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