pm_matrixInit Module Reference

This module contains procedures and generic interfaces relevant to generating and initializing matrices of arbitrary shapes (:, :).
More...

Data Types
interface	getMatInit
	Generate and return a matrix of shape (shape(1), shape(2)) with the upper/lower triangle and the diagonal elements of the matrix set to the corresponding requested input values. More...
interface	setMatInit
	Set the upper/lower triangle and the diagonal elements of the input matrix of arbitrary shape (:,:) to the requested input values. More...

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

Detailed Description

This module contains procedures and generic interfaces relevant to generating and initializing matrices of arbitrary shapes (:, :).

The following guidelines describe the various existing methods within the ParaMonte library for initializing matrices.

• Use the interface getMatInit(..., subset = uppLowDia, ...) or setMatInit(..., subset = uppLowDia, ...) to initialize the upper, diagonal, and lower elements of a rectangular subset of a new or existing matrix.
  
  
  
  
• Use the interface getMatInit(..., subset = uppLow, ...) or setMatInit(..., subset = uppLow, ...) to initialize the lower and upper elements of a rectangular subset of a new or existing matrix.
  
  
  
  
• Use the interface getMatInit(..., subset = lowDia, ...) or setMatInit(..., subset = lowDia, ...) to initialize the diagonal and lower elements of a rectangular subset of a new or existing matrix.
  
  
  
  
• Use the interface getMatInit(..., subset = uppDia, ...) or setMatInit(..., subset = uppDia, ...) to initialize the diagonal and upper elements of a rectangular subset of a new or existing matrix.
  
  
  
  
• Use the interface getMatInit(..., subset = vdia, ...) or setMatInit(..., subset = vdia, ...) to initialize the diagonal elements of a rectangular subset of a new or existing matrix.
  
  
  
  

BLAS/LAPACK equivalent:

The procedures under discussion combine, modernize, and extend the interface and functionalities of Version 3.11 of BLAS/LAPACK routine(s): SLASET, DLASET, CLASET, ZLASET.

See also

pm_arrayInit
pm_matrixCopy
pm_arrayCopy
pm_arrayCopy

Benchmarks:

Benchmark :: The runtime performance of getMatInit vs. setMatInit ⛓

! Test the performance of `getMatInit()` vs. `setMatInit()`.
program benchmark
 
    use iso_fortran_env, only: error_unit
    use pm_bench, only: bench_type
    use pm_kind, only: IK, RKG => RK, RK, SK
 
    implicit none
 
    integer(IK)                         :: i
    integer(IK)                         :: fileUnit
    integer(IK)                         :: rank, irank
    integer(IK) , parameter             :: NRANK = 11_IK
    integer(IK) , parameter             :: NBENCH = 3_IK
    real(RKG)                           :: dummySum = 0._RKG
    real(RKG)   , allocatable           :: MatInit(:,:)
    type(bench_type)                    :: bench(NBENCH)
 
    bench(1) = bench_type(name = SK_"setMatInit", exec = setMatInit , overhead = setOverhead)
    bench(2) = bench_type(name = SK_"getMatInit", exec = getMatInit , overhead = setOverhead)
    bench(3) = bench_type(name = SK_"reshape_looping", exec = getMatInit_D2_reshape , overhead = setOverhead)
 
 
    write(*,"(*(g0,:,' '))")
    write(*,"(*(g0,:,' '))") "setMatInit() vs. getMatInit() vs. getMatInit_D2_reshape()"
    write(*,"(*(g0,:,' '))")
 
    open(newunit = fileUnit, file = "main.out", status = "replace")
 
        write(fileUnit, "(*(g0,:,', '))") "MatrixRank", (bench(i)%name, i = 1, NBENCH)
 
        loopOverMatrixRank: do irank = 1, NRANK
 
            rank = 2_IK**irank
            allocate(MatInit(rank, rank))
            write(*,"(*(g0,:,' '))") "Benchmarking with rank", rank
 
            do i = 1, NBENCH
                bench(i)%timing = bench(i)%getTiming(minsec = 0.07_RK)
            end do
 
            write(fileUnit,"(*(g0,:,', '))") rank, (bench(i)%timing%mean, i = 1, NBENCH)
            deallocate(MatInit)
 
        end do loopOverMatrixRank
        write(*,"(*(g0,:,' '))") dummySum
        write(*,"(*(g0,:,' '))")
 
    close(fileUnit)
 
contains
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! procedure wrappers.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    subroutine setOverhead()
        call getDummy()
    end subroutine
 
    subroutine getDummy()
        dummySum = dummySum + MatInit(1,1)
    end subroutine
 
    subroutine setMatInit()
        block
            use pm_matrixInit, only: setMatInit, dia_type
            call setMatInit(MatInit, dia_type(), 1._RKG, rank, 0_IK, 0_IK)
            call getDummy()
        end block
    end subroutine
 
    subroutine getMatInit()
        block
            use pm_matrixInit, only: getMatInit, dia
            MatInit = getMatInit([rank, rank], dia, 1._RKG)
            call getDummy()
        end block
    end subroutine
 
    subroutine getMatInit_D2_reshape()
        MatInit = reshape_looping(rank)
        call getDummy()
    end subroutine
 
    pure function reshape_looping(n) result(MatInit)
        integer(IK), intent(in) :: n
        real(RKG)               :: MatInit(n,n)
        integer(IK)             :: k, j
        MatInit = reshape([1._RKG, ([(0._RKG, k = 1, n)], 1._RKG, j = 1, n - 1)], shape(MatInit))
    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
 
import os
dirname = os.path.basename(os.getcwd()) 
 
fontsize = 14
 
df = pd.read_csv("main.out", delimiter = ", ")
colnames = list(df.columns.values)
 
 
 
ax = plt.figure(figsize = 1.25 * np.array([6.4,4.6]), dpi = 200)
ax = plt.subplot()
 
for colname in colnames[1:]:
    plt.plot( df[colnames[0]].values
            , df[colname].values
            , linewidth = 2
            )
 
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
ax.set_xlabel(colnames[0], fontsize = fontsize)
ax.set_ylabel("Runtime [ seconds ]", fontsize = fontsize)
ax.set_title(" vs. ".join(colnames[1:])+"\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   ( colnames[1:]
           #, loc='center left'
           #, bbox_to_anchor=(1, 0.5)
            , fontsize = fontsize
            )
 
plt.tight_layout()
plt.savefig("benchmark." + dirname + ".runtime.png")
 
 
 
ax = plt.figure(figsize = 1.25 * np.array([6.4,4.6]), dpi = 200)
ax = plt.subplot()
 
plt.plot( df[colnames[0]].values
        , np.ones(len(df[colnames[0]].values))
        , linestyle = "--"
       #, color = "black"
        , linewidth = 2
        )
for colname in colnames[2:]:
    plt.plot( df[colnames[0]].values
            , df[colname].values / df[colnames[1]].values
            , linewidth = 2
            )
 
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
ax.set_xlabel(colnames[0], fontsize = fontsize)
ax.set_ylabel("Runtime compared to {}".format(colnames[1]), fontsize = fontsize)
ax.set_title("Runtime Ratio Comparison. Lower means faster.\nLower than 1 means faster than {}().".format(colnames[1]), 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   ( colnames[1:]
           #, bbox_to_anchor = (1, 0.5)
           #, loc = "center left"
            , fontsize = fontsize
            )
 
plt.tight_layout()
plt.savefig("benchmark." + dirname + ".runtime.ratio.png")

Visualization of the benchmark output ⛓

Benchmark moral ⛓

1. The procedures under the generic interface getMatInit are functions while the procedures under the generic interface setMatInit are subroutines.
   From the benchmark results, it appears that the functional interface performs less efficiently than the subroutine interface.
   Note that this benchmark does not even include the cost of repeated reallcations, that is, the allocation of matrix happens only once in all tests prior to each benchmark.
   
2. Furthermore, the getMatInit() implementation with Fortran-intrinsic reshape() and implicit-loop appears to be significantly slower than both the subroutine and function implementations.
   

Test:

test_pm_matrixInit

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.

Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, Friday 1:54 AM, April 21, 2017, Institute for Computational Engineering and Sciences (ICES), The University of Texas, Austin, TX

Variable Documentation

MODULE_NAME

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

Definition at line 129 of file pm_matrixInit.F90.