pm_distGeomCyclic::setGeomCyclicLogPMF Interface Reference

Return the natural logarithm of the Probability Mass Function (PMF) of the Cyclic Geometric distribution for an input stepSuccess within the discrete integer support of the distribution \([0, period]\). More...

Detailed Description

Return the natural logarithm of the Probability Mass Function (PMF) of the Cyclic Geometric distribution for an input stepSuccess within the discrete integer support of the distribution \([0, period]\).

Parameters

[out]	logPMF	: The output scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as logProbSuccess, containing the natural logarithm of the PMF of the distribution at the specified stepSuccess.
[in]	stepSuccess	: The input positive scalar (or array of the same rank, shape, and size as other array-like arguments), of type real of the same kind as that of logProbSuccess, type integer of default kind IK, containing the values at which the PMF must be computed. Note that stepSuccess represents the Bernoulli trial step at which the first success occurs.
[in]	logProbSuccess	: The input scalar (or array of the same rank, shape, and size as other array-like arguments), of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the natural logarithm of the probability of success at each Bernoulli step.
[in]	logProbFailure	: The input scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as logProbSuccess containing the natural logarithm of the probability of failure at each Bernoulli step. (optional, default = log(get1mexp(logProbSuccess)))

Possible calling interfaces ⛓

use pm_distGeomCyclic, only: setGeomCyclicLogPMF
 
call setGeomCyclicLogPMF(logPMF, stepSuccess, logProbSuccess, period) ! elemental
call setGeomCyclicLogPMF(logPMF, stepSuccess, logProbSuccess, logProbFailure, period) ! elemental
 
call setGeomCyclicLogPMF(logPMF(:), stepSuccess(:), logProbSuccess, period)
call setGeomCyclicLogPMF(logPMF(:), stepSuccess(:), logProbSuccess, logProbFailure, period)

Warning

The condition all(0 < [stepSuccess]) must hold for the corresponding input arguments.
The condition all([stepSuccess] <= period) must hold for the corresponding input arguments.
The condition logProbSuccess <= 0. must hold for the corresponding input arguments.
The condition logProbFailure < 0. must hold for the corresponding input arguments.
The condition exp(logProbFailure) + exp(logProbSuccess) == 1. 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.

Remarks

The procedures under discussion are elemental.

See also

getGeomCyclicLogCDF
setGeomCyclicLogCDF
getGeomCyclicLogPMF
setGeomCyclicLogPMF

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_kind, only: RKG => RK ! all processor kinds are supported.
    use pm_io, only: display_type
    use pm_distGeomCyclic, only: setGeomCyclicLogPMF
 
    implicit none
 
    real(RKG) :: logPMF(3)
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("call setGeomCyclicLogPMF(logPMF(1), 1_IK, logProbSuccess = log(.2_RKG), period = 1_IK)")
                    call setGeomCyclicLogPMF(logPMF(1), 1_IK, logProbSuccess = log(.2_RKG), period = 1_IK)
    call disp%show("logPMF(1)")
    call disp%show( logPMF(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setGeomCyclicLogPMF(logPMF(1), 1_IK, logProbSuccess = log(.2_RKG), period = 2_IK)")
                    call setGeomCyclicLogPMF(logPMF(1), 1_IK, logProbSuccess = log(.2_RKG), period = 2_IK)
    call disp%show("logPMF(1)")
    call disp%show( logPMF(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setGeomCyclicLogPMF(logPMF(1), 1_IK, logProbSuccess = log(.2_RKG), period = 20_IK)")
                    call setGeomCyclicLogPMF(logPMF(1), 1_IK, logProbSuccess = log(.2_RKG), period = 20_IK)
    call disp%show("logPMF(1)")
    call disp%show( logPMF(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setGeomCyclicLogPMF(logPMF(1), 2_IK, logProbSuccess = log(.2_RKG), period = 2_IK)")
                    call setGeomCyclicLogPMF(logPMF(1), 2_IK, logProbSuccess = log(.2_RKG), period = 2_IK)
    call disp%show("logPMF(1)")
    call disp%show( logPMF(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setGeomCyclicLogPMF(logPMF(1:3), [integer(IK) :: 1, 2, 3], logProbSuccess = log(.2_RKG), logProbFailure = log(1._RKG - .2_RKG), period = 4_IK)")
                    call setGeomCyclicLogPMF(logPMF(1:3), [integer(IK) :: 1, 2, 3], logProbSuccess = log(.2_RKG), logProbFailure = log(1._RKG - .2_RKG), period = 4_IK)
    call disp%show("logPMF(1:3)")
    call disp%show( logPMF(1:3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setGeomCyclicLogPMF(logPMF(1:3), [integer(IK) :: 1, 2, 3], logProbSuccess = log([0.1_RKG, .2_RKG, 1._RKG]), period = 5_IK)")
                    call setGeomCyclicLogPMF(logPMF(1:3), [integer(IK) :: 1, 2, 3], logProbSuccess = log([0.1_RKG, .2_RKG, 1._RKG]), period = 5_IK)
    call disp%show("logPMF(1:3)")
    call disp%show( logPMF(1:3) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
 
        use pm_arrayRange, only: getRange
        integer(IK), allocatable :: stepSuccess(:)
        real(RKG) :: logPMF(4)
        integer :: fileUnit, i
 
        stepSuccess = getRange(1_IK, 10_IK)
        open(newunit = fileUnit, file = "setGeomCyclicLogPMF.IK.txt")
        do i = 1, size(stepSuccess)
            call setGeomCyclicLogPMF(logPMF, stepSuccess(i), log([.05_RKG, .25_RKG, .05_RKG, .25_RKG]), period = [10_IK, 10_IK, 10000_IK, 10000_IK])
            write(fileUnit, "(*(g0,:,','))") stepSuccess(i), exp(logPMF)
        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 setGeomCyclicLogPMF(logPMF(1), 1_IK, logProbSuccess = log(.2_RKG), period = 1_IK)
logPMF(1)
+0.22204460492503131E-15
 
 
call setGeomCyclicLogPMF(logPMF(1), 1_IK, logProbSuccess = log(.2_RKG), period = 2_IK)
logPMF(1)
-0.58778666490211884
 
 
call setGeomCyclicLogPMF(logPMF(1), 1_IK, logProbSuccess = log(.2_RKG), period = 20_IK)
logPMF(1)
-1.5978417206981419
 
 
call setGeomCyclicLogPMF(logPMF(1), 2_IK, logProbSuccess = log(.2_RKG), period = 2_IK)
logPMF(1)
-0.81093021621632855
 
 
call setGeomCyclicLogPMF(logPMF(1:3), [integer(IK) :: 1, 2, 3], logProbSuccess = log(.2_RKG), logProbFailure = log(1._RKG - .2_RKG), period = 4_IK)
logPMF(1:3)
-1.0824829067382260, -1.3056264580524357, -1.5287700093666454
 
 
call setGeomCyclicLogPMF(logPMF(1:3), [integer(IK) :: 1, 2, 3], logProbSuccess = log([0.1_RKG, .2_RKG, 1._RKG]), period = 5_IK)
logPMF(1:3)
-1.4097911370312888, -1.4355606024228085, -709.78271289338397
 
 

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 = "IK"
label = [ r"probSuccess = .05, period = 10"
        , r"probSuccess = .25, period = 10"
        , r"probSuccess = .05, period = 10000"
        , r"probSuccess = .25, period = 10000"
        ]
 
pattern = "*." + kind + ".txt"
fileList = glob.glob(pattern)
if len(fileList) == 1:
 
    df = pd.read_csv(fileList[0], delimiter = ",", header = None)
 
    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]
                    , marker = "."
                    )
 
    plt.xticks(fontsize = fontsize - 2)
    plt.yticks(fontsize = fontsize - 2)
    ax.set_xlim([0, None])
    ax.set_xlabel("stepSuccess", fontsize = fontsize)
    ax.set_ylabel("PMF", 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_distGeomCyclic

Todo:

Normal Priority: This generic interface can be extended to complex arguments.

Final Remarks ⛓

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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, Monday March 6, 2017, 3:22 pm, Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin.

Definition at line 413 of file pm_distGeomCyclic.F90.

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

• src/fortran/main/pm_distGeomCyclic.F90