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

Return the CDF of the Beta distribution for the given parameters \((\alpha, \beta)\) as defined in the details section of pm_distBeta. More...

Detailed Description

Return the CDF of the Beta distribution for the given parameters \((\alpha, \beta)\) as defined in the details section of pm_distBeta.

Parameters
[in]cdf: 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.
  1. 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.
  2. If signed = .true., then the following rules hold:
    1. If the condition x < 0 holds, then the value x = 1 - x < 0 will be used instead of x.
    2. 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 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.
[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, it is set to a non-zero integer whose value depends on the root cause of the lack of convergence.
Convergence typically fails if alpha or beta are too large.
For more information, see the corresponding argument of setBetaInc.
Returns


Possible calling interfaces

call setBetaCDF(cdf, x, alpha, beta, logFuncBeta, signed, info)
Return the CDF of the Beta distribution for the given parameters as defined in the details section o...
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distBeta.F90:99
Warning
All warnings associated with setBetaInc also apply to the procedures of this generic interface.
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
getLogBeta
setBetaCDF
setBetaRand
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_distBeta, only: setBetaCDF
7 use pm_mathBeta, only: getLogBeta
8
9 implicit none
10
11 real(RKG) :: cdf(4)
12 logical(LK) :: signed
13 integer(IK) :: info(4)
14 type(display_type) :: disp
15 disp = display_type(file = "main.out.F90")
16
17 signed = .false.
18
19 call disp%skip()
20 call disp%show("call setBetaCDF(cdf(1), x = 0._RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))")
21 call setBetaCDF(cdf(1), x = 0._RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))
22 call disp%show("if (info(1) /= 0) error stop")
23 if (info(1) /= 0) error stop
24 call disp%show("cdf(1)")
25 call disp%show( cdf(1) )
26 call disp%skip()
27
28 call disp%skip()
29 call disp%show("call setBetaCDF(cdf(1), x = .5_RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))")
30 call setBetaCDF(cdf(1), x = .5_RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))
31 call disp%show("if (info(1) /= 0) error stop")
32 if (info(1) /= 0) error stop
33 call disp%show("cdf(1)")
34 call disp%show( cdf(1) )
35 call disp%skip()
36
37 call disp%skip()
38 call disp%show("call setBetaCDF(cdf(1), x = 1._RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))")
39 call setBetaCDF(cdf(1), x = 1._RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))
40 call disp%show("if (info(1) /= 0) error stop")
41 if (info(1) /= 0) error stop
42 call disp%show("cdf(1)")
43 call disp%show( cdf(1) )
44 call disp%skip()
45
46 call disp%skip()
47 call disp%show("call setBetaCDF(cdf, x = [0._RKG, 0.1_RKG, 0.5_RKG, 1._RKG], alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info)")
48 call setBetaCDF(cdf, x = [0._RKG, 0.1_RKG, 0.5_RKG, 1._RKG], alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info)
49 call disp%show("if (any(info /= 0)) error stop")
50 if (any(info /= 0)) error stop
51 call disp%show("cdf")
52 call disp%show( cdf )
53 call disp%skip()
54
55 call disp%skip()
56 call disp%show("call setBetaCDF(cdf, x = [0._RKG, .1_RKG, 0.5_RKG, 1._RKG], alpha = [0.1_RKG, .5_RKG, 1._RKG, 10._RKG], beta = 3._RKG, logFuncBeta = getLogBeta([0.1_RKG, .5_RKG, 1._RKG, 10._RKG], 3._RKG), signed = signed, info = info)")
57 call setBetaCDF(cdf, x = [0._RKG, .1_RKG, 0.5_RKG, 1._RKG], alpha = [0.1_RKG, .5_RKG, 1._RKG, 10._RKG], beta = 3._RKG, logFuncBeta = getLogBeta([0.1_RKG, .5_RKG, 1._RKG, 10._RKG], 3._RKG), signed = signed, info = info)
58 call disp%show("if (any(info /= 0)) error stop")
59 if (any(info /= 0)) error stop
60 call disp%show("cdf")
61 call disp%show( cdf )
62 call disp%skip()
63
64 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
65 ! Output an example array for visualization.
66 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
67
68 block
69
70 use pm_arraySpace, only: setLinSpace
71 integer(IK) , parameter :: NP = 1000_IK
72 real(RKG) :: cdf(4), X(NP)
73 integer :: fileUnit, i
74
75 call setLinSpace(X, 0._RKG, 1._RKG)
76 open(newunit = fileUnit, file = "setBetaCDF.RK.txt")
77 do i = 1, NP
78 call setBetaCDF(cdf, X(i), [.5_RKG, 5._RKG, .5_RKG, 5._RKG], [.5_RKG, 1.0_RKG, 5.0_RKG, 10._RKG], getLogBeta([.5_RKG, 5._RKG, .5_RKG, 5._RKG], [.5_RKG, 1.0_RKG, 5.0_RKG, 10._RKG]), signed = signed, info = info)
79 if (any(info /= 0)) error stop
80 write(fileUnit, "(*(g0,:,' '))") X(i), cdf
81 end do
82 close(fileUnit)
83
84 end block
85
86end program example
Return the linSpace output argument with size(linSpace) elements of evenly-spaced values over the int...
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
Generate and return the natural logarithm of the Beta Function as defined in the details section of ...
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...
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 LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541
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 RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
Definition: pm_kind.F90:858
This module contains classes and procedures for computing the mathematical Beta Function and its inve...
Definition: pm_mathBeta.F90:84
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
2call setBetaCDF(cdf(1), x = 0._RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))
3if (info(1) /= 0) error stop
4cdf(1)
5+0.00000000000000000000000000000000000
6
7
8call setBetaCDF(cdf(1), x = .5_RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))
9if (info(1) /= 0) error stop
10cdf(1)
11+0.687500000000000000000000000000000096
12
13
14call setBetaCDF(cdf(1), x = 1._RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))
15if (info(1) /= 0) error stop
16cdf(1)
17+1.00000000000000000000000000000000000
18
19
20call setBetaCDF(cdf, x = [0._RKG, 0.1_RKG, 0.5_RKG, 1._RKG], alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info)
21if (any(info /= 0)) error stop
22cdf
23+0.00000000000000000000000000000000000, +0.522999999999999999999999999999999659E-1, +0.687500000000000000000000000000000096, +1.00000000000000000000000000000000000
24
25
26call setBetaCDF(cdf, x = [0._RKG, .1_RKG, 0.5_RKG, 1._RKG], alpha = [0.1_RKG, .5_RKG, 1._RKG, 10._RKG], beta = 3._RKG, logFuncBeta = getLogBeta([0.1_RKG, .5_RKG, 1._RKG, 10._RKG], 3._RKG), signed = signed, info = info)
27if (any(info /= 0)) error stop
28cdf
29+0.00000000000000000000000000000000000, +0.554584444652029525349305955354888178, +0.875000000000000000000000000000000000, +1.00000000000000000000000000000000000
30
31

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"$\alpha, \beta = .5, 0.5$"
13 , r"$\alpha, \beta = 5., 1.0$"
14 , r"$\alpha, \beta = .5, 5.0$"
15 , r"$\alpha, \beta = 5., 10.$"
16 ]
17
18pattern = "*." + kind + ".txt"
19fileList = glob.glob(pattern)
20if len(fileList) == 1:
21
22 df = pd.read_csv(fileList[0], delimiter = " ")
23
24 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
25 ax = plt.subplot()
26
27 for i in range(1,len(df.values[0,:]+1)):
28
29 plt.plot( df.values[:, 0]
30 , df.values[:,i]
31 , linewidth = 2
32 )
33
34 plt.xticks(fontsize = fontsize - 2)
35 plt.yticks(fontsize = fontsize - 2)
36 ax.set_xlabel("x", fontsize = fontsize)
37 ax.set_ylabel("Beta CDF", fontsize = fontsize)
38
39 plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
40 ax.tick_params(axis = "y", which = "minor")
41 ax.tick_params(axis = "x", which = "minor")
42
43 ax.legend ( label
44 , fontsize = fontsize
45 #, loc = "center left"
46 #, bbox_to_anchor = (1, 0.5)
47 )
48
49 plt.savefig(fileList[0].replace(".txt",".png"))
50
51else:
52
53 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 881 of file pm_distBeta.F90.


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