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

Return the natural logarithm of the Cumulative Distribution Function (CDF) of the (Truncated) Poweto distribution for an input logx within the support of the distribution \(x \in [0 < x_\mathrm{min}, x_\mathrm{max} < +\infty]\).
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Detailed Description

Return the natural logarithm of the Cumulative Distribution Function (CDF) of the (Truncated) Poweto distribution for an input logx within the support of the distribution \(x \in [0 < x_\mathrm{min}, x_\mathrm{max} < +\infty]\).

See the documentation of pm_distPoweto for more information on the (Truncated) Poweto distribution.

Parameters
[out]logCDF: The output scalar of the same type and kind the input argument logx, containing the natural logarithm of the CDF 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 x value within the support of the distribution at which the CDF 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 (i.e., the exponent of the power-law function).
[in]logMinX: The input scalar (or array of the same shape 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.
(optional, default = \(-\infty\). It must be present if \(\alpha \leq 0\) holds.)
[in]logCDFNF: The input scalar (or array of the same shape as other array-like arguments) of the same type, kind as logx, containing the natural logarithm of the normalization factor ( \(\eta\)) of power-law function of the (Truncated) Poweto distribution.
Specifying this argument when calling this procedure repeatedly with fixed \((\alpha, x_\mathrm{min}, x_\mathrm{max})\) parameters significantly improves the runtime performance.
(optional, default = getPowetoLogCDFNF(alpha, logMinX). It must be present if \(0 \leq \alpha\) holds.)


Possible calling interfaces

call setPowetoLogCDF(logCDF, logx, alpha, logMinX = logMinX, logCDFNF = logCDFNF)
Return the natural logarithm of the Cumulative Distribution Function (CDF) of the (Truncated) Poweto ...
This module contains classes and procedures for computing various statistical quantities related to t...
Warning
The condition 0 < alpha .or. present(logMinX) must hold for the corresponding input arguments.
The condition alpha < 0 .or. present(logCDFNF) must hold for the corresponding input arguments.
The conditions logMinX <= logx 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
getPowetoLogCDF


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 :: logCDF(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 Cumulative Distribution Function (CDF) of the Poweto distribution.")
18 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
19 call disp%skip()
20
21 call disp%skip()
22 call disp%show("call setPowetoLogCDF(logCDF(1), logx = 3., alpha = -2., logMinX = -2.) ! Poweto distribution.")
23 call setPowetoLogCDF(logCDF(1), logx = 3., alpha = -2., logMinX = -2.) ! Poweto distribution.
24 call disp%show("logCDF(1)")
25 call disp%show( logCDF(1) )
26 call disp%skip()
27
28 call disp%skip()
29 call disp%show("call setPowetoLogCDF(logCDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logMinX = -2.) ! Poweto distribution.")
30 call setPowetoLogCDF(logCDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logMinX = -2.) ! Poweto distribution.
31 call disp%show("logCDF(1:3)")
32 call disp%show( logCDF(1:3) )
33 call disp%skip()
34
35 call disp%skip()
36 call disp%show("call setPowetoLogCDF(logCDF(1), logx = 3., alpha = +2., logCDFNF = getPowetoLogCDFNF(alpha = +2., logMaxX = 5.)) ! Poweto distribution.")
37 call setPowetoLogCDF(logCDF(1), logx = 3., alpha = +2., logCDFNF = getPowetoLogCDFNF(alpha = +2., logMaxX = 5.)) ! Poweto distribution.
38 call disp%show("logCDF(1)")
39 call disp%show( logCDF(1) )
40 call disp%skip()
41
42 call disp%skip()
43 call disp%show("call setPowetoLogCDF(logCDF(1:3), logx = [3., 4., 5.], alpha = [+2., +3., +4.], logCDFNF = getPowetoLogCDFNF(alpha = [+2., +3., +4.], logMaxX = 5.)) ! Poweto distribution.")
44 call setPowetoLogCDF(logCDF(1:3), logx = [3., 4., 5.], alpha = [+2., +3., +4.], logCDFNF = getPowetoLogCDFNF(alpha = [+2., +3., +4.], logMaxX = 5.)) ! Poweto distribution.
45 call disp%show("logCDF(1:3)")
46 call disp%show( logCDF(1:3) )
47 call disp%skip()
48
49 call disp%skip()
50 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
51 call disp%show("! Compute the Cumulative Distribution Function (CDF) of the Truncated Poweto distribution.")
52 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
53 call disp%skip()
54
55 call disp%skip()
56 call disp%show("call setPowetoLogCDF(logCDF(1), logx = 3., alpha = -2., logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.")
57 call setPowetoLogCDF(logCDF(1), logx = 3., alpha = -2., logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
58 call disp%show("logCDF(1)")
59 call disp%show( logCDF(1) )
60 call disp%skip()
61
62 call disp%skip()
63 call disp%show("call setPowetoLogCDF(logCDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.")
64 call setPowetoLogCDF(logCDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
65 call disp%show("logCDF(1:3)")
66 call disp%show( logCDF(1:3) )
67 call disp%skip()
68
69 call disp%skip()
70 call disp%show("call setPowetoLogCDF(logCDF(1), logx = 3., alpha = +2., logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = +2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.")
71 call setPowetoLogCDF(logCDF(1), logx = 3., alpha = +2., logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = +2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
72 call disp%show("logCDF(1)")
73 call disp%show( logCDF(1) )
74 call disp%skip()
75
76 call disp%skip()
77 call disp%show("call setPowetoLogCDF(logCDF(1:3), logx = [3., 4., 5.], alpha = [+2., +3., +4.], logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = [+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.")
78 call setPowetoLogCDF(logCDF(1:3), logx = [3., 4., 5.], alpha = [+2., +3., +4.], logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = [+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
79 call disp%show("logCDF(1:3)")
80 call disp%show( logCDF(1:3) )
81 call disp%skip()
82
83 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
84 ! Output an example array for visualization.
85 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
86
87 block
88 use pm_arraySpace, only: setLinSpace
89 use pm_arrayResize, only: setResized
90 real, allocatable :: alpha(:), logCDF(:)
91 real :: logMinX, logMaxX, logx(2000)
92 integer(IK) :: fileUnit, i
93 alpha = [-2.0, -1., 0., +1., +2.]
94 call setLinSpace(logx, x1 = log(0.1), x2 = log(10.))
95 call setResized(logCDF, size(alpha, 1, IK))
96 logMinX = log(3.)
97 logMaxX = log(8.)
98 open(newunit = fileUnit, file = "setPowetoLogCDF.RK.txt")
99 do i = 1, size(logx, 1, IK)
100 if (logx(i) < logMinX) then
101 logCDF = -huge(0.)
102 elseif (logx(i) < logMaxX) then
103 call setPowetoLogCDF(logCDF, logx(i), alpha, logMinX, getPowetoLogCDFNF(alpha, logMinX, logMaxX))
104 else
105 logCDF = 0.
106 end if
107 write(fileUnit, "(*(g0,:,', '))") exp(logx(i)), exp(logCDF)
108 end do
109 close(fileUnit)
110 end block
111
112end program example
Allocate or resize (shrink or expand) an input allocatable scalar string or array of rank 1....
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 Cumulative Distribution ...
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 resizing allocatable arrays of various typ...
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 Cumulative Distribution Function (CDF) of the Poweto distribution.
4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5
6
7call setPowetoLogCDF(logCDF(1), logx = 3., alpha = -2., logMinX = -2.) ! Poweto distribution.
8logCDF(1)
9-0.454197725E-4
10
11
12call setPowetoLogCDF(logCDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logMinX = -2.) ! Poweto distribution.
13logCDF(1:3)
14-0.454197725E-4, +0.00000000, +0.00000000
15
16
17call setPowetoLogCDF(logCDF(1), logx = 3., alpha = +2., logCDFNF = getPowetoLogCDFNF(alpha = +2., logMaxX = 5.)) ! Poweto distribution.
18logCDF(1)
19-4.00000000
20
21
22call setPowetoLogCDF(logCDF(1:3), logx = [3., 4., 5.], alpha = [+2., +3., +4.], logCDFNF = getPowetoLogCDFNF(alpha = [+2., +3., +4.], logMaxX = 5.)) ! Poweto distribution.
23logCDF(1:3)
24-4.00000000, -3.00000000, +0.00000000
25
26
27!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
28! Compute the Cumulative Distribution Function (CDF) of the Truncated Poweto distribution.
29!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
30
31
32call setPowetoLogCDF(logCDF(1), logx = 3., alpha = -2., logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
33logCDF(1)
34-0.444660982E-4
35
36
37call setPowetoLogCDF(logCDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
38logCDF(1:3)
39-0.444660982E-4, +0.00000000, +0.00000000
40
41
42call setPowetoLogCDF(logCDF(1), logx = 3., alpha = +2., logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = +2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
43logCDF(1)
44-4.00004482
45
46
47call setPowetoLogCDF(logCDF(1:3), logx = [3., 4., 5.], alpha = [+2., +3., +4.], logMinX = -2., logCDFNF = getPowetoLogCDFNF(alpha = [+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.
48logCDF(1:3)
49-4.00004482, -3.00000000, +0.00000000
50
51

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"$\alpha = -2., x_{min} = +3., x_{max} = +8$"
21 , r"$\alpha = -1., x_{min} = +3., x_{max} = +8$"
22 , r"$\alpha = 0.0, x_{min} = +3., x_{max} = +8$"
23 , r"$\alpha = +1., x_{min} = +3., x_{max} = +8$"
24 , r"$\alpha = +2., x_{min} = +3., x_{max} = +8$"
25 ]
26
27for kind in ["IK", "CK", "RK"]:
28
29 pattern = "*." + kind + ".txt"
30 fileList = glob.glob(pattern)
31 if len(fileList) == 1:
32
33 df = pd.read_csv(fileList[0], delimiter = ", ")
34
35 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
36 ax = plt.subplot()
37
38 if kind == "CK":
39 plt.plot( df.values[:, 0]
40 , df.values[:,[2,4]]
41 , marker[kind]
42 , linewidth = linewidth
43 #, color = "r"
44 )
45 plt.plot( df.values[:, 1]
46 , df.values[:,[3,5]]
47 , marker[kind]
48 , linewidth = linewidth
49 #, color = "blue"
50 )
51 else:
52 plt.plot( df.values[:, 0]
53 , df.values[:,1:]
54 , marker[kind]
55 , linewidth = linewidth
56 #, color = "r"
57 )
58 ax.legend ( legends
59 , fontsize = fontsize
60 )
61
62 plt.xticks(fontsize = fontsize - 2)
63 plt.yticks(fontsize = fontsize - 2)
64 ax.set_xlabel(xlab[kind], fontsize = 17)
65 ax.set_ylabel("Cumulative Distribution Function (CDF)", fontsize = 17)
66 #ax.set_xscale("log")
67 #ax.set_yscale("log")
68
69 plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
70 ax.tick_params(axis = "y", which = "minor")
71 ax.tick_params(axis = "x", which = "minor")
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_distPoweto
Todo:
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 877 of file pm_distPoweto.F90.


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