pm_arraySelect Module Reference

This module contains procedures and generic interfaces for selecting the \(k\)th smallest element in unsorted arrays of various types. More...

Data Types
interface	getSelected
	Generate and return the rankth smallest value in the input array by first sorting its elements in ascending order (optionally only between the specified indices [lb, ub]). More...
interface	setSelected
	Return the rankth smallest (or ordered) value in the input array by first sorting its elements in ascending order (optionally only between the specified indices [lb, ub]). More...

Variables
character(*, SK), parameter	MODULE_NAME = "@pm_arraySelect"

Detailed Description

This module contains procedures and generic interfaces for selecting the \(k\)th smallest element in unsorted arrays of various types.

Benchmarks:

Benchmark :: The runtime performance of getSelected vs. setSelected ⛓

! Test the performance of `getSelected()` vs. `setSelected()`.
program benchmark
 
    use iso_fortran_env, only: error_unit
    use pm_kind, only: IK, LK, RK, SK
    use pm_arrayRange, only: getRange
    use pm_bench, only: bench_type
 
    implicit none
 
    integer(IK)                         :: i
    integer(IK)                         :: isize
    integer(IK)                         :: fileUnit
    integer(IK) , parameter             :: NSIZE = 20_IK
    integer(IK) , parameter             :: NBENCH = 2_IK
    integer(IK)                         :: arraySize(NSIZE)
    logical(LK)                         :: dummy = .true._LK
    real(RK)                            :: selection = 1._RK
    real(RK)    , allocatable           :: array(:)
    integer(IK)                         :: rank
    type(bench_type)                    :: bench(NBENCH)
 
    bench(1) = bench_type(name = SK_"setSelected", exec = setSelected , overhead = setOverhead)
    bench(2) = bench_type(name = SK_"getSelected", exec = getSelected , overhead = setOverhead)
 
    arraySize = [( 2_IK**isize, isize = 1_IK, NSIZE )]
 
    write(*,"(*(g0,:,' '))")
    write(*,"(*(g0,:,' '))") "setSelected() vs. getSelected()"
    write(*,"(*(g0,:,' '))")
 
    open(newunit = fileUnit, file = "main.out")
 
        write(fileUnit, "(*(g0,:,','))") "arraySize", (bench(i)%name, i = 1, NBENCH)
 
        loopOverArraySize: do isize = 1, NSIZE
 
            write(*,"(*(g0,:,' '))") "Benchmarking with size", arraySize(isize)
 
            allocate(array(arraySize(isize)))
            rank = 1_IK ! arraySize(isize)
            do i = 1, NBENCH
                bench(i)%timing = bench(i)%getTiming(minsec = 0.05_RK)
            end do
            deallocate(array)
 
            write(fileUnit,"(*(g0,:,','))") arraySize(isize), (bench(i)%timing%mean, i = 1, NBENCH)
 
        end do loopOverArraySize
        write(*,"(*(g0,:,' '))") dummy
        write(*,"(*(g0,:,' '))")
 
    close(fileUnit)
 
contains
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! procedure wrappers.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    subroutine setOverhead()
        call initialize()
        call finalize()
    end subroutine
 
    subroutine initialize()
        call random_number(array)
    end subroutine
 
    subroutine finalize()
        dummy = dummy .and. selection == 0.5_RK
    end subroutine
 
    subroutine setSelected()
        block
            use pm_arraySelect, only: setSelected
            call initialize()
            call setSelected(selection, array, rank)
            call finalize()
        end block
    end subroutine
 
    subroutine getSelected()
        block
            use pm_arraySelect, only: getSelected
            call initialize()
            selection = getSelected(array, rank)
            call finalize()
        end block
    end subroutine
 
end program benchmark

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Postprocessing of the benchmark output ⛓

#!/usr/bin/env python
 
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
 
fontsize = 14
 
methods = ["setSelected", "getSelected"]
 
df = pd.read_csv("main.out")
 
 
 
ax = plt.figure(figsize = 1.25 * np.array([6.4,4.6]), dpi = 200)
ax = plt.subplot()
 
for method in methods:
    plt.plot( df["arraySize"].values
            , df[method].values
            , linewidth = 2
            )
 
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
ax.set_xlabel("Array Size", fontsize = fontsize)
ax.set_ylabel("Runtime [ seconds ]", fontsize = fontsize)
ax.set_title("setSelected() vs. getSelected()\nLower is better.", fontsize = fontsize)
ax.set_xscale("log")
ax.set_yscale("log")
plt.minorticks_on()
plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
ax.tick_params(axis = "y", which = "minor")
ax.tick_params(axis = "x", which = "minor")
ax.legend   ( methods
           #, loc='center left'
           #, bbox_to_anchor=(1, 0.5)
            , fontsize = fontsize
            )
 
plt.tight_layout()
plt.savefig("benchmark.getSelected_vs_setSelected.runtime.png")
 
 
 
ax = plt.figure(figsize = 1.25 * np.array([6.4,4.6]), dpi = 200)
ax = plt.subplot()
 
plt.plot( df["arraySize"].values
        , np.ones(len(df["arraySize"].values))
       #, linestyle = "-"
       #, color = "black"
        , linewidth = 2
        )
plt.plot( df["arraySize"].values
        , df["getSelected"].values / df["setSelected"].values
        , linewidth = 2
        )
 
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
ax.set_xlabel("Array Size", fontsize = fontsize)
ax.set_ylabel("Runtime compared to setSelected()", fontsize = fontsize)
ax.set_title("getSelected() / setSelected()\nLower means faster. Lower than 1 means faster than setSelected().", fontsize = fontsize)
ax.set_xscale("log")
#ax.set_yscale("log")
plt.minorticks_on()
plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
ax.tick_params(axis = "y", which = "minor")
ax.tick_params(axis = "x", which = "minor")
ax.legend   ( ["setSelected", "getSelected"]
           #, bbox_to_anchor = (1, 0.5)
           #, loc = "center left"
            , fontsize = fontsize
            )
 
plt.tight_layout()
plt.savefig("benchmark.getSelected_vs_setSelected.runtime.ratio.png")

Visualization of the benchmark output ⛓

Benchmark moral ⛓

1. The procedures under the generic interface getSelected are functions while the procedures under the generic interface setSelected are subroutines.
   From the benchmark results, it appears that the functional interface performs slightly less efficiently than the subroutine interface.
   This is entirely due to the fact that the functional interface makes a full copy of the input array to keep the input array intact.
   
2. Note that in this benchmark rank = 1 was used to minimize the time spent on sorting, such that only the array copy time becomes the dominant factor.
   Nevertheless, the benchmark results point to the relatively minor effect of array copying on the runtime performance of functional vs. subroutine procedures.
   
3. There is, however, a \(30\%-300\%\) performance loss with the use of the functional interface when size(array) < 10.
   

Test:

test_pm_arraySelect

Final Remarks ⛓

---

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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.

Copyright

Computational Data Science Lab

Author:

Fatemeh Bagheri, Wednesday 12:20 AM, October 13, 2021, Dallas, TX

Variable Documentation

MODULE_NAME

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

Definition at line 53 of file pm_arraySelect.F90.