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

Return the natural logarithm of the Probability Density Function (PDF) of the (Truncated) Pareto distribution for an input log(x) within the support of the distribution \(x \in [0 < x_\mathrm{min}, x_\mathrm{max} < +\infty]\). More...

Detailed Description

Return the natural logarithm of the Probability Density Function (PDF) of the (Truncated) Pareto distribution for an input log(x) within the support of the distribution \(x \in [0 < x_\mathrm{min}, x_\mathrm{max} < +\infty]\).

See the documentation of pm_distPareto for more information on the (Truncated) Pareto distribution.

Parameters
[out]logPDF: The output scalar or array of the same shape as any input array-like argument, of the same type and kind the input argument x, containing the natural logarithm of the PDF of the distribution.
[in]logx: The input scalar or array of the same shape as other array like arguments, of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the natural logarithm of the value at which the PDF must be computed.
[in]alpha: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as logx, containing the shape parameter of the distribution.
[in]logPDFNF: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as logx, containing the natural logarithm of the normalization factor of the PDF 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 getParetoLogPDFNF(alpha, logMinX, logMaxX).


Possible calling interfaces

call setParetoLogPDF(logPDF, logx, alpha, logPDFNF)
Return the natural logarithm of the Probability Density Function (PDF) of the (Truncated) Pareto dist...
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.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.
Be warned that the procedures under this generic interface have no mechanism for checking for the consistency of the specified input arguments with each other.
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
setParetoLogPDF


Example usage

1program example
2
3 use pm_kind, only: SK, IK, LK
6 use pm_io, only: display_type
7
8 implicit none
9
10 real :: logPDF(3)
11
12 type(display_type) :: disp
13 disp = display_type(file = "main.out.F90")
14
15 call disp%skip()
16 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
17 call disp%show("! Compute the Probability Density Function (PDF) of the Pareto distribution.")
18 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
19 call disp%skip()
20
21 call disp%skip()
22 call disp%show("call setParetoLogPDF(logPDF(1), logx = 3., alpha = -2., logPDFNF = getParetoLogPDFNF(alpha = -2., logMinX = -2.)) ! Pareto distribution.")
23 call setParetoLogPDF(logPDF(1), logx = 3., alpha = -2., logPDFNF = getParetoLogPDFNF(alpha = -2., logMinX = -2.)) ! Pareto distribution.
24 call disp%show("logPDF(1)")
25 call disp%show( logPDF(1) )
26 call disp%skip()
27
28 call disp%skip()
29 call disp%show("call setParetoLogPDF(logPDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logPDFNF = getParetoLogPDFNF(alpha = -[+2., +3., +4.], logMinX = -2.)) ! Pareto distribution.")
30 call setParetoLogPDF(logPDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logPDFNF = getParetoLogPDFNF(alpha = -[+2., +3., +4.], logMinX = -2.)) ! Pareto distribution.
31 call disp%show("logPDF(1:3)")
32 call disp%show( logPDF(1:3) )
33 call disp%skip()
34
35 call disp%skip()
36 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
37 call disp%show("! Compute the Probability Density Function (PDF) of the Truncated Pareto distribution.")
38 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
39 call disp%skip()
40
41 call disp%skip()
42 call disp%show("call setParetoLogPDF(logPDF(1), logx = 3., alpha = -2., logPDFNF = getParetoLogPDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.")
43 call setParetoLogPDF(logPDF(1), logx = 3., alpha = -2., logPDFNF = getParetoLogPDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.
44 call disp%show("logPDF(1)")
45 call disp%show( logPDF(1) )
46 call disp%skip()
47
48 call disp%skip()
49 call disp%show("call setParetoLogPDF(logPDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logPDFNF = getParetoLogPDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.")
50 call setParetoLogPDF(logPDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logPDFNF = getParetoLogPDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.
51 call disp%show("logPDF(1:3)")
52 call disp%show( logPDF(1:3) )
53 call disp%skip()
54
55 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
56 ! Output an example logPDF array for visualization.
57 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
58
59 block
60 use pm_arraySpace, only: setLinSpace
61 real :: alpha(2), logMinX, logMaxX, logPDF(4), logx(2000)
62 integer(IK) :: fileUnit, i
63 call setLinSpace(logx, x1 = log(0.1), x2 = log(10.))
64 alpha = -[+0.5, +2.0]
65 logMinX = log(3.)
66 logMaxX = log(8.)
67 open(newunit = fileUnit, file = "setParetoLogPDF.RK.txt")
68 do i = 1, size(logx, 1, IK)
69 logPDF = -huge(0.)
70 if (logMinX <= logx(i)) then
71 call setParetoLogPDF(logPDF(1:2), logx(i), alpha, getParetoLogPDFNF(alpha, logMinX))
72 if (logx(i) <= logMaxX) call setParetoLogPDF(logPDF(3:4), logx(i), alpha, getParetoLogPDFNF(alpha, logMinX, logMaxX))
73 end if
74 write(fileUnit, "(*(g0,:,', '))") exp(logx(i)), exp(logPDF)
75 end do
76 close(fileUnit)
77 end block
78
79end program example
Return the linSpace output argument with size(linSpace) elements of evenly-spaced values over the int...
Generate and return the natural logarithm of the normalization factor of the PDF 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 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 the Probability Density Function (PDF) of the Pareto distribution.
4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5
6
7call setParetoLogPDF(logPDF(1), logx = 3., alpha = -2., logPDFNF = getParetoLogPDFNF(alpha = -2., logMinX = -2.)) ! Pareto distribution.
8logPDF(1)
9-12.3068523
10
11
12call setParetoLogPDF(logPDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logPDFNF = getParetoLogPDFNF(alpha = -[+2., +3., +4.], logMinX = -2.)) ! Pareto distribution.
13logPDF(1:3)
14-12.3068523, -20.9013882, -31.6137047
15
16
17!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
18! Compute the Probability Density Function (PDF) of the Truncated Pareto distribution.
19!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
20
21
22call setParetoLogPDF(logPDF(1), logx = 3., alpha = -2., logPDFNF = getParetoLogPDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.
23logPDF(1)
24-12.3068523
25
26
27call setParetoLogPDF(logPDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logPDFNF = getParetoLogPDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.
28logPDF(1:3)
29-12.3068523, -20.9013882, -31.6137047
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" : "X ( real/imaginary components )"
17 , "IK" : "X ( integer-valued )"
18 , "RK" : "X ( real-valued )"
19 }
20legends = [ r"$\alpha = -.5, x_{min} = +3., x_{max} = +\infty$"
21 , r"$\alpha = -2., x_{min} = +3., x_{max} = +\infty$"
22 , r"$\alpha = -.5, x_{min} = +3., x_{max} = +8$"
23 , r"$\alpha = -2., x_{min} = +3., x_{max} = +8$"
24 ]
25
26for kind in ["IK", "CK", "RK"]:
27
28 pattern = "*." + kind + ".txt"
29 fileList = glob.glob(pattern)
30 if len(fileList) == 1:
31
32 df = pd.read_csv(fileList[0], delimiter = ", ")
33
34 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
35 ax = plt.subplot()
36
37 if kind == "CK":
38 plt.plot( df.values[:, 0]
39 , df.values[:,1:5]
40 , marker[kind]
41 , linewidth = linewidth
42 #, color = "r"
43 )
44 plt.plot( df.values[:, 1]
45 , df.values[:,1:5]
46 , marker[kind]
47 , linewidth = linewidth
48 #, color = "blue"
49 )
50 else:
51 plt.plot( df.values[:, 0]
52 , df.values[:,1:5]
53 , marker[kind]
54 , linewidth = linewidth
55 #, color = "r"
56 )
57 ax.legend ( legends
58 , fontsize = fontsize - 5
59 )
60
61 plt.xticks(fontsize = fontsize - 2)
62 plt.yticks(fontsize = fontsize - 2)
63 ax.set_xlabel(xlab[kind], fontsize = 17)
64 ax.set_ylabel("Probability Density Function (PDF)", fontsize = 17)
65 #ax.set_xscale("log")
66 #ax.set_yscale("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
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_distPareto
Todo:
Very Low Priority: This generic interface can be extended to complex arguments.


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 642 of file pm_distPareto.F90.


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