ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_clusKmeans::setMember Interface Reference

Compute and return the memberships and minimum distances of a set of input points with respect to the an input set of cluster centers.
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Detailed Description

Compute and return the memberships and minimum distances of a set of input points with respect to the an input set of cluster centers.

The membership ID of the ith sample sample(:,i) is determined by computing the distance of the sample from each cluster and choosing the cluster ID j whose center(:,j) has the minimum distance from the sample among all clusters.
This minimum squared distance is output in disq(:,i).
The metric used within this generic interface is the Euclidean distance.

Parameters
[in,out]membership: The output (or input/output) scalar or vector of shape (1:nsam) of type integer of default kind IK, containing the membership of each input sample in sample from its nearest cluster center, such that cluster(membership(i)) is the nearest cluster center to the ith sample sample(:, i) at a squared-distance of disq(i).
  1. If the optional input argument changed is missing, then membership has intent(out).
  2. If the optional input argument changed is present, then membership has intent(inout).
    On input, membership must contain the old cluster membership of the input sample.
[out]disq: The output scalar or vector of shape (1:nsam) of the same type and kind as the input argument sample, containing the Euclidean squared distance of each input sample in sample from its nearest cluster center.
[in]sample: The input scalar, vector, or matrix of,
  1. type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the sample of nsam points in a ndim-dimensional space whose memberships and minimum distances with respect to the input centers must be computed.
  1. If sample is a scalar and center is a vector of shape (1 : ncls), then the input sample must be the coordinate of a single sample in (univariate space) whose distance from ncls cluster centers must be computed.
  2. If sample is a vector of shape (1 : ndim) and center is a matrix of shape (1 : ndim, 1 : ncls), then the input sample must be a single sample (in ndim-dimensional space) whose distance from ncls cluster centers must be computed.
  3. If sample is a vector of shape (1 : nsam) and center is a vector of shape (1 : ncls), then the input sample must be a collection of nsam points (in univariate space) whose distances from ncls cluster centers must be computed.
  4. If sample is a matrix of shape (1 : ndim, 1 : nsam) and center is a matrix of shape (1 : ndim, 1 : ncls), then the input sample must be a collection of nsam points (in ndim-dimensional space) whose distances from ncls cluster centers must be computed.
[in]center: The input vector of shape (1:ncls) or matrix of shape (1 : ndim, 1 : ncls) of the same type and kind as the input argument sample, containing the set of ncls cluster centers (centroids) with respect to which the sample memberships and minimum distances must be computed.
[out]changed: The output scalar of type logical of default kind LK that is .false. if and only if the input values for membership and disq do not change *for any** of the input sample.
In other words, a single membership update is sufficient to set the value of changed to .true. on output.
(optional. If missing, the arguments membership and disq have intent(out) and both will be computed afresh.)


Possible calling interfaces

! The arguments `membership` and `disq` have `intent(out)`.
call setMember(membership , disq , sample , center(1 : ncls))
call setMember(membership(1 : nsam) , disq(1 : nsam), sample(1 : nsam) , center(1 : ncls))
call setMember(membership , disq , sample(1 : ndim) , center(1 : ndim, 1 : ncls))
call setMember(membership(1 : nsam) , disq(1 : nsam), sample(1 : ndim, 1 : nsam), center(1 : ndim, 1 : ncls))
! The arguments `membership` and `disq` have `intent(inout)`.
call setMember(membership , disq , sample , center(1 : ncls), changed)
call setMember(membership(1 : nsam) , disq(1 : nsam), sample(1 : nsam) , center(1 : ncls), changed)
call setMember(membership , disq , sample(1 : ndim) , center(1 : ndim, 1 : ncls), changed)
call setMember(membership(1 : nsam) , disq(1 : nsam), sample(1 : ndim, 1 : nsam), center(1 : ndim, 1 : ncls), changed)
Compute and return the memberships and minimum distances of a set of input points with respect to the...
This module contains procedures and routines for the computing the Kmeans clustering of a given set o...
Warning
The condition ubound(center, rank(center)) > 0 must hold for the corresponding input arguments.
The condition ubound(sample, rank(sample)) == ubound(disq, 1) must hold for the corresponding input arguments.
The condition ubound(sample, rank(sample)) == ubound(membership, 1) must hold for the corresponding input arguments.
The condition ubound(sample, 1) == ubound(center, 1) .or. rank(sample) == 0 .or. rank(center) == 1 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.
Remarks
This generic interface implements one of the two major steps involved in Kmeans clustering.
See also
setKmeans
setCenter
setMember
setKmeansPP


Example usage

1program example
2
3 use pm_kind, only: SK, IK, LK
4 use pm_kind, only: RKG => RKS ! all other real kinds are also supported.
5 use pm_io, only: display_type
6 use pm_distUnif, only: getUnifRand
8 use pm_clusKmeans, only: setMember
9 use pm_arrayRange, only: getRange
10
11 implicit none
12
13 logical(LK) :: changed
14 integer(IK) :: ndim, nsam, ncls
15 real(RKG) , allocatable :: sample(:,:), center(:,:), disq(:)
16 integer(IK) , allocatable :: membership(:)
17 type(display_type) :: disp
18
19 disp = display_type(file = "main.out.F90")
20
21 call disp%skip
22 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
23 call disp%show("! Compute memberships of a sample of points from arbitrary dimensional cluster centers.")
24 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
25 call disp%skip
26
27 call disp%skip()
28 call disp%show("ndim = getUnifRand(1, 5); nsam = getUnifRand(1, 5); ncls = getUnifRand(1, 5);")
29 ndim = getUnifRand(1, 5); nsam = getUnifRand(1, 5); ncls = getUnifRand(1, 5);
30 call disp%show("[ndim, nsam, ncls]")
31 call disp%show( [ndim, nsam, ncls] )
32 call disp%show("center = getUnifRand(0., 5., ndim, ncls) ! initialize random centers.")
33 center = getUnifRand(0., 5., ndim, ncls) ! initialize random centers.
34 call disp%show("center")
35 call disp%show( center )
36 call disp%show("sample = getUnifRand(0., 5., ndim, nsam) ! Create a random sample.")
37 sample = getUnifRand(0., 5., ndim, nsam) ! Create a random sample.
38 call disp%show("sample")
39 call disp%show( sample )
40 call disp%show("call setResized(disq, nsam)")
41 call setResized(disq, nsam)
42 call disp%show("call setResized(membership, nsam)")
43 call setResized(membership, nsam)
44 call disp%skip()
45
46 call disp%show("call setMember(membership, disq, sample, center) ! sample points memberships.")
47 call setMember(membership, disq, sample, center) ! sample points memberships.
48 call disp%show("membership")
49 call disp%show( membership )
50 call disp%show("disq")
51 call disp%show( disq )
52 call disp%skip()
53
54 call disp%show("call setMember(membership, disq, sample, center, changed) ! sample points memberships.")
55 call setMember(membership, disq, sample, center, changed) ! sample points memberships.
56 call disp%show("membership")
57 call disp%show( membership )
58 call disp%show("disq")
59 call disp%show( disq )
60 call disp%show("changed")
61 call disp%show( changed )
62 call disp%skip()
63
64 call disp%show("call setMember(membership(1), disq(1), sample(:,1), center) ! single point membership.")
65 call setMember(membership(1), disq(1), sample(:,1), center) ! single point membership.
66 call disp%show("membership")
67 call disp%show( membership )
68 call disp%show("disq")
69 call disp%show( disq )
70 call disp%skip()
71
72 call disp%show("call setMember(membership(1), disq(1), sample(:,1), center, changed) ! single point membership.")
73 call setMember(membership(1), disq(1), sample(:,1), center, changed) ! single point membership.
74 call disp%show("membership")
75 call disp%show( membership )
76 call disp%show("disq")
77 call disp%show( disq )
78 call disp%show("changed")
79 call disp%show( changed )
80 call disp%skip()
81
82 call disp%show("call setMember(membership, disq, sample(1,:), center(1,:)) ! sample points memberships in one-dimension.")
83 call setMember(membership, disq, sample(1,:), center(1,:)) ! sample points memberships in one-dimension.
84 call disp%show("membership")
85 call disp%show( membership )
86 call disp%show("disq")
87 call disp%show( disq )
88 call disp%skip()
89
90 call disp%show("call setMember(membership, disq, sample(1,:), center(1,:), changed) ! sample points memberships in one-dimension.")
91 call setMember(membership, disq, sample(1,:), center(1,:), changed) ! sample points memberships in one-dimension.
92 call disp%show("membership")
93 call disp%show( membership )
94 call disp%show("disq")
95 call disp%show( disq )
96 call disp%show("changed")
97 call disp%show( changed )
98 call disp%skip()
99
100 call disp%show("call setMember(membership(1), disq(1), sample(1,1), center(1,:)) ! single point membership in one-dimension.")
101 call setMember(membership(1), disq(1), sample(1,1), center(1,:)) ! single point membership in one-dimension.
102 call disp%show("membership")
103 call disp%show( membership )
104 call disp%show("disq")
105 call disp%show( disq )
106 call disp%skip()
107
108 call disp%show("call setMember(membership(1), disq(1), sample(1,1), center(1,:), changed) ! single point membership in one-dimension.")
109 call setMember(membership(1), disq(1), sample(1,1), center(1,:), changed) ! single point membership in one-dimension.
110 call disp%show("membership")
111 call disp%show( membership )
112 call disp%show("disq")
113 call disp%show( disq )
114 call disp%show("changed")
115 call disp%show( changed )
116 call disp%skip()
117
118 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
119 ! Output an example for visualization.
120 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
121
122 block
123 integer(IK) :: funit, i
124 ndim = 2
125 ncls = 5
126 nsam = 5000
127 center = getUnifRand(0., 1., ndim, ncls)
128 sample = getUnifRand(0., 1., ndim, nsam)
129 call setResized(disq, nsam)
130 call setResized(membership, nsam)
131 call setMember(membership, disq, sample, center)
132 call setMember(membership, disq, sample, center, changed)
133 open(newunit = funit, file = "setMember.center.txt")
134 do i = 1, ncls
135 write(funit, "(*(g0,:,','))") i, center(:,i)
136 end do
137 close(funit)
138 open(newunit = funit, file = "setMember.sample.txt")
139 do i = 1, nsam
140 write(funit, "(*(g0,:,','))") membership(i), sample(:,i)
141 end do
142 close(funit)
143 end block
144
145end program example
Generate minimally-spaced character, integer, real sequences or sequences at fixed intervals of size ...
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.
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 procedures and generic interfaces for generating ranges of discrete character,...
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...
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
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541
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
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
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567
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
2!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3! Compute memberships of a sample of points from arbitrary dimensional cluster centers.
4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5
6
7ndim = getUnifRand(1, 5); nsam = getUnifRand(1, 5); ncls = getUnifRand(1, 5);
8[ndim, nsam, ncls]
9+4, +1, +2
10center = getUnifRand(0., 5., ndim, ncls) ! initialize random centers.
11center
12+3.31561542, +2.40937471
13+2.37242699, +3.82513094
14+1.21023655, +2.40704751
15+4.88812494, +0.415560901
16sample = getUnifRand(0., 5., ndim, nsam) ! Create a random sample.
17sample
18+2.37383604
19+4.09437990
20+0.520631671
21+2.15728951
22call setResized(disq, nsam)
23call setResized(membership, nsam)
24
25call setMember(membership, disq, sample, center) ! sample points memberships.
26membership
27+2
28disq
29+6.66594124
30
31call setMember(membership, disq, sample, center, changed) ! sample points memberships.
32membership
33+2
34disq
35+6.66594124
36changed
37F
38
39call setMember(membership(1), disq(1), sample(:,1), center) ! single point membership.
40membership
41+2
42disq
43+6.66594124
44
45call setMember(membership(1), disq(1), sample(:,1), center, changed) ! single point membership.
46membership
47+2
48disq
49+6.66594124
50changed
51F
52
53call setMember(membership, disq, sample(1,:), center(1,:)) ! sample points memberships in one-dimension.
54membership
55+2
56disq
57+0.126299728E-2
58
59call setMember(membership, disq, sample(1,:), center(1,:), changed) ! sample points memberships in one-dimension.
60membership
61+2
62disq
63+0.126299728E-2
64changed
65F
66
67call setMember(membership(1), disq(1), sample(1,1), center(1,:)) ! single point membership in one-dimension.
68membership
69+2
70disq
71+0.126299728E-2
72
73call setMember(membership(1), disq(1), sample(1,1), center(1,:), changed) ! single point membership in one-dimension.
74membership
75+2
76disq
77+0.126299728E-2
78changed
79F
80
81

Postprocessing of the example output
1#!/usr/bin/env python
2
3import matplotlib.pyplot as plt
4import pandas as pd
5import numpy as np
6import glob
7import sys
8import os
9
10fontsize = 17
11fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
12ax = plt.subplot()
13
14parent = os.path.basename(os.path.dirname(__file__))
15pattern = parent + "*.txt"
16
17fileList = glob.glob(pattern)
18legends = []
19if len(fileList) == 2:
20 for file in fileList:
21
22 kind = file.split(".")[1]
23 prefix = file.split(".")[0]
24 df = pd.read_csv(file, delimiter = ",", header = None)
25
26 if kind == "center":
27 ax.scatter ( df.values[:, 1]
28 , df.values[:,2]
29 , zorder = 100
30 , marker = "*"
31 , c = "red"
32 , s = 50
33 )
34 legends.append("center")
35 elif kind == "sample":
36 ax.scatter ( df.values[:, 1]
37 , df.values[:,2]
38 , c = df.values[:, 0]
39 , s = 10
40 )
41 legends.append("sample")
42 else:
43 sys.exit("Ambiguous file exists: {}".format(file))
44
45 ax.legend(legends, fontsize = fontsize)
46 plt.xticks(fontsize = fontsize - 2)
47 plt.yticks(fontsize = fontsize - 2)
48 ax.set_xlabel("X", fontsize = 17)
49 ax.set_ylabel("Y", fontsize = 17)
50 ax.set_title("Membership Scatter Plot", fontsize = fontsize)
51
52 plt.axis('equal')
53 plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
54 ax.tick_params(axis = "y", which = "minor")
55 ax.tick_params(axis = "x", which = "minor")
56 ax.set_axisbelow(True)
57 plt.tight_layout()
58
59 plt.savefig(prefix + ".png")
60else:
61 sys.exit("Ambiguous file list exists.")

Visualization of the example output
Benchmarks:


Benchmark :: The runtime performance of setMember for external membership change verification vs. in place verification by the algorithm.

1! Test the performance of Cholesky factorization computation using an assumed-shape interface vs. explicit-shape interface.
2program benchmark
3
4 use pm_kind, only: IK, LK, RKG => RKD, SK
5 use pm_distUnif, only: setUnifRand
6 use pm_bench, only: bench_type
7
8 implicit none
9
10 integer(IK) :: icls
11 integer(IK) :: ibench
12 integer(IK) :: fileUnit
13 integer(IK) , parameter :: nsam = 1000
14 integer(IK) , parameter :: ndim = 3_IK
15 integer(IK) , parameter :: ncls = 20_IK
16 integer(IK) :: membership(nsam)
17 real(RKG) :: sample(ndim, nsam)
18 real(RKG) :: center(ndim, ncls)
19 real(RKG) :: disq(nsam)
20 type(bench_type), allocatable :: bench(:)
21 real(RKG) :: mean(ndim)
22 integer(IK) :: idum = 0
23 logical(LK) :: mchanged
24
25 bench = [ bench_type(name = SK_"default", exec = default, overhead = setOverhead) &
26 , bench_type(name = SK_"changed", exec = changed, overhead = setOverhead) &
27 ]
28
29 write(*,"(*(g0,:,' '))")
30 write(*,"(*(g0,:,' '))") "membership benchmarking..."
31 write(*,"(*(g0,:,' '))")
32
33 open(newunit = fileUnit, file = "main.out", status = "replace")
34
35 write(fileUnit, "(*(g0,:,','))") "ClusterCount", (bench(ibench)%name, ibench = 1, size(bench))
36
37 do icls = 1, 20
38
39 write(*,"(*(g0,:,' '))") "Benchmarking default() vs. changed()", nsam
40
41 call random_number(disq)
42 call random_number(center)
43 call random_number(sample)
44 call setUnifRand(membership, 1, icls)
45 do ibench = 1, size(bench)
46 bench(ibench)%timing = bench(ibench)%getTiming()
47 end do
48
49 write(fileUnit,"(*(g0,:,','))") icls, (bench(ibench)%timing%mean, ibench = 1, size(bench))
50
51 end do
52 write(*,"(*(g0,:,' '))") idum
53
54 close(fileUnit)
55
56contains
57
58 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
59 ! procedure wrappers.
60 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
61
62 subroutine setOverhead()
63 if (mchanged) idum = idum + 1
64 end subroutine
65
66 subroutine default()
67 use pm_clusKmeans, only: setMember
68 integer(IK) :: membersnew(size(membership))
69 call setMember(membersnew, disq, sample, center(:, 1 : icls))
70 mchanged = all(membersnew == membership)
71 end subroutine
72
73 subroutine changed()
74 use pm_clusKmeans, only: setMember
75 call setMember(membership, disq, sample, center(:, 1 : icls), mchanged)
76 end subroutine
77
78end program benchmark
Generate and return an object of type timing_type containing the benchmark timing information and sta...
Definition: pm_bench.F90:574
Return a uniform random scalar or contiguous array of arbitrary rank of randomly uniformly distribute...
This module contains abstract interfaces and types that facilitate benchmarking of different procedur...
Definition: pm_bench.F90:41
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:568
This is the class for creating benchmark and performance-profiling objects.
Definition: pm_bench.F90:386

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

Postprocessing of the benchmark output
1#!/usr/bin/env python
2
3import matplotlib.pyplot as plt
4import pandas as pd
5import numpy as np
6
7import os
8dirname = os.path.basename(os.getcwd())
9
10fontsize = 14
11
12df = pd.read_csv("main.out", delimiter = ",")
13colnames = list(df.columns.values)
14
15
18
19ax = plt.figure(figsize = 1.25 * np.array([6.4,4.6]), dpi = 200)
20ax = plt.subplot()
21
22for colname in colnames[1:]:
23 plt.plot( df[colnames[0]].values
24 , df[colname].values
25 , linewidth = 2
26 )
27
28plt.xticks(fontsize = fontsize)
29plt.yticks(fontsize = fontsize)
30ax.set_xlabel(colnames[0], fontsize = fontsize)
31ax.set_ylabel("Runtime [ seconds ]", fontsize = fontsize)
32ax.set_title(" vs. ".join(colnames[1:])+"\nLower is better.", fontsize = fontsize)
33ax.set_xscale("log")
34ax.set_yscale("log")
35plt.minorticks_on()
36plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
37ax.tick_params(axis = "y", which = "minor")
38ax.tick_params(axis = "x", which = "minor")
39ax.legend ( colnames[1:]
40 #, loc='center left'
41 #, bbox_to_anchor=(1, 0.5)
42 , fontsize = fontsize
43 )
44
45plt.tight_layout()
46plt.savefig("benchmark." + dirname + ".runtime.png")
47
48
51
52ax = plt.figure(figsize = 1.25 * np.array([6.4,4.6]), dpi = 200)
53ax = plt.subplot()
54
55plt.plot( df[colnames[0]].values
56 , np.ones(len(df[colnames[0]].values))
57 , linestyle = "--"
58 #, color = "black"
59 , linewidth = 2
60 )
61for colname in colnames[2:]:
62 plt.plot( df[colnames[0]].values
63 , df[colname].values / df[colnames[1]].values
64 , linewidth = 2
65 )
66
67plt.xticks(fontsize = fontsize)
68plt.yticks(fontsize = fontsize)
69ax.set_xlabel(colnames[0], fontsize = fontsize)
70ax.set_ylabel("Runtime compared to {}".format(colnames[1]), fontsize = fontsize)
71ax.set_title("Runtime Ratio Comparison. Lower means faster.\nLower than 1 means faster than {}().".format(colnames[1]), fontsize = fontsize)
72ax.set_xscale("log")
73ax.set_yscale("log")
74plt.minorticks_on()
75plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
76ax.tick_params(axis = "y", which = "minor")
77ax.tick_params(axis = "x", which = "minor")
78ax.legend ( colnames[1:]
79 #, bbox_to_anchor = (1, 0.5)
80 #, loc = "center left"
81 , fontsize = fontsize
82 )
83
84plt.tight_layout()
85plt.savefig("benchmark." + dirname + ".runtime.ratio.png")

Visualization of the benchmark output

Benchmark moral The procedures under the generic interface setMember compute the new membership under two different scenarios.
  1. When the input argument changed is missing, the memberships are computed afresh and no comparison with any old membership values is done by the algorithm.
    Consequently, any such comparisons would have to be done externally to the procedure by the user, which requires another pass over the membership values for a comparison.
  2. When the input argument changed is present, the memberships are computed afresh but before overwriting the old values, they are compared against them to detect if any memberships change at all and if so, changed = .true. on output.
From the benchmark results above, it appears that when membership comparison with old values is desired, letting the procedure to perform the comparison (by presenting the optional argument changed) is significantly slower than an external comparison of memberships by the user.
However, the difference is relevant only for small number of clusters involved (1 : 4) and the difference become negligible for more number of clusters.
Where is this situation relevant? Within the Kmeans algorithm this situation repeatedly occurs.
Additionally, note that the above benchmark does not include the cost of maintaining two (old and new) copies of cluster memberships which could potentially lead to additional allocation costs if it happens repeatedly, e.g., within the Kmeans algorithm.
Test:
test_pm_clusKmeans


Final Remarks


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Author:
Amir Shahmoradi, September 1, 2012, 12:00 AM, National Institute for Fusion Studies, The University of Texas Austin

Definition at line 249 of file pm_clusKmeans.F90.


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