Return the natural logarithm of the Probability Density Function (PDF) of the (Truncated) Poweto distribution for an input logx within the support of the distribution \(x \in [0 < x_\mathrm{min}, x_\mathrm{max} < +\infty]\).
More...
Return the natural logarithm of the Probability Density Function (PDF) 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] | logPDF | : The output scalar of the same type and kind the input argument logx, 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 x value within the support of the distribution 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 (i.e., the exponent of the power-law function).
|
| [in] | logPDFNF | : 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.
This argument can be readily obtained by calling getPowetoLogPDFNF(alpha, logMinX, logMaxX).
|
Possible calling interfaces ⛓
Return the natural logarithm of the Probability Density Function (PDF) of the (Truncated) Poweto dist...
This module contains classes and procedures for computing various statistical quantities related to t...
- Warning
- 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
- getPowetoLogPDF
Example usage ⛓
14 type(display_type) :: disp
18 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
19 call disp%show(
"! Compute the Probability Density Function (PDF) of the Poweto distribution.")
20 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
24 call disp%show(
"call setPowetoLogPDF(logPDF(1), logx = 3., alpha = -2., logPDFNF = getPowetoLogPDFNF(alpha = -2., logMinX = -2.)) ! Poweto distribution.")
31 call disp%show(
"call setPowetoLogPDF(logPDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logPDFNF = getPowetoLogPDFNF(alpha = -[+2., +3., +4.], logMinX = -2.)) ! Poweto distribution.")
32 call setPowetoLogPDF(logPDF(
1:
3), logx
= [
3.,
4.,
5.], alpha
= -[
+2.,
+3.,
+4.], logPDFNF
= getPowetoLogPDFNF(alpha
= -[
+2.,
+3.,
+4.], logMinX
= -2.))
38 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
39 call disp%show(
"! Compute the Probability Density Function (PDF) of the Truncated Poweto distribution.")
40 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
44 call disp%show(
"call setPowetoLogPDF(logPDF(1), logx = 3., alpha = -2., logPDFNF = getPowetoLogPDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.")
51 call disp%show(
"call setPowetoLogPDF(logPDF(1:3), logx = [3., 4., 5.], alpha = -[+2., +3., +4.], logPDFNF = getPowetoLogPDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.")
52 call setPowetoLogPDF(logPDF(
1:
3), logx
= [
3.,
4.,
5.], alpha
= -[
+2.,
+3.,
+4.], logPDFNF
= getPowetoLogPDFNF(alpha
= -[
+2.,
+3.,
+4.], logMinX
= -2., logMaxX
= 5.))
58 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
59 call disp%show(
"! Compute the Probability Density Function (PDF) of the Poweto distribution.")
60 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
64 call disp%show(
"call setPowetoLogPDF(logPDF(1), logx = 3., alpha = +2., logPDFNF = getPowetoLogPDFNF(alpha = +2., logMaxX = 5.)) ! Poweto distribution.")
71 call disp%show(
"call setPowetoLogPDF(logPDF(1:3), logx = [3., 4., 5.], alpha = [+2., +3., +4.], logPDFNF = getPowetoLogPDFNF(alpha = [+2., +3., +4.], logMaxX = 5.)) ! Poweto distribution.")
72 call setPowetoLogPDF(logPDF(
1:
3), logx
= [
3.,
4.,
5.], alpha
= [
+2.,
+3.,
+4.], logPDFNF
= getPowetoLogPDFNF(alpha
= [
+2.,
+3.,
+4.], logMaxX
= 5.))
78 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
79 call disp%show(
"! Compute the Probability Density Function (PDF) of the Truncated Poweto distribution.")
80 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
84 call disp%show(
"call setPowetoLogPDF(logPDF(1), logx = 3., alpha = +2., logPDFNF = getPowetoLogPDFNF(alpha = +2., logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.")
91 call disp%show(
"call setPowetoLogPDF(logPDF(1:3), logx = [3., 4., 5.], alpha = [+2., +3., +4.], logPDFNF = getPowetoLogPDFNF(alpha = [+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Poweto distribution.")
92 call setPowetoLogPDF(logPDF(
1:
3), logx
= [
3.,
4.,
5.], alpha
= [
+2.,
+3.,
+4.], logPDFNF
= getPowetoLogPDFNF(alpha
= [
+2.,
+3.,
+4.], logMinX
= -2., logMaxX
= 5.))
104 real,
allocatable :: alpha(:), logPDF(:)
105 real :: logMinX, logMaxX, logx(
2000)
106 integer(IK) :: fileUnit, i
107 alpha
= [
-2.0,
-1.,
0.,
+1.,
+2.]
108 call setLinSpace(logx, x1
= log(
0.1), x2
= log(
10.))
112 open(newunit
= fileUnit, file
= "setPowetoLogPDF.RK.txt")
113 do i
= 1,
size(logx,
1,
IK)
114 if (logMinX
<= logx(i)
.and. logx(i)
<= logMaxX)
then
119 write(fileUnit,
"(*(g0,:,', '))")
exp(logx(i)),
exp(logPDF)
Allocate or resize (shrink or expand) an input allocatable scalar string or array of rank 1....
Generate count evenly-logarithmically-spaced points over the interval [base**logx1,...
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 Probability Density Func...
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 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...
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 ⛓
12call setPowetoLogPDF(logPDF(
1:
3), logx
= [
3.,
4.,
5.], alpha
= -[
+2.,
+3.,
+4.], logPDFNF
= getPowetoLogPDFNF(alpha
= -[
+2.,
+3.,
+4.], logMinX
= -2.))
14-12.3068523,
-20.9013882,
-31.6137047
27call setPowetoLogPDF(logPDF(
1:
3), logx
= [
3.,
4.,
5.], alpha
= -[
+2.,
+3.,
+4.], logPDFNF
= getPowetoLogPDFNF(alpha
= -[
+2.,
+3.,
+4.], logMinX
= -2., logMaxX
= 5.))
29-12.3068523,
-20.9013882,
-31.6137047
42call setPowetoLogPDF(logPDF(
1:
3), logx
= [
3.,
4.,
5.], alpha
= [
+2.,
+3.,
+4.], logPDFNF
= getPowetoLogPDFNF(alpha
= [
+2.,
+3.,
+4.], logMaxX
= 5.))
44-6.30685234,
-5.90138817,
-3.61370468
57call setPowetoLogPDF(logPDF(
1:
3), logx
= [
3.,
4.,
5.], alpha
= [
+2.,
+3.,
+4.], logPDFNF
= getPowetoLogPDFNF(alpha
= [
+2.,
+3.,
+4.], logMinX
= -2., logMaxX
= 5.))
59-6.30685234,
-5.90138817,
-3.61370468
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
16xlab = {
"CK" :
"X ( real/imaginary components )"
17 ,
"IK" :
"X ( integer-valued )"
18 ,
"RK" :
"X ( real-valued )"
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"$\alpha = +2., x_{min} = +3., x_{max} = +8$"
27for kind
in [
"IK",
"CK",
"RK"]:
29 pattern =
"*." + kind +
".txt"
30 fileList = glob.glob(pattern)
31 if len(fileList) == 1:
33 df = pd.read_csv(fileList[0], delimiter =
", ")
35 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
39 plt.plot( df.values[:, 0]
42 , linewidth = linewidth
45 plt.plot( df.values[:, 1]
48 , linewidth = linewidth
52 plt.plot( df.values[:, 0]
55 , linewidth = linewidth
59 , fontsize = fontsize - 5
62 plt.xticks(fontsize = fontsize - 2)
63 plt.yticks(fontsize = fontsize - 2)
64 ax.set_xlabel(xlab[kind], fontsize = 17)
65 ax.set_ylabel(
"Probability Density Function (PDF)", fontsize = 17)
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")
74 plt.savefig(fileList[0].replace(
".txt",
".png"))
76 elif len(fileList) > 1:
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.
-
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 453 of file pm_distPoweto.F90.
1.9.3