This module contains procedures and generic interfaces for finding locations of a pattern in arrays of various types at the specified instances of occurrence of pattern. More...

Data Types
interface	getCountLoc
	Generate and return the number of occurrences of the input `pattern` in the input `array` optionally subject to user-specified memory blindness. More...

interface	getLoc
	Generate and return an `allocatable` array containing the indices of the locations within the input array where the input `pattern` exists. More...

interface	setLoc
	Return an `allocatable` array containing the indices of the locations within the input array where the input `pattern` exists. More...

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

Detailed Description

This module contains procedures and generic interfaces for finding locations of a pattern in arrays of various types at the specified instances of occurrence of pattern.

Benchmarks:

Benchmark :: The runtime performance of setLoc for scalar vs. vector input pattern argument. ⛓

! Test the performance of setLoc() with a vector `pattern` vs. scalar `pattern`.
program benchmark
 
    use iso_fortran_env, only: error_unit
    use pm_kind, only: IK, LK, RK, SK
    use pm_bench, only: bench_type
 
    implicit none
 
    integer(IK)                         :: i
    integer(IK)                         :: nloc
    integer(IK)                         :: isize
    integer(IK)                         :: fileUnit
    integer(IK)     , parameter         :: NSIZE = 18_IK
    integer(IK)     , parameter         :: NBENCH = 2_IK
    integer(IK)                         :: arraySize(NSIZE)
    logical(LK)                         :: dummy = .true._LK
    integer(IK)     , allocatable       :: loc(:)
    integer(IK)     , allocatable       :: array(:)
    integer(IK)     , parameter         :: pattern(1) = 0_IK
    type(bench_type)                    :: bench(NBENCH)
 
    bench(1) = bench_type(name = SK_"scalarPattern", exec = scalarPattern , overhead = setOverhead)
    bench(2) = bench_type(name = SK_"vectorPattern", exec = vectorPattern , overhead = setOverhead)
 
    arraySize = [( 2_IK**isize, isize = 1_IK, NSIZE )]
    loc = [integer(IK) ::] ! essential for `setLoc()`.
    nloc = 0_IK
 
    write(*,"(*(g0,:,' '))")
    write(*,"(*(g0,:,' '))") "scalarPattern() vs. vectorPattern()"
    write(*,"(*(g0,:,' '))")
 
    open(newunit = fileUnit, file = "main.out", status = "replace")
 
        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)))
 
            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()
        array(:) = 1_IK
    end subroutine
 
    subroutine finalize()
        dummy = dummy .and. size(loc, 1, IK) == nloc
    end subroutine
 
    subroutine scalarPattern()
        use pm_arrayFind, only: setLoc
        call initialize()
        call setLoc(loc, nloc, array, pattern(1), 1_IK)
        call finalize()
    end subroutine
 
    subroutine vectorPattern()
        block
            use pm_arrayFind, only: setLoc
            call initialize()
            call setLoc(loc, nloc, array, pattern, 1_IK)
            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 = ["scalarPattern", "vectorPattern"]
 
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("Finding array segments with pattern(1) (scalar) vs. pattern(1:1) (vector).\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.setLoc-scalarPattern_vs_vectorPattern.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["vectorPattern"].values / df["scalarPattern"].values
        , linewidth = 2
        )
 
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
ax.set_xlabel("Array Size", fontsize = fontsize)
ax.set_ylabel("Runtime compared to scalarPattern()", fontsize = fontsize)
ax.set_title("Runtime Ratio: Find pattern(1:1) / Find pattern(1).\nLower means faster. Lower than 1 means faster than scalarPattern.", 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   ( ["scalarPattern", "vectorPattern"]
           #, bbox_to_anchor = (1, 0.5)
           #, loc = "center left"
            , fontsize = fontsize
            )
 
plt.tight_layout()
plt.savefig("benchmark.setLoc-scalarPattern_vs_vectorPattern.runtime.ratio.png")

Visualization of the benchmark output ⛓

Benchmark moral ⛓

The procedures under the generic interface setLoc take both scalar and vector pattern arguments.
As evidenced by the above benchmark, when the input pattern is vector of length 1, it is much faster, possibly up to 4X, to pass pattern as a scalar instead of a whole array of length 1.
Note that this benchmark is likely irrelevant to finding substrings in Fortran strings.

Benchmark :: The runtime performance of getLoc vs. setLoc ⛓

! Test the performance of `getLoc()` vs. `setLoc()`.
program benchmark
 
    use iso_fortran_env, only: error_unit
    use pm_kind, only: IK, LK, RK, SK
    use pm_bench, only: bench_type
 
    implicit none
 
    integer(IK)                         :: i
    integer(IK)                         :: nloc
    integer(IK)                         :: isize
    integer(IK)                         :: fileUnit
    integer(IK)     , parameter         :: blindness = 1
    integer(IK)     , parameter         :: NSIZE = 18_IK
    integer(IK)     , parameter         :: NBENCH = 2_IK
    integer(IK)                         :: arraySize(NSIZE)
    logical(LK)                         :: dummy = .true._LK
    integer(IK)     , allocatable       :: loc(:)
    character(:, SK), allocatable       :: array
    character(1,SK)                     :: pattern
    type(bench_type)                    :: bench(NBENCH)
 
    bench(1) = bench_type(name = SK_"setLoc", exec = setLoc , overhead = setOverhead)
    bench(2) = bench_type(name = SK_"getLoc", exec = getLoc , overhead = setOverhead)
 
    arraySize = [( 2_IK**isize, isize = 1_IK, NSIZE )]
    loc = [integer(IK) ::] ! essential for `setLoc()`.
    nloc = 0_IK
 
    write(*,"(*(g0,:,' '))")
    write(*,"(*(g0,:,' '))") "setLoc() vs. getLoc()"
    write(*,"(*(g0,:,' '))")
 
    open(newunit = fileUnit, file = "main.out", status = "replace")
 
        write(fileUnit, "(*(g0,:,','))") "arraySize", (bench(i)%name, i = 1, NBENCH)
 
        loopOverArraySize: do isize = 1, NSIZE
 
            write(*,"(*(g0,:,' '))") "Benchmarking with size", arraySize(isize)
 
            allocate(character(arraySize(isize)) :: array)
            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()
        use pm_distUnif, only: setUnifRand
        !allocate( character(arraySize(isize)) :: array )
        call setUnifRand(pattern)
        array(:) = repeat(pattern, len(array))
    end subroutine
 
    subroutine finalize()
        dummy = dummy .and. size(loc, 1, IK) == nloc
        !deallocate(array)
    end subroutine
 
    subroutine setLoc()
        block
            use pm_arrayFind, only: setLoc
            call initialize()
            call setLoc(loc, nloc, array, pattern, blindness)
            call finalize()
        end block
    end subroutine
 
    subroutine getLoc()
        block
            use pm_arrayFind, only: getLoc
            call initialize()
            loc = getLoc(array, pattern)
            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 = ["setLoc", "getLoc"]
 
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("setLoc() vs. getLoc()\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.getLoc_vs_setLoc.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["getLoc"].values / df["setLoc"].values
        , linewidth = 2
        )
 
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
ax.set_xlabel("Array Size", fontsize = fontsize)
ax.set_ylabel("Runtime compared to setLoc()", fontsize = fontsize)
ax.set_title("getLoc() / setLoc()\nLower means faster. Lower than 1 means faster than setLoc().", 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   ( ["setLoc", "getLoc"]
           #, bbox_to_anchor = (1, 0.5)
           #, loc = "center left"
            , fontsize = fontsize
            )
 
plt.tight_layout()
plt.savefig("benchmark.getLoc_vs_setLoc.runtime.ratio.png")

Visualization of the benchmark output ⛓

Benchmark moral ⛓

The procedures under the generic interface getLoc are functions while the procedures under the generic interface setLoc are subroutines.
From the benchmark results, it appears that the functional interface performs slightly less efficiently than the subroutine interface when the input array size is small.
Nevertheless, the difference appears to be marginal and insignificant in most practical situations.
Note that this benchmark considers the worst-case scenario where all elements of the input array match the input pattern and must be therefore indexed.

Benchmark :: The runtime performance of setLoc with and without sorted = .true. and positive = .true. optional input arguments. ⛓

! Test the performance of setLoc() with and without the optional `sorted = .true._LK, positive = .true.` input arguments.
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)                         :: nloc
    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
    integer(IK)     , allocatable       :: instance(:)
    integer(IK)     , allocatable       :: loc(:)
    integer(IK)     , allocatable       :: array(:)
    integer(IK)                         :: pattern
    type(bench_type)                    :: bench(NBENCH)
    real(RK)                            :: unifrnd
 
    bench(1) = bench_type(name = SK_"sortedPositive", exec = sortedPositive , overhead = setOverhead)
    bench(2) = bench_type(name = SK_"defaultOptions", exec = defaultOptions , overhead = setOverhead)
 
    arraySize = [( 2_IK**isize, isize = 1_IK, NSIZE )]
    loc = [integer(IK) ::] ! essential for `setLoc()`.
    nloc = 0_IK
 
    write(*,"(*(g0,:,' '))")
    write(*,"(*(g0,:,' '))") "sortedPositive() vs. defaultOptions()"
    write(*,"(*(g0,:,' '))")
 
    open(newunit = fileUnit, file = "main.out", status = "replace")
 
        write(fileUnit, "(*(g0,:,','))") "arraySize", (bench(i)%name, i = 1_IK, NBENCH)
 
        loopOverArraySize: do isize = 1_IK, NSIZE
 
            write(*,"(*(g0,:,' '))") "Benchmarking with size", arraySize(isize)
            instance = getRange(1_IK, arraySize(isize))
            allocate(array(arraySize(isize)))
 
            do i = 1_IK, NBENCH
                bench(i)%timing = bench(i)%getTiming(minsec = 0.05_RK)
            end do
 
            deallocate(array, instance)
            write(fileUnit,"(*(g0,:,','))") arraySize(isize), (bench(i)%timing%mean, i = 1_IK, 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(unifrnd)
        pattern = nint(unifrnd, kind = IK)
        array(:) = pattern + 1_IK
    end subroutine
 
    subroutine finalize()
        dummy = dummy .and. size(loc, kind = IK) == nloc
    end subroutine
 
    subroutine sortedPositive()
        use pm_arrayFind, only: setLoc
        call initialize()
        call setLoc(loc, nloc, array, pattern, instance, .true._LK, .true._LK, 1_IK)
        call finalize()
    end subroutine
 
    subroutine defaultOptions()
        block
            use pm_arrayFind, only: setLoc
            call initialize()
            call setLoc(loc, nloc, array, pattern, instance, .false._LK, .false._LK, 1_IK)
            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 = ["sortedPositive", "defaultOptions"]
 
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("Finding pattern with `sorted = .true._LK, positive = .true.` vs. the default.\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.setLoc-sortedPositive_vs_defaultOptions.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["defaultOptions"].values / df["sortedPositive"].values
        , linewidth = 2
        )
 
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
ax.set_xlabel("Array Size", fontsize = fontsize)
ax.set_ylabel("Runtime compared to sortedPositive", fontsize = fontsize)
ax.set_title("Runtime Ratio: Find with sortedPositive / Find with defaultOptions.\nLower means faster. Lower than 1 means faster than finding with sortedPositive.", 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   ( ["sortedPositive", "defaultOptions"]
           #, bbox_to_anchor = (1, 0.5)
           #, loc = "center left"
            , fontsize = fontsize
            )
 
plt.tight_layout()
plt.savefig("benchmark.setLoc-sortedPositive_vs_defaultOptions.runtime.ratio.png")

Visualization of the benchmark output ⛓

Benchmark moral ⛓

The procedures under the generic interface setLoc take two optional sorted and positive input arguments when the input array of instances instance is also specified. Setting sorted = .true._LK, positive = .true. guarantees to the procedures that all elements of instance are sorted in ascending-order and that no negative or zero value is present in instance. Hence, the maximum value in instance corresponds to instance(size(instance)), saving the procedures the time to find the maximum value of the input instance.
As evidenced by the above benchmark, when sorted = .true._LK, positive = .true. can be guaranteed by the user, the runtime performance of the procedures could possibly increase 2-3 times compared to when the default values have to be assumed, corresponding to the worst case scenario (sorted = .false._LK, positive = .false.).
The results of this benchmark equally hold for the functions under the generic interface getLoc.

Benchmark :: The runtime performance of setLoc with and without iseq external optional input argument. ⛓

! Test the performance of setLoc() with and without the optional external function `iseq` input argument.
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)                         :: nloc
    integer(IK)                         :: isize
    integer(IK)                         :: fileUnit
    integer(IK)     , parameter         :: blindness = 1
    integer(IK)     , parameter         :: NSIZE = 20_IK
    integer(IK)     , parameter         :: NBENCH = 2_IK
    integer(IK)                         :: arraySize(NSIZE)
    logical(LK)                         :: dummy = .true._LK
    integer(IK)     , allocatable       :: instance(:)
    integer(IK)     , allocatable       :: loc(:)
    integer(IK)     , allocatable       :: array(:)
    integer(IK)                         :: pattern
    type(bench_type)                    :: bench(NBENCH)
    real(RK)                            :: unifrnd, MeanTime(2) = 0._RK
 
    bench(1) = bench_type(name = SK_"default", exec = default , overhead = setOverhead)
    bench(2) = bench_type(name = SK_"iseqArg", exec = iseqArg , overhead = setOverhead)
 
    arraySize = [( 2_IK**isize, isize = 1_IK, NSIZE )]
    loc = [integer(IK) ::] ! essential for `setLoc()`.
    nloc = 0_IK
 
    write(*,"(*(g0,:,' '))")
    write(*,"(*(g0,:,' '))") "iseqArg vs. default"
    write(*,"(*(g0,:,' '))")
 
    open(newunit = fileUnit, file = "main.out", status = "replace")
 
        write(fileUnit, "(*(g0,:,','))") "arraySize", (bench(i)%name, i = 1_IK, NBENCH)
 
        loopOverArraySize: do isize = 1_IK, NSIZE
 
            write(*,"(*(g0,:,' '))") "Benchmarking with size", arraySize(isize)
            instance = getRange(1_IK, arraySize(isize))
            allocate(array(arraySize(isize)))
 
            do i = 1_IK, NBENCH
                bench(i)%timing = bench(i)%getTiming(minsec = 0.03_RK)
                MeanTime(i) = MeanTime(i) + bench(i)%timing%mean
            end do
 
            do i = NBENCH, 1_IK, -1_IK
                bench(i)%timing = bench(i)%getTiming(minsec = 0.03_RK)
                MeanTime(i) = MeanTime(i) + bench(i)%timing%mean
            end do
 
            deallocate(array, instance)
            write(fileUnit,"(*(g0,:,','))") arraySize(isize), MeanTime / 2_IK
 
        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(unifrnd)
        pattern = nint(unifrnd, kind = IK)
        array(:) = pattern + 1_IK
    end subroutine
 
    subroutine finalize()
        dummy = dummy .and. size(loc, 1, IK) == nloc
    end subroutine
 
    subroutine iseqArg()
        use pm_arrayFind, only: setLoc
        call initialize()
        call setLoc(loc, nloc, array, pattern, iseq, 1_IK)
        call finalize()
    end subroutine
 
    subroutine default()
        block
            use pm_arrayFind, only: setLoc
            call initialize()
            call setLoc(loc, nloc, array, pattern, 1_IK)
            call finalize()
        end block
    end subroutine
 
    pure function iseq(arraysegment, pattern) result(equivalent)
        use pm_kind, only: IK, LK
        integer(IK) , intent(in)    :: pattern, arraySegment
        logical(LK)                 :: equivalent
        equivalent = arraySegment == pattern
    end function
 
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 = ["default", "iseqArg"]
 
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("Finding pattern with external `iseq()` vs. default comparison.\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.setLoc-iseqArg_vs_default.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["iseqArg"].values / df["default"].values
        , linewidth = 2
        )
 
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
ax.set_xlabel("Array Size", fontsize = fontsize)
ax.set_ylabel("Runtime compared to iseqArg", fontsize = fontsize)
ax.set_title("Runtime Ratio: Comparison with `iseq()` / default.\nLower means faster. Lower than 1 means faster than finding with `iseq()`.", 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
           #, bbox_to_anchor = (1, 0.5)
           #, loc = "center left"
            , fontsize = fontsize
            )
 
plt.tight_layout()
plt.savefig("benchmark.setLoc-iseqArg_vs_default.runtime.ratio.png")

Visualization of the benchmark output ⛓

Benchmark moral ⛓

The procedures under the generic interface setLoc take an optional iseq() external-function input argument which can perform custom user-defined equivalence checks between the input pattern and array segments. By default, the equivalence check is equality (or equivalence for logical values).
The presence of an external iseq argument does appear to deteriorate the runtime performance of setLoc.
However, the exact amount of this penalty appears to significantly depend on the computing platform and the ability of the compiler to inline the external function.
The results of this benchmark equally hold for the functions under the generic interface getLoc.

Test:: test_pm_arrayFind

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

Variable Documentation

◆ MODULE_NAME

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

Definition at line 103 of file pm_arrayFind.F90.

Data Types

Variables

Detailed Description

Variable Documentation

◆ MODULE_NAME