ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_mathCumSum Module Reference

This module contains the procedures and interfaces for computing the cumulative sum of an array. More...

Data Types

interface  getCumSum
 Generate and return the cumulative sum of the input array, optionally in the backward direction and, optionally reverse the output cumulative sum array upon return. More...
 
interface  setCumSum
 Return the cumulative sum of the input array, optionally in the backward direction and optionally, reverse the output cumulative sum array upon return. More...
 

Variables

character(*, SK), parameter MODULE_NAME = "@pm_mathCumSum"
 

Detailed Description

This module contains the procedures and interfaces for computing the cumulative sum of an array.

Benchmarks:


Benchmark :: The runtime performance of getCumSum vs. setCumSum

1! Test the performance of `getCumSum()` vs. `setCumSum()`.
2program benchmark
3
4 use iso_fortran_env, only: error_unit
5 use pm_kind, only: IK, RK, SK
6 use pm_bench, only: bench_type
7
8 implicit none
9
10 integer(IK) :: i
11 integer(IK) :: iarr
12 integer(IK) :: fileUnit
13 integer(IK) , parameter :: NARR = 11_IK
14 integer(IK) :: arraySize(NARR)
15 real(RK) :: dummySum = 0._RK
16 real(RK) , allocatable :: array(:)
17 real(RK) , allocatable :: cumsum(:)
18 type(bench_type), allocatable :: bench(:)
19
20 bench = [ bench_type(name = SK_"setCumSum", exec = setCumSum, overhead = setOverhead) &
21 , bench_type(name = SK_"getCumSum", exec = getCumSum, overhead = setOverhead) &
22 , bench_type(name = SK_"setCumSum_overwrite", exec = setCumSum_overwrite, overhead = setOverhead) &
23 , bench_type(name = SK_"getCumSum_withBounds", exec = getCumSum_withBounds, overhead = setOverhead) &
24 ]
25
26 arraySize = [( 2_IK**iarr, iarr = 1_IK, NARR )]
27
28 write(*,"(*(g0,:,' '))")
29 write(*,"(*(g0,:,' '))") "setCumSum() vs. getCumSum() vs. getCumSum_withBounds()"
30 write(*,"(*(g0,:,' '))")
31
32 open(newunit = fileUnit, file = "main.out", status = "replace")
33
34 write(fileUnit, "(*(g0,:,','))") "arraySize", (bench(i)%name, i = 1, size(bench))
35
36 loopOverArraySize: do iarr = 1, NARR
37
38 allocate(array(arraySize(iarr)))
39 allocate(cumsum(arraySize(iarr)), source = 0._RK)
40 write(*,"(*(g0,:,' '))") "Benchmarking with array size", arraySize(iarr)
41
42 do i = 1, size(bench)
43 bench(i)%timing = bench(i)%getTiming() !, minsec = 0.1_RK)
44 end do
45 write(fileUnit,"(*(g0,:,','))") arraySize(iarr), (bench(i)%timing%mean, i = 1, size(bench))
46
47 deallocate(array, cumsum)
48
49 end do loopOverArraySize
50 write(*,"(*(g0,:,' '))") dummySum
51 write(*,"(*(g0,:,' '))")
52
53 close(fileUnit)
54
55contains
56
57 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
58 ! procedure wrappers.
59 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
60
61 subroutine setOverhead()
62 call setArray()
63 call getDummy()
64 end subroutine
65
66 subroutine setArray()
67 call random_number(array)
68 end subroutine
69
70 subroutine getDummy()
71 dummySum = dummySum + cumsum(1) + array(1)
72 end subroutine
73
74 subroutine setCumSum()
75 block
76 use pm_mathCumSum, only: setCumSum
77 call setArray()
78 call setCumSum(cumsum, array)
79 call getDummy()
80 end block
81 end subroutine
82
83 subroutine setCumSum_overwrite()
84 block
85 use pm_mathCumSum, only: setCumSum
86 call setArray()
87 call setCumSum(array)
88 call getDummy()
89 end block
90 end subroutine
91
92 subroutine getCumSum()
93 block
94 use pm_mathCumSum, only: getCumSum
95 call setArray()
96 cumsum = getCumSum(array)
97 call getDummy()
98 end block
99 end subroutine
100
101 subroutine getCumSum_withBounds()
102 block
103 use pm_mathCumSum, only: getCumSum
104 call setArray()
105 cumsum(:) = getCumSum(array)
106 call getDummy()
107 end block
108 end subroutine
109
110end program benchmark
Generate and return an object of type timing_type containing the benchmark timing information and sta...
Definition: pm_bench.F90:574
Generate and return the cumulative sum of the input array, optionally in the backward direction and,...
Return the cumulative sum of the input array, optionally in the backward direction and optionally,...
This module contains abstract interfaces and types that facilitate benchmarking of different procedur...
Definition: pm_bench.F90:41
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
integer, parameter RK
The default real kind in the ParaMonte library: real64 in Fortran, c_double in C-Fortran Interoperati...
Definition: pm_kind.F90:543
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
This module contains the procedures and interfaces for computing the cumulative sum of an array.
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")
73#ax.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
  1. The procedures under the generic interface getCumSum are functions while the procedures under the generic interface setCumSum are subroutines.
    From the benchmark results, it appears that the functional interface performs less efficiently than the subroutine interface.
  2. Furthermore, specifying the array bounds on the left-hand-side (LHS) assignment in the case of the functional interface (to avoid automatic reallocation) does not appear to enhance the performance of the functional interface in any meaningful way.
    In other words, the compiler appears to be smart enough to not reallocate the LHS needlessly.
Test:
test_pm_mathCumSum


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.

  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.
  2. 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.

Author:
Amir Shahmoradi, April 25, 2015, 2:21 PM, National Institute for Fusion Studies, The University of Texas Austin

Variable Documentation

◆ MODULE_NAME

character(*, SK), parameter pm_mathCumSum::MODULE_NAME = "@pm_mathCumSum"

Definition at line 58 of file pm_mathCumSum.F90.