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

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

See the documentation of pm_distPareto for more information on generating random numbers from the (Truncated) Pareto 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.
[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) Pareto 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 getParetoLogCDFNF(alpha, logMinX, logMaxX).
(optional, default = getParetoLogCDFNF(alpha, logMinX, logMaxX). If present, it implies a (Truncated) Pareto distribution.)


Possible calling interfaces

call setParetoLogRand(logRand, negExpRand, alpha, logMinX) ! Pareto distributed.
call setParetoLogRand(logRand, negExpRand, alpha, logMinX, logCDFNF) ! Truncated Pareto distributed.
!
Return a scalar (or array of arbitrary rank) of the natural logarithm(s) of random value(s) from the ...
This module contains classes and procedures for computing various statistical quantities related to t...
Warning
The condition alpha < 0 must hold for the corresponding input arguments.
The condition 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
getParetoLogRand


Example usage

1program example
2
3 use pm_kind, only: SK, IK, LK
7 use pm_io, only: display_type
8
9 implicit none
10
11 real :: logx(3)
12
13 type(display_type) :: disp
14 disp = display_type(file = "main.out.F90")
15
16 call disp%skip()
17 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
18 call disp%show("! Compute random value(s) from the Pareto distribution.")
19 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
20 call disp%skip()
21
22 call disp%skip()
23 call disp%show("call setParetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2.) ! Pareto distribution.")
24 call setParetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2.) ! Pareto distribution.
25 call disp%show("logx(1)")
26 call disp%show( logx(1) )
27 call disp%skip()
28
29 call disp%skip()
30 call disp%show("call setParetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2.) ! Pareto distribution.")
31 call setParetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2.) ! Pareto distribution.
32 call disp%show("logx(1:3)")
33 call disp%show( logx(1:3) )
34 call disp%skip()
35
36 call disp%skip()
37 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
38 call disp%show("! Compute random value(s) from the Truncated Pareto distribution.")
39 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
40 call disp%skip()
41
42 call disp%skip()
43 call disp%show("call setParetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2., logCDFNF = getParetoLogCDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.")
44 call setParetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2., logCDFNF = getParetoLogCDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.
45 call disp%show("logx(1)")
46 call disp%show( logx(1) )
47 call disp%skip()
48
49 call disp%skip()
50 call disp%show("call setParetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2., logCDFNF = getParetoLogCDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.")
51 call setParetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2., logCDFNF = getParetoLogCDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.
52 call disp%show("logx(1:3)")
53 call disp%show( logx(1:3) )
54 call disp%skip()
55
56 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
57 ! Output an example array for visualization.
58 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
59
60 block
61 use pm_arraySpace, only: setLinSpace
62 real :: alpha(3), logMinX(3), logMaxX(3), logx(3)
63 integer(IK) :: fileUnit, i
64 alpha = -[.5, 1., 10.]
65 logMinX = log([3., 1., 2.])
66 logMaxX = log([5., 4., huge(0.)])
67 open(newunit = fileUnit, file = "setParetoLogRand.RK.txt")
68 do i = 1, 2000_IK
69 call setParetoLogRand(logx(1:2), getNegExpRand([1., 1.]), alpha(1:2), logMinX(1:2), getParetoLogCDFNF(alpha(1:2), logMinX(1:2), logMaxX(1:2)))
70 call setParetoLogRand(logx(3), getNegExpRand(1.), alpha(3), logMinX(3), 0.)
71 write(fileUnit, "(*(g0,:,', '))") exp(logx)
72 end do
73 close(fileUnit)
74 end block
75
76end program example
Return the linSpace output argument with size(linSpace) elements of evenly-spaced values over the int...
Return a scalar (or array of arbitrary rank of) random value(s) from the Negative Exponential distrib...
Generate and return the natural logarithm of the normalization factor of the CDF of the (Truncated) P...
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 procedures and generic interfaces for generating arrays with linear or logarithm...
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 LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541
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
1
2!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3! Compute random value(s) from the Pareto distribution.
4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5
6
7call setParetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2.) ! Pareto distribution.
8logx(1)
9-1.51465178
10
11
12call setParetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2.) ! Pareto distribution.
13logx(1:3)
14-1.56825864, -1.95504391, -1.90944815
15
16
17!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
18! Compute random value(s) from the Truncated Pareto distribution.
19!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
20
21
22call setParetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2., logCDFNF = getParetoLogCDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.
23logx(1)
24-1.61313891
25
26
27call setParetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2., logCDFNF = getParetoLogCDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.
28logx(1:3)
29-1.72224069, -1.67550266, -1.55328679
30
31

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"$\alpha = -.5, x_{min} = +3., x_{max} = +5$"
21 , r"$\alpha = -1., x_{min} = +1., x_{max} = +4$"
22 , r"$\alpha = -10, x_{min} = +2., x_{max} = +\infty$"
23 ]
24
25for kind in ["IK", "CK", "RK"]:
26
27 pattern = "*." + kind + ".txt"
28 fileList = glob.glob(pattern)
29 if len(fileList) == 1:
30
31 df = pd.read_csv(fileList[0], delimiter = ", ")
32
33 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
34 ax = plt.subplot()
35
36 if kind == "CK":
37 ax.hist ( df.values[:, 0]
38 , bins = 30
39 , histtype = "stepfilled"
40 , density = True
41 , alpha = 0.7
42 )
43 ax.hist ( df.values[:, 1]
44 , bins = 30
45 , histtype = "stepfilled"
46 , density = True
47 , alpha = 0.7
48 )
49 else:
50 ax.hist ( df.values[:,:]
51 , bins = 50
52 , histtype = "stepfilled"
53 , density = True
54 , alpha = 0.7
55 )
56 ax.legend ( legends[::-1]
57 , fontsize = fontsize
58 )
59
60 plt.xticks(fontsize = fontsize - 2)
61 plt.yticks(fontsize = fontsize - 2)
62 ax.set_xlabel(xlab[kind], fontsize = 17)
63 ax.set_ylabel("Density", fontsize = 17)
64 ax.set_title("Histogram of {} randomly generated values".format(len(df.values)), fontsize = fontsize)
65 #ax.set_yscale("log")
66 #ax.set_xscale("log")
67
68 plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
69 ax.tick_params(axis = "y", which = "minor")
70 ax.tick_params(axis = "x", which = "minor")
71 ax.set_axisbelow(True)
72
73 plt.tight_layout()
74 plt.savefig(fileList[0].replace(".txt",".png"))
75
76 elif len(fileList) > 1:
77
78 sys.exit("Ambiguous file list exists.")

Visualization of the example output
Test:
test_pm_distPareto
Todo:
Critical 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.

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

Definition at line 1925 of file pm_distPareto.F90.


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