ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_distNegExp::setNegExpRand Interface Reference

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

Detailed Description

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

See the documentation of pm_distNegExp for more details.

Parameters
[out]rand: 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 random value(s) from the distribution.
[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 uniformly-distributed random value(s) with the range 0 <= urand < 1.
Such random value(s) can be readily obtained via the Fortran intrinsic procedure random_number() or via getUnifRand().
Supplying this argument 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 urand, 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 urand, 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

call setNegExpRand(rand, urand)
call setNegExpRand(rand, urand, sigma)
call setNegExpRand(rand, urand, sigma, mu)
Return a scalar (or array of arbitrary rank of) random value(s) from the Negative Exponential distrib...
This module contains classes and procedures for computing various statistical quantities related to t...
Warning
The condition 0 < sigma must hold for the corresponding input arguments.
The condition 0 <= urand < 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
getNegExpRand


Example usage

1program example
2
3 use pm_kind, only: SK, IK
4 use pm_io, only: display_type
6 use pm_distUnif, only: setUnifRand
7
8 implicit none
9
10 integer(IK) , parameter :: NP = 5_IK
11 real :: rand(NP,NP), UnifRand(NP,NP)
12
13 type(display_type) :: disp
14 disp = display_type(file = "main.out.F90")
15
16
17 call disp%show("call setUnifRand(UnifRand(1,1))")
18 call setUnifRand(UnifRand(1,1))
19 call disp%show("call setNegExpRand(rand(1,1), UnifRand(1,1))")
20 call setNegExpRand(rand(1,1), UnifRand(1,1))
21 call disp%show("rand(1,1)")
22 call disp%show( rand(1,1) )
23 call disp%skip()
24
25 call disp%skip()
26 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
27 call disp%show("! Generate a scalar real random number.")
28 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
29 call disp%skip()
30
31 call disp%show("call setUnifRand(UnifRand(1,1))")
32 call setUnifRand(UnifRand(1,1))
33 call disp%show("call setNegExpRand(rand(1,1), UnifRand(1,1), sigma = 2.) ! random real number with the Negative Exponential mean 2..")
34 call setNegExpRand(rand(1,1), UnifRand(1,1), sigma = 2.)
35 call disp%show("rand(1,1)")
36 call disp%show( rand(1,1) )
37 call disp%skip()
38
39 call disp%skip()
40 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
41 call disp%show("! Generate a vector of real random numbers.")
42 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
43 call disp%skip()
44
45 call disp%show("call setUnifRand(UnifRand(:,1))")
46 call setUnifRand(UnifRand(:,1))
47 call disp%show("call setNegExpRand(rand(:,1), UnifRand(:,1)) ! random real vector with the default Negative Exponential mean (1,1).")
48 call setNegExpRand(rand(:,1), UnifRand(:,1))
49 call disp%show("rand(:,1)")
50 call disp%show( rand(:,1) )
51 call disp%skip()
52
53 call disp%show("call setNegExpRand(rand(:,1), UnifRand(:,1), sigma = 10.) ! random real vector with mean 10..")
54 call setNegExpRand(rand(:,1), UnifRand(:,1), sigma = 10.)
55 call disp%show("rand(:,1)")
56 call disp%show( rand(:,1) )
57 call disp%skip()
58
59 call disp%skip()
60 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
61 call disp%show("! Generate a matrix of real random numbers.")
62 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
63 call disp%skip()
64
65 call disp%show("call setUnifRand(UnifRand)")
66 call setUnifRand(UnifRand)
67 call disp%show("call setNegExpRand(rand, UnifRand) ! random matrix with the default Negative Exponential mean 1..")
68 call setNegExpRand(rand, UnifRand)
69 call disp%show("rand")
70 call disp%show( rand )
71 call disp%skip()
72
73 call disp%show("call setUnifRand(UnifRand)")
74 call setUnifRand(UnifRand)
75 call disp%show("call setNegExpRand(rand, UnifRand, sigma = 100.) ! random real vector with mean 100..")
76 call setNegExpRand(rand, UnifRand, sigma = 100.)
77 call disp%show("rand")
78 call disp%show( rand )
79 call disp%skip()
80
81 block
82 integer :: fileUnit, i
83 real :: rand(2), UnifRand(2)
84 open(newunit = fileUnit, file = "setNegExpRand.RK.txt")
85 do i = 1, 1000
86 call setUnifRand(UnifRand)
87 call setNegExpRand(rand, UnifRand, sigma = [3., 2.], mu = [0., 2.])
88 write(fileUnit,"(2(g0,:,', '))") rand
89 end do
90 close(fileUnit)
91 end block
92
93end program example
Return a uniform random scalar or contiguous array of arbitrary rank of randomly uniformly distribute...
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508
This module contains classes and procedures for computing various statistical quantities related to t...
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler
1#!/usr/bin/env sh
2rm main.exe
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example Windows Batch compile command via Intel ifort compiler
1del main.exe
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler
1#!/usr/bin/env sh
2rm main.exe
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example output
1call setUnifRand(UnifRand(1,1))
2call setNegExpRand(rand(1,1), UnifRand(1,1))
3rand(1,1)
4-1.09794593
5
6
7!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
8! Generate a scalar real random number.
9!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
10
11call setUnifRand(UnifRand(1,1))
12call setNegExpRand(rand(1,1), UnifRand(1,1), sigma = 2.) ! random real number with the Negative Exponential mean 2..
13rand(1,1)
14-0.448050350
15
16
17!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
18! Generate a vector of real random numbers.
19!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
20
21call setUnifRand(UnifRand(:,1))
22call setNegExpRand(rand(:,1), UnifRand(:,1)) ! random real vector with the default Negative Exponential mean (1,1).
23rand(:,1)
24-1.52162027, -1.83445907, -2.86113453, -4.46776390, -0.294508278
25
26call setNegExpRand(rand(:,1), UnifRand(:,1), sigma = 10.) ! random real vector with mean 10..
27rand(:,1)
28-15.2162027, -18.3445911, -28.6113453, -44.6776390, -2.94508266
29
30
31!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
32! Generate a matrix of real random numbers.
33!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
34
35call setUnifRand(UnifRand)
36call setNegExpRand(rand, UnifRand) ! random matrix with the default Negative Exponential mean 1..
37rand
38-0.518573999, -0.522917733E-1, -0.628596663, -0.126085505, -0.231478050
39-0.304433644, -0.342581421, -0.641192913, -0.322895676, -0.781829655
40-1.38752198, -1.34395111, -0.955975115, -0.360046774, -1.92723393
41-0.769591749, -3.52962351, -0.418258071, -0.318158776, -0.818661094
42-3.01987481, -3.55651498, -0.334773004, -0.561813340E-1, -1.97906172
43
44call setUnifRand(UnifRand)
45call setNegExpRand(rand, UnifRand, sigma = 100.) ! random real vector with mean 100..
46rand
47-43.4835091, -33.1509399, -126.326324, -134.784012, -20.5806103
48-166.942566, -62.7924995, -100.445534, -158.372803, -54.2476768
49-88.2515717, -553.304443, -9.72706318, -45.1378365, -89.4859085
50-73.2710876, -76.1558380, -4.93615961, -214.761978, -13.6604700
51-64.8366241, -66.6357651, -123.942169, -29.4970570, -97.5288391
52
53

Postprocessing of the example output
1#!/usr/bin/env python
2
3import matplotlib.pyplot as plt
4import pandas as pd
5import numpy as np
6import glob
7import sys
8
9linewidth = 2
10fontsize = 17
11
12marker ={ "CK" : "-"
13 , "IK" : "."
14 , "RK" : "-"
15 }
16xlab = { "CK" : "Random Value ( Real / Imaginary ))"
17 , "IK" : "Random Value ( Integer )"
18 , "RK" : "Random Value ( Real )"
19 }
20legends = [ r"$\sigma, \mu = 2., 2.$"
21 , r"$\sigma = 3.$"
22 ]
23
24for kind in ["IK", "CK", "RK"]:
25
26 pattern = "*." + kind + ".txt"
27 fileList = glob.glob(pattern)
28 if len(fileList) == 1:
29
30 df = pd.read_csv(fileList[0], delimiter = ", ")
31
32 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
33 ax = plt.subplot()
34
35 if kind == "CK":
36 ax.hist ( df.values[:, 0]
37 , bins = 30
38 , histtype = "stepfilled"
39 , density = True
40 , alpha = 0.7
41 )
42 ax.hist ( df.values[:, 1]
43 , bins = 30
44 , histtype = "stepfilled"
45 , density = True
46 , alpha = 0.7
47 )
48 else:
49 ax.hist ( df.values[:,0:2]
50 , bins = 50
51 , histtype = "stepfilled"
52 , density = True
53 , alpha = 0.7
54 )
55 ax.legend ( legends
56 , fontsize = fontsize
57 )
58
59 plt.xticks(fontsize = fontsize - 2)
60 plt.yticks(fontsize = fontsize - 2)
61 ax.set_xlabel(xlab[kind], fontsize = 17)
62 ax.set_ylabel("Density", fontsize = 17)
63 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)
64 #ax.set_yscale("log")
65 #ax.set_xscale("log")
66
67 plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
68 ax.tick_params(axis = "y", which = "minor")
69 ax.tick_params(axis = "x", which = "minor")
70 ax.set_axisbelow(True)
71
72 plt.tight_layout()
73 plt.savefig(fileList[0].replace(".txt",".png"))
74
75 elif len(fileList) > 1:
76
77 sys.exit("Ambiguous file list exists.")

Visualization of the example output
Test:
test_pm_distNegExp
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


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.

Author:
Amir Shahmoradi, Oct 16, 2009, 11:14 AM, Michigan

Definition at line 1139 of file pm_distNegExp.F90.


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