pm_distPoweto::setPowetoLogRand Interface Reference

Return a scalar (or array of arbitrary rank) of the natural logarithm(s) of random value(s) from the (Truncated) Poweto distribution with parameters \((\alpha, x_\mathrm{min}, x_\mathrm{max})\). More...

Detailed Description

Return a scalar (or array of arbitrary rank) of the natural logarithm(s) of random value(s) from the (Truncated) Poweto distribution with parameters \((\alpha, x_\mathrm{min}, x_\mathrm{max})\).

See the documentation of pm_distPoweto for more information on generating random numbers from the (Truncated) Poweto distribution.

Parameters

[out]	logRand	: The output scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha, containing the random value(s) from the specified distribution.
[in]	negExpRand	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha, containing a random value from the standard Negative Exponential distribution ( \(\mu = 0, \sigma = 1.\)). This argument can be readily obtained by calling getNegExpRand(sigma = 1.).
[in]	alpha	: 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 shape parameter ( \(\alpha\)) of the distribution.
[in]	logMinX	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha, containing the natural logarithm of the first scale parameter of the distribution, representing the minimum of the support of the distribution. (optional, default = \(-\infty\). It can be present if and only if logCDFNF is also present.)
[in]	logCDFNF	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha, containing the natural logarithm of the normalization factor of the CDF of the (Truncated) Poweto distribution. Specifying this argument when calling this procedure repeatedly with fixed \((\alpha, x_\mathrm{min}, x_\mathrm{max})\) parameters will significantly improve the runtime performance. This argument can be readily obtained by calling getPowetoLogCDFNF(alpha, logMinX, logMaxX). (optional, default = getPowetoLogCDFNF(alpha, logMinX). It must be present if \(0 \leq \alpha\) holds.)

Possible calling interfaces ⛓

use pm_distPoweto, only: setPowetoLogRand
 
call setPowetoLogRand(logRand, negExpRand, alpha, logMinX = logMinX, logCDFNF = logCDFNF)
!

Warning

The condition 0 < alpha .or. present(logMinX) must hold for the corresponding input arguments.
The condition alpha < 0 .or. present(logMaxX) must hold for the corresponding input arguments.
The conditions logMinX < logMaxX must hold for the corresponding input arguments.
The conditions negExpRand <= 0. 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

getPowetoLogRand

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_distPoweto, only: getPowetoLogCDFNF
    use pm_distPoweto, only: setPowetoLogRand
    use pm_distNegExp, only: getNegExpRand
    use pm_io, only: display_type
 
    implicit none
 
    real                    :: logx(3)
 
    type(display_type)      :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute random value(s) from the Poweto distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setPowetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2.) ! Poweto distribution.")
                    call setPowetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2.) ! Poweto distribution.
    call disp%show("logx(1)")
    call disp%show( logx(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setPowetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2.) ! Poweto distribution.")
                    call setPowetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2.) ! Poweto distribution.
    call disp%show("logx(1:3)")
    call disp%show( logx(1:3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setPowetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = +2., logCDFNF = getPowetoLogCDFNF(alpha = +2., logMaxX = -2.)) ! Poweto distribution.")
                    call setPowetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = +2., logCDFNF = getPowetoLogCDFNF(alpha = +2., logMaxX = -2.)) ! Poweto distribution.
    call disp%show("logx(1)")
    call disp%show( logx(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setPowetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = [+2., +3., +4.], logCDFNF = getPowetoLogCDFNF(alpha = [+2., +3., +4.], logMaxX = -2.)) ! Poweto distribution.")
                    call setPowetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = [+2., +3., +4.], logCDFNF = getPowetoLogCDFNF(alpha = [+2., +3., +4.], logMaxX = -2.)) ! Poweto distribution.
    call disp%show("logx(1:3)")
    call disp%show( logx(1:3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute random value(s) from the Truncated Poweto distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setPowetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.")
                    call setPowetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
    call disp%show("logx(1)")
    call disp%show( logx(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setPowetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.")
                    call setPowetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
    call disp%show("logx(1:3)")
    call disp%show( logx(1:3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setPowetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = +2., logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = +2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.")
                    call setPowetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = +2., logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = +2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
    call disp%show("logx(1)")
    call disp%show( logx(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setPowetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = +[+2., +3., +4.], logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = +[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.")
                    call setPowetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = +[+2., +3., +4.], logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = +[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
    call disp%show("logx(1:3)")
    call disp%show( logx(1:3) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        use pm_arraySpace, only: setLinSpace
        use pm_arrayResize, only: setResized
        use pm_arrayRefill, only: setRefilled
        real, allocatable :: alpha(:), logx(:), sigma(:)
        real :: logMinX, logMaxX
        integer(IK) :: fileUnit, i
        alpha = [-2.0, -1., 0., +1., +2.]
        call setRefilled(sigma, 1., size(alpha, 1, IK))
        call setResized(logx, size(alpha, 1, IK))
        logMinX = log(3.)
        logMaxX = log(8.)
        open(newunit = fileUnit, file = "setPowetoLogRand.RK.txt")
        do i = 1, 2000
            call setPowetoLogRand(logx, getNegExpRand(1.), alpha, logMinX, getPowetoLogCDFNF(alpha, logMinX, logMaxX))
            write(fileUnit, "(*(g0,:,', '))") exp(logx)
        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 random value(s) from the Poweto distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
call setPowetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2.) ! Poweto distribution.
logx(1)
-1.68862128
 
 
call setPowetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2.) ! Poweto distribution.
logx(1:3)
-1.79726696, -1.45848942, -1.95481551
 
 
call setPowetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = +2., logCDFNF = getPowetoLogCDFNF(alpha = +2., logMaxX = -2.)) ! Poweto distribution.
logx(1)
-2.00723505
 
 
call setPowetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = [+2., +3., +4.], logCDFNF = getPowetoLogCDFNF(alpha = [+2., +3., +4.], logMaxX = -2.)) ! Poweto distribution.
logx(1:3)
-2.17782259, -2.28644991, -2.16453886
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute random value(s) from the Truncated Poweto distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
call setPowetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
logx(1)
-1.97997415
 
 
call setPowetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
logx(1:3)
-1.76483643, -1.88575745, -1.87818265
 
 
call setPowetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = +2., logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = +2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
logx(1)
+3.89004993
 
 
call setPowetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = +[+2., +3., +4.], logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = +[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
logx(1:3)
+3.68919134, +4.98029566, +4.78703690
 
 

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
 
linewidth = 2
fontsize = 17
 
marker ={ "CK" : "-"
        , "IK" : "."
        , "RK" : "-"
        }
xlab =  { "CK" : "Random Value ( Real / Imaginary ))"
        , "IK" : "Random Value ( Integer )"
        , "RK" : "Random Value ( Real )"
        }
legends =   [ r"$\alpha = -2., x_{min} = +3., x_{max} = +8$"
            , r"$\alpha = -1., x_{min} = +3., x_{max} = +8$"
            , r"$\alpha = 0.0, x_{min} = +3., x_{max} = +8$"
            , r"$\alpha = +1., x_{min} = +3., x_{max} = +8$"
            , r"$\alpha = +2., x_{min} = +3., x_{max} = +8$"
            ]
 
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":
            ax.hist ( df.values[:, 0]
                    , bins = 30
                    , histtype = "step"
                    , density = True
                    , alpha = 1
                    )
            ax.hist ( df.values[:, 1]
                    , bins = 30
                    , histtype = "step"
                    , density = True
                    , alpha = 1
                    )
        else:
            ax.hist ( df.values[:,:]
                    , bins = 50
                    , histtype = "step"
                    , density = True
                    , alpha = 1
                    )
            ax.legend   ( legends[::-1]
                        , fontsize = fontsize
                        )
 
        plt.xticks(fontsize = fontsize - 2)
        plt.yticks(fontsize = fontsize - 2)
        ax.set_xlabel(xlab[kind], fontsize = 17)
        ax.set_ylabel("Density", fontsize = 17)
        ax.set_title("Histogram of {} randomly generated values".format(len(df.values)), fontsize = fontsize)
        #ax.set_yscale("log")
        #ax.set_xscale("log")
 
        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.set_axisbelow(True)
 
        plt.tight_layout()
        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_distPoweto

Todo:

Low Priority: This interface can be extended to support vector-like logRand arguments other than the elemental approach.
Such an extension would be sensible only if the new interface improves the performance against the elemental approach.

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 1445 of file pm_distPoweto.F90.

---

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

• src/fortran/main/pm_distPoweto.F90