Generate and return the natural logarithm of the Beta Function \(\mathrm{B}(\alpha, \beta)\) as defined in the details section of pm_mathBeta.
More...
Generate and return the natural logarithm of the Beta Function \(\mathrm{B}(\alpha, \beta)\) as defined in the details section of pm_mathBeta.
 Parameters

[in]  alpha  : The input scalar (or array of the same shape as other arraylike arguments) of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128).

[in]  beta  : The input scalar (or array of the same shape as other arraylike arguments) of the same type and kind as alpha . 
 Returns
logFuncBeta
: The output object of the same type, kind, and rank as highestrank input argument containing the natural logarithm of the Beta Function.
Possible calling interfaces ⛓
Generate and return the natural logarithm of the Beta Function as defined in the details section of ...
This module contains classes and procedures for computing the mathematical Beta Function and its inve...
 Warning
 The conditions
0 < alpha .and. 0 < beta
must hold for the corresponding input arguments.
This condition is 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.
 See also
 getLogBeta
getBetaInc
getBetaLogPDF
Example usage ⛓
10 type(display_type) :: disp
14 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
15 call disp%show(
"! Compute the regularized (lower) Incomplete Beta Function using its series representation.")
16 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
20 call disp%show(
"getLogBeta(alpha = 2._RK, beta = 3._RK) ! 2.484906649788000")
25 call disp%show(
"getLogBeta(alpha = 5._RK, beta = 3._RK) ! 4.653960350157524")
30 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
31 call disp%show(
"! Compute the regularized Incomplete Beta Function for a vector of input parameters.")
32 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
36 call disp%show(
"getLogBeta(alpha = [0.1_RK, 1._RK, 10._RK], beta = 3._RK) ! 2.158484749020289 1.098612288668110 6.492239835020470")
47 integer(IK) ,
parameter :: NP
= 1000_IK
48 integer :: fileUnit, i
52 open(newunit
= fileUnit, file
= "getLogBeta.RK.txt")
54 write(fileUnit,
"(*(g0,:,' '))") A_RK(i),
exp(
getLogBeta(A_RK(i), [
0.1_RK,
1.0_RK,
10._RK]))
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
This is a generic method of the derived type display_type with pass attribute.
This is a generic method of the derived type display_type with pass attribute.
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...
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
This module defines the relevant Fortran kind typeparameters frequently used in the ParaMonte librar...
integer, parameter RK
The default real kind in the ParaMonte library: real64 in Fortran, c_double in CFortran Interoperati...
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in CFortran Interoper...
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in CFortran Intero...
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort fpp standardsemantics O3 Wl,rpath,../../../lib I../../../inc main.F90 ../../../lib/libparamonte* o main.exe
Example Windows Batch compile command via Intel ifort
compiler ⛓
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standardsemantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran cpp ffreelinelengthnone O3 Wl,rpath,../../../lib I../../../inc main.F90 ../../../lib/libparamonte* o main.exe
Example output ⛓
20getLogBeta(alpha
= [
0.1_RK,
1._RK,
10._RK], beta
= 3._RK)
21+2.1584847490202885,
1.0986122886681096,
6.4922398350204720
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
12label = [
r"$\beta = 0.1$"
17pattern =
"*." + kind +
".txt"
18fileList = glob.glob(pattern)
21 df = pd.read_csv(fileList[0], delimiter =
" ")
23 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
26 for i
in range(1,len(df.values[0,:]+1)):
28 plt.plot( df.values[:, 0]
33 plt.xticks(fontsize = fontsize  2)
34 plt.yticks(fontsize = fontsize  2)
35 ax.set_xlabel(
"a", fontsize = fontsize)
36 ax.set_ylabel(
"Beta Function", fontsize = fontsize)
40 plt.grid(visible =
True, which =
"both", axis =
"both", color =
"0.85", linestyle =
"")
41 ax.tick_params(axis =
"y", which =
"minor")
42 ax.tick_params(axis =
"x", which =
"minor")
50 plt.savefig(fileList[0].replace(
".txt",
".png"))
54 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 144 of file pm_mathBeta.F90.