コード例 #1
0
ファイル: sggqrf.c プロジェクト: 3deggi/levmar-ndk
/* Subroutine */ int sggqrf_(integer *n, integer *m, integer *p, real *a, 
	integer *lda, real *taua, real *b, integer *ldb, real *taub, real *
	work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;

    /* Local variables */
    integer nb, nb1, nb2, nb3, lopt;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *);
    extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *, integer *), sgerqf_(integer *, 
	    integer *, real *, integer *, real *, real *, integer *, integer *
);
    integer lwkopt;
    logical lquery;
    extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, real *, integer *, real *, 
	    integer *, integer *);


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  SGGQRF computes a generalized QR factorization of an N-by-M matrix A */
/*  and an N-by-P matrix B: */

/*              A = Q*R,        B = Q*T*Z, */

/*  where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal */
/*  matrix, and R and T assume one of the forms: */

/*  if N >= M,  R = ( R11 ) M  ,   or if N < M,  R = ( R11  R12 ) N, */
/*                  (  0  ) N-M                         N   M-N */
/*                     M */

/*  where R11 is upper triangular, and */

/*  if N <= P,  T = ( 0  T12 ) N,   or if N > P,  T = ( T11 ) N-P, */
/*                   P-N  N                           ( T21 ) P */
/*                                                       P */

/*  where T12 or T21 is upper triangular. */

/*  In particular, if B is square and nonsingular, the GQR factorization */
/*  of A and B implicitly gives the QR factorization of inv(B)*A: */

/*               inv(B)*A = Z'*(inv(T)*R) */

/*  where inv(B) denotes the inverse of the matrix B, and Z' denotes the */
/*  transpose of the matrix Z. */

/*  Arguments */
/*  ========= */

/*  N       (input) INTEGER */
/*          The number of rows of the matrices A and B. N >= 0. */

/*  M       (input) INTEGER */
/*          The number of columns of the matrix A.  M >= 0. */

/*  P       (input) INTEGER */
/*          The number of columns of the matrix B.  P >= 0. */

/*  A       (input/output) REAL array, dimension (LDA,M) */
/*          On entry, the N-by-M matrix A. */
/*          On exit, the elements on and above the diagonal of the array */
/*          contain the min(N,M)-by-M upper trapezoidal matrix R (R is */
/*          upper triangular if N >= M); the elements below the diagonal, */
/*          with the array TAUA, represent the orthogonal matrix Q as a */
/*          product of min(N,M) elementary reflectors (see Further */
/*          Details). */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A. LDA >= max(1,N). */

/*  TAUA    (output) REAL array, dimension (min(N,M)) */
/*          The scalar factors of the elementary reflectors which */
/*          represent the orthogonal matrix Q (see Further Details). */

/*  B       (input/output) REAL array, dimension (LDB,P) */
/*          On entry, the N-by-P matrix B. */
/*          On exit, if N <= P, the upper triangle of the subarray */
/*          B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T; */
/*          if N > P, the elements on and above the (N-P)-th subdiagonal */
/*          contain the N-by-P upper trapezoidal matrix T; the remaining */
/*          elements, with the array TAUB, represent the orthogonal */
/*          matrix Z as a product of elementary reflectors (see Further */
/*          Details). */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B. LDB >= max(1,N). */

/*  TAUB    (output) REAL array, dimension (min(N,P)) */
/*          The scalar factors of the elementary reflectors which */
/*          represent the orthogonal matrix Z (see Further Details). */

/*  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

/*  LWORK   (input) INTEGER */
/*          The dimension of the array WORK. LWORK >= max(1,N,M,P). */
/*          For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3), */
/*          where NB1 is the optimal blocksize for the QR factorization */
/*          of an N-by-M matrix, NB2 is the optimal blocksize for the */
/*          RQ factorization of an N-by-P matrix, and NB3 is the optimal */
/*          blocksize for a call of SORMQR. */

/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates the optimal size of the WORK array, returns */
/*          this value as the first entry of the WORK array, and no error */
/*          message related to LWORK is issued by XERBLA. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */

/*  Further Details */
/*  =============== */

/*  The matrix Q is represented as a product of elementary reflectors */

/*     Q = H(1) H(2) . . . H(k), where k = min(n,m). */

/*  Each H(i) has the form */

/*     H(i) = I - taua * v * v' */

/*  where taua is a real scalar, and v is a real vector with */
/*  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */
/*  and taua in TAUA(i). */
/*  To form Q explicitly, use LAPACK subroutine SORGQR. */
/*  To use Q to update another matrix, use LAPACK subroutine SORMQR. */

/*  The matrix Z is represented as a product of elementary reflectors */

/*     Z = H(1) H(2) . . . H(k), where k = min(n,p). */

/*  Each H(i) has the form */

/*     H(i) = I - taub * v * v' */

/*  where taub is a real scalar, and v is a real vector with */
/*  v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in */
/*  B(n-k+i,1:p-k+i-1), and taub in TAUB(i). */
/*  To form Z explicitly, use LAPACK subroutine SORGRQ. */
/*  To use Z to update another matrix, use LAPACK subroutine SORMRQ. */

/*  ===================================================================== */

/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --taua;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --taub;
    --work;

    /* Function Body */
    *info = 0;
    nb1 = ilaenv_(&c__1, "SGEQRF", " ", n, m, &c_n1, &c_n1);
    nb2 = ilaenv_(&c__1, "SGERQF", " ", n, p, &c_n1, &c_n1);
    nb3 = ilaenv_(&c__1, "SORMQR", " ", n, m, p, &c_n1);
/* Computing MAX */
    i__1 = max(nb1,nb2);
    nb = max(i__1,nb3);
/* Computing MAX */
    i__1 = max(*n,*m);
    lwkopt = max(i__1,*p) * nb;
    work[1] = (real) lwkopt;
    lquery = *lwork == -1;
    if (*n < 0) {
	*info = -1;
    } else if (*m < 0) {
	*info = -2;
    } else if (*p < 0) {
	*info = -3;
    } else if (*lda < max(1,*n)) {
	*info = -5;
    } else if (*ldb < max(1,*n)) {
	*info = -8;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = max(1,*n), i__1 = max(i__1,*m);
	if (*lwork < max(i__1,*p) && ! lquery) {
	    *info = -11;
	}
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGGQRF", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     QR factorization of N-by-M matrix A: A = Q*R */

    sgeqrf_(n, m, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
    lopt = work[1];

/*     Update B := Q'*B. */

    i__1 = min(*n,*m);
    sormqr_("Left", "Transpose", n, p, &i__1, &a[a_offset], lda, &taua[1], &b[
	    b_offset], ldb, &work[1], lwork, info);
/* Computing MAX */
    i__1 = lopt, i__2 = (integer) work[1];
    lopt = max(i__1,i__2);

/*     RQ factorization of N-by-P matrix B: B = T*Z. */

    sgerqf_(n, p, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
/* Computing MAX */
    i__1 = lopt, i__2 = (integer) work[1];
    work[1] = (real) max(i__1,i__2);

    return 0;

/*     End of SGGQRF */

} /* sggqrf_ */
コード例 #2
0
ファイル: stimrq.c プロジェクト: zangel/uquad
/* Subroutine */ int stimrq_(char *line, integer *nm, integer *mval, integer *
	nval, integer *nk, integer *kval, integer *nnb, integer *nbval, 
	integer *nxval, integer *nlda, integer *ldaval, real *timmin, real *a,
	 real *tau, real *b, real *work, real *reslts, integer *ldr1, integer 
	*ldr2, integer *ldr3, integer *nout, ftnlen line_len)
{
    /* Initialized data */

    static char subnam[6*3] = "SGERQF" "SORGRQ" "SORMRQ";
    static char sides[1*2] = "L" "R";
    static char transs[1*2] = "N" "T";
    static integer iseed[4] = { 0,0,0,1 };

    /* Format strings */
    static char fmt_9999[] = "(1x,a6,\002 timing run not attempted\002,/)";
    static char fmt_9998[] = "(/\002 *** Speed of \002,a6,\002 in megaflops "
	    "***\002)";
    static char fmt_9997[] = "(5x,\002line \002,i2,\002 with LDA = \002,i5)";
    static char fmt_9996[] = "(5x,\002K = min(M,N)\002,/)";
    static char fmt_9995[] = "(/5x,a6,\002 with SIDE = '\002,a1,\002', TRANS"
	    " = '\002,a1,\002', \002,a1,\002 =\002,i6,/)";
    static char fmt_9994[] = "(\002 *** No pairs (M,N) found with M <= N: "
	    " \002,a6,\002 not timed\002)";

    /* System generated locals */
    integer reslts_dim1, reslts_dim2, reslts_dim3, reslts_offset, i__1, i__2, 
	    i__3, i__4, i__5, i__6;

    /* Builtin functions   
       Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
    integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void),
	     s_wsle(cilist *), e_wsle(void);

    /* Local variables */
    static integer ilda;
    static char labm[1], side[1];
    static integer info;
    static char path[3];
    static real time;
    static integer isub, muse[12], nuse[12], i__, k, m, n;
    static char cname[6];
    static integer iside, itoff, itran, minmn;
    extern doublereal sopla_(char *, integer *, integer *, integer *, integer 
	    *, integer *);
    extern /* Subroutine */ int icopy_(integer *, integer *, integer *, 
	    integer *, integer *);
    static char trans[1];
    static integer k1, i4, m1, n1;
    static real s1, s2;
    static integer ic;
    extern /* Subroutine */ int sprtb4_(char *, char *, char *, integer *, 
	    integer *, integer *, integer *, integer *, integer *, integer *, 
	    real *, integer *, integer *, integer *, ftnlen, ftnlen, ftnlen), 
	    sprtb5_(char *, char *, char *, integer *, integer *, integer *, 
	    integer *, integer *, integer *, real *, integer *, integer *, 
	    integer *, ftnlen, ftnlen, ftnlen);
    static integer nb, ik, im, lw, nx, reseed[4];
    extern /* Subroutine */ int atimck_(integer *, char *, integer *, integer 
	    *, integer *, integer *, integer *, integer *, ftnlen);
    extern doublereal second_(void);
    extern /* Subroutine */ int atimin_(char *, char *, integer *, char *, 
	    logical *, integer *, integer *, ftnlen, ftnlen, ftnlen), sgerqf_(
	    integer *, integer *, real *, integer *, real *, real *, integer *
	    , integer *), slacpy_(char *, integer *, integer *, real *, 
	    integer *, real *, integer *), xlaenv_(integer *, integer 
	    *);
    extern doublereal smflop_(real *, real *, integer *);
    static real untime;
    extern /* Subroutine */ int stimmg_(integer *, integer *, integer *, real 
	    *, integer *, integer *, integer *);
    static logical timsub[3];
    extern /* Subroutine */ int slatms_(integer *, integer *, char *, integer 
	    *, char *, real *, integer *, real *, real *, integer *, integer *
	    , char *, real *, integer *, real *, integer *), sorgrq_(integer *, integer *, integer *, real *, integer 
	    *, real *, real *, integer *, integer *), sormrq_(char *, char *, 
	    integer *, integer *, integer *, real *, integer *, real *, real *
	    , integer *, real *, integer *, integer *);
    static integer lda, icl, inb, imx;
    static real ops;

    /* Fortran I/O blocks */
    static cilist io___9 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___29 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___31 = { 0, 0, 0, fmt_9997, 0 };
    static cilist io___32 = { 0, 0, 0, 0, 0 };
    static cilist io___33 = { 0, 0, 0, fmt_9996, 0 };
    static cilist io___34 = { 0, 0, 0, fmt_9999, 0 };
    static cilist io___49 = { 0, 0, 0, fmt_9998, 0 };
    static cilist io___50 = { 0, 0, 0, fmt_9997, 0 };
    static cilist io___51 = { 0, 0, 0, fmt_9995, 0 };
    static cilist io___53 = { 0, 0, 0, fmt_9995, 0 };
    static cilist io___54 = { 0, 0, 0, fmt_9994, 0 };



#define subnam_ref(a_0,a_1) &subnam[(a_1)*6 + a_0 - 6]
#define reslts_ref(a_1,a_2,a_3,a_4) reslts[(((a_4)*reslts_dim3 + (a_3))*\
reslts_dim2 + (a_2))*reslts_dim1 + a_1]


/*  -- 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   


    Purpose   
    =======   

    STIMRQ times the LAPACK routines to perform the RQ factorization of   
    a REAL 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 SORMRQ.   

    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.   

    TAU     (workspace) REAL array, dimension (min(M,N))   

    B       (workspace) REAL array, dimension (LDAMAX*NMAX)   

    WORK    (workspace) REAL array, dimension (LDAMAX*NBMAX)   
            where NBMAX is the maximum value of NB.   

    RESLTS  (workspace) REAL 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 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.   

    =====================================================================   

       Parameter adjustments */
    --mval;
    --nval;
    --kval;
    --nbval;
    --nxval;
    --ldaval;
    --a;
    --tau;
    --b;
    --work;
    reslts_dim1 = *ldr1;
    reslts_dim2 = *ldr2;
    reslts_dim3 = *ldr3;
    reslts_offset = 1 + reslts_dim1 * (1 + reslts_dim2 * (1 + reslts_dim3 * 1)
	    );
    reslts -= reslts_offset;

    /* Function Body   

       Extract the timing request from the input line. */

    s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
    s_copy(path + 1, "RQ", (ftnlen)2, (ftnlen)2);
    atimin_(path, line, &c__3, subnam, timsub, nout, &info, (ftnlen)3, (
	    ftnlen)80, (ftnlen)6);
    if (info != 0) {
	goto L230;
    }

/*     Check that M <= LDA for the input values. */

    s_copy(cname, line, (ftnlen)6, (ftnlen)6);
    atimck_(&c__1, cname, nm, &mval[1], nlda, &ldaval[1], nout, &info, (
	    ftnlen)6);
    if (info > 0) {
	io___9.ciunit = *nout;
	s_wsfe(&io___9);
	do_fio(&c__1, cname, (ftnlen)6);
	e_wsfe();
	goto L230;
    }

/*     Do for each pair of values (M,N): */

    i__1 = *nm;
    for (im = 1; im <= i__1; ++im) {
	m = mval[im];
	n = nval[im];
	minmn = min(m,n);
	icopy_(&c__4, iseed, &c__1, reseed, &c__1);

/*        Do for each value of LDA: */

	i__2 = *nlda;
	for (ilda = 1; ilda <= i__2; ++ilda) {
	    lda = ldaval[ilda];

/*           Do for each pair of values (NB, NX) in NBVAL and NXVAL. */

	    i__3 = *nnb;
	    for (inb = 1; inb <= i__3; ++inb) {
		nb = nbval[inb];
		xlaenv_(&c__1, &nb);
		nx = nxval[inb];
		xlaenv_(&c__3, &nx);
/* Computing MAX */
		i__4 = 1, i__5 = m * max(1,nb);
		lw = max(i__4,i__5);

/*              Generate a test matrix of size M by N. */

		icopy_(&c__4, reseed, &c__1, iseed, &c__1);
		slatms_(&m, &n, "Uniform", iseed, "Nonsymm", &tau[1], &c__3, &
			c_b24, &c_b25, &m, &n, "No packing", &b[1], &lda, &
			work[1], &info);

		if (timsub[0]) {

/*                 SGERQF:  RQ factorization */

		    slacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
		    ic = 0;
		    s1 = second_();
L10:
		    sgerqf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &
			    info);
		    s2 = second_();
		    time = s2 - s1;
		    ++ic;
		    if (time < *timmin) {
			slacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
			goto L10;
		    }

/*                 Subtract the time used in SLACPY. */

		    icl = 1;
		    s1 = second_();
L20:
		    s2 = second_();
		    untime = s2 - s1;
		    ++icl;
		    if (icl <= ic) {
			slacpy_("Full", &m, &n, &a[1], &lda, &b[1], &lda);
			goto L20;
		    }

		    time = (time - untime) / (real) ic;
		    ops = sopla_("SGERQF", &m, &n, &c__0, &c__0, &nb);
		    reslts_ref(inb, im, ilda, 1) = smflop_(&ops, &time, &info)
			    ;
		} else {

/*                 If SGERQF was not timed, generate a matrix and factor   
                   it using SGERQF anyway so that the factored form of   
                   the matrix can be used in timing the other routines. */

		    slacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
		    sgerqf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &
			    info);
		}

		if (timsub[1]) {

/*                 SORGRQ:  Generate orthogonal matrix Q from the RQ   
                   factorization */

		    slacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
		    ic = 0;
		    s1 = second_();
L30:
		    sorgrq_(&minmn, &n, &minmn, &b[1], &lda, &tau[1], &work[1]
			    , &lw, &info);
		    s2 = second_();
		    time = s2 - s1;
		    ++ic;
		    if (time < *timmin) {
			slacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
			goto L30;
		    }

/*                 Subtract the time used in SLACPY. */

		    icl = 1;
		    s1 = second_();
L40:
		    s2 = second_();
		    untime = s2 - s1;
		    ++icl;
		    if (icl <= ic) {
			slacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
			goto L40;
		    }

		    time = (time - untime) / (real) ic;
		    ops = sopla_("SORGRQ", &minmn, &n, &minmn, &c__0, &nb);
		    reslts_ref(inb, im, ilda, 2) = smflop_(&ops, &time, &info)
			    ;
		}

/* L50: */
	    }
/* L60: */
	}
/* L70: */
    }

/*     Print tables of results */

    for (isub = 1; isub <= 2; ++isub) {
	if (! timsub[isub - 1]) {
	    goto L90;
	}
	io___29.ciunit = *nout;
	s_wsfe(&io___29);
	do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
	e_wsfe();
	if (*nlda > 1) {
	    i__1 = *nlda;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		io___31.ciunit = *nout;
		s_wsfe(&io___31);
		do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(integer));
		do_fio(&c__1, (char *)&ldaval[i__], (ftnlen)sizeof(integer));
		e_wsfe();
/* L80: */
	    }
	}
	io___32.ciunit = *nout;
	s_wsle(&io___32);
	e_wsle();
	if (isub == 2) {
	    io___33.ciunit = *nout;
	    s_wsfe(&io___33);
	    e_wsfe();
	}
	sprtb4_("(  NB,  NX)", "M", "N", nnb, &nbval[1], &nxval[1], nm, &mval[
		1], &nval[1], nlda, &reslts_ref(1, 1, 1, isub), ldr1, ldr2, 
		nout, (ftnlen)11, (ftnlen)1, (ftnlen)1);
L90:
	;
    }

/*     Time SORMRQ separately.  Here the starting matrix is M by N, and   
       K is the free dimension of the matrix multiplied by Q. */

    if (timsub[2]) {

/*        Check that K <= LDA for the input values. */

	atimck_(&c__3, cname, nk, &kval[1], nlda, &ldaval[1], nout, &info, (
		ftnlen)6);
	if (info > 0) {
	    io___34.ciunit = *nout;
	    s_wsfe(&io___34);
	    do_fio(&c__1, subnam_ref(0, 3), (ftnlen)6);
	    e_wsfe();
	    goto L230;
	}

/*        Use only the pairs (M,N) where M <= N. */

	imx = 0;
	i__1 = *nm;
	for (im = 1; im <= i__1; ++im) {
	    if (mval[im] <= nval[im]) {
		++imx;
		muse[imx - 1] = mval[im];
		nuse[imx - 1] = nval[im];
	    }
/* L100: */
	}

/*        SORMRQ:  Multiply by Q stored as a product of elementary   
          transformations   

          Do for each pair of values (M,N): */

	i__1 = imx;
	for (im = 1; im <= i__1; ++im) {
	    m = muse[im - 1];
	    n = nuse[im - 1];

/*           Do for each value of LDA: */

	    i__2 = *nlda;
	    for (ilda = 1; ilda <= i__2; ++ilda) {
		lda = ldaval[ilda];

/*              Generate an M by N matrix and form its RQ decomposition. */

		slatms_(&m, &n, "Uniform", iseed, "Nonsymm", &tau[1], &c__3, &
			c_b24, &c_b25, &m, &n, "No packing", &a[1], &lda, &
			work[1], &info);
/* Computing MAX */
		i__3 = 1, i__4 = m * max(1,nb);
		lw = max(i__3,i__4);
		sgerqf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &info);

/*              Do first for SIDE = 'L', then for SIDE = 'R' */

		i4 = 0;
		for (iside = 1; iside <= 2; ++iside) {
		    *(unsigned char *)side = *(unsigned char *)&sides[iside - 
			    1];

/*                 Do for each pair of values (NB, NX) in NBVAL and   
                   NXVAL. */

		    i__3 = *nnb;
		    for (inb = 1; inb <= i__3; ++inb) {
			nb = nbval[inb];
			xlaenv_(&c__1, &nb);
			nx = nxval[inb];
			xlaenv_(&c__3, &nx);

/*                    Do for each value of K in KVAL */

			i__4 = *nk;
			for (ik = 1; ik <= i__4; ++ik) {
			    k = kval[ik];

/*                       Sort out which variable is which */

			    if (iside == 1) {
				k1 = m;
				m1 = n;
				n1 = k;
/* Computing MAX */
				i__5 = 1, i__6 = n1 * max(1,nb);
				lw = max(i__5,i__6);
			    } else {
				k1 = m;
				n1 = n;
				m1 = k;
/* Computing MAX */
				i__5 = 1, i__6 = m1 * max(1,nb);
				lw = max(i__5,i__6);
			    }

/*                       Do first for TRANS = 'N', then for TRANS = 'T' */

			    itoff = 0;
			    for (itran = 1; itran <= 2; ++itran) {
				*(unsigned char *)trans = *(unsigned char *)&
					transs[itran - 1];
				stimmg_(&c__0, &m1, &n1, &b[1], &lda, &c__0, &
					c__0);
				ic = 0;
				s1 = second_();
L110:
				sormrq_(side, trans, &m1, &n1, &k1, &a[1], &
					lda, &tau[1], &b[1], &lda, &work[1], &
					lw, &info);
				s2 = second_();
				time = s2 - s1;
				++ic;
				if (time < *timmin) {
				    stimmg_(&c__0, &m1, &n1, &b[1], &lda, &
					    c__0, &c__0);
				    goto L110;
				}

/*                          Subtract the time used in STIMMG. */

				icl = 1;
				s1 = second_();
L120:
				s2 = second_();
				untime = s2 - s1;
				++icl;
				if (icl <= ic) {
				    stimmg_(&c__0, &m1, &n1, &b[1], &lda, &
					    c__0, &c__0);
				    goto L120;
				}

				time = (time - untime) / (real) ic;
				i__5 = iside - 1;
				ops = sopla_("SORMRQ", &m1, &n1, &k1, &i__5, &
					nb);
				reslts_ref(inb, im, ilda, i4 + itoff + ik) = 
					smflop_(&ops, &time, &info);
				itoff = *nk;
/* L130: */
			    }
/* L140: */
			}
/* L150: */
		    }
		    i4 = *nk << 1;
/* L160: */
		}
/* L170: */
	    }
/* L180: */
	}

/*        Print tables of results */

	isub = 3;
	i4 = 1;
	if (imx >= 1) {
	    for (iside = 1; iside <= 2; ++iside) {
		*(unsigned char *)side = *(unsigned char *)&sides[iside - 1];
		if (iside == 1) {
		    io___49.ciunit = *nout;
		    s_wsfe(&io___49);
		    do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
		    e_wsfe();
		    if (*nlda > 1) {
			i__1 = *nlda;
			for (i__ = 1; i__ <= i__1; ++i__) {
			    io___50.ciunit = *nout;
			    s_wsfe(&io___50);
			    do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(
				    integer));
			    do_fio(&c__1, (char *)&ldaval[i__], (ftnlen)
				    sizeof(integer));
			    e_wsfe();
/* L190: */
			}
		    }
		}
		for (itran = 1; itran <= 2; ++itran) {
		    *(unsigned char *)trans = *(unsigned char *)&transs[itran 
			    - 1];
		    i__1 = *nk;
		    for (ik = 1; ik <= i__1; ++ik) {
			if (iside == 1) {
			    n = kval[ik];
			    io___51.ciunit = *nout;
			    s_wsfe(&io___51);
			    do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
			    do_fio(&c__1, side, (ftnlen)1);
			    do_fio(&c__1, trans, (ftnlen)1);
			    do_fio(&c__1, "N", (ftnlen)1);
			    do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
				    ;
			    e_wsfe();
			    *(unsigned char *)labm = 'M';
			} else {
			    m = kval[ik];
			    io___53.ciunit = *nout;
			    s_wsfe(&io___53);
			    do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
			    do_fio(&c__1, side, (ftnlen)1);
			    do_fio(&c__1, trans, (ftnlen)1);
			    do_fio(&c__1, "M", (ftnlen)1);
			    do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer))
				    ;
			    e_wsfe();
			    *(unsigned char *)labm = 'N';
			}
			sprtb5_("NB", "K", labm, nnb, &nbval[1], &imx, muse, 
				nuse, nlda, &reslts_ref(1, 1, 1, i4), ldr1, 
				ldr2, nout, (ftnlen)2, (ftnlen)1, (ftnlen)1);
			++i4;
/* L200: */
		    }
/* L210: */
		}
/* L220: */
	    }
	} else {
	    io___54.ciunit = *nout;
	    s_wsfe(&io___54);
	    do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
	    e_wsfe();
	}
    }
L230:
    return 0;

/*     End of STIMRQ */

} /* stimrq_ */