pm_distNegExp::setNegExpCDF Interface Reference

Return the Cumulative Distribution Function (CDF) of the Negative Exponential distribution for an input x within the support of the distribution \((-\infty, \mu]\). More...

Detailed Description

Return the Cumulative Distribution Function (CDF) of the Negative Exponential distribution for an input x within the support of the distribution \((-\infty, \mu]\).

Parameters

[out]	cdf	: The output scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as x, containing the CDF of the distribution at the specified point.
[in]	x	: 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 values at which the CDF must be computed.
[in]	mu	: The input scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as x containing the location parameter of the distribution. (optional, default = 0. It can be present if and only if invSigma is also present.)
[in]	invSigma	: The input scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as x containing the inverse scale (i.e., the rate or the inverse mean) parameter of the distribution. (optional, default = 1..)

Possible calling interfaces ⛓

use pm_distNegExp, only: setNegExpCDF
 
call setNegExpCDF(cdf, x)
call setNegExpCDF(cdf, x, invSigma)
call setNegExpCDF(cdf, x, mu, invSigma)

Warning

The condition x <= mu must hold for the corresponding input arguments.
The condition 0 < invSigma 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

getNegExpCDF

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK
    use pm_io, only: display_type
    use pm_distNegExp, only: setNegExpCDF
 
    implicit none
 
    real :: CDF(3)
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the Cumulative Distribution Function (CDF) of Negative Exponential distribution at the specified values.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the CDF at an input scalar real value.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setNegExpCDF(CDF(1), x = -.5)")
                    call setNegExpCDF(CDF(1), x = -.5)
    call disp%show("CDF(1)")
    call disp%show( CDF(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setNegExpCDF(CDF(1), x = -.5, invSigma = 1.)")
                    call setNegExpCDF(CDF(1), x = -.5, invSigma = 1.)
    call disp%show("CDF(1)")
    call disp%show( CDF(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setNegExpCDF(CDF(1), x = -.5, mu = 0., invSigma = 1.)")
                    call setNegExpCDF(CDF(1), x = -.5, mu = 0., invSigma = 1.)
    call disp%show("CDF(1)")
    call disp%show( CDF(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the CDF at an input vector real value with different parameter values.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setNegExpCDF(CDF(1:3), x = -[.5, 1., 2.])")
                    call setNegExpCDF(CDF(1:3), x = -[.5, 1., 2.])
    call disp%show("CDF(1:3)")
    call disp%show( CDF(1:3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setNegExpCDF(CDF(1:3), x = -[.5, 1., 2.], invSigma = [2., 1., .5])")
                    call setNegExpCDF(CDF(1:3), x = -[.5, 1., 2.], invSigma = [2., 1., .5])
    call disp%show("CDF(1:3)")
    call disp%show( CDF(1:3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setNegExpCDF(CDF(1:3), x = -[5., 1., 2.], mu = [-1., 0., +1.], invSigma = 1.)")
                    call setNegExpCDF(CDF(1:3), x = -[5., 1., 2.], mu = [-1., 0., +1.], invSigma = 1.)
    call disp%show("CDF(1:3)")
    call disp%show( CDF(1:3) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        use pm_arraySpace, only: getLinSpace
        real, parameter :: invSigma(3) = [2., 1., .5]
        real, parameter :: mu(3) = [-2., 0., 2.]
        real :: Point(1000)
        integer :: fileUnit, i, j
        Point = -getLinSpace(-4., +8., size(Point,1,IK))
        open(newunit = fileUnit, file = "setNegExpCDF.RK.txt")
        do i = 1, size(Point)
            do j = 1, size(CDF)
                CDF(j) = 0.
                if (Point(i) <= mu(j)) call setNegExpCDF(CDF(j), Point(i), mu(j), invSigma(j))
            end do
            write(fileUnit,"(*(g0,:,', '))") Point(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 ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the Cumulative Distribution Function (CDF) of Negative Exponential distribution at the specified values.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the CDF at an input scalar real value.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
call setNegExpCDF(CDF(1), x = -.5)
CDF(1)
+0.606530666
 
 
call setNegExpCDF(CDF(1), x = -.5, invSigma = 1.)
CDF(1)
+0.606530666
 
 
call setNegExpCDF(CDF(1), x = -.5, mu = 0., invSigma = 1.)
CDF(1)
+0.606530666
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the CDF at an input vector real value with different parameter values.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
call setNegExpCDF(CDF(1:3), x = -[.5, 1., 2.])
CDF(1:3)
+0.606530666, +0.367879450, +0.135335281
 
 
call setNegExpCDF(CDF(1:3), x = -[.5, 1., 2.], invSigma = [2., 1., .5])
CDF(1:3)
+0.367879450, +0.367879450, +0.367879450
 
 
call setNegExpCDF(CDF(1:3), x = -[5., 1., 2.], mu = [-1., 0., +1.], invSigma = 1.)
CDF(1:3)
+0.183156393E-1, +0.367879450, +0.497870669E-1
 
 

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
 
marker ={ "CK" : "-"
        , "IK" : "."
        , "RK" : "-"
        }
xlab =  { "CK" : "X ( real/imaginary components )"
        , "IK" : "X ( integer-valued )"
        , "RK" : "X ( real-valued )"
        }
legends =   [ r"$\mu = -2., invSigma = +2.$"
            , r"$\mu = +0., invSigma = +1.$"
            , r"$\mu = +2., invSigma = +.5$"
            ]
 
for kind in ["IK", "CK", "RK"]:
 
    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()
 
        if kind == "CK":
            plt.plot( df.values[:, 0]
                    , df.values[:,2]
                    , marker[kind]
                    , color = "r"
                    )
            plt.plot( df.values[:,1]
                    , df.values[:,3]
                    , marker[kind]
                    , color = "blue"
                    )
            ax.legend   ( ["real", "imaginary"]
                        , fontsize = fontsize
                        )
        else:
            plt.plot( df.values[:, 0]
                    , df.values[:,1:4]
                    , marker[kind]
                    )
        ax.legend   ( legends
                    , fontsize = fontsize - 5
                    )
 
        plt.xticks(fontsize = fontsize - 2)
        plt.yticks(fontsize = fontsize - 2)
        ax.set_xlabel(xlab[kind], fontsize = 17)
        ax.set_ylabel("Cumulative Distribution Function (CDF)", fontsize = 17)
 
        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")
 
        plt.savefig(fileList[0].replace(".txt",".png"))
 
    elif len(fileList) > 1:
 
        sys.exit("Ambiguous file list exists.")

Visualization of the example output ⛓

Test:

test_pm_distNegExp

Todo:

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

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 754 of file pm_distNegExp.F90.

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

• src/fortran/main/pm_distNegExp.F90