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

[out]  logPDF  : The output scalar or array of the same shape as the input arraylike arguments, of,

type
real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
representing the natural logarithm of the PDF of the Normal distribution at x .

[in]  x  : The input scalar or array of the same shape as other arraylike arguments, of the same type and kind as the output logPDF , representing the point(s) at which the PDF must be computed.

[in]  mu  : The input scalar or array of the same shape as other arraylike arguments of the same type and kind as the output logPDF representing the mean of the distribution.
(optional, default = 0. ) 
[in]  invSigma  : The input scalar or array of the same shape as other arraylike arguments, of the same type and kind as the output logPDF representing the inverse of the standard deviation of the distribution.
(optional, default = 1. , must be present if and only if logInvSigma is also present.) 
[in]  logInvSigma  : The input scalar or array of the same shape as other arraylike arguments, of the same type and kind as the output logPDF representing the natural logarithm of the inverse of the standard deviation 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 Normal distrib...
This module contains classes and procedures for computing various statistical quantities related to t...
 Warning
 The condition
0. < invSigma
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
 getNormLogPDF
getLogNormLogPDF
setLogNormLogPDF
Example usage ⛓
12 integer(IK),
parameter :: NP
= 1000_IK
13 real(RK), dimension(NP) :: Point, mu, invSigma, logPDF
15 type(display_type) :: disp
20 call setLogSpace(invSigma, logx1
= log(
0.1_RK), logx2
= log(
10._RK))
23 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
24 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
25 call disp%show(
"! Compute the Probability Density Function (PDF) of the (Standard) Normal distribution.")
26 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
27 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
39 call disp%show(
"call setNormLogPDF(logPDF(1), Point(NP/2))")
56 call disp%show(
"call setNormLogPDF(logPDF(1), Point(1), mu(1))")
63 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
64 call disp%show(
"! PDF with a standard deviation.")
65 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
73 call disp%show(
"call setNormLogPDF(logPDF(1), Point(1), invSigma(1), log(invSigma(1)))")
74 call setNormLogPDF(logPDF(
1), Point(
1), invSigma(
1),
log(invSigma(
1)))
80 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
81 call disp%show(
"! PDF with a mean and a standard deviation.")
82 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
92 call disp%show(
"call setNormLogPDF(logPDF(1), Point(1), mu(1), invSigma(1), log(invSigma(1)))")
93 call setNormLogPDF(logPDF(
1), Point(
1), mu(
1), invSigma(
1),
log(invSigma(
1)))
99 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
100 call disp%show(
"! A vector of PDF at different points with the same mean and standard deviation.")
101 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
111 call disp%show(
"call setNormLogPDF(logPDF(1:NP:NP/5), Point(1:NP:NP/5), mu(1), invSigma(1), log(invSigma(1)))")
112 call setNormLogPDF(logPDF(
1:NP:NP
/5), Point(
1:NP:NP
/5), mu(
1), invSigma(
1),
log(invSigma(
1)))
118 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
119 call disp%show(
"! A vector of PDF at the same point but with different means and standard deviations.")
120 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
126 call disp%show(
"invSigma(1:NP:NP/5)")
127 call disp%show( invSigma(
1:NP:NP
/5) )
130 call disp%show(
"call setNormLogPDF(logPDF(1:NP:NP/5), Point(1), mu(1:NP:NP/5), invSigma(1:NP:NP/5), log(invSigma(1:NP:NP/5)))")
131 call setNormLogPDF(logPDF(
1:NP:NP
/5), Point(
1), mu(
1:NP:NP
/5), invSigma(
1:NP:NP
/5),
log(invSigma(
1:NP:NP
/5)))
137 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
138 call disp%show(
"! A vector of PDF at different points with different means and a standard deviations.")
139 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
145 call disp%show(
"invSigma(1:NP:NP/5)")
146 call disp%show( invSigma(
1:NP:NP
/5) )
149 call disp%show(
"call setNormLogPDF(logPDF(1:NP:NP/5), Point(1:NP:NP/5), mu(1:NP:NP/5), invSigma(1:NP:NP/5), log(invSigma(1:NP:NP/5)))")
150 call setNormLogPDF(logPDF(
1:NP:NP
/5), Point(
1:NP:NP
/5), mu(
1:NP:NP
/5), invSigma(
1:NP:NP
/5),
log(invSigma(
1:NP:NP
/5)))
160 integer(IK) :: fileUnit, i
161 real(RK),
parameter :: mu(
*)
= [
0.00_RK,
0.00_RK,
0.00_RK,
2.00_RK]
162 real(RK),
parameter :: invSigma(
*)
= 1._RK / [
3.0_RK,
1.00_RK,
0.30_RK,
1.00_RK]
163 open(newunit
= fileUnit, file
= "setNormLogPDF.RK.txt")
165 call setNormLogPDF(logPDF(
1:
4), Point(i),
+0._RK, invSigma,
log(invSigma))
166 write(fileUnit,
"(*(f0.8,:,','))") Point(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 ⛓
150.10010010010010006E1
44call setNormLogPDF(logPDF(
1), Point(
1), invSigma(
1),
log(invSigma(
1)))
60call setNormLogPDF(logPDF(
1), Point(
1), mu(
1), invSigma(
1),
log(invSigma(
1)))
7510.000000000000000,
5.9959959959959956,
1.9919919919919913,
+2.0120120120120113,
+6.0160160160160174
76call setNormLogPDF(logPDF(
1:NP:NP
/5), Point(
1:NP:NP
/5), mu(
1), invSigma(
1),
log(invSigma(
1)))
783.3465236261987181,
3.2264836663189183,
3.2667641870799198,
3.4673651884817218,
3.8282866705243257
875.0000000000000000,
2.9979979979979978,
0.99599599599599564,
+1.0060060060060056,
+3.0080080080080087
89+0.10000000000000003,
+0.25142033481427983,
+0.63212184758124557,
+1.5892828656229783,
+3.9957803018952722
92call setNormLogPDF(logPDF(
1:NP:NP
/5), Point(
1), mu(
1:NP:NP
/5), invSigma(
1:NP:NP
/5),
log(invSigma(
1:NP:NP
/5)))
943.3465236261987181,
3.8491521427026156,
17.574924273815174,
153.43468382647370,
1350.3453534890459
1035.0000000000000000,
2.9979979979979978,
0.99599599599599564,
+1.0060060060060056,
+3.0080080080080087
105+0.10000000000000003,
+0.25142033481427983,
+0.63212184758124557,
+1.5892828656229783,
+3.9957803018952722
10710.000000000000000,
5.9959959959959956,
1.9919919919919913,
+2.0120120120120113,
+6.0160160160160174
108call setNormLogPDF(logPDF(
1:NP:NP
/5), Point(
1:NP:NP
/5), mu(
1:NP:NP
/5), invSigma(
1:NP:NP
/5),
log(invSigma(
1:NP:NP
/5)))
1103.3465236261987181,
2.5836429383357573,
1.5758039459061650,
1.7337813061862941,
71.765956410825737
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_distNorm
 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 437 of file pm_distNorm.F90.