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SUBROUTINE STIMTD( LINE, NM, MVAL, NN, NVAL, 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, NLDA, NM, NN, NNB, NOUT
REAL TIMMIN
* ..
* .. Array Arguments ..
INTEGER LDAVAL( * ), MVAL( * ), NBVAL( * ), NVAL( * ),
$ NXVAL( * )
REAL A( * ), B( * ), D( * ),
$ RESLTS( LDR1, LDR2, LDR3, * ), TAU( * ),
$ WORK( * )
* ..
*
* Purpose
* =======
*
* STIMTD times the LAPACK routines SSYTRD, SORGTR, and SORMTR and the
* EISPACK routine TRED1.
*
* 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 size 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.
*
* 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) REAL array, dimension (LDAMAX*NMAX)
* where LDAMAX and NMAX are the maximum values of LDA and N.
*
* B (workspace) REAL array, dimension (LDAMAX*NMAX)
*
* D (workspace) REAL array, dimension (2*NMAX-1)
*
* TAU (workspace) REAL array, dimension (NMAX)
*
* WORK (workspace) REAL array, dimension (NMAX*NBMAX)
* where NBMAX is the maximum value of NB.
*
* RESLTS (workspace) REAL array, dimension
* (LDR1,LDR2,LDR3,4*NN+3)
* The timing results for each subroutine over the relevant
* values of M, (NB,NX), LDA, and N.
*
* 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(1,2*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 SLATMS 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 = 4 )
INTEGER MODE
REAL COND, DMAX
PARAMETER ( MODE = 3, COND = 100.0E0, DMAX = 1.0E0 )
* ..
* .. Local Scalars ..
CHARACTER LAB1, LAB2, SIDE, TRANS, UPLO
CHARACTER*3 PATH
CHARACTER*6 CNAME
INTEGER I, I3, I4, IC, ICL, ILDA, IM, IN, INB, INFO,
$ ISIDE, ISUB, ITOFF, ITRAN, IUPLO, LDA, LW, M,
$ M1, N, N1, NB, NX
REAL OPS, S1, S2, TIME, UNTIME
* ..
* .. Local Arrays ..
LOGICAL TIMSUB( NSUBS )
CHARACTER SIDES( 2 ), TRANSS( 2 ), UPLOS( 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, ICOPY, SLACPY, SLATMS, SORGTR,
$ SORMTR, SPRTB3, SPRTBL, SSYTRD, STIMMG, TRED1,
$ XLAENV
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, REAL
* ..
* .. Data statements ..
DATA SUBNAM / 'SSYTRD', 'TRED1', 'SORGTR',
$ 'SORMTR' /
DATA SIDES / 'L', 'R' / , TRANSS / 'N', 'T' / ,
$ UPLOS / 'U', 'L' /
DATA ISEED / 0, 0, 0, 1 /
* ..
* .. Executable Statements ..
*
* Extract the timing request from the input line.
*
PATH( 1: 1 ) = 'Single precision'
PATH( 2: 3 ) = 'TD'
CALL ATIMIN( PATH, LINE, NSUBS, SUBNAM, TIMSUB, NOUT, INFO )
IF( INFO.NE.0 )
$ GO TO 240
*
* Check that M <= LDA for the input values.
*
CNAME = LINE( 1: 6 )
CALL ATIMCK( 2, CNAME, NM, MVAL, NLDA, LDAVAL, NOUT, INFO )
IF( INFO.GT.0 ) THEN
WRITE( NOUT, FMT = 9999 )CNAME
GO TO 240
END IF
*
* Check that K <= LDA for SORMTR
*
IF( TIMSUB( 4 ) ) THEN
CALL ATIMCK( 3, CNAME, NN, NVAL, NLDA, LDAVAL, NOUT, INFO )
IF( INFO.GT.0 ) THEN
WRITE( NOUT, FMT = 9999 )SUBNAM( 4 )
TIMSUB( 4 ) = .FALSE.
END IF
END IF
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
DO 150 IUPLO = 1, 2
UPLO = UPLOS( IUPLO )
*
* Do for each value of M:
*
DO 140 IM = 1, NM
M = MVAL( IM )
CALL ICOPY( 4, ISEED, 1, RESEED, 1 )
*
* Do for each value of LDA:
*
DO 130 ILDA = 1, NLDA
LDA = LDAVAL( ILDA )
I3 = ( IUPLO-1 )*NLDA + 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( 1, M*MAX( 1, NB ) )
*
* Generate a test matrix of order M.
*
CALL ICOPY( 4, RESEED, 1, ISEED, 1 )
CALL SLATMS( M, M, 'Uniform', ISEED, 'Symmetric', TAU,
$ MODE, COND, DMAX, M, M, 'No packing', B,
$ LDA, WORK, INFO )
*
IF( TIMSUB( 2 ) .AND. INB.EQ.1 .AND. IUPLO.EQ.2 ) THEN
*
* TRED1: Eispack reduction using orthogonal
* transformations.
*
CALL SLACPY( UPLO, M, M, B, LDA, A, LDA )
IC = 0
S1 = SECOND( )
10 CONTINUE
CALL TRED1( LDA, M, A, D, D( M+1 ), D( M+1 ) )
S2 = SECOND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL SLACPY( UPLO, M, M, B, LDA, A, LDA )
GO TO 10
END IF
*
* Subtract the time used in SLACPY.
*
ICL = 1
S1 = SECOND( )
20 CONTINUE
S2 = SECOND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL SLACPY( UPLO, M, M, B, LDA, A, LDA )
GO TO 20
END IF
*
TIME = ( TIME-UNTIME ) / REAL( IC )
OPS = SOPLA( 'SSYTRD', M, M, -1, -1, NB )
RESLTS( INB, IM, ILDA, 2 ) = SMFLOP( OPS, TIME,
$ INFO )
END IF
*
IF( TIMSUB( 1 ) ) THEN
*
* SSYTRD: Reduction to tridiagonal form
*
CALL SLACPY( UPLO, M, M, B, LDA, A, LDA )
IC = 0
S1 = SECOND( )
30 CONTINUE
CALL SSYTRD( UPLO, M, A, LDA, D, D( M+1 ), TAU,
$ WORK, LW, INFO )
S2 = SECOND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL SLACPY( UPLO, M, M, B, LDA, A, LDA )
GO TO 30
END IF
*
* Subtract the time used in SLACPY.
*
ICL = 1
S1 = SECOND( )
40 CONTINUE
S2 = SECOND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL SLACPY( UPLO, M, M, A, LDA, B, LDA )
GO TO 40
END IF
*
TIME = ( TIME-UNTIME ) / REAL( IC )
OPS = SOPLA( 'SSYTRD', M, M, -1, -1, NB )
RESLTS( INB, IM, I3, 1 ) = SMFLOP( OPS, TIME,
$ INFO )
ELSE
*
* If SSYTRD was not timed, generate a matrix and
* factor it using SSYTRD anyway so that the factored
* form of the matrix can be used in timing the other
* routines.
*
CALL SLACPY( UPLO, M, M, B, LDA, A, LDA )
CALL SSYTRD( UPLO, M, A, LDA, D, D( M+1 ), TAU,
$ WORK, LW, INFO )
END IF
*
IF( TIMSUB( 3 ) ) THEN
*
* SORGTR: Generate the orthogonal matrix Q from the
* reduction to Hessenberg form A = Q*H*Q'
*
CALL SLACPY( UPLO, M, M, A, LDA, B, LDA )
IC = 0
S1 = SECOND( )
50 CONTINUE
CALL SORGTR( UPLO, M, B, LDA, TAU, WORK, LW, INFO )
S2 = SECOND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL SLACPY( UPLO, M, M, A, LDA, B, LDA )
GO TO 50
END IF
*
* Subtract the time used in SLACPY.
*
ICL = 1
S1 = SECOND( )
60 CONTINUE
S2 = SECOND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL SLACPY( UPLO, M, M, A, LDA, B, LDA )
GO TO 60
END IF
*
TIME = ( TIME-UNTIME ) / REAL( IC )
*
* Op count for SORGTR: same as
* SORGQR( N-1, N-1, N-1, ... )
*
OPS = SOPLA( 'SORGQR', M-1, M-1, M-1, -1, NB )
RESLTS( INB, IM, I3, 3 ) = SMFLOP( OPS, TIME,
$ INFO )
END IF
*
IF( TIMSUB( 4 ) ) THEN
*
* SORMTR: Multiply by Q stored as a product of
* elementary transformations
*
I4 = 3
DO 110 ISIDE = 1, 2
SIDE = SIDES( ISIDE )
DO 100 IN = 1, NN
N = NVAL( IN )
LW = MAX( 1, MAX( 1, NB )*N )
IF( ISIDE.EQ.1 ) THEN
M1 = M
N1 = N
ELSE
M1 = N
N1 = M
END IF
ITOFF = 0
DO 90 ITRAN = 1, 2
TRANS = TRANSS( ITRAN )
CALL STIMMG( 0, M1, N1, B, LDA, 0, 0 )
IC = 0
S1 = SECOND( )
70 CONTINUE
CALL SORMTR( SIDE, UPLO, TRANS, M1, N1, A,
$ LDA, TAU, B, LDA, WORK, LW,
$ INFO )
S2 = SECOND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL STIMMG( 0, M1, N1, B, LDA, 0, 0 )
GO TO 70
END IF
*
* Subtract the time used in STIMMG.
*
ICL = 1
S1 = SECOND( )
80 CONTINUE
S2 = SECOND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL STIMMG( 0, M1, N1, B, LDA, 0, 0 )
GO TO 80
END IF
*
TIME = ( TIME-UNTIME ) / REAL( IC )
*
* Op count for SORMTR, SIDE='L': same as
* SORMQR( 'L', TRANS, M-1, N, M-1, ...)
*
* Op count for SORMTR, SIDE='R': same as
* SORMQR( 'R', TRANS, M, N-1, N-1, ...)
*
IF( ISIDE.EQ.1 ) THEN
OPS = SOPLA( 'SORMQR', M1-1, N1, M1-1,
$ -1, NB )
ELSE
OPS = SOPLA( 'SORMQR', M1, N1-1, N1-1,
$ 1, NB )
END IF
*
RESLTS( INB, IM, I3,
$ I4+ITOFF+IN ) = SMFLOP( OPS, TIME,
$ INFO )
ITOFF = NN
90 CONTINUE
100 CONTINUE
I4 = I4 + 2*NN
110 CONTINUE
END IF
*
120 CONTINUE
130 CONTINUE
140 CONTINUE
150 CONTINUE
*
* Print tables of results for SSYTRD, TRED1, and SORGTR
*
DO 180 ISUB = 1, NSUBS - 1
IF( .NOT.TIMSUB( ISUB ) )
$ GO TO 180
WRITE( NOUT, FMT = 9998 )SUBNAM( ISUB )
IF( NLDA.GT.1 ) THEN
DO 160 I = 1, NLDA
WRITE( NOUT, FMT = 9997 )I, LDAVAL( I )
160 CONTINUE
END IF
IF( ISUB.EQ.2 ) THEN
WRITE( NOUT, FMT = * )
CALL SPRTB3( ' ', 'N', 1, NBVAL, NXVAL, NM, MVAL, NLDA,
$ RESLTS( 1, 1, 1, ISUB ), LDR1, LDR2, NOUT )
ELSE
I3 = 1
DO 170 IUPLO = 1, 2
WRITE( NOUT, FMT = 9996 )SUBNAM( ISUB ), UPLOS( IUPLO )
CALL SPRTB3( '( NB, NX)', 'N', NNB, NBVAL, NXVAL, NM,
$ MVAL, NLDA, RESLTS( 1, 1, I3, ISUB ), LDR1,
$ LDR2, NOUT )
I3 = I3 + NLDA
170 CONTINUE
END IF
180 CONTINUE
*
* Print tables of results for SORMTR
*
ISUB = 4
IF( TIMSUB( ISUB ) ) THEN
I4 = 3
DO 230 ISIDE = 1, 2
IF( ISIDE.EQ.1 ) THEN
LAB1 = 'M'
LAB2 = 'N'
IF( NLDA.GT.1 ) THEN
WRITE( NOUT, FMT = 9998 )SUBNAM( ISUB )
DO 190 I = 1, NLDA
WRITE( NOUT, FMT = 9997 )I, LDAVAL( I )
190 CONTINUE
END IF
ELSE
LAB1 = 'N'
LAB2 = 'M'
END IF
DO 220 ITRAN = 1, 2
DO 210 IN = 1, NN
I3 = 1
DO 200 IUPLO = 1, 2
WRITE( NOUT, FMT = 9995 )SUBNAM( ISUB ),
$ SIDES( ISIDE ), UPLOS( IUPLO ), TRANSS( ITRAN ),
$ LAB2, NVAL( IN )
CALL SPRTBL( 'NB', LAB1, NNB, NBVAL, NM, MVAL,
$ NLDA, RESLTS( 1, 1, I3, I4+IN ), LDR1,
$ LDR2, NOUT )
I3 = I3 + NLDA
200 CONTINUE
210 CONTINUE
I4 = I4 + NN
220 CONTINUE
230 CONTINUE
END IF
240 CONTINUE
*
* Print a table of results for each timed routine.
*
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 UPLO = ''', A1, '''', / )
9995 FORMAT( / 5X, A6, ' with SIDE = ''', A1, ''', UPLO = ''', A1,
$ ''', TRANS = ''', A1, ''', ', A1, ' =', I6, / )
RETURN
*
* End of STIMTD
*
END
|
