. The loss of precision near `1` occurs because of inadequate resolution of `real` number representations in digital computers near `1` which is orders of magnitude worse than the precision near `0`.
[in]	reltol	: The input scalar argument of the same type and kind as `betaInc`, representing the relative tolerance of integration in the definition of the Incomplete Beta function. If the relative accuracy of integration reaches a value below this threshold, the computation of the Incomplete Beta function is assumed to have converged. Specifying this argument will lead to brute-force numerical integration of the integrand of the Beta function to compute the integral. This approach can be useful when the continued-fraction representation of the Incomplete Beta Function fails to converge or is extremely costly or a bound on the numerical error is needed. Convergence failure or costly computations frequently occur for large values of `alpha` and `beta`. This argument can be set to any positive value significantly larger (e.g., $\times10000$) than `epsilon(real(0., kind(reltol))`. A good rule of thumb is to set `reltol = epsilon(real(0, kind(integral)))(2./3.)`. The integration result is generally orders of magnitude more precise than the specified `reltol`. (optional**. If missing, the continued-fraction representation of the Incomplete Beta function will be used to approximate the output.)
[out]	info	: The output scalar (or array of the same shape as other array-like arguments) of type `integer` of default kind IK. It is `0` if and only if the computation converges, otherwise, if the input argument `reltol` is missing, it is set to `1` to signal lack of convergence in the computation of the continued-fraction representation of the Incomplete Beta function. Convergence fails if `alpha` or `beta` are too large, in which case a brute-force integration method by specifying the input argument `reltol` might resolve it. if the input argument `reltol` is present, it is set to the non-zero `info` output of getQuadErr to signal lack of convergence in the computation of the integral. See the documentation of the output argument `info` of getQuadErr for possible output error codes and their meanings. The failure may be resolved by increasing the preset value of `MAX_ITER` in the implementation.

Returns

Possible calling interfaces ⛓

: use pm_mathBeta, only: setBetaInc

call setBetaInc(betaInc, x, alpha, beta, logFuncBeta, signed, info)

call setBetaInc(betaInc, x, alpha, beta, logFuncBeta, reltol, signed, info)

pm_mathBeta::setBetaInc
Return the regularized Incomplete Beta Function as defined in the details section of pm_mathBeta.
Definition: pm_mathBeta.F90:443

pm_mathBeta
This module contains classes and procedures for computing the mathematical Beta Function and its inve...
Definition: pm_mathBeta.F90:84

Warning: The conditions 0 <= x .and. x <= 1 must hold for the corresponding input arguments.
The conditions 0 < alpha .and. 0 < beta 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. The procedures of this generic interface are always impure when the input argument reltol is present.

Remarks: The procedures under discussion are elemental.

See also: getLogBeta
setBetaInc
getBetaLogPDF

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_kind, only: RKG => RKH ! all processor kinds are supported.

5 use pm_io, only: display_type

6 use pm_mathBeta, only: setBetaInc

7 use pm_mathBeta, only: getLogBeta

8 use pm_err, only: setAsserted

9

10 implicit none

11

12 integer(IK) :: info(3)

13 real(RKG) :: betaInc(3), alpha, beta, reltol

14 real(RKG) , allocatable :: alphas(:), betas(:)

15 type(display_type) :: disp

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

17

18 call disp%skip()

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

20 call disp%show("! Compute the regularized (lower) Incomplete Beta Function using its series representation.")

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

22 call disp%skip()

23

24 call disp%skip()

25 call disp%show("alpha = 2.; beta = 3.")

26 alpha = 2.; beta = 3.

27 call disp%show("call setBetaInc(betaInc(1), 0._RKG, alpha, beta, getLogBeta(alpha, beta), signed = .false._LK, info = info(1))")

28 call setBetaInc(betaInc(1), 0._RKG, alpha, beta, getLogBeta(alpha, beta), signed = .false._LK, info = info(1))

29 call disp%show(.not."call setAsserted( info(1) < 0)")

30 call setAsserted(.not. info(1) < 0)

31 call disp%show("betaInc(1)")

32 call disp%show( betaInc(1) )

33 call disp%skip()

34

35 call disp%skip()

36 call disp%show("alpha = 2.; beta = 3.")

37 alpha = 2.; beta = 3.

38 call disp%show("call setBetaInc(betaInc(1), .5_RKG, alpha, beta, getLogBeta(alpha, beta), signed = .false._LK, info = info(1)) ! 0.6875")

39 call setBetaInc(betaInc(1), .5_RKG, alpha, beta, getLogBeta(alpha, beta), signed = .false._LK, info = info(1))

40 call disp%show(.not."call setAsserted( info(1) < 0)")

41 call setAsserted(.not. info(1) < 0)

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

43 call disp%show( betaInc(1) )

44 call disp%skip()

45

46 call disp%skip()

47 call disp%show("alpha = 2.; beta = 3.")

48 alpha = 2.; beta = 3.

49 call disp%show("call setBetaInc(betaInc(1), 1._RKG, alpha, beta, getLogBeta(alpha, beta), signed = .false._LK, info = info(1))")

50 call setBetaInc(betaInc(1), 1._RKG, alpha, beta, getLogBeta(alpha, beta), signed = .false._LK, info = info(1))

51 call disp%show(.not."call setAsserted( info(1) < 0)")

52 call setAsserted(.not. info(1) < 0)

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

54 call disp%show( betaInc(1) )

55 call disp%skip()

56

57 call disp%skip()

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

59 call disp%show("! Compute the regularized (lower) Incomplete Beta Function for a vector of points.")

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

61 call disp%skip()

62

63 call disp%skip()

64 call disp%show("alpha = 2.; beta = 3.")

65 alpha = 2.; beta = 3.

66 call disp%show("call setBetaInc(betaInc, [0._RKG, 0.5_RKG, 1._RKG], alpha, beta, getLogBeta(alpha, beta), signed = .false._LK, info = info)")

67 call setBetaInc(betaInc, [0._RKG, 0.5_RKG, 1._RKG], alpha, beta, getLogBeta(alpha, beta), signed = .false._LK, info = info)

68 call disp%show("info")

69 call disp%show( info )

70 call disp%show("betaInc")

71 call disp%show( betaInc )

72 call disp%skip()

73

74 call disp%skip()

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

76 call disp%show("! Compute the regularized Incomplete Beta Function for a vector of input parameters.")

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

78 call disp%skip()

79

80 call disp%skip()

81 call disp%show("alphas = [real(RKG) :: 0.1, 1., 10.]; beta = 3.")

82 alphas = [real(RKG) :: 0.1, 1., 10.]; beta = 3.

83 call disp%show("call setBetaInc(betaInc, [0._RKG, 0.5_RKG, 1._RKG], alphas, beta, getLogBeta(alphas, beta), signed = .false._LK, info = info)")

84 call setBetaInc(betaInc, [0._RKG, 0.5_RKG, 1._RKG], alphas, beta, getLogBeta(alphas, beta), signed = .false._LK, info = info)

85 call disp%show("info")

86 call disp%show( info )

87 call disp%show("betaInc")

88 call disp%show( betaInc )

89 call disp%skip()

90

91 call disp%skip()

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

93 call disp%show("! Compute the regularized (lower) Incomplete Beta Function using brute-force integration.")

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

95 call disp%skip()

96

97 call disp%skip()

98 call disp%show("reltol = epsilon(reltol)**.7")

99 reltol = epsilon(reltol)**.7

100 call disp%show("alphas = 5000.**[1, -1]; betas = 5000.**[1, -1]")

101 alphas = 5000.**[1, -1]; betas = 5000.**[1, -1]

102 call disp%show("call setBetaInc(betaInc(1:2), .5_RKG, alphas, betas, getLogBeta(alphas, betas), reltol, signed = .false._LK, info = info(1:2))")

103 call setBetaInc(betaInc(1:2), .5_RKG, alphas, betas, getLogBeta(alphas, betas), reltol, signed = .false._LK, info = info(1:2))

104 call disp%show("info(1:2)")

105 call disp%show( info(1:2) )

106 call disp%show("betaInc(1:2)")

107 call disp%show( betaInc(1:2) )

108 call disp%skip()

109

110 call disp%skip()

111 call disp%show("reltol = epsilon(reltol)**.7")

112 reltol = epsilon(reltol)**.7

113 call disp%show("reltol")

114 call disp%show( reltol )

115 call disp%show("alphas = 5000.**[1, -1]; betas = 5000.**[1, -1]")

116 alphas = 5000.**[1, -1]; betas = 5000.**[1, -1]

117 call disp%show("call setBetaInc(betaInc(1:2), .5_RKG, alphas, betas, getLogBeta(alphas, betas), signed = .false._LK, info = info(1:2))")

118 call setBetaInc(betaInc(1:2), .5_RKG, alphas, betas, getLogBeta(alphas, betas), signed = .false._LK, info = info(1:2))

119 call disp%show("info(1:2)")

120 call disp%show( info(1:2) )

121 call disp%show("betaInc(1:2)")

122 call disp%show( betaInc(1:2) )

123 call disp%skip()

124

125 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

126 ! Output an example array of the regularized Incomplete Beta function for visualization.

127 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

128

129 !block

130 ! use pm_arraySpace, only: setLinSpace

131 ! integer(IK) , parameter :: n1000_IK

132 ! real(RK) :: betaInc(3), x(nx)

133 ! integer :: fileUnit, i

134 ! call setLinSpace(x, 0._RKG, 1._RKG)

135 ! open(newunit = fileUnit, file = "setBetaInc.RK.txt")

136 ! do i = 1, nx

137 ! call setBetaInc(betaInc, x(i), 5._RKG, [1.0_RKG, 5.0_RKG, 10._RKG], getLogBeta(5._RKG, [1.0_RKG, 5.0_RKG, 10._RKG]), err)

138 ! write(fileUnit, "(*(g0,:,' '))") x_RK(i), betaInc

139 ! end do

140 ! close(fileUnit)

141 !end block

142

143 block

144 use pm_kind, only: RKG => RKH, RKH

145 use pm_arraySpace, only: setLinSpace

146 integer(IK) , parameter :: nx = 1000

147 real(RKG) , parameter :: alphas(*) = [0.1_RKG, 10._RKG, 1._RKG, 0.1_RKG, 10._RKG], betas(*) = [0.1_RKG, 0.1_RKG, 1._RKG, 10._RKG, 10._RKG]

148 real(RKG) :: betaInc(max(size(alphas), size(betas)))

149 integer(IK) :: fileUnit, i, info(size(betaInc))

150 real(RKG) :: x(nx)

151 call setLinSpace(x, 0._RKG, 1._RKG, fopen = .true._LK, lopen = .true._LK)

152 open(newunit = fileUnit, file = "setBetaInc.RK.txt")

153 do i = 1, nx

154 call setBetaInc(betaInc, x(i), alphas, betas, getLogBeta(alphas, betas), signed = .false._LK, info = info)

155 if (any(info /= 0)) error stop

156 write(fileUnit, "(*(g0,:,','))") x(i), betaInc

157 end do

158 close(fileUnit)

159 end block

160

161end 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_err::setAsserted
Verify the input assertion holds and if it does not, print the (optional) input message on stdout and...
Definition: pm_err.F90:735

pm_err::show
Generate and return an object of type stop_type with the user-specified input attributes.
Definition: pm_err.F90:1618

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

pm_mathBeta::getLogBeta
Generate and return the natural logarithm of the Beta Function as defined in the details section of ...
Definition: pm_mathBeta.F90:144

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

pm_err
This module contains classes and procedures for reporting and handling errors.
Definition: pm_err.F90:52

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::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_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 regularized (lower) Incomplete Beta Function using its series representation.

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

5

6

7alpha = 2.; beta = 3.

8call setBetaInc(betaInc(1), 0._RKG, alpha, beta, getLogBeta(alpha, beta), signed = .false._LK, info = info(1))

9call setAsserted(.not. info(1) < 0)

10betaInc(1)

11+0.00000000000000000000000000000000000

12

13

14alpha = 2.; beta = 3.

15call setBetaInc(betaInc(1), .5_RKG, alpha, beta, getLogBeta(alpha, beta), signed = .false._LK, info = info(1)) ! 0.6875

16call setAsserted(.not. info(1) < 0)

17betaInc(1)

18+0.687500000000000000000000000000000096

19

20

21alpha = 2.; beta = 3.

22call setBetaInc(betaInc(1), 1._RKG, alpha, beta, getLogBeta(alpha, beta), signed = .false._LK, info = info(1))

23call setAsserted(.not. info(1) < 0)

24betaInc(1)

25+1.00000000000000000000000000000000000

26

27

28!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

29! Compute the regularized (lower) Incomplete Beta Function for a vector of points.

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

31

32

33alpha = 2.; beta = 3.

34call setBetaInc(betaInc, [0._RKG, 0.5_RKG, 1._RKG], alpha, beta, getLogBeta(alpha, beta), signed = .false._LK, info = info)

35info

36+0, +0, +0

37betaInc

38+0.00000000000000000000000000000000000, +0.687500000000000000000000000000000096, +1.00000000000000000000000000000000000

39

40

41!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

42! Compute the regularized Incomplete Beta Function for a vector of input parameters.

43!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

44

45

46alphas = [real(RKG) :: 0.1, 1., 10.]; beta = 3.

47call setBetaInc(betaInc, [0._RKG, 0.5_RKG, 1._RKG], alphas, beta, getLogBeta(alphas, beta), signed = .false._LK, info = info)

48info

49+0, +0, +0

50betaInc

51+0.00000000000000000000000000000000000, +0.875000000000000000000000000000000000, +1.00000000000000000000000000000000000

52

53

54!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

55! Compute the regularized (lower) Incomplete Beta Function using brute-force integration.

56!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

57

58

59reltol = epsilon(reltol)**.7

60alphas = 5000.**[1, -1]; betas = 5000.**[1, -1]

61call setBetaInc(betaInc(1:2), .5_RKG, alphas, betas, getLogBeta(alphas, betas), reltol, signed = .false._LK, info = info(1:2))

62info(1:2)

63+0, +5

64betaInc(1:2)

65+0.499999999999999999999999999995890258, +0.499999999999999999999999999656137679

66

67

68reltol = epsilon(reltol)**.7

69reltol

70+0.250754503649549880673038532701962290E-23

71alphas = 5000.**[1, -1]; betas = 5000.**[1, -1]

72call setBetaInc(betaInc(1:2), .5_RKG, alphas, betas, getLogBeta(alphas, betas), signed = .false._LK, info = info(1:2))

73info(1:2)

74+0, +0

75betaInc(1:2)

76+0.499999999999999999999999999995924251, +0.499999999999999999999999999999999567

77

78

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"

12#label = [ r"$\alpha, \beta = 5., 1.0$"

13# , r"$\alpha, \beta = 5., 5.0$"

14# , r"$\alpha, \beta = 5., 10.$"

15# ]

16label = [ r"$\alpha, \beta = .1, .1$"

17 , r"$\alpha, \beta = 10, .1$"

18 , r"$\alpha, \beta = 1., 1.$"

19 , r"$\alpha, \beta = .1, 10$"

20 , r"$\alpha, \beta = 10, 10$"

21 ]

22

23pattern = "*." + kind + ".txt"

24fileList = glob.glob(pattern)

25if len(fileList) == 1:

26

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

28

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

30 ax = plt.subplot()

31

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

33

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

35 , df.values[:,i]

36 , linewidth = 2

37 )

38

39 plt.xticks(fontsize = fontsize - 2)

40 plt.yticks(fontsize = fontsize - 2)

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

42 ax.set_ylabel("Regularized Lower\nIncomplete Beta Function", fontsize = fontsize)

43 #ax.set_xscale("log")

44 #ax.set_yscale("log")

45

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

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

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

49

50 ax.legend ( label

51 , fontsize = fontsize

52 #, loc = "center left"

53 #, bbox_to_anchor = (1, 0.5)

54 )

55

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

57

58else:

59

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

Visualization of the example output ⛓

Test:: test_pm_mathBeta

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 443 of file pm_mathBeta.F90.

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

src/fortran/main/pm_mathBeta.F90