497 lines
17 KiB
FortranFixed
497 lines
17 KiB
FortranFixed
SUBROUTINE ZTIMLQ( LINE, NM, MVAL, NVAL, NK, KVAL, NNB, NBVAL,
|
|
$ NXVAL, NLDA, LDAVAL, TIMMIN, A, TAU, B, WORK,
|
|
$ RWORK, RESLTS, LDR1, LDR2, LDR3, NOUT )
|
|
*
|
|
* -- LAPACK timing routine (version 3.1) --
|
|
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
|
|
* October 2006
|
|
*
|
|
* .. 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 RESLTS( LDR1, LDR2, LDR3, * ), RWORK( * )
|
|
COMPLEX*16 A( * ), B( * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* ZTIMLQ times the LAPACK routines to perform the LQ factorization of
|
|
* a COMPLEX*16 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 ZUNMLQ.
|
|
*
|
|
* 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) COMPLEX*16 array, dimension (LDAMAX*NMAX)
|
|
* where LDAMAX and NMAX are the maximum values of LDA and N.
|
|
*
|
|
* TAU (workspace) COMPLEX*16 array, dimension (min(M,N))
|
|
*
|
|
* B (workspace) COMPLEX*16 array, dimension (LDAMAX*NMAX)
|
|
*
|
|
* WORK (workspace) COMPLEX*16 array, dimension (LDAMAX*NBMAX)
|
|
* where NBMAX is the maximum value of NB.
|
|
*
|
|
* RWORK (workspace) DOUBLE PRECISION array, dimension
|
|
* (min(MMAX,NMAX))
|
|
*
|
|
* 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 ZLATMS 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(32) 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(32) SUBNAM( NSUBS )
|
|
INTEGER ISEED( 4 ), MUSE( 12 ), NUSE( 12 ), RESEED( 4 )
|
|
* ..
|
|
* .. External Functions ..
|
|
INTEGER ILA_LEN_TRIM
|
|
EXTERNAL ILA_LEN_TRIM
|
|
DOUBLE PRECISION DMFLOP, DOPLA, DSECND
|
|
EXTERNAL DMFLOP, DOPLA, DSECND
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL ATIMCK, ATIMIN, DPRTB4, DPRTB5, ICOPY, XLAENV,
|
|
$ ZGELQF, ZLACPY, ZLATMS, ZTIMMG, ZUNGLQ, ZUNMLQ
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC DBLE, MAX, MIN
|
|
* ..
|
|
* .. Data statements ..
|
|
DATA SUBNAM / 'ZGELQF', 'ZUNGLQ', 'ZUNMLQ' /
|
|
DATA SIDES / 'L', 'R' / , TRANSS / 'N', 'C' /
|
|
DATA ISEED / 0, 0, 0, 1 /
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Extract the timing request from the input line.
|
|
*
|
|
PATH( 1: 1 ) = 'Zomplex precision'
|
|
PATH( 2: 3 ) = 'LQ'
|
|
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(1:ILA_LEN_TRIM(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, M*MAX( 1, NB ) )
|
|
*
|
|
* Generate a test matrix of size M by N.
|
|
*
|
|
CALL ICOPY( 4, RESEED, 1, ISEED, 1 )
|
|
CALL ZLATMS( M, N, 'Uniform', ISEED, 'Nonsymm', RWORK,
|
|
$ MODE, COND, DMAX, M, N, 'No packing', B,
|
|
$ LDA, WORK, INFO )
|
|
*
|
|
IF( TIMSUB( 1 ) ) THEN
|
|
*
|
|
* ZGELQF: LQ factorization
|
|
*
|
|
CALL ZLACPY( 'Full', M, N, B, LDA, A, LDA )
|
|
IC = 0
|
|
S1 = DSECND( )
|
|
10 CONTINUE
|
|
CALL ZGELQF( M, N, A, LDA, TAU, WORK, LW, INFO )
|
|
S2 = DSECND( )
|
|
TIME = S2 - S1
|
|
IC = IC + 1
|
|
IF( TIME.LT.TIMMIN ) THEN
|
|
CALL ZLACPY( 'Full', M, N, B, LDA, A, LDA )
|
|
GO TO 10
|
|
END IF
|
|
*
|
|
* Subtract the time used in ZLACPY.
|
|
*
|
|
ICL = 1
|
|
S1 = DSECND( )
|
|
20 CONTINUE
|
|
S2 = DSECND( )
|
|
UNTIME = S2 - S1
|
|
ICL = ICL + 1
|
|
IF( ICL.LE.IC ) THEN
|
|
CALL ZLACPY( 'Full', M, N, A, LDA, B, LDA )
|
|
GO TO 20
|
|
END IF
|
|
*
|
|
TIME = ( TIME-UNTIME ) / DBLE( IC )
|
|
OPS = DOPLA( 'ZGELQF', M, N, 0, 0, NB )
|
|
RESLTS( INB, IM, ILDA, 1 ) = DMFLOP( OPS, TIME, INFO )
|
|
ELSE
|
|
*
|
|
* If ZGELQF was not timed, generate a matrix and factor
|
|
* it using ZGELQF anyway so that the factored form of
|
|
* the matrix can be used in timing the other routines.
|
|
*
|
|
CALL ZLACPY( 'Full', M, N, B, LDA, A, LDA )
|
|
CALL ZGELQF( M, N, A, LDA, TAU, WORK, LW, INFO )
|
|
END IF
|
|
*
|
|
IF( TIMSUB( 2 ) ) THEN
|
|
*
|
|
* ZUNGLQ: Generate orthogonal matrix Q from the LQ
|
|
* factorization
|
|
*
|
|
CALL ZLACPY( 'Full', MINMN, N, A, LDA, B, LDA )
|
|
IC = 0
|
|
S1 = DSECND( )
|
|
30 CONTINUE
|
|
CALL ZUNGLQ( MINMN, N, MINMN, B, LDA, TAU, WORK, LW,
|
|
$ INFO )
|
|
S2 = DSECND( )
|
|
TIME = S2 - S1
|
|
IC = IC + 1
|
|
IF( TIME.LT.TIMMIN ) THEN
|
|
CALL ZLACPY( 'Full', MINMN, N, A, LDA, B, LDA )
|
|
GO TO 30
|
|
END IF
|
|
*
|
|
* Subtract the time used in ZLACPY.
|
|
*
|
|
ICL = 1
|
|
S1 = DSECND( )
|
|
40 CONTINUE
|
|
S2 = DSECND( )
|
|
UNTIME = S2 - S1
|
|
ICL = ICL + 1
|
|
IF( ICL.LE.IC ) THEN
|
|
CALL ZLACPY( 'Full', MINMN, N, A, LDA, B, LDA )
|
|
GO TO 40
|
|
END IF
|
|
*
|
|
TIME = ( TIME-UNTIME ) / DBLE( IC )
|
|
OPS = DOPLA( 'ZUNGLQ', MINMN, N, 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 )(1:ILA_LEN_TRIM( 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 ZUNMLQ 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 )(1:ILA_LEN_TRIM( 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 ).LE.NVAL( IM ) ) THEN
|
|
IMX = IMX + 1
|
|
MUSE( IMX ) = MVAL( IM )
|
|
NUSE( IMX ) = NVAL( IM )
|
|
END IF
|
|
100 CONTINUE
|
|
*
|
|
* ZUNMLQ: 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 LQ decomposition.
|
|
*
|
|
CALL ZLATMS( M, N, 'Uniform', ISEED, 'Nonsymm', RWORK,
|
|
$ MODE, COND, DMAX, M, N, 'No packing', A,
|
|
$ LDA, WORK, INFO )
|
|
LW = MAX( 1, M*MAX( 1, NB ) )
|
|
CALL ZGELQF( 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
|
|
K1 = M
|
|
M1 = N
|
|
N1 = K
|
|
LW = MAX( 1, N1*MAX( 1, NB ) )
|
|
ELSE
|
|
K1 = M
|
|
N1 = 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 ZTIMMG( 0, M1, N1, B, LDA, 0, 0 )
|
|
IC = 0
|
|
S1 = DSECND( )
|
|
110 CONTINUE
|
|
CALL ZUNMLQ( 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 ZTIMMG( 0, M1, N1, B, LDA, 0, 0 )
|
|
GO TO 110
|
|
END IF
|
|
*
|
|
* Subtract the time used in ZTIMMG.
|
|
*
|
|
ICL = 1
|
|
S1 = DSECND( )
|
|
120 CONTINUE
|
|
S2 = DSECND( )
|
|
UNTIME = S2 - S1
|
|
ICL = ICL + 1
|
|
IF( ICL.LE.IC ) THEN
|
|
CALL ZTIMMG( 0, M1, N1, B, LDA, 0, 0 )
|
|
GO TO 120
|
|
END IF
|
|
*
|
|
TIME = ( TIME-UNTIME ) / DBLE( IC )
|
|
OPS = DOPLA( 'ZUNMLQ', 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 )(1:ILA_LEN_TRIM( 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 )(1:ILA_LEN_TRIM( SUBNAM( ISUB ) )), SIDE,
|
|
$ TRANS, 'N', N
|
|
LABM = 'M'
|
|
ELSE
|
|
M = KVAL( IK )
|
|
WRITE( NOUT, FMT = 9995 )
|
|
$ SUBNAM( ISUB )(1:ILA_LEN_TRIM( SUBNAM( ISUB ) )), SIDE,
|
|
$ TRANS, 'M', M
|
|
LABM = 'N'
|
|
END IF
|
|
CALL DPRTB5( 'NB', 'K', LABM, 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 )(1:ILA_LEN_TRIM( SUBNAM( ISUB ) ))
|
|
END IF
|
|
END IF
|
|
230 CONTINUE
|
|
9999 FORMAT( 1X, A, ' timing run not attempted', / )
|
|
9998 FORMAT( / ' *** Speed of ', A, ' in megaflops ***' )
|
|
9997 FORMAT( 5X, 'line ', I2, ' with LDA = ', I5 )
|
|
9996 FORMAT( 5X, 'K = min(M,N)', / )
|
|
9995 FORMAT( / 5X, A, ' with SIDE = ''', A1, ''', TRANS = ''', A1,
|
|
$ ''', ', A1, ' =', I6, / )
|
|
9994 FORMAT( ' *** No pairs (M,N) found with M <= N: ', A,
|
|
$ ' not timed' )
|
|
RETURN
|
|
*
|
|
* End of ZTIMLQ
|
|
*
|
|
END
|