Generate and return the number of points that are members (i.e., inside) of the specified \(\ndim\)-dimensional ellipsoid.
More...
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 ⛓
integer(IK) :: countMemberEll
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...
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
- 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 ⛓
9 type(display_type) :: disp
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])) )
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])) )
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])) )
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])) )
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.
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.
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort -fpp -standard-semantics -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 /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example output ⛓
2getCountMemberEll(radius
= 1., point
= reshape([
0.,
0.,
1.,
0.,
1.,
1.,
-1.,
-1.], [
2,
4]))
6getCountMemberEll(radius
= 2., center
= [
-1.5,
0.], point
= reshape([
0.,
0.,
1.,
0.,
1.,
1.,
-1.,
-1.], [
2,
4]))
10getCountMemberEll(invGram
= reshape([
1.,
0. ,
0.,
1.], [
2,
2]), point
= reshape([
0.,
0.,
1.,
0.,
1.,
1.,
-1.,
-1.], [
2,
4]))
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]))
- 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.
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, 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.