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...
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 ⛓
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.
- See also
- getNegExpRand
Example usage ⛓
10 integer(IK) ,
parameter :: NP
= 5_IK
11 real :: rand(NP,NP), UnifRand(NP,NP)
13 type(display_type) :: disp
17 call disp%show(
"call setUnifRand(UnifRand(1,1))")
19 call disp%show(
"call setNegExpRand(rand(1,1), UnifRand(1,1))")
26 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
27 call disp%show(
"! Generate a scalar real random number.")
28 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
31 call disp%show(
"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..")
40 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
41 call disp%show(
"! Generate a vector of real random numbers.")
42 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
45 call disp%show(
"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).")
53 call disp%show(
"call setNegExpRand(rand(:,1), UnifRand(:,1), sigma = 10.) ! random real vector with mean 10..")
60 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
61 call disp%show(
"! Generate a matrix of real random numbers.")
62 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
65 call disp%show(
"call setUnifRand(UnifRand)")
67 call disp%show(
"call setNegExpRand(rand, UnifRand) ! random matrix with the default Negative Exponential mean 1..")
73 call disp%show(
"call setUnifRand(UnifRand)")
75 call disp%show(
"call setNegExpRand(rand, UnifRand, sigma = 100.) ! random real vector with mean 100..")
82 integer :: fileUnit, i
83 real :: rand(
2), UnifRand(
2)
84 open(newunit
= fileUnit, file
= "setNegExpRand.RK.txt")
87 call setNegExpRand(rand, UnifRand, sigma
= [
3.,
2.], mu
= [
0.,
2.])
88 write(fileUnit,
"(2(g0,:,', '))") rand
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.
This is a generic method of the derived type display_type with pass attribute.
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...
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example Windows Batch compile command via Intel ifort
compiler ⛓
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example output ⛓
24-0.211218894,
-1.26994133,
-0.367250890E-1,
-0.105256706,
-0.385029882
28-2.11218882,
-12.6994133,
-0.367250890,
-1.05256701,
-3.85029888
38-1.23722541,
-1.58830237,
-0.225943580,
-0.125766620,
-0.833915025E-1
39-2.21887851,
-0.239219278,
-0.506664515,
-0.265766233,
-1.51896703
40-0.796975076,
-0.327081233E-1,
-0.468215942,
-3.38063312,
-1.36250365
41-2.03107142,
-0.776478171,
-0.440493412E-2,
-1.50323021,
-0.117614195
42-3.30969930,
-0.977683216E-1,
-0.913202822,
-3.91387939,
-2.23203349
47-38.5687637,
-75.2509689,
-214.603500,
-2.64045215,
-51.1450996
48-7.57232904,
-140.433167,
-8.15944672,
-49.6121178,
-0.594981790
49-110.778030,
-49.6635361,
-42.4721413,
-24.5701466,
-136.782211
50-171.428131,
-2.00855517,
-234.657974,
-62.6613159,
-246.140106
51-4.09265137,
-67.0322266,
-97.3456345,
-80.5629959,
-15.0108223
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
16xlab = {
"CK" :
"Random Value ( Real / Imaginary ))"
17 ,
"IK" :
"Random Value ( Integer )"
18 ,
"RK" :
"Random Value ( Real )"
20legends = [
r"$\sigma, \mu = 2., 2.$"
24for kind
in [
"IK",
"CK",
"RK"]:
26 pattern =
"*." + kind +
".txt"
27 fileList = glob.glob(pattern)
28 if len(fileList) == 1:
30 df = pd.read_csv(fileList[0], delimiter =
", ")
32 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
36 ax.hist ( df.values[:, 0]
38 , histtype =
"stepfilled"
42 ax.hist ( df.values[:, 1]
44 , histtype =
"stepfilled"
49 ax.hist ( df.values[:,0:2]
51 , histtype =
"stepfilled"
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)
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)
73 plt.savefig(fileList[0].replace(
".txt",
".png"))
75 elif len(fileList) > 1:
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.
-
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.
-
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 1139 of file pm_distNegExp.F90.