pm_distExp::setExpRand Interface Reference

Return a scalar (or array of arbitrary rank of) random value(s) from the Exponential distribution, optionally with the specified input location and scale parameters mu, sigma.
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Detailed Description

Return a scalar (or array of arbitrary rank of) random value(s) from the Exponential distribution, optionally with the specified input location and scale parameters mu, sigma.

See the documentation of pm_distExp for more details.

Parameters

[in,out]	rand	: The input/output 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), that, must contain uniformly-distributed random value(s) in range \([0, 1)\) on input, and will contain exponentially-distributed random value(s) in range \([0, +\infty)\) on output. The uniformly-distributed random value(s) can be readily obtained via the Fortran intrinsic procedure random_number() or, via getUnifRand(). Supplying this argument as an input ensures the purity of the procedures, allowing further compiler optimizations.
[in]	sigma	: The input scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as rand, representing the scale parameter of the distribution. (optional, default = 1..)
[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 rand, representing the location parameter of the distribution. (optional, default = 0. It can be present if and only if sigma is also present.)

Possible calling interfaces ⛓

use pm_distExp, only: setExpRand
 
call setExpRand(rand)
call setExpRand(rand, sigma)
call setExpRand(rand, sigma, mu)

Warning

The condition 0 < sigma must hold for the corresponding input arguments.
The condition 0 <= rand < 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

getExpRand

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK
    use pm_io, only: display_type
    use pm_distExp, only: setExpRand
    use pm_distUnif, only: setUnifRand
 
    implicit none
 
    integer(IK) , parameter :: NP = 5_IK
    real :: rand(NP,NP)
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
 
    call disp%show("call setUnifRand(rand(1,1))")
                    call setUnifRand(rand(1,1))
    call disp%show("call setExpRand(rand(1,1))")
                    call setExpRand(rand(1,1))
    call disp%show("rand(1,1)")
    call disp%show( rand(1,1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Generate a scalar real random number.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%show("call setUnifRand(rand(1,1))")
                    call setUnifRand(rand(1,1))
    call disp%show("call setExpRand(rand(1,1), sigma = 2.) ! random real number with the Exponential mean 2..")
                    call setExpRand(rand(1,1), sigma = 2.)
    call disp%show("rand(1,1)")
    call disp%show( rand(1,1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Generate a vector of real random numbers.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%show("call setUnifRand(rand(:,1))")
                    call setUnifRand(rand(:,1))
    call disp%show("call setExpRand(rand(:,1)) ! random real vector with the default Exponential mean (1,1).")
                    call setExpRand(rand(:,1))
    call disp%show("rand(:,1)")
    call disp%show( rand(:,1) )
    call disp%skip()
 
    call disp%show("call setUnifRand(rand(:,1))")
                    call setUnifRand(rand(:,1))
    call disp%show("call setExpRand(rand(:,1), sigma = 10.) ! random real vector with mean 10..")
                    call setExpRand(rand(:,1), sigma = 10.)
    call disp%show("rand(:,1)")
    call disp%show( rand(:,1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Generate a matrix of real random numbers.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%show("call setUnifRand(rand)")
                    call setUnifRand(rand)
    call disp%show("call setExpRand(rand) ! random matrix with the default Exponential mean 1..")
                    call setExpRand(rand)
    call disp%show("rand")
    call disp%show( rand )
    call disp%skip()
 
    call disp%show("call setUnifRand(rand)")
                    call setUnifRand(rand)
    call disp%show("call setExpRand(rand, sigma = 100.) ! random real vector with mean 100..")
                    call setExpRand(rand, sigma = 100.)
    call disp%show("rand")
    call disp%show( rand )
    call disp%skip()
 
    block
        integer :: fileUnit, i
        real :: rand(2)
        open(newunit = fileUnit, file = "setExpRand.RK.txt")
        do i = 1, 1000
            call setUnifRand(rand)
            call setExpRand(rand, sigma = [3., 2.], mu = [0., 2.])
            write(fileUnit,"(2(g0,:,', '))") rand
        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 setUnifRand(rand(1,1))
call setExpRand(rand(1,1))
rand(1,1)
+0.251435816
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Generate a scalar real random number.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
call setUnifRand(rand(1,1))
call setExpRand(rand(1,1), sigma = 2.) ! random real number with the Exponential mean 2..
rand(1,1)
+3.86267900
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Generate a vector of real random numbers.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
call setUnifRand(rand(:,1))
call setExpRand(rand(:,1)) ! random real vector with the default Exponential mean (1,1).
rand(:,1)
+0.552730821E-1, +3.93697023, +0.421984613, +0.864686728, +0.738922477
 
call setUnifRand(rand(:,1))
call setExpRand(rand(:,1), sigma = 10.) ! random real vector with mean 10..
rand(:,1)
+11.0956306, +18.1514454, +20.0629902, +23.4371872, +7.77758503
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Generate a matrix of real random numbers.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
call setUnifRand(rand)
call setExpRand(rand) ! random matrix with the default Exponential mean 1..
rand
+0.899216413, +2.62834001, +0.573873073E-1, +0.321793169, +0.404808074
+2.64986062, +0.577117980, +0.101723067, +0.104271762, +0.165630266
+0.317576170, +3.60960054, +0.329711348, +1.82449853, +0.157025144
+0.648605973E-1, +0.137604848, +2.29776311, +0.103087291, +2.29863787
+0.836691558, +0.534402609, +0.244067505, +1.87467337, +3.00282621
 
call setUnifRand(rand)
call setExpRand(rand, sigma = 100.) ! random real vector with mean 100..
rand
+15.1922550, +100.378540, +31.0162067, +10.2884789, +149.706528
+32.8152275, +165.936783, +73.0224991, +13.9237747, +6.38782883
+2.70236850, +0.540984035, +255.904465, +59.2662621, +28.0014763
+150.235168, +66.6014328, +0.625269338E-1, +201.909302, +110.492279
+53.3583527, +104.062950, +130.024673, +192.447845, +33.1473427
 
 

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"$\sigma, \mu = 2., 2.$"
            , r"$\sigma = 3.$"
            ]
 
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[:,0:2]
                    , bins = 50
                    , histtype = "stepfilled"
                    , density = True
                    , alpha = 0.7
                    )
            ax.legend   ( legends
                        , 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 {} Exponential random numbers\nMean = {}".format(len(df.values), np.round(np.mean(np.double(df.values), axis = 0), 2)), 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_distExp

Todo:

Critical Priority: The Intel ifort bug (described below) appears to have been resolved in ifort 2021.4.
Therefore, once TACC and other relevant supercomputers have ifort >=2021.4 installed, the bug workaround must be resolved.

Bug:

Status: possibly Resolved in Intel Classic Fortran Compiler ifort version 2021.4
Source: Intel Classic Fortran Compiler ifort version 2021.2
Description: The Intel Classic Fortran Compiler ifort version 2021.2 yields an ICE for passing complex components to random_number() or log().
This appears to have been fixed in Intel Classic Fortran Compiler ifort version 2021.4.

Remedy (as of ParaMonte Library version 1.5): For now, the implementations are kept separately, since the installation of the new Intel Classic Fortran Compiler ifort versions on supercomputers often lags.

Remedy (as of ParaMonte Library version Oct, 2022): The complex interface of the routines is now deprecated and removed.

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, Oct 16, 2009, 11:14 AM, Michigan

Definition at line 1177 of file pm_distExp.F90.

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

• src/fortran/main/pm_distExp.F90