pm_distGeomCyclic::getGeomCyclicLogPMF Interface Reference

Generate and 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 \([0, \ms{period}]\). More...

Detailed Description

Generate and 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 \([0, \ms{period}]\).

Parameters

[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 probSuccess, 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. As such, it must never exceed the value of the input argument period.
[in]	probSuccess	: 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 probability of success at each Bernoulli step.
[in]	period	: The input positive scalar (or array of the same rank, shape, and size as other array-like arguments), of type integer of default kind IK, containing the period of the Cyclic Geometric distribution. The period represents the maximum number of Bernoulli trials in the experiment.

Returns

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 probSuccess, containing the natural logarithm of the PMF of the distribution at the specified point stepSuccess.

Possible calling interfaces ⛓

use pm_distGeomCyclic, only: getGeomCyclicLogPMF
 
logPMF = getGeomCyclicLogPMF(stepSuccess, probSuccess, period)

Warning

The condition 0. < probSuccess must hold for the corresponding input arguments.
The condition probSuccess <= 1 must hold for the corresponding input arguments.
The condition 1 <= stepSuccess must hold for the corresponding input arguments.
The condition stepSuccess <= period 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: getGeomCyclicLogPMF
 
    implicit none
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("getGeomCyclicLogPMF(1_IK, probSuccess = .5_RKG, period = 2_IK)")
    call disp%show( getGeomCyclicLogPMF(1_IK, probSuccess = .5_RKG, period = 2_IK) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getGeomCyclicLogPMF(2_IK, probSuccess = .5_RKG, period = 2_IK)")
    call disp%show( getGeomCyclicLogPMF(2_IK, probSuccess = .5_RKG, period = 2_IK) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getGeomCyclicLogPMF(2_IK, probSuccess = .2_RKG, period = 2_IK)")
    call disp%show( getGeomCyclicLogPMF(2_IK, probSuccess = .2_RKG, period = 2_IK) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getGeomCyclicLogPMF([integer(IK) :: 1, 2, 3], probSuccess = .9_RKG, period = 3_IK)")
    call disp%show( getGeomCyclicLogPMF([integer(IK) :: 1, 2, 3], probSuccess = .9_RKG, period = 3_IK) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getGeomCyclicLogPMF([integer(IK) :: 1, 2, 3, 4], probSuccess = [0.01_RKG, 0.1_RKG, .1_RKG, 1._RKG], period = 10_IK)")
    call disp%show( getGeomCyclicLogPMF([integer(IK) :: 1, 2, 3, 4], probSuccess = [0.01_RKG, 0.1_RKG, .1_RKG, 1._RKG], period = 10_IK) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
 
        use pm_arrayRange, only: getRange
        integer(IK), allocatable :: count(:)
        integer :: fileUnit, i
 
        count = getRange(1_IK, 10_IK)
        open(newunit = fileUnit, file = "getGeomCyclicLogPMF.IK.txt")
        do i = 1, size(count)
            write(fileUnit, "(*(g0,:,','))") count(i), exp(getGeomCyclicLogPMF(count(i), [.05_RKG, .25_RKG, .05_RKG, .25_RKG], period = [10_IK, 10_IK, 10000_IK, 10000_IK]))
        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 ⛓

 
getGeomCyclicLogPMF(1_IK, probSuccess = .5_RKG, period = 2_IK)
-0.40546510810816438
 
 
getGeomCyclicLogPMF(2_IK, probSuccess = .5_RKG, period = 2_IK)
-1.0986122886681096
 
 
getGeomCyclicLogPMF(2_IK, probSuccess = .2_RKG, period = 2_IK)
-0.81093021621632855
 
 
getGeomCyclicLogPMF([integer(IK) :: 1, 2, 3], probSuccess = .9_RKG, period = 3_IK)
-0.10436001532424274, -2.4069451083182885, -4.7095302013123330
 
 
getGeomCyclicLogPMF([integer(IK) :: 1, 2, 3, 4], probSuccess = [0.01_RKG, 0.1_RKG, .1_RKG, 1._RKG], period = 10_IK)
-2.2577752093953025, -1.9791937975453833, -2.0845543132032098, -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

Final Remarks ⛓

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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.
   
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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 198 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