pm_distLogUnif::setLogUnifLogRand Interface Reference

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

Detailed Description

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

See the documentation of pm_distLogUnif for more information on the LogUniform 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 urand, containing the natural logarithm of the randomly-generated value(s) from the specified distribution. By definition, the condition logMinX <= logRand < logMaxX holds.
[in]	urand	: 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 a random value from the standard Uniform distribution with support [0, 1). This argument can be readily obtained by calling getUnifRand(0., 1.) for the desired real kind.
[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 urand, containing the natural logarithm of the first scale parameter of the distribution, representing the minimum of the support of the distribution.
[in]	pdfnf	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as urand, containing the natural logarithm of the normalization factor of the PDF of the LogUniform distribution. Specifying this argument when calling this procedure repeatedly with fixed \((x_\mathrm{min}, x_\mathrm{max})\) parameters will significantly improve the runtime performance. This argument can be readily obtained by calling getLogUnifPDFNF(logMinX, logMaxX).

Possible calling interfaces ⛓

use pm_distLogUnif, only: setLogUnifLogRand
 
call setLogUnifLogRand(logRand, urand, logMinX, pdfnf)

Warning

The condition 0 <= urand <= 1 must hold for the corresponding input arguments.
This condition is 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

getLogUnifRand

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_io, only: display_type
    use pm_distUnif, only: getUnifRand
    use pm_distUnif, only: setUnifRand
    use pm_distLogUnif, only: getLogUnifPDFNF
    use pm_distLogUnif, only: setLogUnifLogRand
 
    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("! Generate random value(s) from the LogUniform distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setLogUnifLogRand(logx(1), urand = getUnifRand(0., 1.), logMinX = log(2.), pdfnf = getLogUnifPDFNF(logMinX = log(2.), logMaxX = log(5.)))")
                    call setLogUnifLogRand(logx(1), urand = getUnifRand(0., 1.), logMinX = log(2.), pdfnf = getLogUnifPDFNF(logMinX = log(2.), logMaxX = log(5.)))
    call disp%show("logx(1)")
    call disp%show( logx(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setLogUnifLogRand(logx(1:3), urand = getUnifRand(0., 1.), logMinX = log(2.), pdfnf = getLogUnifPDFNF(logMinX = log(2.), logMaxX = log(5.)))")
                    call setLogUnifLogRand(logx(1:3), urand = getUnifRand(0., 1.), logMinX = log(2.), pdfnf = getLogUnifPDFNF(logMinX = log(2.), logMaxX = log(5.)))
    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
        real :: logMinX(2), logMaxX(2), LogRand(2), UnifRand(2000)
        integer(IK) :: fileUnit, i
        call setUnifRand(UnifRand)
        logMinX = log([3., 2.0])
        logMaxX = log([7., 10.])
        open(newunit = fileUnit, file = "setLogUnifLogRand.RK.txt")
        do i = 1, size(UnifRand)
            call setLogUnifLogRand(LogRand, UnifRand(i), logMinX, getLogUnifPDFNF(logMinX, logMaxX))
            write(fileUnit, "(*(g0,:,', '))") exp(LogRand)
        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 ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Generate random value(s) from the LogUniform distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
call setLogUnifLogRand(logx(1), urand = getUnifRand(0., 1.), logMinX = log(2.), pdfnf = getLogUnifPDFNF(logMinX = log(2.), logMaxX = log(5.)))
logx(1)
+1.50923300
 
 
call setLogUnifLogRand(logx(1:3), urand = getUnifRand(0., 1.), logMinX = log(2.), pdfnf = getLogUnifPDFNF(logMinX = log(2.), logMaxX = log(5.)))
logx(1:3)
+0.862717390, +0.862717390, +0.862717390
 
 

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"$x_{min} = +3., x_{max} = +7.$"
            , r"$x_{min} = +2., x_{max} = +10.$"
            ]
 
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 = "stepfilled"
                    , density = True
                    , alpha = 0.7
                    )
            ax.hist ( df.values[:,1]
                    , bins = 30
                    , histtype = "stepfilled"
                    , density = True
                    , alpha = 0.7
                    )
        else:
            ax.hist ( df.values[:,:]
                    , bins = 50
                    , histtype = "stepfilled"
                    , density = True
                    , alpha = 0.7
                    )
            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_distLogUnif

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.
   
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.
   

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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 1291 of file pm_distLogUnif.F90.

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

• src/fortran/main/pm_distLogUnif.F90