Decrease the computation time for DGELSD subroutine - matlab

Question

I am writing a code in Fortran that involve computation of linear least squares (A^(-1)*b). For this I have used the subroutine "DGELSD". I am able to get the correct answer from my code. I have cross checked my solution with that of the data available from MATLAB.
Now when it comes to the computation time, MATLAB is taking much less time than that of my .f90 code. The main motivation for me to write the .f90 code was to do heavy computations, as MATLAB was unable to handle this problem (as the matrix size is increased, it takes more and more time). I am talking of the order of matrix around (10^6 x 10^6).
I know that I may be lacking somewhere around the vectorization or parallelization of code (as I am new to it). But would it make any difference? As the subroutine "DGELSD" is already highly optimized. Also I am using Intel ifort compiler and visual studio as an editor.
I have attached the part of the main code (.f90) below for reference. Please suggest what can be done to decrease the computation time. I am having good hardware configuration to run heavy computation.
Workstation specification: Intel Xeon 32 core - 64 bit processor, 64 GB RAM.
Code information:
a) I have used 'DGELSD' example available on Intel MKL example site..
b) I am using x64 architecture.
c) This is the code I am using in MATLAB for comparison.
function min_norm_check(m,n)
tic
a=15*m*n;
b=15*m*n;
c=6;
A=rand(a,b);
B=rand(b,c);
C=A\B;
toc
end
This is the Fotran code given below:
! Program to check the time required to
! calculate linear least square solution
! using DGELSD subroutine
PROGRAM MAIN
IMPLICIT NONE
INTEGER :: M,N,LDA,LDB,NRHS,NB,NG
REAL :: T1,T2,START,FINISH
DOUBLE PRECISION, DIMENSION (:,:), ALLOCATABLE :: D_CAP,A,B,TG,DG
INTEGER :: I=0
NB=10
NG=10
M = 15*NB*NG
N = 15*NB*NG
NRHS = 6
!!
LDA = MAX(M,N)
LDB = MAX(M,NRHS)
!
ALLOCATE (A(LDA,N))
ALLOCATE (B(LDB,NRHS))
A = 0
B = 0
CALL RANDOM_NUMBER(A)
CALL RANDOM_NUMBER(B)
CALL CPU_TIME(START)
DO I=1,1
WRITE(*,*) I
CALL CALC_MIN_NORM_D(M,N,LDA,LDB,NRHS,A,B,D_CAP)
ENDDO
CALL CPU_TIME(FINISH)
WRITE(*,*)'("TIME =',FINISH-START,'SECONDS.")'
END
SUBROUTINE CALC_MIN_NORM_D(M,N,LDA,LDB,NRHS,A,B,D_CAP)
!
! SUBROUTINE DEFINITION TO CALCULATE THE
! LINEAR LEAST SQUARE SOLUTION OF ([A]^-1*B)
!
IMPLICIT NONE
INTEGER :: M,N,NRHS,LDA,LDB,LWMAX,INFO,LWORK,RANK
DOUBLE PRECISION RCOND
INTEGER, ALLOCATABLE, DIMENSION(:) :: IWORK
DOUBLE PRECISION :: A(LDA,N),B(LDB,NRHS),D_CAP(LDB,NRHS)
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:) :: S,WORK
!
WRITE(*,*)'IN CALC MIN NORM BEGINING'
WRITE(*,*)'DGELSD EXAMPLE PROGRAM RESULTS'
LWMAX = 1E8
ALLOCATE(S(M))
ALLOCATE(IWORK(3*M*0+11*M))
ALLOCATE(WORK(LWMAX))
! NEGATIVE RCOND MEANS USING DEFAULT (MACHINE PRECISION) VALUE
RCOND = -1.0
!
! QUERY THE OPTIMAL WORKSPACE.
!
LWORK = -1
CALL DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK,LWORK, IWORK, INFO )
LWORK = MIN( LWMAX, INT( WORK( 1 ) ) )
!WRITE(*,*) 'AFTER FIRST DGELSD'
!
! SOLVE THE EQUATIONS A*X = B.
!!!
CALL DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK,LWORK, IWORK, INFO )
!
! CHECK FOR CONVERGENCE.
!
IF( INFO.GT.0 ) THEN
WRITE(*,*)'THE ALGORITHM COMPUTING SVD FAILED TO CONVERGE;'
WRITE(*,*)'THE LEAST SQUARES SOLUTION COULD NOT BE COMPUTED.'
STOP
END IF
!
!
WRITE(*,*)' EFFECTIVE RANK = ', RANK
!D_CAP = B
END
This is the build log for successful compilation of the file. As I am using Visual studio with intel visual fortran, I can compile my program using Compile option available in the editor. I mean to say I don't have to use command line interface to run my program.
Compiling with Intel(R) Visual Fortran Compiler 17.0.2.187 [IA-32]...
ifort /nologo /debug:full /Od /warn:interfaces /module:&quotDebug\\&quot /object:&quotDebug\\&quot /Fd&quotDebug\vc110.pdb&quot /traceback /check:bounds /check:stack /libs:dll /threads /dbglibs /c /Qlocation,link,&quotC:\Program Files (x86)\Microsoft Visual Studio 11.0\VC\\bin&quot /Qm32 &quotD:\Google Drive\Friday_May_27_2016\Mtech Thesis Job\All new work\Fortran coding\fortran hfgmc\Console6\Console6\Console6.f90&quot
Linking...
Link /OUT:&quotDebug\Console6.exe&quot /INCREMENTAL:NO /NOLOGO /MANIFEST /MANIFESTFILE:&quotDebug\Console6.exe.intermediate.manifest&quot /MANIFESTUAC:&quotlevel='asInvoker' uiAccess='false'&quot /DEBUG /PDB:&quotD:\Google Drive\Friday_May_27_2016\Mtech Thesis Job\All new work\Fortran coding\Console6\Console6\Debug\Console6.pdb&quot /SUBSYSTEM:CONSOLE /IMPLIB:&quotD:\Google Drive\Friday_May_27_2016\Mtech Thesis Job\All new work\Fortran coding\fortran hfgmc\Console6\Console6\Debug\Console6.lib&quot -qm32 &quotDebug\Console6.obj&quot
Embedding manifest...
mt.exe /nologo /outputresource:&quotD:\Google Drive\Friday_May_27_2016\Mtech Thesis Job\All new work\Fortran coding\fortran hfgmc\Console6\Console6\Debug\Console6.exe;#1&quot /manifest &quotDebug\Console6.exe.intermediate.manifest&quot
Console6 - 0 error(s), 0 warning(s)
Also I have included the intel mkl library, shown in the figure below:
I have compiled the program and the output has been written in file 'OUTPUT_FILE.TXT'.
IN CALC MIN NORM BEGINING
DGELSD EXAMPLE PROGRAM RESULTS
EFFECTIVE RANK = 1500
IN CALC MIN NORM ENDING
("TIME TAKEN TO SOLVE DGELSD= 4.290028 SECONDS.")
On the other hand MATLAB gives the following result in the output command window:
min_norm_check(10,10)
Elapsed time is 0.224172 seconds.
Also I don't want to outperform MATLAB, its easy and simple. But with increase in the size of the problem, MATLAB stops responding. I have left my program to run on MATLAB for more than two days. It still haven't produced any results.