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SUBROUTINE DTIMQL( LINE, NM, MVAL, NVAL, NK, KVAL, NNB, NBVAL,
$ NXVAL, NLDA, LDAVAL, TIMMIN, A, TAU, B, WORK,
$ RESLTS, LDR1, LDR2, LDR3, NOUT )
*
* -- LAPACK timing routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* March 31, 1993
*
* .. Scalar Arguments ..
CHARACTER*80 LINE
INTEGER LDR1, LDR2, LDR3, NK, NLDA, NM, NNB, NOUT
DOUBLE PRECISION TIMMIN
* ..
* .. Array Arguments ..
INTEGER KVAL( * ), LDAVAL( * ), MVAL( * ), NBVAL( * ),
$ NVAL( * ), NXVAL( * )
DOUBLE PRECISION A( * ), B( * ), RESLTS( LDR1, LDR2, LDR3, * ),
$ TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DTIMQL times the LAPACK routines to perform the QL factorization of
* a DOUBLE PRECISION general matrix.
*
* 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 and N contained in the vectors
* MVAL and NVAL. The matrix sizes are used in pairs (M,N).
*
* MVAL (input) INTEGER array, dimension (NM)
* The values of the matrix row dimension M.
*
* NVAL (input) INTEGER array, dimension (NM)
* The values of the matrix column dimension N.
*
* NK (input) INTEGER
* The number of values of K in the vector KVAL.
*
* KVAL (input) INTEGER array, dimension (NK)
* The values of the matrix dimension K, used in DORMQL.
*
* 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 (LDAMAX*NMAX)
* where LDAMAX and NMAX are the maximum values of LDA and N.
*
* TAU (workspace) DOUBLE PRECISION array, dimension (min(M,N))
*
* B (workspace) DOUBLE PRECISION array, dimension (LDAMAX*NMAX)
*
* WORK (workspace) DOUBLE PRECISION array, dimension (LDAMAX*NBMAX)
* where NBMAX is the maximum value of NB.
*
* RESLTS (workspace) DOUBLE PRECISION array, dimension
* (LDR1,LDR2,LDR3,2*NK)
* The timing results for each subroutine over the relevant
* values of (M,N), (NB,NX), and LDA.
*
* LDR1 (input) INTEGER
* The first dimension of RESLTS. LDR1 >= max(1,NNB).
*
* LDR2 (input) INTEGER
* The second dimension of RESLTS. LDR2 >= max(1,NM).
*
* LDR3 (input) INTEGER
* The third dimension of RESLTS. LDR3 >= max(1,NLDA).
*
* NOUT (input) INTEGER
* The unit number for output.
*
* Internal Parameters
* ===================
*
* MODE INTEGER
* The matrix type. MODE = 3 is a geometric distribution of
* eigenvalues. See DLATMS for further details.
*
* COND DOUBLE PRECISION
* The condition number of the matrix. The singular values are
* set to values from DMAX to DMAX/COND.
*
* DMAX DOUBLE PRECISION
* The magnitude of the largest singular value.
*
* =====================================================================
*
* .. Parameters ..
INTEGER NSUBS
PARAMETER ( NSUBS = 3 )
INTEGER MODE
DOUBLE PRECISION COND, DMAX
PARAMETER ( MODE = 3, COND = 100.0D0, DMAX = 1.0D0 )
* ..
* .. Local Scalars ..
CHARACTER LABM, SIDE, TRANS
CHARACTER*3 PATH
CHARACTER*6 CNAME
INTEGER I, I4, IC, ICL, IK, ILDA, IM, IMX, INB, INFO,
$ ISIDE, ISUB, ITOFF, ITRAN, K, K1, LDA, LW, M,
$ M1, MINMN, N, N1, NB, NX
DOUBLE PRECISION OPS, S1, S2, TIME, UNTIME
* ..
* .. Local Arrays ..
LOGICAL TIMSUB( NSUBS )
CHARACTER SIDES( 2 ), TRANSS( 2 )
CHARACTER*6 SUBNAM( NSUBS )
INTEGER ISEED( 4 ), MUSE( 12 ), NUSE( 12 ), RESEED( 4 )
* ..
* .. External Functions ..
DOUBLE PRECISION DMFLOP, DOPLA, DSECND
EXTERNAL DMFLOP, DOPLA, DSECND
* ..
* .. External Subroutines ..
EXTERNAL ATIMCK, ATIMIN, DGEQLF, DLACPY, DLATMS, DORGQL,
$ DORMQL, DPRTB4, DPRTB5, DTIMMG, ICOPY, XLAENV
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX, MIN
* ..
* .. Data statements ..
DATA SUBNAM / 'DGEQLF', 'DORGQL', 'DORMQL' /
DATA SIDES / 'L', 'R' / , TRANSS / 'N', 'T' /
DATA ISEED / 0, 0, 0, 1 /
* ..
* .. Executable Statements ..
*
* Extract the timing request from the input line.
*
PATH( 1: 1 ) = 'Double precision'
PATH( 2: 3 ) = 'QL'
CALL ATIMIN( PATH, LINE, NSUBS, SUBNAM, TIMSUB, NOUT, INFO )
IF( INFO.NE.0 )
$ GO TO 230
*
* Check that M <= LDA for the input values.
*
CNAME = LINE( 1: 6 )
CALL ATIMCK( 1, CNAME, NM, MVAL, NLDA, LDAVAL, NOUT, INFO )
IF( INFO.GT.0 ) THEN
WRITE( NOUT, FMT = 9999 )CNAME
GO TO 230
END IF
*
* Do for each pair of values (M,N):
*
DO 70 IM = 1, NM
M = MVAL( IM )
N = NVAL( IM )
MINMN = MIN( M, N )
CALL ICOPY( 4, ISEED, 1, RESEED, 1 )
*
* Do for each value of LDA:
*
DO 60 ILDA = 1, NLDA
LDA = LDAVAL( ILDA )
*
* Do for each pair of values (NB, NX) in NBVAL and NXVAL.
*
DO 50 INB = 1, NNB
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
NX = NXVAL( INB )
CALL XLAENV( 3, NX )
LW = MAX( 1, N*MAX( 1, NB ) )
*
* Generate a test matrix of size M by N.
*
CALL ICOPY( 4, RESEED, 1, ISEED, 1 )
CALL DLATMS( M, N, 'Uniform', ISEED, 'Nonsymm', TAU,
$ MODE, COND, DMAX, M, N, 'No packing', B,
$ LDA, WORK, INFO )
*
IF( TIMSUB( 1 ) ) THEN
*
* DGEQLF: QL factorization
*
CALL DLACPY( 'Full', M, N, B, LDA, A, LDA )
IC = 0
S1 = DSECND( )
10 CONTINUE
CALL DGEQLF( M, N, A, LDA, TAU, WORK, LW, INFO )
S2 = DSECND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL DLACPY( 'Full', M, N, B, LDA, A, LDA )
GO TO 10
END IF
*
* Subtract the time used in DLACPY.
*
ICL = 1
S1 = DSECND( )
20 CONTINUE
S2 = DSECND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL DLACPY( 'Full', M, N, A, LDA, B, LDA )
GO TO 20
END IF
*
TIME = ( TIME-UNTIME ) / DBLE( IC )
OPS = DOPLA( 'DGEQLF', M, N, 0, 0, NB )
RESLTS( INB, IM, ILDA, 1 ) = DMFLOP( OPS, TIME, INFO )
ELSE
*
* If DGEQLF was not timed, generate a matrix and factor
* it using DGEQLF anyway so that the factored form of
* the matrix can be used in timing the other routines.
*
CALL DLACPY( 'Full', M, N, B, LDA, A, LDA )
CALL DGEQLF( M, N, A, LDA, TAU, WORK, LW, INFO )
END IF
*
IF( TIMSUB( 2 ) ) THEN
*
* DORGQL: Generate orthogonal matrix Q from the QL
* factorization
*
CALL DLACPY( 'Full', M, MINMN, A, LDA, B, LDA )
IC = 0
S1 = DSECND( )
30 CONTINUE
CALL DORGQL( M, MINMN, MINMN, B, LDA, TAU, WORK, LW,
$ INFO )
S2 = DSECND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL DLACPY( 'Full', M, MINMN, A, LDA, B, LDA )
GO TO 30
END IF
*
* Subtract the time used in DLACPY.
*
ICL = 1
S1 = DSECND( )
40 CONTINUE
S2 = DSECND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL DLACPY( 'Full', M, MINMN, A, LDA, B, LDA )
GO TO 40
END IF
*
TIME = ( TIME-UNTIME ) / DBLE( IC )
OPS = DOPLA( 'DORGQL', M, MINMN, MINMN, 0, NB )
RESLTS( INB, IM, ILDA, 2 ) = DMFLOP( OPS, TIME, INFO )
END IF
*
50 CONTINUE
60 CONTINUE
70 CONTINUE
*
* Print tables of results
*
DO 90 ISUB = 1, NSUBS - 1
IF( .NOT.TIMSUB( ISUB ) )
$ GO TO 90
WRITE( NOUT, FMT = 9998 )SUBNAM( ISUB )
IF( NLDA.GT.1 ) THEN
DO 80 I = 1, NLDA
WRITE( NOUT, FMT = 9997 )I, LDAVAL( I )
80 CONTINUE
END IF
WRITE( NOUT, FMT = * )
IF( ISUB.EQ.2 )
$ WRITE( NOUT, FMT = 9996 )
CALL DPRTB4( '( NB, NX)', 'M', 'N', NNB, NBVAL, NXVAL, NM,
$ MVAL, NVAL, NLDA, RESLTS( 1, 1, 1, ISUB ), LDR1,
$ LDR2, NOUT )
90 CONTINUE
*
* Time DORMQL separately. Here the starting matrix is M by N, and
* K is the free dimension of the matrix multiplied by Q.
*
IF( TIMSUB( 3 ) ) THEN
*
* Check that K <= LDA for the input values.
*
CALL ATIMCK( 3, CNAME, NK, KVAL, NLDA, LDAVAL, NOUT, INFO )
IF( INFO.GT.0 ) THEN
WRITE( NOUT, FMT = 9999 )SUBNAM( 3 )
GO TO 230
END IF
*
* Use only the pairs (M,N) where M >= N.
*
IMX = 0
DO 100 IM = 1, NM
IF( MVAL( IM ).GE.NVAL( IM ) ) THEN
IMX = IMX + 1
MUSE( IMX ) = MVAL( IM )
NUSE( IMX ) = NVAL( IM )
END IF
100 CONTINUE
*
* DORMQL: Multiply by Q stored as a product of elementary
* transformations
*
* Do for each pair of values (M,N):
*
DO 180 IM = 1, IMX
M = MUSE( IM )
N = NUSE( IM )
*
* Do for each value of LDA:
*
DO 170 ILDA = 1, NLDA
LDA = LDAVAL( ILDA )
*
* Generate an M by N matrix and form its QL decomposition.
*
CALL DLATMS( M, N, 'Uniform', ISEED, 'Nonsymm', TAU,
$ MODE, COND, DMAX, M, N, 'No packing', A,
$ LDA, WORK, INFO )
LW = MAX( 1, N*MAX( 1, NB ) )
CALL DGEQLF( M, N, A, LDA, TAU, WORK, LW, INFO )
*
* Do first for SIDE = 'L', then for SIDE = 'R'
*
I4 = 0
DO 160 ISIDE = 1, 2
SIDE = SIDES( ISIDE )
*
* Do for each pair of values (NB, NX) in NBVAL and
* NXVAL.
*
DO 150 INB = 1, NNB
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
NX = NXVAL( INB )
CALL XLAENV( 3, NX )
*
* Do for each value of K in KVAL
*
DO 140 IK = 1, NK
K = KVAL( IK )
*
* Sort out which variable is which
*
IF( ISIDE.EQ.1 ) THEN
M1 = M
K1 = N
N1 = K
LW = MAX( 1, N1*MAX( 1, NB ) )
ELSE
N1 = M
K1 = N
M1 = K
LW = MAX( 1, M1*MAX( 1, NB ) )
END IF
*
* Do first for TRANS = 'N', then for TRANS = 'T'
*
ITOFF = 0
DO 130 ITRAN = 1, 2
TRANS = TRANSS( ITRAN )
CALL DTIMMG( 0, M1, N1, B, LDA, 0, 0 )
IC = 0
S1 = DSECND( )
110 CONTINUE
CALL DORMQL( SIDE, TRANS, M1, N1, K1, A, LDA,
$ TAU, B, LDA, WORK, LW, INFO )
S2 = DSECND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL DTIMMG( 0, M1, N1, B, LDA, 0, 0 )
GO TO 110
END IF
*
* Subtract the time used in DTIMMG.
*
ICL = 1
S1 = DSECND( )
120 CONTINUE
S2 = DSECND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL DTIMMG( 0, M1, N1, B, LDA, 0, 0 )
GO TO 120
END IF
*
TIME = ( TIME-UNTIME ) / DBLE( IC )
OPS = DOPLA( 'DORMQL', M1, N1, K1, ISIDE-1,
$ NB )
RESLTS( INB, IM, ILDA,
$ I4+ITOFF+IK ) = DMFLOP( OPS, TIME, INFO )
ITOFF = NK
130 CONTINUE
140 CONTINUE
150 CONTINUE
I4 = 2*NK
160 CONTINUE
170 CONTINUE
180 CONTINUE
*
* Print tables of results
*
ISUB = 3
I4 = 1
IF( IMX.GE.1 ) THEN
DO 220 ISIDE = 1, 2
SIDE = SIDES( ISIDE )
IF( ISIDE.EQ.1 ) THEN
WRITE( NOUT, FMT = 9998 )SUBNAM( ISUB )
IF( NLDA.GT.1 ) THEN
DO 190 I = 1, NLDA
WRITE( NOUT, FMT = 9997 )I, LDAVAL( I )
190 CONTINUE
END IF
END IF
DO 210 ITRAN = 1, 2
TRANS = TRANSS( ITRAN )
DO 200 IK = 1, NK
IF( ISIDE.EQ.1 ) THEN
N = KVAL( IK )
WRITE( NOUT, FMT = 9995 )SUBNAM( ISUB ), SIDE,
$ TRANS, 'N', N
LABM = 'M'
ELSE
M = KVAL( IK )
WRITE( NOUT, FMT = 9995 )SUBNAM( ISUB ), SIDE,
$ TRANS, 'M', M
LABM = 'N'
END IF
CALL DPRTB5( 'NB', LABM, 'K', NNB, NBVAL, IMX,
$ MUSE, NUSE, NLDA,
$ RESLTS( 1, 1, 1, I4 ), LDR1, LDR2,
$ NOUT )
I4 = I4 + 1
200 CONTINUE
210 CONTINUE
220 CONTINUE
ELSE
WRITE( NOUT, FMT = 9994 )SUBNAM( ISUB )
END IF
END IF
230 CONTINUE
9999 FORMAT( 1X, A6, ' timing run not attempted', / )
9998 FORMAT( / ' *** Speed of ', A6, ' in megaflops ***' )
9997 FORMAT( 5X, 'line ', I2, ' with LDA = ', I5 )
9996 FORMAT( 5X, 'K = min(M,N)', / )
9995 FORMAT( / 5X, A6, ' with SIDE = ''', A1, ''', TRANS = ''', A1,
$ ''', ', A1, ' =', I6, / )
9994 FORMAT( ' *** No pairs (M,N) found with M >= N: ', A6,
$ ' not timed' )
RETURN
*
* End of DTIMQL
*
END
|
