Generate and return the natural logarithm of the Probability Density Function (PDF) of the uniform distribution on an \(n\)sphere embedded in an \(\ndim\)dimensional space.
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Generate and return the natural logarithm of the Probability Density Function (PDF) of the uniform distribution on an \(n\)sphere embedded in an \(\ndim\)dimensional space.
See the documentation of pm_distUnifSphere for details of the definition of the PDF.
 Note
 Note that the procedures of this generic interface do not require an input
X
value representing a location within the domain of the density function.
This is fine and intentional by design because the PDF is uniform across the entire support of the PDF.
 Parameters

[in]  logRadius  : The input scalar of the same type and kind as the output logPDF , containing the natural logarithm of the radius of the \(n\)sphere embedded in the \(\ndim\)dimensional space.
A value of 1 corresponds to unit \(n\)sphere.

[in]  ndim  : The input positive scalar of type integer of default kind IK, containing the dimension of space within which the \(n\)sphere is embedded.
In other words, \(\ndim = n + 1\).

 Returns
logPDF
: The output scalar of,

type
real
of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the natural logarithm of the PDF of the uniform distribution on the surface of \(n\)sphere.
Possible calling interfaces ⛓
Generate and return the natural logarithm of the Probability Density Function (PDF) of the uniform di...
This module contains classes and procedures for computing various statistical quantities related to t...
 Warning
 The condition
0 < ndim
must hold for the corresponding input arguments.
This condition is 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.
Example usage ⛓
10 type(display_type) :: disp
14 call disp%show(
"1. / exp(getUnifSphereLogPDF(log(1.), ndim = [1, 2, 3, 4])) ! area of the sphere embedded in ndim dimensions with unit radius.")
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.
Generate and return a matrix of shape (shape(1), shape(2)) with the upper/lower triangle and the diag...
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 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...
This module contains procedures and generic interfaces relevant to generating and initializing matric...
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 ⛓
3+2.00000024,
+6.28318596,
+12.5663738,
+19.7392120
 Test:
 test_pm_distUnifSphere
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, Monday March 6, 2017, 3:22 pm, Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin.
Definition at line 232 of file pm_distUnifSphere.F90.