Return the full or a subset of the Euclidean (squared) distance matrix of the input set of npnt points in ndim dimensions.
More...
Return the full or a subset of the Euclidean (squared) distance matrix of the input set of npnt points in ndim dimensions.
- Parameters
-
| [in] | pack | : The input scalar that can be:
-
the constant rdpack or an object of type rdpack_type, implying the use of Rectangular Default Packing format for the output matrix.
|
| [in] | subset | : The input scalar that can be:
-
the constant uppLowDia or an object of type uppLowDia_type, indicating that the output
distance must contain the full distance matrix of shape (1:npnt, 1:npnt) including the zero-valued diagonals.
-
the constant uppLow or an object of type uppLow_type, indicating that the output
distance must exclude the zero-valued diagonals from the distance matrix yielding a distance matrix of shape (1:npnt - 1, 1:npnt).
Motivation: The zero-valued diagonal elements of the distance matrix are are frequently troubling for subsequent vector operations on the output distance matrix.
Such vector operations include but are not limited to finding the extrema of distances, for example, the nearest and farthest neighbors.
This subset value offers a fast convenient method of excluding self-distance values from the output distance matrix such that each column (1:npnt-1 , i) of the distance matrix contains only the distances of point(1:ndim, i) with all other npnt - 1 points in point.
For example, finding the nearest neighbor of the points using the output distance matrix would be as simple as minval(distance, 1).
Finding the actual index of the point that is the nearest neighbor to each point would be slightly more involved as a two-step process:
nn1loc(1 : npnt) = minloc(distance(1 : npnt - 1, 1 : npnt), 1)
nn1loc = merge(nn1loc, nn1loc + 1, getRange(1, npnt) <= nn1loc)
nn1loc is the vector of indices of the first nearest neighbors such that point(:,nn1loc(i)) is the nearest neighbor to point(:,i).
|
| [in] | point | : The input contiguous 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 in the ndim-dimensional Euclidean space whose distances with respect to each other must be computed and returned.
|
| [in] | method | : The input scalar that can be,
-
the constant euclid or an object of type euclid_type, implying that all distance calculations must be done without undue numerical overflow.
This option is computationally the most expensive method.
-
the constant euclidu or an object of type euclidu_type, implying that all distance calculations must be without runtime checks for numerical overflow.
This option is computationally faster than the euclid method.
-
the constant euclidsq or an object of type euclidsq_type implying that the squared values of all distance calculations must be returned without runtime checks for numerical overflow.
This option is computationally the fastest approach to constructing the distance matrix because it avoid costly sqrt() operations and runtime overflow checks.
(optional, default = euclid) |
- Returns
distance : The output contiguous array of rank 2 of the same type and kind as the input argument point.
On output, it contains the requested subset of the (squared) distance matrix in the specified packing format pack.
Any element of distance that is not included in the specified subset will remain intact, if any such element exists.
Possible calling interfaces ⛓
distance(
1:npnt,
1:npnt)
= getDisMatEuclid(pack, subset, point(
1:ndim,
1:npnt), method)
distance(
1:npnt
-1,
1:npnt)
= getDisMatEuclid(pack, subset, point(
1:ndim,
1:npnt), method)
!
Return the full or a subset of the Euclidean (squared) distance matrix of the input set of npnt point...
This module contains procedures and generic interfaces for computing the Euclidean norm of a single p...
- Warning
- The condition
size(point, 1) == size(point, 2) must hold for the corresponding input arguments.
The condition shape(distance) == [size(point, 1), size(point, 1)] .or. .not. same_type_as(subset, uppLowDia) must hold for the corresponding input arguments.
The condition shape(distance) == [size(point, 1) - 1, size(point, 1)] .or. .not. same_type_as(subset, uppLow) must hold for the corresponding input arguments.
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.
- Developer Remark:
- The input arguments
pack, subset appear first for a good reason: To allow the possibility of adding of similarly-named arguments for the input point matrix.
- See also
- euclid
euclidu
euclidsq
euclid_type
euclidu_type
euclidsq_type
getDisEuclid
setDisEuclid
getDisMatEuclid
setDisMatEuclid
Example usage ⛓
12 integer(IK) :: ndim, npnt, itry, ntry
= 5
13 type(display_type) :: disp
17 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
18 call disp%show(
"! Compute the distance matrix of a set of points.")
19 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
23 real(RKG),
allocatable :: distance(:,:), point(:,:)
26 call disp%show(
"ndim = getUnifRand(1, 3); npnt = getUnifRand(1, 7)")
30 call disp%show(
"point = getUnifRand(1, 10, ndim, npnt)")
34 call disp%show(
"distance = getDisMatEuclid(point)")
38 call disp%show(
"distance = getDisMatEuclid(rdpack, uppLow, point) ! drop the zero-valued diagonal elements of the distance matrix.")
42 call disp%show(
"distance = getDisMatEuclid(point, euclid)")
46 call disp%show(
"distance = getDisMatEuclid(rdpack, uppLow, point, euclid) ! drop the zero-valued diagonal elements of the distance matrix.")
50 call disp%show(
"distance = getDisMatEuclid(point, euclidu)")
54 call disp%show(
"distance = getDisMatEuclid(rdpack, uppLow, point, euclidsq) ! drop the zero-valued diagonal elements of the distance matrix.")
58 call disp%show(
"distance = getDisMatEuclid(point, euclidsq)")
62 call disp%show(
"distance = getDisMatEuclid(rdpack, uppLow, point, euclidsq) ! drop the zero-valued diagonal elements of the distance matrix.")
Allocate or resize (shrink or expand) an input allocatable scalar string or array of rank 1....
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
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 procedures and generic interfaces for resizing allocatable arrays of various typ...
This module contains classes and procedures for computing various statistical quantities related to t...
type(euclidu_type), parameter euclidu
This is a scalar parameter object of type euclidu_typethat is exclusively used to request unsafe meth...
type(euclid_type), parameter euclid
This is a scalar parameter object of type euclid_type that is exclusively used to request safe method...
type(euclidsq_type), parameter euclidsq
This is a scalar parameter object of type euclidsq_typethat is exclusively used to request computing ...
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.
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
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 ⛓
12+10.0000000,
+3.00000000
13+9.00000000,
+1.00000000
16+0.00000000,
+10.6301460
17+10.6301460,
+0.00000000
20+10.6301460,
+10.6301460
23+0.00000000,
+10.6301460
24+10.6301460,
+0.00000000
27+10.6301460,
+10.6301460
30+0.00000000,
+10.6301460
31+10.6301460,
+0.00000000
34+113.000000,
+113.000000
37+0.00000000,
+113.000000
38+113.000000,
+0.00000000
41+113.000000,
+113.000000
78+3.00000000,
+7.00000000,
+5.00000000
79+6.00000000,
+1.00000000,
+10.0000000
82+0.00000000,
+6.40312433,
+4.47213602
83+6.40312433,
+0.00000000,
+9.21954441
84+4.47213602,
+9.21954441,
+0.00000000
87+6.40312433,
+6.40312433,
+4.47213602
88+4.47213602,
+9.21954441,
+9.21954441
91+0.00000000,
+6.40312433,
+4.47213602
92+6.40312433,
+0.00000000,
+9.21954441
93+4.47213602,
+9.21954441,
+0.00000000
96+6.40312433,
+6.40312433,
+4.47213602
97+4.47213602,
+9.21954441,
+9.21954441
100+0.00000000,
+6.40312433,
+4.47213602
101+6.40312433,
+0.00000000,
+9.21954441
102+4.47213602,
+9.21954441,
+0.00000000
105+41.0000000,
+41.0000000,
+20.0000000
106+20.0000000,
+85.0000000,
+85.0000000
109+0.00000000,
+41.0000000,
+20.0000000
110+41.0000000,
+0.00000000,
+85.0000000
111+20.0000000,
+85.0000000,
+0.00000000
114+41.0000000,
+41.0000000,
+20.0000000
115+20.0000000,
+85.0000000,
+85.0000000
- Test:
- test_pm_distanceEuclid
- Todo:
- High Priority: This generic interface must be extended to allow other packing and subsets of the output distance matrix.
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, September 1, 2017, 12:00 AM, Institute for Computational Engineering and Sciences (ICES), The University of Texas Austin
Definition at line 3110 of file pm_distanceEuclid.F90.
1.9.3