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|
SUBROUTINE DTIMLS( LINE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
$ NBVAL, NXVAL, NLDA, LDAVAL, TIMMIN, A, COPYA,
$ B, COPYB, S, COPYS, OPCTBL, TIMTBL, FLPTBL,
$ WORK, IWORK, NOUT )
*
* -- LAPACK timing routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* December 22, 1999
*
* .. Scalar Arguments ..
CHARACTER*80 LINE
INTEGER NLDA, NM, NN, NNB, NNS, NOUT
DOUBLE PRECISION TIMMIN
* ..
* .. Array Arguments ..
INTEGER IWORK( * ), LDAVAL( * ), MVAL( * ), NBVAL( * ),
$ NSVAL( * ), NVAL( * ), NXVAL( * )
DOUBLE PRECISION A( * ), B( * ), COPYA( * ), COPYB( * ),
$ COPYS( * ), FLPTBL( 6, 6,
$ NM*NN*NNS*NLDA*( NNB+1 ), * ),
$ OPCTBL( 6, 6, NM*NN*NNS*NLDA*( NNB+1 ), * ),
$ S( * ), TIMTBL( 6, 6, NM*NN*NNS*NLDA*( NNB+1 ),
$ * ), WORK( * )
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, IOUNIT, OK, LERR
COMMON / LSTIME / OPCNT, TIMNG
COMMON / SRNAMC / SRNAMT
* ..
* .. Arrays in Common ..
DOUBLE PRECISION OPCNT( 6 ), TIMNG( 6 )
* ..
*
* Purpose
* =======
*
* DTIMLS times the least squares driver routines DGELS, SGELSS, SGELSX,
* DGELSY and SGELSD.
*
* Arguments
* =========
*
* LINE (input) CHARACTER*80
* The input line that requested this routine. The first six
* characters contain either the name of a subroutine or a
* generic path name. The remaining characters may be used to
* specify the individual routines to be timed. See ATIMIN for
* a full description of the format of the input line.
*
* NM (input) INTEGER
* The number of values of M contained in the vector MVAL.
*
* MVAL (input) INTEGER array, dimension (NM)
* The values of the matrix row dimension M.
*
* NN (input) INTEGER
* The number of values of N contained in the vector NVAL.
*
* NVAL (input) INTEGER array, dimension (NN)
* The values of the matrix column dimension N.
*
* NNS (input) INTEGER
* The number of values of NRHS contained in the vector NSVAL.
*
* NSVAL (input) INTEGER array, dimension (NNS)
* The values of the number of right hand sides NRHS.
*
* NNB (input) INTEGER
* The number of values of NB and NX contained in the
* vectors NBVAL and NXVAL. The blocking parameters are used
* in pairs (NB,NX).
*
* NBVAL (input) INTEGER array, dimension (NNB)
* The values of the blocksize NB.
*
* NXVAL (input) INTEGER array, dimension (NNB)
* The values of the crossover point NX.
*
* NLDA (input) INTEGER
* The number of values of LDA contained in the vector LDAVAL.
*
* LDAVAL (input) INTEGER array, dimension (NLDA)
* The values of the leading dimension of the array A.
*
* TIMMIN (input) DOUBLE PRECISION
* The minimum time a subroutine will be timed.
*
* A (workspace) DOUBLE PRECISION array, dimension (MMAX*NMAX)
* where MMAX is the maximum value of M in MVAL and NMAX is the
* maximum value of N in NVAL.
*
* COPYA (workspace) DOUBLE PRECISION array, dimension (MMAX*NMAX)
*
* B (workspace) DOUBLE PRECISION array, dimension (MMAX*NSMAX)
* where MMAX is the maximum value of M in MVAL and NSMAX is the
* maximum value of NRHS in NSVAL.
*
* COPYB (workspace) DOUBLE PRECISION array, dimension (MMAX*NSMAX)
*
* S (workspace) DOUBLE PRECISION array, dimension
* (min(MMAX,NMAX))
*
* COPYS (workspace) DOUBLE PRECISION array, dimension
* (min(MMAX,NMAX))
*
* OPZTBL (workspace) DOUBLE PRECISION array, dimension
* (6,6,(NNB+1)*NLDA,NM*NN*NNS,5)
*
* TIMTBL (workspace) DOUBLE PRECISION array, dimension
* (6,6,(NNB+1)*NLDA,NM*NN*NNS,5)
*
* FLPTBL (workspace) DOUBLE PRECISION array, dimension
* (6,6,(NNB+1)*NLDA,NM*NN*NNS,5)
*
* WORK (workspace) DOUBLE PRECISION array,
* dimension (MMAX*NMAX + 4*NMAX + MMAX).
*
* IWORK (workspace) INTEGER array, dimension (NMAX)
*
* NOUT (input) INTEGER
* The unit number for output.
*
* =====================================================================
*
* .. Parameters ..
INTEGER MTYPE, NSUBS
PARAMETER ( MTYPE = 6, NSUBS = 5 )
INTEGER SMLSIZ
PARAMETER ( SMLSIZ = 25 )
DOUBLE PRECISION ONE, TWO, ZERO
PARAMETER ( ONE = 1.0D0, TWO = 2.0D0, ZERO = 0.0D0 )
* ..
* .. Local Scalars ..
CHARACTER TRANS
CHARACTER*3 PATH
INTEGER CRANK, I, ILDA, IM, IN, INB, INFO, INS, IRANK,
$ ISCALE, ISUB, ITBL, ITRAN, ITYPE, LDA, LDB,
$ LDWORK, LWLSY, LWORK, M, MNMIN, N, NB, NCALL,
$ NCLS, NCLSD, NCLSS, NCLSX, NCLSY, NCOLS, NLVL,
$ NRHS, NROWS, RANK
DOUBLE PRECISION EPS, NORMA, NORMB, RCOND, S1, S2, TIME
* ..
* .. Local Arrays ..
LOGICAL TIMSUB( NSUBS )
CHARACTER*6 SUBNAM( NSUBS )
INTEGER ISEED( 4 ), ISEEDY( 4 ), NDATA( NSUBS )
* ..
* .. External Functions ..
DOUBLE PRECISION DASUM, DLAMCH, DMFLOP, DSECND
EXTERNAL DASUM, DLAMCH, DMFLOP, DSECND
* ..
* .. External Subroutines ..
EXTERNAL ATIMIN, DCOPY, DGELS, DGELSD, DGELSS, DGELSX,
$ DGELSY, DGEMM, DLACPY, DLARNV, DLASET, DQRT13,
$ DQRT15, DSCAL, DPRTLS, XLAENV
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, LOG, MAX, MIN, SQRT
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*6 SRNAMT
INTEGER INFOT, IOUNIT
* ..
* .. Common blocks ..
* ..
* .. Data statements ..
DATA SUBNAM / 'DGELS ', 'DGELSX', 'DGELSY',
$ 'DGELSS', 'DGELSD' /
DATA ISEEDY / 1988, 1989, 1990, 1991 /
DATA NDATA / 4, 6, 6, 6, 5 /
* ..
* .. Executable Statements ..
*
* Extract the timing request from the input line.
*
PATH( 1: 1 ) = 'Double precision'
PATH( 2: 3 ) = 'LS'
CALL ATIMIN( PATH, LINE, NSUBS, SUBNAM, TIMSUB, NOUT, INFO )
IF( INFO.NE.0 )
$ GO TO 230
*
* Initialize constants and the random number seed.
*
NCLS = 0
NCLSD = 0
NCLSS = 0
NCLSX = 0
NCLSY = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
EPS = DLAMCH( 'Epsilon' )
*
* Threshold for rank estimation
*
RCOND = SQRT( EPS ) - ( SQRT( EPS )-EPS ) / 2
*
INFOT = 0
CALL XLAENV( 2, 2 )
CALL XLAENV( 9, SMLSIZ )
*
DO 200 IM = 1, NM
M = MVAL( IM )
*
DO 190 IN = 1, NN
N = NVAL( IN )
MNMIN = MIN( M, N )
*
DO 180 INS = 1, NNS
NRHS = NSVAL( INS )
NLVL = MAX( INT( LOG( MAX( ONE, DBLE( MNMIN ) ) /
$ DBLE( SMLSIZ+1 ) ) / LOG( TWO ) ) + 1, 0 )
LWORK = MAX( 1, ( M+NRHS )*( N+2 ), ( N+NRHS )*( M+2 ),
$ M*N+4*MNMIN+MAX( M, N ), 12*MNMIN+2*MNMIN*SMLSIZ+
$ 8*MNMIN*NLVL+MNMIN*NRHS+(SMLSIZ+1)**2 )
*
DO 170 ILDA = 1, NLDA
LDA = MAX( 1, LDAVAL( ILDA ) )
LDB = MAX( 1, LDAVAL( ILDA ), M, N )
*
DO 160 IRANK = 1, 2
*
DO 150 ISCALE = 1, 3
*
IF( IRANK.EQ.1 .AND. TIMSUB( 1 ) ) THEN
*
* Time DGELS
*
* Generate a matrix of scaling type ISCALE
*
CALL DQRT13( ISCALE, M, N, COPYA, LDA, NORMA,
$ ISEED )
DO 50 INB = 1, NNB
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
CALL XLAENV( 3, NXVAL( INB ) )
*
DO 40 ITRAN = 1, 2
ITYPE = ( ITRAN-1 )*3 + ISCALE
IF( ITRAN.EQ.1 ) THEN
TRANS = 'N'
NROWS = M
NCOLS = N
ELSE
TRANS = 'T'
NROWS = N
NCOLS = M
END IF
LDWORK = MAX( 1, NCOLS )
*
* Set up a consistent rhs
*
IF( NCOLS.GT.0 ) THEN
CALL DLARNV( 2, ISEED, NCOLS*NRHS,
$ WORK )
CALL DSCAL( NCOLS*NRHS,
$ ONE / DBLE( NCOLS ),
$ WORK, 1 )
END IF
CALL DGEMM( TRANS, 'No transpose',
$ NROWS, NRHS, NCOLS, ONE,
$ COPYA, LDA, WORK, LDWORK,
$ ZERO, B, LDB )
CALL DLACPY( 'Full', NROWS, NRHS, B,
$ LDB, COPYB, LDB )
*
* Solve LS or overdetermined system
*
NCALL = 0
TIME = ZERO
CALL DLASET( 'Full', NDATA( 1 ), 1,
$ ZERO, ZERO, OPCNT,
$ NDATA( 1 ) )
CALL DLASET( 'Full', NDATA( 1 ), 1,
$ ZERO, ZERO, TIMNG,
$ NDATA( 1 ) )
20 CONTINUE
IF( M.GT.0 .AND. N.GT.0 ) THEN
CALL DLACPY( 'Full', M, N, COPYA,
$ LDA, A, LDA )
CALL DLACPY( 'Full', NROWS, NRHS,
$ COPYB, LDB, B, LDB )
END IF
SRNAMT = 'DGELS '
NCALL = NCALL + 1
S1 = DSECND( )
CALL DGELS( TRANS, M, N, NRHS, A, LDA,
$ B, LDB, WORK, LWORK, INFO )
S2 = DSECND( )
TIME = TIME + ( S2-S1 )
IF( INFO.EQ.0 .AND. TIME.LT.TIMMIN )
$ GO TO 20
TIMNG( 1 ) = TIME
OPCNT( 1 ) = DASUM( NDATA( 1 ), OPCNT,
$ 1 )
CALL DSCAL( NDATA( 1 ),
$ ONE / DBLE( NCALL ), OPCNT,
$ 1 )
CALL DSCAL( NDATA( 1 ),
$ ONE / DBLE( NCALL ), TIMNG,
$ 1 )
CALL DCOPY( NDATA( 1 ), OPCNT, 1,
$ OPCTBL( 1, ITYPE, NCLS+INB,
$ 1 ), 1 )
CALL DCOPY( NDATA( 1 ), TIMNG, 1,
$ TIMTBL( 1, ITYPE, NCLS+INB,
$ 1 ), 1 )
DO 30 I = 1, NDATA( 1 )
FLPTBL( I, ITYPE, NCLS+INB,
$ 1 ) = DMFLOP( OPCNT( I ),
$ TIMNG( I ), INFO )
30 CONTINUE
40 CONTINUE
50 CONTINUE
*
END IF
*
* Generate a matrix of scaling type ISCALE and
* rank type IRANK.
*
ITYPE = ( IRANK-1 )*3 + ISCALE
CALL DQRT15( ISCALE, IRANK, M, N, NRHS, COPYA,
$ LDA, COPYB, LDB, COPYS, RANK,
$ NORMA, NORMB, ISEED, WORK, LWORK )
*
IF( TIMSUB( 2 ) ) THEN
*
* Time DGELSX
*
* workspace used:
* MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
*
LDWORK = MAX( 1, M )
*
* DGELSX: Compute the minimum-norm
* solution X to min( norm( A * X - B ) )
* using a complete orthogonal factorization.
*
NCALL = 0
TIME = ZERO
CALL DLASET( 'Full', NDATA( 2 ), 1, ZERO,
$ ZERO, OPCNT, NDATA( 2 ) )
CALL DLASET( 'Full', NDATA( 2 ), 1, ZERO,
$ ZERO, TIMNG, NDATA( 2 ) )
60 CONTINUE
CALL DLACPY( 'Full', M, N, COPYA, LDA, A,
$ LDA )
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, B,
$ LDB )
SRNAMT = 'DGELSX'
NCALL = NCALL + 1
S1 = DSECND( )
CALL DGELSX( M, N, NRHS, A, LDA, B, LDB,
$ IWORK, RCOND, CRANK, WORK,
$ INFO )
S2 = DSECND( )
TIME = TIME + ( S2-S1 )
IF( INFO.EQ.0 .AND. TIME.LT.TIMMIN )
$ GO TO 60
TIMNG( 1 ) = TIME
OPCNT( 1 ) = DASUM( NDATA( 2 ), OPCNT, 1 )
CALL DSCAL( NDATA( 2 ), ONE / DBLE( NCALL ),
$ OPCNT, 1 )
CALL DSCAL( NDATA( 2 ), ONE / DBLE( NCALL ),
$ TIMNG, 1 )
CALL DCOPY( NDATA( 2 ), OPCNT, 1,
$ OPCTBL( 1, ITYPE, NCLSX+1, 2 ),
$ 1 )
CALL DCOPY( NDATA( 2 ), TIMNG, 1,
$ TIMTBL( 1, ITYPE, NCLSX+1, 2 ),
$ 1 )
DO 70 I = 1, NDATA( 2 )
FLPTBL( I, ITYPE, NCLSX+1,
$ 2 ) = DMFLOP( OPCNT( I ), TIMNG( I ),
$ INFO )
70 CONTINUE
*
END IF
*
* Loop for timing different block sizes.
*
DO 140 INB = 1, NNB
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
CALL XLAENV( 3, NXVAL( INB ) )
*
IF( TIMSUB( 3 ) ) THEN
*
* Time DGELSY
*
* DGELSY: Compute the minimum-norm solution X
* to min( norm( A * X - B ) ) using the
* rank-revealing orthogonal factorization.
*
* Set LWLSY to the adequate value.
*
LWLSY = MAX( 1, MNMIN+2*N+NB*( N+1 ),
$ 2*MNMIN+NB*NRHS )
*
NCALL = 0
TIME = ZERO
CALL DLASET( 'Full', NDATA( 3 ), 1, ZERO,
$ ZERO, OPCNT, NDATA( 3 ) )
CALL DLASET( 'Full', NDATA( 3 ), 1, ZERO,
$ ZERO, TIMNG, NDATA( 3 ) )
80 CONTINUE
CALL DLACPY( 'Full', M, N, COPYA, LDA, A,
$ LDA )
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB,
$ B, LDB )
SRNAMT = 'DGELSY'
NCALL = NCALL + 1
S1 = DSECND( )
CALL DGELSY( M, N, NRHS, A, LDA, B, LDB,
$ IWORK, RCOND, CRANK, WORK,
$ LWLSY, INFO )
S2 = DSECND( )
TIME = TIME + ( S2-S1 )
IF( INFO.EQ.0 .AND. TIME.LT.TIMMIN )
$ GO TO 80
TIMNG( 1 ) = TIME
OPCNT( 1 ) = DASUM( NDATA( 3 ), OPCNT, 1 )
CALL DSCAL( NDATA( 3 ),
$ ONE / DBLE( NCALL ), OPCNT,
$ 1 )
CALL DSCAL( NDATA( 3 ),
$ ONE / DBLE( NCALL ), TIMNG,
$ 1 )
CALL DCOPY( NDATA( 3 ), OPCNT, 1,
$ OPCTBL( 1, ITYPE, NCLSY+INB,
$ 3 ), 1 )
CALL DCOPY( NDATA( 3 ), TIMNG, 1,
$ TIMTBL( 1, ITYPE, NCLSY+INB,
$ 3 ), 1 )
DO 90 I = 1, NDATA( 3 )
FLPTBL( I, ITYPE, NCLSY+INB,
$ 3 ) = DMFLOP( OPCNT( I ),
$ TIMNG( I ), INFO )
90 CONTINUE
*
END IF
*
IF( TIMSUB( 4 ) ) THEN
*
* Time DGELSS
*
* DGELSS: Compute the minimum-norm solution X
* to min( norm( A * X - B ) ) using the SVD.
*
NCALL = 0
TIME = ZERO
CALL DLASET( 'Full', NDATA( 4 ), 1, ZERO,
$ ZERO, OPCNT, NDATA( 4 ) )
CALL DLASET( 'Full', NDATA( 4 ), 1, ZERO,
$ ZERO, TIMNG, NDATA( 4 ) )
100 CONTINUE
CALL DLACPY( 'Full', M, N, COPYA, LDA, A,
$ LDA )
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB,
$ B, LDB )
SRNAMT = 'DGELSS'
NCALL = NCALL + 1
S1 = DSECND( )
CALL DGELSS( M, N, NRHS, A, LDA, B, LDB,
$ S, RCOND, CRANK, WORK, LWORK,
$ INFO )
S2 = DSECND( )
TIME = TIME + ( S2-S1 )
IF( INFO.EQ.0 .AND. TIME.LT.TIMMIN )
$ GO TO 100
TIMNG( 1 ) = TIME
OPCNT( 1 ) = DASUM( NDATA( 4 ), OPCNT, 1 )
CALL DSCAL( NDATA( 4 ),
$ ONE / DBLE( NCALL ), OPCNT,
$ 1 )
CALL DSCAL( NDATA( 4 ),
$ ONE / DBLE( NCALL ), TIMNG,
$ 1 )
CALL DCOPY( NDATA( 4 ), OPCNT, 1,
$ OPCTBL( 1, ITYPE, NCLSS+INB,
$ 4 ), 1 )
CALL DCOPY( NDATA( 4 ), TIMNG, 1,
$ TIMTBL( 1, ITYPE, NCLSS+INB,
$ 4 ), 1 )
DO 110 I = 1, NDATA( 4 )
FLPTBL( I, ITYPE, NCLSS+INB,
$ 4 ) = DMFLOP( OPCNT( I ),
$ TIMNG( I ), INFO )
110 CONTINUE
*
END IF
*
IF( TIMSUB( 5 ) ) THEN
*
* Time DGELSD
*
* DGELSD: Compute the minimum-norm solution X
* to min( norm( A * X - B ) ) using a
* divide-and-conquer SVD.
*
NCALL = 0
TIME = ZERO
CALL DLASET( 'Full', NDATA( 5 ), 1, ZERO,
$ ZERO, OPCNT, NDATA( 5 ) )
CALL DLASET( 'Full', NDATA( 5 ), 1, ZERO,
$ ZERO, TIMNG, NDATA( 5 ) )
120 CONTINUE
CALL DLACPY( 'Full', M, N, COPYA, LDA, A,
$ LDA )
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB,
$ B, LDB )
SRNAMT = 'DGELSD'
NCALL = NCALL + 1
S1 = DSECND( )
CALL DGELSD( M, N, NRHS, A, LDA, B, LDB,
$ S, RCOND, CRANK, WORK, LWORK,
$ IWORK, INFO )
S2 = DSECND( )
TIME = TIME + ( S2-S1 )
IF( INFO.EQ.0 .AND. TIME.LT.TIMMIN )
$ GO TO 120
TIMNG( 1 ) = TIME
OPCNT( 1 ) = DASUM( NDATA( 5 ), OPCNT, 1 )
CALL DSCAL( NDATA( 5 ),
$ ONE / DBLE( NCALL ), OPCNT,
$ 1 )
CALL DSCAL( NDATA( 5 ),
$ ONE / DBLE( NCALL ), TIMNG,
$ 1 )
CALL DCOPY( NDATA( 5 ), OPCNT, 1,
$ OPCTBL( 1, ITYPE, NCLSD+INB,
$ 5 ), 1 )
CALL DCOPY( NDATA( 5 ), TIMNG, 1,
$ TIMTBL( 1, ITYPE, NCLSD+INB,
$ 5 ), 1 )
DO 130 I = 1, NDATA( 5 )
FLPTBL( I, ITYPE, NCLSD+INB,
$ 5 ) = DMFLOP( OPCNT( I ),
$ TIMNG( I ), INFO )
130 CONTINUE
*
END IF
*
140 CONTINUE
150 CONTINUE
160 CONTINUE
NCLS = NCLS + NNB
NCLSY = NCLSY + NNB
NCLSS = NCLSS + NNB
NCLSD = NCLSD + NNB
170 CONTINUE
NCLSX = NCLSX + 1
180 CONTINUE
190 CONTINUE
200 CONTINUE
*
* Print a summary of the results.
*
DO 220 ISUB = 1, NSUBS
IF( TIMSUB( ISUB ) ) THEN
WRITE( NOUT, FMT = 9999 )SUBNAM( ISUB )
IF( ISUB.EQ.1 ) THEN
WRITE( NOUT, FMT = 9998 )
ELSE IF( ISUB.EQ.2 ) THEN
WRITE( NOUT, FMT = 9997 )
ELSE IF( ISUB.EQ.3 ) THEN
WRITE( NOUT, FMT = 9996 )
ELSE IF( ISUB.EQ.4 ) THEN
WRITE( NOUT, FMT = 9995 )
ELSE IF( ISUB.EQ.5 ) THEN
WRITE( NOUT, FMT = 9994 )
END IF
DO 210 ITBL = 1, 3
IF( ITBL.EQ.1 ) THEN
WRITE( NOUT, FMT = 9993 )
CALL DPRTLS( ISUB, SUBNAM( ISUB ), NDATA( ISUB ), NM,
$ MVAL, NN, NVAL, NNS, NSVAL, NNB, NBVAL,
$ NXVAL, NLDA, LDAVAL, MTYPE,
$ TIMTBL( 1, 1, 1, ISUB ), NOUT )
ELSE IF( ITBL.EQ.2 ) THEN
WRITE( NOUT, FMT = 9992 )
CALL DPRTLS( ISUB, SUBNAM( ISUB ), NDATA( ISUB ), NM,
$ MVAL, NN, NVAL, NNS, NSVAL, NNB, NBVAL,
$ NXVAL, NLDA, LDAVAL, MTYPE,
$ OPCTBL( 1, 1, 1, ISUB ), NOUT )
ELSE IF( ITBL.EQ.3 ) THEN
WRITE( NOUT, FMT = 9991 )
CALL DPRTLS( ISUB, SUBNAM( ISUB ), NDATA( ISUB ), NM,
$ MVAL, NN, NVAL, NNS, NSVAL, NNB, NBVAL,
$ NXVAL, NLDA, LDAVAL, MTYPE,
$ FLPTBL( 1, 1, 1, ISUB ), NOUT )
END IF
210 CONTINUE
END IF
220 CONTINUE
*
230 CONTINUE
9999 FORMAT( / / / ' ****** Results for ', A, ' ******' )
9998 FORMAT( / ' DGELS : overall performance',
$ / ' comp. 1 : if M>=N, DGEQRF, QR factorization',
$ / ' if M< N, DGELQF, QR factorization',
$ / ' comp. 2 : if M>=N, DORMQR, multiplication by',
$ ' reflectors', /
$ ' if M< N, DORMLQ, multiplication by',
$ ' reflectors', /
$ ' comp. 3 : DTRSM, solution of the triangular', ' system',
$ / / ' Types 4 to 6 are the transpose', ' of types 1 to 3' )
9997 FORMAT( / ' DGELSX : overall performance',
$ / ' comp. 1 : DGEQPF, QR factorization with column',
$ ' pivoting', / ' comp. 2 : if RANK<N, DTZRQF, reduction to',
$ ' triangular form', /
$ ' comp. 3 : DORM2R, multiplication by reflectors',
$ / ' comp. 4 : DTRSM, solution of the triangular', ' system',
$ / ' comp. 5 : if RANK<N, DLATZM, multiplication by',
$ ' reflectors' )
9996 FORMAT( / ' DGELSY : overall performance',
$ / ' comp. 1 : DGEQP3, QR factorization with column',
$ ' pivoting', / ' comp. 2 : if RANK<N, DTZRZF, reduction to',
$ ' triangular form', /
$ ' comp. 3 : DORMQR, multiplication by reflectors',
$ / ' comp. 4 : DTRSM, solution of the triangular', ' system',
$ / ' comp. 5 : if RANK<N, DORMRZ, multiplication by',
$ ' reflectors' )
9995 FORMAT( / ' DGELSS: overall performance',
$ / ' comp. 1 : if M>>N, DGEQRF, QR factorization',
$ / ' DORMQR, multiplication by',
$ ' reflectors', /
$ ' if N>>M, DGELQF, QL factorization',
$ / ' comp. 2 : DGEBRD, reduction to bidiagonal form',
$ / ' comp. 3 : DORMBR, multiplication by left',
$ ' bidiagonalizing vectors', /
$ ' DORGBR, generation of right',
$ ' bidiagonalizing vectors', /
$ ' comp. 4 : DBDSQR, singular value decomposition',
$ ' of the bidiagonal matrix',
$ / ' comp. 5 : multiplication by right bidiagonalizing',
$ ' vectors', /
$ ' (DGEMM or SGEMV, and DORMLQ if N>>M)' )
9994 FORMAT( / ' DGELSD: overall performance',
$ / ' comp. 1 : if M>>N, DGEQRF, QR factorization',
$ / ' DORMQR, multiplication by',
$ ' reflectors', /
$ ' if N>>M, DGELQF, QL factorization',
$ / ' comp. 2 : DGEBRD, reduction to bidiagonal form',
$ / ' comp. 3 : DORMBR, multiplication by left ',
$ ' bidiagonalizing vectors', /
$ ' multiplication by right',
$ ' bidiagonalizing vectors', /
$ ' comp. 4 : DLALSD, singular value decomposition',
$ ' of the bidiagonal matrix' )
9993 FORMAT( / / ' *** Time in seconds *** ' )
9992 FORMAT( / / ' *** Number of floating-point operations *** ' )
9991 FORMAT( / / ' *** Speed in megaflops *** ' )
RETURN
*
* End of DTIMLS
*
END
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