pm_distUnifSphere::getUnifSphereLogPDF Interface Reference

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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Detailed Description

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,

1. 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 ⛓

use pm_distUnifSphere, only: getUnifSphereLogPDF
 
logPDF = getUnifSphereLogPDF(logRadius, ndim

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.

Remarks

The procedures under discussion are elemental.

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK
    use pm_matrixInit, only: uppLowDia, getMatInit
    use pm_distUnifSphere, only: getUnifSphereLogPDF
    use pm_io, only: display_type
 
    implicit none
 
    type(display_type)      :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("1. / exp(getUnifSphereLogPDF(log(1.), ndim = [1, 2, 3, 4])) ! area of the sphere embedded in ndim dimensions with unit radius.")
    call disp%show( 1. / exp(getUnifSphereLogPDF(log(1.), ndim = [1, 2, 3, 4])) )
    call disp%skip()
 
end program example

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example output ⛓

 
1. / exp(getUnifSphereLogPDF(log(1.), ndim = [1, 2, 3, 4])) ! area of the sphere embedded in ndim dimensions with unit radius.
+2.00000024, +6.28318596, +12.5663738, +19.7392120
 
 

Test:

test_pm_distUnifSphere

Final Remarks ⛓

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For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
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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.

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

• src/fortran/main/pm_distUnifSphere.F90