Generate the natural logarithm of probability density function (PDF) of the univariate Lognormal distribution.
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Generate the natural logarithm of probability density function (PDF) of the univariate Lognormal distribution.
 Parameters

[out]  logPDF  : The output scalar or array of the same shape as the input arraylike arguments, of the same type and kind as the input logx representing the PDF of the Lognormal distribution at exp(logx) . 
[in]  logx  : The input scalar or array of the same shape as other arraylike arguments, of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), representing the natural logarithms of the point(s) at which the PDF must be computed (i.e., \(\log(x)\)). 
[in]  mu  : The input scalar or array of the same shape as other arraylike arguments of the same type and kind as logx representing the location parameter of the distribution.
(optional, default = 0 ) 
[in]  invSigma  : The input scalar of the same type and kind as logx representing the inverse of the scale parameter of the distribution.
(optional, default = 1. , must be present if and only if logInvSigma is also present) 
[in]  logInvSigma  : The input scalar of the same type and kind as logx representing the natural logarithm of the inverse of the scale parameter of the distribution.
(optional, default = 0 , must be present if and only if invSigma is also present). 
Possible calling interfaces ⛓
Generate the natural logarithm of probability density function (PDF) of the univariate Lognormal dist...
This module contains classes and procedures for computing various statistical quantities related to t...
 Warning
 The condition
invSigma > 0.
must hold for the corresponding procedure argument.
The condition log(invSigma) == logInvSigma
must hold within a small range of computer precision for the corresponding procedure 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
 getLogNormLogPDF
getNormLogPDF
setNormLogPDF
Example usage ⛓
12 integer(IK),
parameter :: NP
= 1000_IK
13 real(RK), dimension(NP) :: logx, mu, invSigma, logPDF
15 type(display_type) :: disp
19 call setLinSpace(logx, x1
= log(
0.0001_RK), x2
= log(
5._RK))
20 call setLogSpace(invSigma, logx1
= log(
0.1_RK), logx2
= log(
10._RK))
23 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
24 call disp%show(
"! Compute the Probability Density Function (PDF) of the (Standard) LogNormal distribution.")
25 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
37 call disp%show(
"call setLogNormLogPDF(logPDF(1), logx(NP/2))")
54 call disp%show(
"call setLogNormLogPDF(logPDF(1), logx(1), mu(1))")
61 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
62 call disp%show(
"! PDF with a standard deviation.")
63 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
71 call disp%show(
"call setLogNormLogPDF(logPDF(1), logx(1), invSigma(1), log(invSigma(1)))")
78 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
79 call disp%show(
"! PDF with a mean and a standard deviation.")
80 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
90 call disp%show(
"call setLogNormLogPDF(logPDF(1), logx(1), mu(1), invSigma(1), log(invSigma(1)))")
91 call setLogNormLogPDF(logPDF(
1), logx(
1), mu(
1), invSigma(
1),
log(invSigma(
1)))
97 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
98 call disp%show(
"! A vector of PDF at different points with the same mean and standard deviation.")
99 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
109 call disp%show(
"call setLogNormLogPDF(logPDF(1:NP:NP/5), logx(1:NP:NP/5), mu(1), invSigma(1), log(invSigma(1)))")
110 call setLogNormLogPDF(logPDF(
1:NP:NP
/5), logx(
1:NP:NP
/5), mu(
1), invSigma(
1),
log(invSigma(
1)))
116 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
117 call disp%show(
"! A vector of PDF at the same point but with different means and standard deviations.")
118 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
124 call disp%show(
"invSigma(1:NP:NP/5)")
125 call disp%show( invSigma(
1:NP:NP
/5) )
128 call disp%show(
"call setLogNormLogPDF(logPDF(1:NP:NP/5), logx(1), mu(1:NP:NP/5), invSigma(1:NP:NP/5), log(invSigma(1:NP:NP/5)))")
129 call setLogNormLogPDF(logPDF(
1:NP:NP
/5), logx(
1), mu(
1:NP:NP
/5), invSigma(
1:NP:NP
/5),
log(invSigma(
1:NP:NP
/5)))
135 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
136 call disp%show(
"! A vector of PDF at different points with different means and a standard deviations.")
137 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
143 call disp%show(
"invSigma(1:NP:NP/5)")
144 call disp%show( invSigma(
1:NP:NP
/5) )
147 call disp%show(
"call setLogNormLogPDF(logPDF(1:NP:NP/5), logx(1:NP:NP/5), mu(1:NP:NP/5), invSigma(1:NP:NP/5), log(invSigma(1:NP:NP/5)))")
148 call setLogNormLogPDF(logPDF(
1:NP:NP
/5), logx(
1:NP:NP
/5), mu(
1:NP:NP
/5), invSigma(
1:NP:NP
/5),
log(invSigma(
1:NP:NP
/5)))
158 integer(IK) :: fileUnit, i
159 real(RK),
parameter :: invSigma(
*)
= 1._RK / [
2.00_RK,
1.00_RK,
0.50_RK,
0.25_RK]
160 open(newunit
= fileUnit, file
= "setLogNormLogPDF.RK.txt")
162 call setLogNormLogPDF(logPDF(
1:
4), logx(i),
+0._RK, invSigma,
log(invSigma))
163 write(fileUnit,
"(*(E20.8e4,:,' '))")
exp(logx(i)),
exp(logPDF(
1:
4))
Return the linSpace output argument with size(linSpace) elements of evenlyspaced values over the int...
Return the logSpace output argument with size(logSpace) elements of logarithmicallyevenlyspaced val...
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 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 typeparameters frequently used in the ParaMonte librar...
integer, parameter RK
The default real kind in the ParaMonte library: real64 in Fortran, c_double in CFortran Interoperati...
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in CFortran Interoper...
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in CFortran Intero...
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort fpp standardsemantics 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 /standardsemantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran cpp ffreelinelengthnone O3 Wl,rpath,../../../lib I../../../inc main.F90 ../../../lib/libparamonte* o main.exe
Example output ⛓
58call setLogNormLogPDF(logPDF(
1), logx(
1), mu(
1), invSigma(
1),
log(invSigma(
1)))
739.2103403719761818,
7.0442185933154651,
4.8780968146547474,
2.7119750359940307,
0.54585325733331302
74call setLogNormLogPDF(logPDF(
1:NP:NP
/5), logx(
1:NP:NP
/5), mu(
1), invSigma(
1),
log(invSigma(
1)))
76+5.9001819155380009,
+3.8018008188304635,
+1.6564988865230426,
0.53572388138426019,
2.7748674848914465
855.0000000000000000,
2.9979979979979978,
0.99599599599599564,
+1.0060060060060056,
+3.0080080080080087
87+0.10000000000000003,
+0.25142033481427983,
+0.63212184758124557,
+1.5892828656229783,
+3.9957803018952722
90call setLogNormLogPDF(logPDF(
1:NP:NP
/5), logx(
1), mu(
1:NP:NP
/5), invSigma(
1:NP:NP
/5),
log(invSigma(
1:NP:NP
/5)))
92+5.9001819155380009,
+5.6909925649980364,
5.6481256711121706,
123.05994822248609,
1182.1091836696894
1015.0000000000000000,
2.9979979979979978,
0.99599599599599564,
+1.0060060060060056,
+3.0080080080080087
103+0.10000000000000003,
+0.25142033481427983,
+0.63212184758124557,
+1.5892828656229783,
+3.9957803018952722
1059.2103403719761818,
7.0442185933154651,
4.8780968146547474,
2.7119750359940307,
0.54585325733331302
106call setLogNormLogPDF(logPDF(
1:NP:NP
/5), logx(
1:NP:NP
/5), mu(
1:NP:NP
/5), invSigma(
1:NP:NP
/5),
log(invSigma(
1:NP:NP
/5)))
108+5.9001819155380009,
+4.2271991415313570,
+0.48952351323037480,
15.201369457730461,
99.814220020847046
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
16xlab = {
"CK" :
"X ( real/imaginary components )"
17 ,
"IK" :
"X ( integervalued )"
18 ,
"RK" :
"X ( realvalued )"
20legends = [
r"$\mu = 0.0,~\sigma = 2.00$"
21 ,
r"$\mu = 0.0,~\sigma = 1.00$"
22 ,
r"$\mu = 0.0,~\sigma = 0.50$"
23 ,
r"$\mu = 0.0,~\sigma = 0.25$"
26for kind
in [
"IK",
"CK",
"RK"]:
28 pattern =
"*." + kind +
".txt"
29 fileList = glob.glob(pattern)
30 if len(fileList) == 1:
32 df = pd.read_csv(fileList[0], delimiter =
" ")
34 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
38 plt.plot( df.values[:, 0]
41 , linewidth = linewidth
44 plt.plot( df.values[:, 1]
47 , linewidth = linewidth
51 plt.plot( df.values[:, 0]
54 , linewidth = linewidth
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)
66 plt.grid(visible =
True, which =
"both", axis =
"both", color =
"0.85", linestyle =
"")
67 ax.tick_params(axis =
"y", which =
"minor")
68 ax.tick_params(axis =
"x", which =
"minor")
71 plt.savefig(fileList[0].replace(
".txt",
".png"))
73 elif len(fileList) > 1:
75 sys.exit(
"Ambiguous file list exists.")
Visualization of the example output ⛓
 Test:
 test_pm_distLogNorm
 Todo:
 Normal Priority: A performant vectorized
logPDF(:)
version of the subroutines under this generic interface could be added in the future.
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 292 of file pm_distLogNorm.F90.