pm_ellipsoid::setVolUnitBall Interface Reference

Return the volume of an \(\ndim\)-dimensional ball of unit-radius. More...

Detailed Description

Return the volume of an \(\ndim\)-dimensional ball of unit-radius.

The computation of the volume of an n-ball requires involves factorials which are computed in the procedures of this generic interface iteratively.
This generic subroutine interface is an exact functional-interface replacement for the generic functional interface getVolUnitBall.

Parameters

[out]	volUnitBall	: The output scalar (or array of the same rank as other input array-like arguments) of, type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing natural logarithm of the volume of the unit-radius hyper-ball.
[in]	ndim	: The input scalar containing the number of dimensions of the unit-radius hyper-ball. It can be, of type integer of default kind IK.

Possible calling interfaces ⛓

use pm_ellipsoid, only: setVolUnitBall
 
call setVolUnitBall(volUnitBall, 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.

See also

getLogVolUnitBall
Volume of an n-ball
Particular values of the Gamma function

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK, RKG => RKH
    use pm_ellipsoid, only: setVolUnitBall
    use pm_io, only: display_type
 
    implicit none
 
    real(RKG) :: volUnitBall(5)
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("call setVolUnitBall(volUnitBall(1), ndim = 2_IK)")
                    call setVolUnitBall(volUnitBall(1), ndim = 2_IK)
    call disp%show("volUnitBall(1)")
    call disp%show( volUnitBall(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setVolUnitBall(volUnitBall(1:5), ndim = [integer(IK) :: 0, 1, 2, 3, 4])")
                    call setVolUnitBall(volUnitBall(1:5), ndim = [integer(IK) :: 0, 1, 2, 3, 4])
    call disp%show("volUnitBall(1:5)")
    call disp%show( volUnitBall(1:5) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        use pm_kind, only: RKD
        use pm_arrayRange, only: getRange
        integer(IK), parameter :: nsim = 30_IK
        integer(IK) :: ndim(0 : nsim)
        real(RKD) :: volUnitBall(0 : nsim)
        integer(IK) :: fileUnit, i
        open(newunit = fileUnit, file = "setVolUnitBall.RK.txt")
        ndim(0 : nsim) = getRange(0_IK, nsim)
        call setVolUnitBall(volUnitBall, ndim)
        do i = 0, nsim
            write(fileUnit, "(*(g0,:,','))") ndim(i), volUnitBall(i)
        end do
        close(fileUnit)
    end block
 
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 ⛓

 
call setVolUnitBall(volUnitBall(1), ndim = 2_IK)
volUnitBall(1)
+3.14159265358979323846264338327950280
 
 
call setVolUnitBall(volUnitBall(1:5), ndim = [integer(IK) :: 0, 1, 2, 3, 4])
volUnitBall(1:5)
+1.00000000000000000000000000000000000, +2.00000000000000000000000000000000000, +3.14159265358979323846264338327950280, +4.18879020478639098461685784437267065, +4.93480220054467930941724549993807541
 
 

Postprocessing of the example output ⛓

#!/usr/bin/env python
 
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import glob
import sys
 
linewidth = 2
fontsize = 17
 
for kind in ["RK"]:
 
    pattern = "*." + kind + ".txt"
    fileList = glob.glob(pattern)
 
    for file in fileList:
 
        df = pd.read_csv(file, delimiter = ",", header = None)
 
        # definitions for the axes
       #left, width = 0.1, 0.65
       #bottom, height = 0.1, 0.65
       #spacing = 0.015
 
        # start with a square Figure
        fig = plt.figure() # figsize = (8, 6)
 
        plt.rcParams.update({'font.size': fontsize - 2})
        ax = plt.subplot()
       #ax = fig.add_axes([left, bottom, width, height]) # scatter plot
       #ax_histx = fig.add_axes([left, bottom + height + spacing, width, 0.2], sharex = ax) # histx
       #ax_histy = fig.add_axes([left + width + spacing, bottom, 0.2, height], sharey = ax) # histy
       #
       #for axes in [ax, ax_histx, ax_histy]:
       #    axes.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
       #    axes.tick_params(axis = "y", which = "minor")
       #    axes.tick_params(axis = "x", which = "minor")
       #
       
 
        # the scatter plot:
        for i in range(0, len(df.values[0,:]), 2):
            ax.scatter  ( df.values[:,i]
                        , df.values[:,i+1]
                        , s = 8
                        , zorder = 1000
                        )
 
       #ax_histx.hist(df.values[:, 0], bins = 50, zorder = 1000)
       #ax_histy.hist(df.values[:,1], bins = 50, orientation = "horizontal", zorder= 1000)
 
        #ax.set_aspect("equal")
        ax.set_xlim([0, df.values[-1,:].max()])
        ax.set_xlabel("ndim", fontsize = 17)
        ax.set_ylabel("Volume of ndim unit-ball", fontsize = 17)
        plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
        plt.minorticks_on()
 
        plt.tight_layout()
        plt.savefig(file.replace(".txt",".png"))

Visualization of the example output ⛓

Test:

test_pm_ellipsoid

Final Remarks ⛓

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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.

1. 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.
   
2. 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, April 23, 2017, 1:36 AM, Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin

Definition at line 291 of file pm_ellipsoid.F90.

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

• src/fortran/main/pm_ellipsoid.F90