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. 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 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 ⛓

use pm_distBeta, only: setBetaCDF
 
call setBetaCDF(cdf, x, alpha, beta, logFuncBeta, signed, info)

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 ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_kind, only: RKG => RKH ! all processor kinds are supported.
    use pm_io, only: display_type
    use pm_distBeta, only: setBetaCDF
    use pm_mathBeta, only: getLogBeta
 
    implicit none
 
    real(RKG) :: cdf(4)
    logical(LK) :: signed
    integer(IK) :: info(4)
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    signed = .false.
 
    call disp%skip()
    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))")
                    call setBetaCDF(cdf(1), x = 0._RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))
    call disp%show("if (info(1) /= 0) error stop")
                    if (info(1) /= 0) error stop
    call disp%show("cdf(1)")
    call disp%show( cdf(1) )
    call disp%skip()
 
    call disp%skip()
    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))")
                    call setBetaCDF(cdf(1), x = .5_RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))
    call disp%show("if (info(1) /= 0) error stop")
                    if (info(1) /= 0) error stop
    call disp%show("cdf(1)")
    call disp%show( cdf(1) )
    call disp%skip()
 
    call disp%skip()
    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))")
                    call setBetaCDF(cdf(1), x = 1._RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))
    call disp%show("if (info(1) /= 0) error stop")
                    if (info(1) /= 0) error stop
    call disp%show("cdf(1)")
    call disp%show( cdf(1) )
    call disp%skip()
 
    call disp%skip()
    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)")
                    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)
    call disp%show("if (any(info /= 0)) error stop")
                    if (any(info /= 0)) error stop
    call disp%show("cdf")
    call disp%show( cdf )
    call disp%skip()
 
    call disp%skip()
    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)")
                    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)
    call disp%show("if (any(info /= 0)) error stop")
                    if (any(info /= 0)) error stop
    call disp%show("cdf")
    call disp%show( cdf )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
 
        use pm_arraySpace, only: setLinSpace
        integer(IK) , parameter :: NP = 1000_IK
        real(RKG) :: cdf(4), X(NP)
        integer :: fileUnit, i
 
        call setLinSpace(X, 0._RKG, 1._RKG)
        open(newunit = fileUnit, file = "setBetaCDF.RK.txt")
        do i = 1, NP
            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)
            if (any(info /= 0)) error stop
            write(fileUnit, "(*(g0,:,' '))") X(i), cdf
        end do
        close(fileUnit)
 
    end block
 
end program example

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example output ⛓

 
call setBetaCDF(cdf(1), x = 0._RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))
if (info(1) /= 0) error stop
cdf(1)
+0.00000000000000000000000000000000000
 
 
call setBetaCDF(cdf(1), x = .5_RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))
if (info(1) /= 0) error stop
cdf(1)
+0.687500000000000000000000000000000096
 
 
call setBetaCDF(cdf(1), x = 1._RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))
if (info(1) /= 0) error stop
cdf(1)
+1.00000000000000000000000000000000000
 
 
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)
if (any(info /= 0)) error stop
cdf
+0.00000000000000000000000000000000000, +0.522999999999999999999999999999999659E-1, +0.687500000000000000000000000000000096, +1.00000000000000000000000000000000000
 
 
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)
if (any(info /= 0)) error stop
cdf
+0.00000000000000000000000000000000000, +0.554584444652029525349305955354888178, +0.875000000000000000000000000000000000, +1.00000000000000000000000000000000000
 
 

Postprocessing of the example output ⛓

#!/usr/bin/env python
 
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import glob
import sys
 
fontsize = 17
 
kind = "RK"
label = [ r"$\alpha, \beta = .5, 0.5$"
        , r"$\alpha, \beta = 5., 1.0$"
        , r"$\alpha, \beta = .5, 5.0$"
        , r"$\alpha, \beta = 5., 10.$"
        ]
 
pattern = "*." + kind + ".txt"
fileList = glob.glob(pattern)
if len(fileList) == 1:
 
    df = pd.read_csv(fileList[0], delimiter = " ")
 
    fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
    ax = plt.subplot()
 
    for i in range(1,len(df.values[0,:]+1)):
 
            plt.plot( df.values[:, 0]
                    , df.values[:,i]
                    , linewidth = 2
                    )
 
    plt.xticks(fontsize = fontsize - 2)
    plt.yticks(fontsize = fontsize - 2)
    ax.set_xlabel("x", fontsize = fontsize)
    ax.set_ylabel("Beta CDF", fontsize = fontsize)
 
    plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
    ax.tick_params(axis = "y", which = "minor")
    ax.tick_params(axis = "x", which = "minor")
 
    ax.legend   ( label
                , fontsize = fontsize
               #, loc = "center left"
               #, bbox_to_anchor = (1, 0.5)
                )
 
    plt.savefig(fileList[0].replace(".txt",".png"))
 
else:
 
    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.

Copyright

Computational Data Science Lab

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:

• src/fortran/main/pm_distBeta.F90