ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
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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,
  1. 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
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)))
Generate and return the number of points that are members (i.e., inside) of the specified -dimensiona...
This module contains classes and procedures for setting up and computing the properties of the hyper-...
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540
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

1program example
2
3 use pm_kind, only: SK, IK, LK
4 use pm_io, only: display_type
6
7 implicit none
8
9 type(display_type) :: disp
10 disp = display_type(file = "main.out.F90")
11
12 call disp%skip()
13 call disp%show("getCountMemberEll(radius = 1., point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4]))")
14 call disp%show( getCountMemberEll(radius = 1., point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4])) )
15 call disp%skip()
16
17 call disp%skip()
18 call disp%show("getCountMemberEll(radius = 2., center = [-1.5, 0.], point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4]))")
19 call disp%show( getCountMemberEll(radius = 2., center = [-1.5, 0.], point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4])) )
20 call disp%skip()
21
22 call disp%skip()
23 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.")
24 call disp%show( getCountMemberEll(invGram = reshape([1., 0. , 0., 1.], [2,2]), point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4])) )
25 call disp%skip()
26
27 call disp%skip()
28 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")
29 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])) )
30 call disp%skip()
31
32end program example
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler
1#!/usr/bin/env sh
2rm main.exe
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example Windows Batch compile command via Intel ifort compiler
1del main.exe
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler
1#!/usr/bin/env sh
2rm main.exe
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example output
1
2getCountMemberEll(radius = 1., point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4]))
3+2
4
5
6getCountMemberEll(radius = 2., center = [-1.5, 0.], point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4]))
7+1
8
9
10getCountMemberEll(invGram = reshape([1., 0. , 0., 1.], [2,2]), point = reshape([0., 0., 1., 0., 1., 1., -1., -1.], [2, 4])) ! correlation 0.
11+2
12
13
14getCountMemberEll(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
15+1
16
17
Test:
test_pm_ellipsoid


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.
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  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.
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Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

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.


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