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SUBROUTINE CTIMBR( LINE, NM, MVAL, NVAL, NK, KVAL, NNB, NBVAL,
$ NXVAL, NLDA, LDAVAL, TIMMIN, A, B, D, TAU,
$ 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
REAL TIMMIN
* ..
* .. Array Arguments ..
INTEGER KVAL( * ), LDAVAL( * ), MVAL( * ), NBVAL( * ),
$ NVAL( * ), NXVAL( * )
REAL D( * ), RESLTS( LDR1, LDR2, LDR3, * )
COMPLEX A( * ), B( * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* CTIMBR times CGEBRD, CUNGBR, and CUNMBR.
*
* 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 contained in the vector KVAL.
*
* KVAL (input) INTEGER array, dimension (NK)
* The values of the matrix dimension K.
*
* 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) REAL
* The minimum time a subroutine will be timed.
*
* A (workspace) COMPLEX array, dimension (LDAMAX*NMAX)
* where LDAMAX and NMAX are the maximum values of LDA and N.
*
* B (workspace) COMPLEX array, dimension (LDAMAX*NMAX)
*
* D (workspace) REAL array, dimension
* (2*max(min(M,N))-1)
*
* TAU (workspace) COMPLEX array, dimension
* (2*max(min(M,N)))
*
* WORK (workspace) COMPLEX array, dimension (LDAMAX*NBMAX)
* where NBMAX is the maximum value of NB.
*
* RESLTS (output) REAL array, dimension (LDR1,LDR2,LDR3,6)
* 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 CLATMS for further details.
*
* COND REAL
* The condition number of the matrix. The singular values are
* set to values from DMAX to DMAX/COND.
*
* DMAX REAL
* The magnitude of the largest singular value.
*
* =====================================================================
*
* .. Parameters ..
INTEGER NSUBS
PARAMETER ( NSUBS = 3 )
INTEGER MODE
REAL COND, DMAX
PARAMETER ( MODE = 3, COND = 100.0E0, DMAX = 1.0E0 )
* ..
* .. Local Scalars ..
CHARACTER LABK, LABM, LABN, SIDE, TRANS, VECT
CHARACTER*3 PATH
CHARACTER*6 CNAME
INTEGER I, I3, I4, IC, ICL, IK, ILDA, IM, INB, INFO,
$ INFO2, ISIDE, ISUB, ITOFF, ITRAN, IVECT, K, K1,
$ LDA, LW, M, M1, MINMN, N, N1, NB, NQ, NX
REAL OPS, S1, S2, TIME, UNTIME
* ..
* .. Local Arrays ..
LOGICAL TIMSUB( NSUBS )
CHARACTER SIDES( 2 ), TRANSS( 2 ), VECTS( 2 )
CHARACTER*6 SUBNAM( NSUBS )
INTEGER ISEED( 4 ), RESEED( 4 )
* ..
* .. External Functions ..
REAL SECOND, SMFLOP, SOPLA
EXTERNAL SECOND, SMFLOP, SOPLA
* ..
* .. External Subroutines ..
EXTERNAL ATIMCK, ATIMIN, CGEBRD, CLACPY, CLATMS, CTIMMG,
$ CUNGBR, CUNMBR, ICOPY, SPRTB4, SPRTB5, XLAENV
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, REAL
* ..
* .. Data statements ..
DATA SUBNAM / 'CGEBRD', 'CUNGBR', 'CUNMBR' / ,
$ SIDES / 'L', 'R' / , VECTS / 'Q', 'P' / ,
$ TRANSS / 'N', 'C' /
DATA ISEED / 0, 0, 0, 1 /
* ..
* .. Executable Statements ..
*
* Extract the timing request from the input line.
*
PATH( 1: 1 ) = 'Complex precision'
PATH( 2: 3 ) = 'BR'
CALL ATIMIN( PATH, LINE, NSUBS, SUBNAM, TIMSUB, NOUT, INFO )
IF( INFO.NE.0 )
$ GO TO 220
*
* 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 220
END IF
*
* Check that N <= LDA and K <= LDA for SORMBR
*
IF( TIMSUB( 3 ) ) THEN
CALL ATIMCK( 2, CNAME, NM, NVAL, NLDA, LDAVAL, NOUT, INFO )
CALL ATIMCK( 3, CNAME, NK, KVAL, NLDA, LDAVAL, NOUT, INFO2 )
IF( INFO.GT.0 .OR. INFO2.GT.0 ) THEN
WRITE( NOUT, FMT = 9999 )SUBNAM( 3 )
TIMSUB( 3 ) = .FALSE.
END IF
END IF
*
* Do for each pair of values (M,N):
*
DO 140 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 130 ILDA = 1, NLDA
LDA = LDAVAL( ILDA )
*
* Do for each pair of values (NB, NX) in NBVAL and NXVAL.
*
DO 120 INB = 1, NNB
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
NX = NXVAL( INB )
CALL XLAENV( 3, NX )
LW = MAX( M+N, MAX( 1, NB )*( M+N ) )
*
* Generate a test matrix of size M by N.
*
CALL ICOPY( 4, RESEED, 1, ISEED, 1 )
CALL CLATMS( M, N, 'Uniform', ISEED, 'Nonsymm', D, MODE,
$ COND, DMAX, M, N, 'No packing', B, LDA,
$ WORK, INFO )
*
IF( TIMSUB( 1 ) ) THEN
*
* CGEBRD: Block reduction to bidiagonal form
*
CALL CLACPY( 'Full', M, N, B, LDA, A, LDA )
IC = 0
S1 = SECOND( )
10 CONTINUE
CALL CGEBRD( M, N, A, LDA, D, D( MINMN ), TAU,
$ TAU( MINMN+1 ), WORK, LW, INFO )
S2 = SECOND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL CLACPY( 'Full', M, N, B, LDA, A, LDA )
GO TO 10
END IF
*
* Subtract the time used in CLACPY.
*
ICL = 1
S1 = SECOND( )
20 CONTINUE
S2 = SECOND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL CLACPY( 'Full', M, N, A, LDA, B, LDA )
GO TO 20
END IF
*
TIME = ( TIME-UNTIME ) / REAL( IC )
OPS = SOPLA( 'CGEBRD', M, N, 0, 0, NB )
RESLTS( INB, IM, ILDA, 1 ) = SMFLOP( OPS, TIME, INFO )
ELSE
*
* If CGEBRD was not timed, generate a matrix and reduce
* it using CGEBRD anyway so that the orthogonal
* transformations may be used in timing the other
* routines.
*
CALL CLACPY( 'Full', M, N, B, LDA, A, LDA )
CALL CGEBRD( M, N, A, LDA, D, D( MINMN ), TAU,
$ TAU( MINMN+1 ), WORK, LW, INFO )
*
END IF
*
IF( TIMSUB( 2 ) ) THEN
*
* CUNGBR: Generate one of the orthogonal matrices Q or
* P' from the reduction to bidiagonal form
* A = Q * B * P'.
*
DO 50 IVECT = 1, 2
IF( IVECT.EQ.1 ) THEN
VECT = 'Q'
M1 = M
N1 = MIN( M, N )
K1 = N
ELSE
VECT = 'P'
M1 = MIN( M, N )
N1 = N
K1 = M
END IF
I3 = ( IVECT-1 )*NLDA
LW = MAX( 1, MAX( 1, NB )*MIN( M, N ) )
CALL CLACPY( 'Full', M, N, A, LDA, B, LDA )
IC = 0
S1 = SECOND( )
30 CONTINUE
CALL CUNGBR( VECT, M1, N1, K1, B, LDA, TAU, WORK,
$ LW, INFO )
S2 = SECOND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL CLACPY( 'Full', M, N, A, LDA, B, LDA )
GO TO 30
END IF
*
* Subtract the time used in CLACPY.
*
ICL = 1
S1 = SECOND( )
40 CONTINUE
S2 = SECOND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL CLACPY( 'Full', M, N, A, LDA, B, LDA )
GO TO 40
END IF
*
TIME = ( TIME-UNTIME ) / REAL( IC )
*
* Op count for CUNGBR:
*
IF( IVECT.EQ.1 ) THEN
IF( M1.GE.K1 ) THEN
OPS = SOPLA( 'CUNGQR', M1, N1, K1, -1, NB )
ELSE
OPS = SOPLA( 'CUNGQR', M1-1, M1-1, M1-1, -1,
$ NB )
END IF
ELSE
IF( K1.LT.N1 ) THEN
OPS = SOPLA( 'CUNGLQ', M1, N1, K1, -1, NB )
ELSE
OPS = SOPLA( 'CUNGLQ', N1-1, N1-1, N1-1, -1,
$ NB )
END IF
END IF
*
RESLTS( INB, IM, I3+ILDA, 2 ) = SMFLOP( OPS, TIME,
$ INFO )
50 CONTINUE
END IF
*
IF( TIMSUB( 3 ) ) THEN
*
* CUNMBR: Multiply an m by n matrix B by one of the
* orthogonal matrices Q or P' from the reduction to
* bidiagonal form A = Q * B * P'.
*
DO 110 IVECT = 1, 2
IF( IVECT.EQ.1 ) THEN
VECT = 'Q'
K1 = N
NQ = M
ELSE
VECT = 'P'
K1 = M
NQ = N
END IF
I3 = ( IVECT-1 )*NLDA
I4 = 2
DO 100 ISIDE = 1, 2
SIDE = SIDES( ISIDE )
DO 90 IK = 1, NK
K = KVAL( IK )
IF( ISIDE.EQ.1 ) THEN
M1 = NQ
N1 = K
LW = MAX( 1, MAX( 1, NB )*N1 )
ELSE
M1 = K
N1 = NQ
LW = MAX( 1, MAX( 1, NB )*M1 )
END IF
ITOFF = 0
DO 80 ITRAN = 1, 2
TRANS = TRANSS( ITRAN )
CALL CTIMMG( 0, M1, N1, B, LDA, 0, 0 )
IC = 0
S1 = SECOND( )
60 CONTINUE
CALL CUNMBR( VECT, SIDE, TRANS, M1, N1,
$ K1, A, LDA, TAU, B, LDA,
$ WORK, LW, INFO )
S2 = SECOND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL CTIMMG( 0, M1, N1, B, LDA, 0, 0 )
GO TO 60
END IF
*
* Subtract the time used in CTIMMG.
*
ICL = 1
S1 = SECOND( )
70 CONTINUE
S2 = SECOND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL CTIMMG( 0, M1, N1, B, LDA, 0, 0 )
GO TO 70
END IF
*
TIME = ( TIME-UNTIME ) / REAL( IC )
IF( IVECT.EQ.1 ) THEN
*
* Op count for CUNMBR, VECT = 'Q':
*
IF( NQ.GE.K1 ) THEN
OPS = SOPLA( 'CUNMQR', M1, N1, K1,
$ ISIDE-1, NB )
ELSE IF( ISIDE.EQ.1 ) THEN
OPS = SOPLA( 'CUNMQR', M1-1, N1,
$ NQ-1, ISIDE-1, NB )
ELSE
OPS = SOPLA( 'CUNMQR', M1, N1-1,
$ NQ-1, ISIDE-1, NB )
END IF
ELSE
*
* Op count for CUNMBR, VECT = 'P':
*
IF( NQ.GE.K1 ) THEN
OPS = SOPLA( 'CUNMLQ', M1, N1, K1,
$ ISIDE-1, NB )
ELSE IF( ISIDE.EQ.1 ) THEN
OPS = SOPLA( 'CUNMLQ', M1-1, N1,
$ NQ-1, ISIDE-1, NB )
ELSE
OPS = SOPLA( 'CUNMLQ', M1, N1-1,
$ NQ-1, ISIDE-1, NB )
END IF
END IF
*
RESLTS( INB, IM, I3+ILDA,
$ I4+ITOFF+IK ) = SMFLOP( OPS, TIME,
$ INFO )
ITOFF = NK
80 CONTINUE
90 CONTINUE
I4 = 2*NK + 2
100 CONTINUE
110 CONTINUE
END IF
120 CONTINUE
130 CONTINUE
140 CONTINUE
*
* Print a table of results for each timed routine.
*
DO 210 ISUB = 1, NSUBS
IF( .NOT.TIMSUB( ISUB ) )
$ GO TO 210
WRITE( NOUT, FMT = 9998 )SUBNAM( ISUB )
IF( NLDA.GT.1 ) THEN
DO 150 I = 1, NLDA
WRITE( NOUT, FMT = 9997 )I, LDAVAL( I )
150 CONTINUE
END IF
IF( ISUB.EQ.1 ) THEN
WRITE( NOUT, FMT = * )
CALL SPRTB4( '( NB, NX)', 'M', 'N', NNB, NBVAL, NXVAL, NM,
$ MVAL, NVAL, NLDA, RESLTS( 1, 1, 1, ISUB ),
$ LDR1, LDR2, NOUT )
ELSE IF( ISUB.EQ.2 ) THEN
DO 160 IVECT = 1, 2
I3 = ( IVECT-1 )*NLDA + 1
IF( IVECT.EQ.1 ) THEN
LABK = 'N'
LABM = 'M'
LABN = 'K'
ELSE
LABK = 'M'
LABM = 'K'
LABN = 'N'
END IF
WRITE( NOUT, FMT = 9996 )SUBNAM( ISUB ), VECTS( IVECT ),
$ LABK, LABM, LABN
CALL SPRTB4( '( NB, NX)', LABM, LABN, NNB, NBVAL,
$ NXVAL, NM, MVAL, NVAL, NLDA,
$ RESLTS( 1, 1, I3, ISUB ), LDR1, LDR2, NOUT )
160 CONTINUE
ELSE IF( ISUB.EQ.3 ) THEN
DO 200 IVECT = 1, 2
I3 = ( IVECT-1 )*NLDA + 1
I4 = 3
DO 190 ISIDE = 1, 2
IF( ISIDE.EQ.1 ) THEN
IF( IVECT.EQ.1 ) THEN
LABM = 'M'
LABN = 'K'
ELSE
LABM = 'K'
LABN = 'M'
END IF
LABK = 'N'
ELSE
IF( IVECT.EQ.1 ) THEN
LABM = 'N'
LABN = 'K'
ELSE
LABM = 'K'
LABN = 'N'
END IF
LABK = 'M'
END IF
DO 180 ITRAN = 1, 2
DO 170 IK = 1, NK
WRITE( NOUT, FMT = 9995 )SUBNAM( ISUB ),
$ VECTS( IVECT ), SIDES( ISIDE ),
$ TRANSS( ITRAN ), LABK, KVAL( IK )
CALL SPRTB5( 'NB', LABM, LABN, NNB, NBVAL, NM,
$ MVAL, NVAL, NLDA,
$ RESLTS( 1, 1, I3, I4 ), LDR1, LDR2,
$ NOUT )
I4 = I4 + 1
170 CONTINUE
180 CONTINUE
190 CONTINUE
200 CONTINUE
END IF
210 CONTINUE
220 CONTINUE
RETURN
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, A6, ' with VECT = ''', A1, ''', ', A1, ' = MIN(',
$ A1, ',', A1, ')', / )
9995 FORMAT( / 5X, A6, ' with VECT = ''', A1, ''', SIDE = ''', A1,
$ ''', TRANS = ''', A1, ''', ', A1, ' =', I6, / )
*
* End of CTIMBR
*
END
|
