ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_distBeta::setBetaRand Interface Reference

Return a scalar or array of arbitrary rank of Beta-distributed random values in range \([0, 1]\) (or \((0, 1)\), depending on the specific parameter values) with the specified two shape parameters \((\alpha, \beta)\) of the Beta distribution corresponding to the procedure arguments (alpha, beta). More...

Detailed Description

Return a scalar or array of arbitrary rank of Beta-distributed random values in range \([0, 1]\) (or \((0, 1)\), depending on the specific parameter values) with the specified two shape parameters \((\alpha, \beta)\) of the Beta distribution corresponding to the procedure arguments (alpha, beta).

See the documentation of pm_distBeta for more information on the Probability Density Function (PDF) of the Beta distribution and RNG.

Parameters
[in,out]rng: The input/output scalar that can be an object of,
  1. type rngf_type, implying the use of intrinsic Fortran uniform RNG.
  2. type xoshiro256ssw_type, implying the use of xoshiro256** uniform RNG.
(optional, default = rngf_type, implying the use of the intrinsic Fortran URNG.)
[out]rand: The output scalar or
  1. array of rank 1, or
  2. array of arbitrary rank if the rng argument is missing or set to rngf_type, or
of,
  1. type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128).
On output, it contains Beta-distributed random value(s).
[in]alpha: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as rand, containing the first shape parameter of the distribution.
[in]beta: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as rand, containing the second shape parameter of the distribution.


Possible calling interfaces

call setBetaRand(rand, alpha, beta)
call setBetaRand(rand(..), alpha, beta)
call setBetaRand(rng, rand, alpha, beta)
call setBetaRand(rng, rand(:), alpha, beta)
Return a scalar or array of arbitrary rank of Beta-distributed random values in range (or ,...
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distBeta.F90:99
Warning
The conditions \(0. < \alpha\) and \(0. < \beta\) must hold for the input arguments (alpha, beta).
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.
The procedures under discussion are recursive.
Note
For repeated Beta RNG with fixed alpha, it is best to pass a vector of rand to be filled with random numbers rather than calling the procedures with scalar rand argument repeatedly.
In addition to avoiding procedure call overhead, vectorized RGN in this particular case also avoids an unnecessary division and square-root operation.
See also
getBetaLogPDF
setBetaLogPDF
getBetaCDF
setBetaCDF


Example usage

1program example
2
3 use pm_kind, only: SK, IK
4 use pm_kind, only: RKG => RKS ! all real kinds are supported.
6 use pm_distBeta, only: setBetaRand
9 use pm_io, only: display_type
10
11 implicit none
12
13 type(xoshiro256ssw_type) :: rng
14 integer(IK), parameter :: NP = 1000_IK
15 real(RKG), dimension(NP) :: alpha, beta, rand
16
17 type(display_type) :: disp
18 disp = display_type(file = "main.out.F90")
19
20 call setLogSpace(alpha, logx1 = log(0.1_RKG), logx2 = log(10._RKG))
21 call setLogSpace(beta, logx1 = log(0.1_RKG), logx2 = log(10._RKG))
22
23 call disp%skip()
24 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
25 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
26 call disp%show("! Generate random numbers from the Beta distribution.")
27 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
28 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
29 call disp%skip()
30
31 call disp%skip()
32 call disp%show("alpha(1)")
33 call disp%show( alpha(1) )
34 call disp%show("beta(1)")
35 call disp%show( beta(1) )
36 call disp%show("call setBetaRand(rand(1), 1._RKG, beta = beta(1))")
37 call setBetaRand(rand(1), 1._RKG, beta = beta(1))
38 call disp%show("rand(1)")
39 call disp%show( rand(1) )
40 call disp%skip()
41
42 call disp%skip()
43 call disp%show("alpha(1)")
44 call disp%show( alpha(1) )
45 call disp%show("beta(1)")
46 call disp%show( beta(1) )
47 call disp%show("rng = xoshiro256ssw_type()")
48 rng = xoshiro256ssw_type()
49 call disp%show("call setBetaRand(rng, rand(1:2), 1._RKG, beta = beta(1))")
50 call setBetaRand(rng, rand(1:2), 1._RKG, beta = beta(1))
51 call disp%show("rand(1:2)")
52 call disp%show( rand(1:2) )
53 call disp%skip()
54
55 call disp%skip()
56 call disp%show("alpha(1)")
57 call disp%show( alpha(1) )
58 call disp%show("beta(1)")
59 call disp%show( beta(1) )
60 call disp%show("call setBetaRand(rand(1:2), alpha(1), beta = beta(1))")
61 call setBetaRand(rand(1:2), alpha(1), beta = beta(1))
62 call disp%show("rand(1:2)")
63 call disp%show( rand(1:2) )
64 call disp%skip()
65
66 call disp%skip()
67 call disp%show("alpha(1:NP:NP/3)")
68 call disp%show( alpha(1:NP:NP/3) )
69 call disp%show("beta(1:NP:NP/3)")
70 call disp%show( beta(1:NP:NP/3) )
71 call disp%show("call setBetaRand(rand(1:NP:NP/3), alpha(1:NP:NP/3), beta = beta(1:NP:NP/3))")
72 call setBetaRand(rand(1:NP:NP/3), alpha(1:NP:NP/3), beta = beta(1:NP:NP/3))
73 call disp%show("rand(1:NP:NP/3)")
74 call disp%show( rand(1:NP:NP/3) )
75 call disp%skip()
76
77 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
78 ! Output an example rand array for visualization.
79 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
80
81 block
82 use pm_io, only: getErrTableWrite
83 real(RKG) :: rand(5000, 4)
84 call setBetaRand(rand(:, 1), alpha = 0.5_RKG, beta = 0.5_RKG)
85 call setBetaRand(rand(:, 2), alpha = 2.0_RKG, beta = 2.0_RKG)
86 call setBetaRand(rand(:, 3), alpha = 2.0_RKG, beta = 5.0_RKG)
87 call setBetaRand(rand(:, 4), alpha = 5.0_RKG, beta = 2.0_RKG)
88 if (0 /= getErrTableWrite(SK_"setBetaRand.RK.txt", rand)) error stop "Failed to write table."
89 end block
90
91end program example
Return the linSpace output argument with size(linSpace) elements of evenly-spaced values over the int...
Return the logSpace output argument with size(logSpace) elements of logarithmically-evenly-spaced val...
Generate and return the iostat code resulting from writing the input table of rank 1 or 2 to the spec...
Definition: pm_io.F90:5940
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 computing various statistical quantities related to t...
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 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
This is the derived type for declaring and generating objects of type xoshiro256ssw_type containing a...
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! Generate random numbers from the Beta distribution.
5!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7
8
9alpha(1)
10+0.999999940E-1
11beta(1)
12+0.999999940E-1
13call setBetaRand(rand(1), 1._RKG, beta = beta(1))
14rand(1)
15+0.100168034
16
17
18alpha(1)
19+0.999999940E-1
20beta(1)
21+0.999999940E-1
23call setBetaRand(rng, rand(1:2), 1._RKG, beta = beta(1))
24rand(1:2)
25+0.573816597, +1.00000000
26
27
28alpha(1)
29+0.999999940E-1
30beta(1)
31+0.999999940E-1
32call setBetaRand(rand(1:2), alpha(1), beta = beta(1))
33rand(1:2)
34+0.664646104E-1, +0.421227198E-14
35
36
37alpha(1:NP:NP/3)
38+0.999999940E-1, +0.464158833, +2.15443444, +10.0000010
39beta(1:NP:NP/3)
40+0.999999940E-1, +0.464158833, +2.15443444, +10.0000010
41call setBetaRand(rand(1:NP:NP/3), alpha(1:NP:NP/3), beta = beta(1:NP:NP/3))
42rand(1:NP:NP/3)
43+0.976444542, +0.900211811, +0.672374189, +0.372821599
44
45

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
9linewidth = 2
10fontsize = 17
11
12marker ={ "CK" : "-"
13 , "IK" : "."
14 , "RK" : "-"
15 }
16xlab = { "CK" : "Beta Random Value ( real/imaginary components )"
17 , "IK" : "Beta Random Value ( integer-valued )"
18 , "RK" : "Beta Random Value ( real-valued )"
19 }
20legends = [ r"$\alpha = 0.5, \beta = 0.5$"
21 , r"$\alpha = 2.0, \beta = 2.0$"
22 , r"$\alpha = 2.0, \beta = 5.0$"
23 , r"$\alpha = 5.0, \beta = 2.0$"
24 ]
25
26for kind in ["IK", "CK", "RK"]:
27
28 pattern = "*." + kind + ".txt"
29 fileList = glob.glob(pattern)
30 if len(fileList) == 1:
31
32 df = pd.read_csv(fileList[0], delimiter = ",", header = None)
33
34 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
35 ax = plt.subplot()
36
37 for j in range(len(df.values[0,:])):
38 if kind == "CK":
39 plt.hist( df.values[:,j]
40 , histtype = "stepfilled"
41 , alpha = 0.5
42 , bins = 75
43 )
44 else:
45 plt.hist( df.values[:,j]
46 , histtype = "stepfilled"
47 , alpha = 0.5
48 , bins = 75
49 )
50 ax.legend ( legends
51 , fontsize = fontsize
52 )
53 plt.xticks(fontsize = fontsize - 2)
54 plt.yticks(fontsize = fontsize - 2)
55 ax.set_xlabel(xlab[kind], fontsize = 17)
56 ax.set_ylabel("Count", fontsize = 17)
57 ax.set_title("Histograms of {} Beta random values".format(len(df.values[:, 0])), fontsize = 17)
58
59 plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
60 ax.tick_params(axis = "y", which = "minor")
61 ax.tick_params(axis = "x", which = "minor")
62
63 plt.savefig(fileList[0].replace(".txt",".png"))
64
65 elif len(fileList) > 1:
66
67 sys.exit("Ambiguous file list exists.")

Visualization of the example output
Test:
test_pm_distBeta


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.

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.

Author:
Amir Shahmoradi, Oct 16, 2009, 11:14 AM, Michigan

Definition at line 1039 of file pm_distBeta.F90.


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