pm_ellipsoid::getCountMemberEll Interface Reference

Generate and return the number of points that are members (i.e., inside) of the specified \(\ndim\)-dimensional ellipsoid.
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Detailed Description

Generate and return the number of points that are members (i.e., inside) of the specified \(\ndim\)-dimensional ellipsoid.

See the documentation of pm_ellipsoid for computational and algorithmic details.

Parameters

[in]	radius	: The input positive scalar of the same type and kind as the input argument point, containing the full inverse representative Gramian matrix of the \(\ndim\)-dimensional ellipsoid. (optional. If present, the ellipsoid is assumed to be a ball. It must be present if and only if the input argument invGram is missing.)
[in]	invGram	: The input square matrix of shape (1:ndim, 1:ndim) of the same type and kind as the input argument point, containing the full inverse representative Gramian matrix of the \(\ndim\)-dimensional ellipsoid. (optional. It must be present if and only if the input argument radius is missing.)
[in]	center	: The input vector of shape (1:ndim) of the same type and kind as the input invGram, containing the center of the ellipsoid. (optional. default = [(0., i = 1, ndim)].)
[in]	point	: The input matrix of shape (1:ndim, 1:npnt) of, type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing npnt points whose presence within the ellipsoid is to be checked.

Returns

countMemberEll : The output scalar of type integer of default kind IK, containing the number of points that are within the specified ellipsoid.

Possible calling interfaces ⛓

use pm_kind, only: IK
use pm_ellipsoid, only: getCountMemberEll
integer(IK) :: countMemberEll
 
countMemberEll = getCountMemberEll(radius, point(1:ndim, 1:npnt))
countMemberEll = getCountMemberEll(radius, center(1:ndim), point(1:ndim, 1:npnt))
countMemberEll = getCountMemberEll(invGram(1:ndim, 1:ndim), point(1:ndim, 1:npnt)))
countMemberEll = getCountMemberEll(invGram(1:ndim, 1:ndim), center(1:ndim), point(1:ndim, 1:npnt)))

Warning

The condition 0. < radius must hold for the corresponding input arguments.
The condition size(point, 1) == size(center) must hold for the corresponding input arguments.
The condition all(size(point, 1) == shape(invGram)) must hold for the corresponding input arguments.
The condition \(0. < \left|\ms{invGram}\right|\) must hold for the corresponding input arguments.
In other words, the input inverse Gramian must be a positive definite matrix.
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

isMemberEll
getCountMemberEll

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_io, only: display_type
    use pm_ellipsoid, only: getCountMemberEll
 
    implicit none
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("getCountMemberEll(radius = 1., point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4]))")
    call disp%show( getCountMemberEll(radius = 1., point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4])) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getCountMemberEll(radius = 2., center = [-1.5, 0.], point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4]))")
    call disp%show( getCountMemberEll(radius = 2., center = [-1.5, 0.], point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4])) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getCountMemberEll(invGram = reshape([1., 0. , 0., 1.], [2,2]), point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4])) ! correlation 0.")
    call disp%show( getCountMemberEll(invGram = reshape([1., 0. , 0., 1.], [2,2]), point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4])) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getCountMemberEll(invGram = reshape([5.2632, -4.7368, -4.7368, 5.2632], [2,2]), center = [0., 0.], point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4])) ! correlation 0.9")
    call disp%show( getCountMemberEll(invGram = reshape([5.2632, -4.7368, -4.7368, 5.2632], [2,2]), center = [0., 0.], point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 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 ⛓

 
getCountMemberEll(radius = 1., point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4]))
+2
 
 
getCountMemberEll(radius = 2., center = [-1.5, 0.], point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4]))
+1
 
 
getCountMemberEll(invGram = reshape([1., 0. , 0., 1.], [2,2]), point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4])) ! correlation 0.
+2
 
 
getCountMemberEll(invGram = reshape([5.2632, -4.7368, -4.7368, 5.2632], [2,2]), center = [0., 0.], point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4])) ! correlation 0.9
+1
 
 

Test:

test_pm_ellipsoid

Final Remarks ⛓

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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.

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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 1236 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