Пример #1
0
/* Subroutine */ int dgelqs_(integer *m, integer *n, integer *nrhs, 
	doublereal *a, integer *lda, doublereal *tau, doublereal *b, integer *
	ldb, doublereal *work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1;

    /* Local variables */
    extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, 
	    integer *, integer *, doublereal *, doublereal *, integer *, 
	    doublereal *, integer *), dlaset_(
	    char *, integer *, integer *, doublereal *, doublereal *, 
	    doublereal *, integer *), xerbla_(char *, integer *), dormlq_(char *, char *, integer *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
	    doublereal *, integer *, integer *);


/*  -- LAPACK routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  Compute a minimum-norm solution */
/*      min || A*X - B || */
/*  using the LQ factorization */
/*      A = L*Q */
/*  computed by DGELQF. */

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

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

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

/*  NRHS    (input) INTEGER */
/*          The number of columns of B.  NRHS >= 0. */

/*  A       (input) DOUBLE PRECISION array, dimension (LDA,N) */
/*          Details of the LQ factorization of the original matrix A as */
/*          returned by DGELQF. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= M. */

/*  TAU     (input) DOUBLE PRECISION array, dimension (M) */
/*          Details of the orthogonal matrix Q. */

/*  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */
/*          On entry, the m-by-nrhs right hand side matrix B. */
/*          On exit, the n-by-nrhs solution matrix X. */

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

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK) */

/*  LWORK   (input) INTEGER */
/*          The length of the array WORK.  LWORK must be at least NRHS, */
/*          and should be at least NRHS*NB, where NB is the block size */
/*          for this environment. */

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

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

/*     .. Parameters .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

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

    /* Function Body */
    *info = 0;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0 || *m > *n) {
	*info = -2;
    } else if (*nrhs < 0) {
	*info = -3;
    } else if (*lda < max(1,*m)) {
	*info = -5;
    } else if (*ldb < max(1,*n)) {
	*info = -8;
    } else if (*lwork < 1 || *lwork < *nrhs && *m > 0 && *n > 0) {
	*info = -10;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DGELQS", &i__1);
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0 || *nrhs == 0 || *m == 0) {
	return 0;
    }

/*     Solve L*X = B(1:m,:) */

    dtrsm_("Left", "Lower", "No transpose", "Non-unit", m, nrhs, &c_b7, &a[
	    a_offset], lda, &b[b_offset], ldb);

/*     Set B(m+1:n,:) to zero */

    if (*m < *n) {
	i__1 = *n - *m;
	dlaset_("Full", &i__1, nrhs, &c_b9, &c_b9, &b[*m + 1 + b_dim1], ldb);
    }

/*     B := Q' * B */

    dormlq_("Left", "Transpose", n, nrhs, m, &a[a_offset], lda, &tau[1], &b[
	    b_offset], ldb, &work[1], lwork, info);

    return 0;

/*     End of DGELQS */

} /* dgelqs_ */
Пример #2
0
/* Subroutine */ int dormbr_(char *vect, char *side, char *trans, integer *m, 
	integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, 
	doublereal *c, integer *ldc, doublereal *work, integer *lwork, 
	integer *info)
{
/*  -- LAPACK routine (version 2.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    Purpose   
    =======   

    If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C   
    with   
                    SIDE = 'L'     SIDE = 'R'   
    TRANS = 'N':      Q * C          C * Q   
    TRANS = 'T':      Q**T * C       C * Q**T   

    If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C   
    with   
                    SIDE = 'L'     SIDE = 'R'   
    TRANS = 'N':      P * C          C * P   
    TRANS = 'T':      P**T * C       C * P**T   

    Here Q and P**T are the orthogonal matrices determined by DGEBRD when 
  
    reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and 
  
    P**T are defined as products of elementary reflectors H(i) and G(i)   
    respectively.   

    Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the   
    order of the orthogonal matrix Q or P**T that is applied.   

    If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:   
    if nq >= k, Q = H(1) H(2) . . . H(k);   
    if nq < k, Q = H(1) H(2) . . . H(nq-1).   

    If VECT = 'P', A is assumed to have been a K-by-NQ matrix:   
    if k < nq, P = G(1) G(2) . . . G(k);   
    if k >= nq, P = G(1) G(2) . . . G(nq-1).   

    Arguments   
    =========   

    VECT    (input) CHARACTER*1   
            = 'Q': apply Q or Q**T;   
            = 'P': apply P or P**T.   

    SIDE    (input) CHARACTER*1   
            = 'L': apply Q, Q**T, P or P**T from the Left;   
            = 'R': apply Q, Q**T, P or P**T from the Right.   

    TRANS   (input) CHARACTER*1   
            = 'N':  No transpose, apply Q  or P;   
            = 'T':  Transpose, apply Q**T or P**T.   

    M       (input) INTEGER   
            The number of rows of the matrix C. M >= 0.   

    N       (input) INTEGER   
            The number of columns of the matrix C. N >= 0.   

    K       (input) INTEGER   
            If VECT = 'Q', the number of columns in the original   
            matrix reduced by DGEBRD.   
            If VECT = 'P', the number of rows in the original   
            matrix reduced by DGEBRD.   
            K >= 0.   

    A       (input) DOUBLE PRECISION array, dimension   
                                  (LDA,min(nq,K)) if VECT = 'Q'   
                                  (LDA,nq)        if VECT = 'P'   
            The vectors which define the elementary reflectors H(i) and   
            G(i), whose products determine the matrices Q and P, as   
            returned by DGEBRD.   

    LDA     (input) INTEGER   
            The leading dimension of the array A.   
            If VECT = 'Q', LDA >= max(1,nq);   
            if VECT = 'P', LDA >= max(1,min(nq,K)).   

    TAU     (input) DOUBLE PRECISION array, dimension (min(nq,K))   
            TAU(i) must contain the scalar factor of the elementary   
            reflector H(i) or G(i) which determines Q or P, as returned   
            by DGEBRD in the array argument TAUQ or TAUP.   

    C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)   
            On entry, the M-by-N matrix C.   
            On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q   
            or P*C or P**T*C or C*P or C*P**T.   

    LDC     (input) INTEGER   
            The leading dimension of the array C. LDC >= max(1,M).   

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

    LWORK   (input) INTEGER   
            The dimension of the array WORK.   
            If SIDE = 'L', LWORK >= max(1,N);   
            if SIDE = 'R', LWORK >= max(1,M).   
            For optimum performance LWORK >= N*NB if SIDE = 'L', and   
            LWORK >= M*NB if SIDE = 'R', where NB is the optimal   
            blocksize.   

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

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


       Test the input arguments   

    
   Parameter adjustments   
       Function Body */
    /* System generated locals */
    integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2;
    /* Local variables */
    static logical left;
    extern logical lsame_(char *, char *);
    static integer iinfo, i1, i2, mi, ni, nq, nw;
    extern /* Subroutine */ int xerbla_(char *, integer *), dormlq_(
	    char *, char *, integer *, integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, integer *);
    static logical notran;
    extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *, integer *);
    static logical applyq;
    static char transt[1];


#define TAU(I) tau[(I)-1]
#define WORK(I) work[(I)-1]

#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define C(I,J) c[(I)-1 + ((J)-1)* ( *ldc)]

    *info = 0;
    applyq = lsame_(vect, "Q");
    left = lsame_(side, "L");
    notran = lsame_(trans, "N");

/*     NQ is the order of Q or P and NW is the minimum dimension of WORK 
*/

    if (left) {
	nq = *m;
	nw = *n;
    } else {
	nq = *n;
	nw = *m;
    }
    if (! applyq && ! lsame_(vect, "P")) {
	*info = -1;
    } else if (! left && ! lsame_(side, "R")) {
	*info = -2;
    } else if (! notran && ! lsame_(trans, "T")) {
	*info = -3;
    } else if (*m < 0) {
	*info = -4;
    } else if (*n < 0) {
	*info = -5;
    } else if (*k < 0) {
	*info = -6;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = 1, i__2 = min(nq,*k);
	if (applyq && *lda < max(1,nq) || ! applyq && *lda < max(i__1,i__2)) {
	    *info = -8;
	} else if (*ldc < max(1,*m)) {
	    *info = -11;
	} else if (*lwork < max(1,nw)) {
	    *info = -13;
	}
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DORMBR", &i__1);
	return 0;
    }

/*     Quick return if possible */

    WORK(1) = 1.;
    if (*m == 0 || *n == 0) {
	return 0;
    }

    if (applyq) {

/*        Apply Q */

	if (nq >= *k) {

/*           Q was determined by a call to DGEBRD with nq >= k */

	    dormqr_(side, trans, m, n, k, &A(1,1), lda, &TAU(1), &C(1,1), ldc, &WORK(1), lwork, &iinfo);
	} else if (nq > 1) {

/*           Q was determined by a call to DGEBRD with nq < k */

	    if (left) {
		mi = *m - 1;
		ni = *n;
		i1 = 2;
		i2 = 1;
	    } else {
		mi = *m;
		ni = *n - 1;
		i1 = 1;
		i2 = 2;
	    }
	    i__1 = nq - 1;
	    dormqr_(side, trans, &mi, &ni, &i__1, &A(2,1), lda, &TAU(1)
		    , &C(i1,i2), ldc, &WORK(1), lwork, &iinfo);
	}
    } else {

/*        Apply P */

	if (notran) {
	    *(unsigned char *)transt = 'T';
	} else {
	    *(unsigned char *)transt = 'N';
	}
	if (nq > *k) {

/*           P was determined by a call to DGEBRD with nq > k */

	    dormlq_(side, transt, m, n, k, &A(1,1), lda, &TAU(1), &C(1,1), ldc, &WORK(1), lwork, &iinfo);
	} else if (nq > 1) {

/*           P was determined by a call to DGEBRD with nq <= k */

	    if (left) {
		mi = *m - 1;
		ni = *n;
		i1 = 2;
		i2 = 1;
	    } else {
		mi = *m;
		ni = *n - 1;
		i1 = 1;
		i2 = 2;
	    }
	    i__1 = nq - 1;
	    dormlq_(side, transt, &mi, &ni, &i__1, &A(1,2), lda,
		     &TAU(1), &C(i1,i2), ldc, &WORK(1), lwork, &
		    iinfo);
	}
    }
    return 0;

/*     End of DORMBR */

} /* dormbr_ */
Пример #3
0
/* Subroutine */ int dgelsd_(integer *m, integer *n, integer *nrhs, 
	doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
	s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork,
	 integer *iwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;

    /* Builtin functions */
    double log(doublereal);

    /* Local variables */
    static doublereal anrm, bnrm;
    static integer itau, nlvl, iascl, ibscl;
    static doublereal sfmin;
    static integer minmn, maxmn, itaup, itauq, mnthr, nwork;
    extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
    static integer ie, il;
    extern /* Subroutine */ int dgebrd_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, doublereal *, doublereal *,
	     doublereal *, integer *, integer *);
    extern doublereal dlamch_(char *);
    static integer mm;
    extern doublereal dlange_(char *, integer *, integer *, doublereal *, 
	    integer *, doublereal *);
    extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *, integer *), 
	    dlalsd_(char *, integer *, integer *, integer *, doublereal *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, integer *, integer *), dlascl_(char *, 
	    integer *, integer *, doublereal *, doublereal *, integer *, 
	    integer *, doublereal *, integer *, integer *), dgeqrf_(
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    doublereal *, integer *, integer *), dlacpy_(char *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, integer *), dlaset_(char *, integer *, integer *, doublereal *, 
	    doublereal *, doublereal *, integer *), xerbla_(char *, 
	    integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    static doublereal bignum;
    extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *, integer *);
    static integer wlalsd;
    extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *, integer *);
    static integer ldwork;
    extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *, integer *);
    static integer minwrk, maxwrk;
    static doublereal smlnum;
    static logical lquery;
    static integer smlsiz;
    static doublereal eps;


#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]


/*  -- LAPACK driver routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       October 31, 1999   


    Purpose   
    =======   

    DGELSD computes the minimum-norm solution to a real linear least   
    squares problem:   
        minimize 2-norm(| b - A*x |)   
    using the singular value decomposition (SVD) of A. A is an M-by-N   
    matrix which may be rank-deficient.   

    Several right hand side vectors b and solution vectors x can be   
    handled in a single call; they are stored as the columns of the   
    M-by-NRHS right hand side matrix B and the N-by-NRHS solution   
    matrix X.   

    The problem is solved in three steps:   
    (1) Reduce the coefficient matrix A to bidiagonal form with   
        Householder transformations, reducing the original problem   
        into a "bidiagonal least squares problem" (BLS)   
    (2) Solve the BLS using a divide and conquer approach.   
    (3) Apply back all the Householder tranformations to solve   
        the original least squares problem.   

    The effective rank of A is determined by treating as zero those   
    singular values which are less than RCOND times the largest singular   
    value.   

    The divide and conquer algorithm makes very mild assumptions about   
    floating point arithmetic. It will work on machines with a guard   
    digit in add/subtract, or on those binary machines without guard   
    digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or   
    Cray-2. It could conceivably fail on hexadecimal or decimal machines   
    without guard digits, but we know of none.   

    Arguments   
    =========   

    M       (input) INTEGER   
            The number of rows of A. M >= 0.   

    N       (input) INTEGER   
            The number of columns of A. N >= 0.   

    NRHS    (input) INTEGER   
            The number of right hand sides, i.e., the number of columns   
            of the matrices B and X. NRHS >= 0.   

    A       (input) DOUBLE PRECISION array, dimension (LDA,N)   
            On entry, the M-by-N matrix A.   
            On exit, A has been destroyed.   

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

    B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)   
            On entry, the M-by-NRHS right hand side matrix B.   
            On exit, B is overwritten by the N-by-NRHS solution   
            matrix X.  If m >= n and RANK = n, the residual   
            sum-of-squares for the solution in the i-th column is given   
            by the sum of squares of elements n+1:m in that column.   

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

    S       (output) DOUBLE PRECISION array, dimension (min(M,N))   
            The singular values of A in decreasing order.   
            The condition number of A in the 2-norm = S(1)/S(min(m,n)).   

    RCOND   (input) DOUBLE PRECISION   
            RCOND is used to determine the effective rank of A.   
            Singular values S(i) <= RCOND*S(1) are treated as zero.   
            If RCOND < 0, machine precision is used instead.   

    RANK    (output) INTEGER   
            The effective rank of A, i.e., the number of singular values   
            which are greater than RCOND*S(1).   

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

    LWORK   (input) INTEGER   
            The dimension of the array WORK. LWORK must be at least 1.   
            The exact minimum amount of workspace needed depends on M,   
            N and NRHS. As long as LWORK is at least   
                12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2,   
            if M is greater than or equal to N or   
                12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2,   
            if M is less than N, the code will execute correctly.   
            SMLSIZ is returned by ILAENV and is equal to the maximum   
            size of the subproblems at the bottom of the computation   
            tree (usually about 25), and   
               NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )   
            For good performance, LWORK should generally be larger.   

            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.   

    IWORK   (workspace) INTEGER array, dimension (LIWORK)   
            LIWORK >= 3 * MINMN * NLVL + 11 * MINMN,   
            where MINMN = MIN( M,N ).   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value.   
            > 0:  the algorithm for computing the SVD failed to converge;   
                  if INFO = i, i off-diagonal elements of an intermediate   
                  bidiagonal form did not converge to zero.   

    Further Details   
    ===============   

    Based on contributions by   
       Ming Gu and Ren-Cang Li, Computer Science Division, University of   
         California at Berkeley, USA   
       Osni Marques, LBNL/NERSC, USA   

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


       Test the input arguments.   

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

    /* Function Body */
    *info = 0;
    minmn = min(*m,*n);
    maxmn = max(*m,*n);
    mnthr = ilaenv_(&c__6, "DGELSD", " ", m, n, nrhs, &c_n1, (ftnlen)6, (
	    ftnlen)1);
    lquery = *lwork == -1;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*nrhs < 0) {
	*info = -3;
    } else if (*lda < max(1,*m)) {
	*info = -5;
    } else if (*ldb < max(1,maxmn)) {
	*info = -7;
    }

    smlsiz = ilaenv_(&c__9, "DGELSD", " ", &c__0, &c__0, &c__0, &c__0, (
	    ftnlen)6, (ftnlen)1);

/*     Compute workspace.   
       (Note: Comments in the code beginning "Workspace:" describe the   
       minimal amount of workspace needed at that point in the code,   
       as well as the preferred amount for good performance.   
       NB refers to the optimal block size for the immediately   
       following subroutine, as returned by ILAENV.) */

    minwrk = 1;
    minmn = max(1,minmn);
/* Computing MAX */
    i__1 = (integer) (log((doublereal) minmn / (doublereal) (smlsiz + 1)) / 
	    log(2.)) + 1;
    nlvl = max(i__1,0);

    if (*info == 0) {
	maxwrk = 0;
	mm = *m;
	if (*m >= *n && *m >= mnthr) {

/*           Path 1a - overdetermined, with many more rows than columns. */

	    mm = *n;
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "DGEQRF", " ", m, 
		    n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, "DORMQR", "LT", 
		    m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2);
	    maxwrk = max(i__1,i__2);
	}
	if (*m >= *n) {

/*           Path 1 - overdetermined or exactly determined.   

   Computing MAX */
	    i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, "DGEBRD"
		    , " ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, "DORMBR", 
		    "QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, "DORMBR",
		     "PLN", n, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
	    maxwrk = max(i__1,i__2);
/* Computing 2nd power */
	    i__1 = smlsiz + 1;
	    wlalsd = *n * 9 + (*n << 1) * smlsiz + (*n << 3) * nlvl + *n * *
		    nrhs + i__1 * i__1;
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n * 3 + wlalsd;
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,i__2), 
		    i__2 = *n * 3 + wlalsd;
	    minwrk = max(i__1,i__2);
	}
	if (*n > *m) {
/* Computing 2nd power */
	    i__1 = smlsiz + 1;
	    wlalsd = *m * 9 + (*m << 1) * smlsiz + (*m << 3) * nlvl + *m * *
		    nrhs + i__1 * i__1;
	    if (*n >= mnthr) {

/*              Path 2a - underdetermined, with many more columns   
                than rows. */

		maxwrk = *m + *m * ilaenv_(&c__1, "DGELQF", " ", m, n, &c_n1, 
			&c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) * 
			ilaenv_(&c__1, "DGEBRD", " ", m, m, &c_n1, &c_n1, (
			ftnlen)6, (ftnlen)1);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(&
			c__1, "DORMBR", "QLT", m, nrhs, m, &c_n1, (ftnlen)6, (
			ftnlen)3);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) * 
			ilaenv_(&c__1, "DORMBR", "PLN", m, nrhs, m, &c_n1, (
			ftnlen)6, (ftnlen)3);
		maxwrk = max(i__1,i__2);
		if (*nrhs > 1) {
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
		    maxwrk = max(i__1,i__2);
		} else {
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * *m + (*m << 1);
		    maxwrk = max(i__1,i__2);
		}
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, "DORMLQ", 
			"LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + wlalsd;
		maxwrk = max(i__1,i__2);
	    } else {

/*              Path 2 - remaining underdetermined cases. */

		maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, "DGEBRD", " ", m,
			 n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, "DORMBR"
			, "QLT", m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR", 
			"PLN", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * 3 + wlalsd;
		maxwrk = max(i__1,i__2);
	    }
/* Computing MAX */
	    i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *m, i__1 = max(i__1,i__2), 
		    i__2 = *m * 3 + wlalsd;
	    minwrk = max(i__1,i__2);
	}
	minwrk = min(minwrk,maxwrk);
	work[1] = (doublereal) maxwrk;
	if (*lwork < minwrk && ! lquery) {
	    *info = -12;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DGELSD", &i__1);
	return 0;
    } else if (lquery) {
	goto L10;
    }

/*     Quick return if possible. */

    if (*m == 0 || *n == 0) {
	*rank = 0;
	return 0;
    }

/*     Get machine parameters. */

    eps = dlamch_("P");
    sfmin = dlamch_("S");
    smlnum = sfmin / eps;
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);

/*     Scale A if max entry outside range [SMLNUM,BIGNUM]. */

    anrm = dlange_("M", m, n, &a[a_offset], lda, &work[1]);
    iascl = 0;
    if (anrm > 0. && anrm < smlnum) {

/*        Scale matrix norm up to SMLNUM. */

	dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, 
		info);
	iascl = 1;
    } else if (anrm > bignum) {

/*        Scale matrix norm down to BIGNUM. */

	dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
		info);
	iascl = 2;
    } else if (anrm == 0.) {

/*        Matrix all zero. Return zero solution. */

	i__1 = max(*m,*n);
	dlaset_("F", &i__1, nrhs, &c_b82, &c_b82, &b[b_offset], ldb);
	dlaset_("F", &minmn, &c__1, &c_b82, &c_b82, &s[1], &c__1);
	*rank = 0;
	goto L10;
    }

/*     Scale B if max entry outside range [SMLNUM,BIGNUM]. */

    bnrm = dlange_("M", m, nrhs, &b[b_offset], ldb, &work[1]);
    ibscl = 0;
    if (bnrm > 0. && bnrm < smlnum) {

/*        Scale matrix norm up to SMLNUM. */

	dlascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
		 info);
	ibscl = 1;
    } else if (bnrm > bignum) {

/*        Scale matrix norm down to BIGNUM. */

	dlascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
		 info);
	ibscl = 2;
    }

/*     If M < N make sure certain entries of B are zero. */

    if (*m < *n) {
	i__1 = *n - *m;
	dlaset_("F", &i__1, nrhs, &c_b82, &c_b82, &b_ref(*m + 1, 1), ldb);
    }

/*     Overdetermined case. */

    if (*m >= *n) {

/*        Path 1 - overdetermined or exactly determined. */

	mm = *m;
	if (*m >= mnthr) {

/*           Path 1a - overdetermined, with many more rows than columns. */

	    mm = *n;
	    itau = 1;
	    nwork = itau + *n;

/*           Compute A=Q*R.   
             (Workspace: need 2*N, prefer N+N*NB) */

	    i__1 = *lwork - nwork + 1;
	    dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1,
		     info);

/*           Multiply B by transpose(Q).   
             (Workspace: need N+NRHS, prefer N+NRHS*NB) */

	    i__1 = *lwork - nwork + 1;
	    dormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
		    b_offset], ldb, &work[nwork], &i__1, info);

/*           Zero out below R. */

	    if (*n > 1) {
		i__1 = *n - 1;
		i__2 = *n - 1;
		dlaset_("L", &i__1, &i__2, &c_b82, &c_b82, &a_ref(2, 1), lda);
	    }
	}

	ie = 1;
	itauq = ie + *n;
	itaup = itauq + *n;
	nwork = itaup + *n;

/*        Bidiagonalize R in A.   
          (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */

	i__1 = *lwork - nwork + 1;
	dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
		work[itaup], &work[nwork], &i__1, info);

/*        Multiply B by transpose of left bidiagonalizing vectors of R.   
          (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */

	i__1 = *lwork - nwork + 1;
	dormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], 
		&b[b_offset], ldb, &work[nwork], &i__1, info);

/*        Solve the bidiagonal least squares problem. */

	dlalsd_("U", &smlsiz, n, nrhs, &s[1], &work[ie], &b[b_offset], ldb, 
		rcond, rank, &work[nwork], &iwork[1], info);
	if (*info != 0) {
	    goto L10;
	}

/*        Multiply B by right bidiagonalizing vectors of R. */

	i__1 = *lwork - nwork + 1;
	dormbr_("P", "L", "N", n, nrhs, n, &a[a_offset], lda, &work[itaup], &
		b[b_offset], ldb, &work[nwork], &i__1, info);

    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = *m, i__2 = (*m << 1) - 4, i__1 = max(i__1,i__2), i__1 = max(
		i__1,*nrhs), i__2 = *n - *m * 3;
	if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__1,i__2)) {

/*        Path 2a - underdetermined, with many more columns than rows   
          and sufficient workspace for an efficient algorithm. */

	    ldwork = *m;
/* Computing MAX   
   Computing MAX */
	    i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = 
		    max(i__3,*nrhs), i__4 = *n - *m * 3;
	    i__1 = (*m << 2) + *m * *lda + max(i__3,i__4), i__2 = *m * *lda + 
		    *m + *m * *nrhs;
	    if (*lwork >= max(i__1,i__2)) {
		ldwork = *lda;
	    }
	    itau = 1;
	    nwork = *m + 1;

/*        Compute A=L*Q.   
          (Workspace: need 2*M, prefer M+M*NB) */

	    i__1 = *lwork - nwork + 1;
	    dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1,
		     info);
	    il = nwork;

/*        Copy L to WORK(IL), zeroing out above its diagonal. */

	    dlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork);
	    i__1 = *m - 1;
	    i__2 = *m - 1;
	    dlaset_("U", &i__1, &i__2, &c_b82, &c_b82, &work[il + ldwork], &
		    ldwork);
	    ie = il + ldwork * *m;
	    itauq = ie + *m;
	    itaup = itauq + *m;
	    nwork = itaup + *m;

/*        Bidiagonalize L in WORK(IL).   
          (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */

	    i__1 = *lwork - nwork + 1;
	    dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], 
		    &work[itaup], &work[nwork], &i__1, info);

/*        Multiply B by transpose of left bidiagonalizing vectors of L.   
          (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */

	    i__1 = *lwork - nwork + 1;
	    dormbr_("Q", "L", "T", m, nrhs, m, &work[il], &ldwork, &work[
		    itauq], &b[b_offset], ldb, &work[nwork], &i__1, info);

/*        Solve the bidiagonal least squares problem. */

	    dlalsd_("U", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], 
		    ldb, rcond, rank, &work[nwork], &iwork[1], info);
	    if (*info != 0) {
		goto L10;
	    }

/*        Multiply B by right bidiagonalizing vectors of L. */

	    i__1 = *lwork - nwork + 1;
	    dormbr_("P", "L", "N", m, nrhs, m, &work[il], &ldwork, &work[
		    itaup], &b[b_offset], ldb, &work[nwork], &i__1, info);

/*        Zero out below first M rows of B. */

	    i__1 = *n - *m;
	    dlaset_("F", &i__1, nrhs, &c_b82, &c_b82, &b_ref(*m + 1, 1), ldb);
	    nwork = itau + *m;

/*        Multiply transpose(Q) by B.   
          (Workspace: need M+NRHS, prefer M+NRHS*NB) */

	    i__1 = *lwork - nwork + 1;
	    dormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[
		    b_offset], ldb, &work[nwork], &i__1, info);

	} else {

/*        Path 2 - remaining underdetermined cases. */

	    ie = 1;
	    itauq = ie + *m;
	    itaup = itauq + *m;
	    nwork = itaup + *m;

/*        Bidiagonalize A.   
          (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */

	    i__1 = *lwork - nwork + 1;
	    dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
		    work[itaup], &work[nwork], &i__1, info);

/*        Multiply B by transpose of left bidiagonalizing vectors.   
          (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */

	    i__1 = *lwork - nwork + 1;
	    dormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, &work[itauq]
		    , &b[b_offset], ldb, &work[nwork], &i__1, info);

/*        Solve the bidiagonal least squares problem. */

	    dlalsd_("L", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], 
		    ldb, rcond, rank, &work[nwork], &iwork[1], info);
	    if (*info != 0) {
		goto L10;
	    }

/*        Multiply B by right bidiagonalizing vectors of A. */

	    i__1 = *lwork - nwork + 1;
	    dormbr_("P", "L", "N", n, nrhs, m, &a[a_offset], lda, &work[itaup]
		    , &b[b_offset], ldb, &work[nwork], &i__1, info);

	}
    }

/*     Undo scaling. */

    if (iascl == 1) {
	dlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
		 info);
	dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
		minmn, info);
    } else if (iascl == 2) {
	dlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
		 info);
	dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
		minmn, info);
    }
    if (ibscl == 1) {
	dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
		 info);
    } else if (ibscl == 2) {
	dlascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
		 info);
    }

L10:
    work[1] = (doublereal) maxwrk;
    return 0;

/*     End of DGELSD */

} /* dgelsd_ */
Пример #4
0
/* Subroutine */ int dgels_(char *trans, integer *m, integer *n, integer *
	nrhs, doublereal *a, integer *lda, doublereal *b, integer *ldb, 
	doublereal *work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;

    /* Local variables */
    integer i__, j, nb, mn;
    doublereal anrm, bnrm;
    integer brow;
    logical tpsd;
    integer iascl, ibscl;
    extern logical lsame_(char *, char *);
    integer wsize;
    doublereal rwork[1];
    extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
    extern doublereal dlamch_(char *), dlange_(char *, integer *, 
	    integer *, doublereal *, integer *, doublereal *);
    extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *, integer *), 
	    dlascl_(char *, integer *, integer *, doublereal *, doublereal *, 
	    integer *, integer *, doublereal *, integer *, integer *),
	     dgeqrf_(integer *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *, integer *), dlaset_(char *, 
	     integer *, integer *, doublereal *, doublereal *, doublereal *, 
	    integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *);
    integer scllen;
    doublereal bignum;
    extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *, integer *), 
	    dormqr_(char *, char *, integer *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
	    doublereal *, integer *, integer *);
    doublereal smlnum;
    logical lquery;
    extern /* Subroutine */ int dtrtrs_(char *, char *, char *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, integer *, 
	    integer *);


/*  -- LAPACK driver routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  DGELS solves overdetermined or underdetermined real linear systems */
/*  involving an M-by-N matrix A, or its transpose, using a QR or LQ */
/*  factorization of A.  It is assumed that A has full rank. */

/*  The following options are provided: */

/*  1. If TRANS = 'N' and m >= n:  find the least squares solution of */
/*     an overdetermined system, i.e., solve the least squares problem */
/*                  minimize || B - A*X ||. */

/*  2. If TRANS = 'N' and m < n:  find the minimum norm solution of */
/*     an underdetermined system A * X = B. */

/*  3. If TRANS = 'T' and m >= n:  find the minimum norm solution of */
/*     an undetermined system A**T * X = B. */

/*  4. If TRANS = 'T' and m < n:  find the least squares solution of */
/*     an overdetermined system, i.e., solve the least squares problem */
/*                  minimize || B - A**T * X ||. */

/*  Several right hand side vectors b and solution vectors x can be */
/*  handled in a single call; they are stored as the columns of the */
/*  M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
/*  matrix X. */

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

/*  TRANS   (input) CHARACTER*1 */
/*          = 'N': the linear system involves A; */
/*          = 'T': the linear system involves A**T. */

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

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

/*  NRHS    (input) INTEGER */
/*          The number of right hand sides, i.e., the number of */
/*          columns of the matrices B and X. NRHS >=0. */

/*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/*          On entry, the M-by-N matrix A. */
/*          On exit, */
/*            if M >= N, A is overwritten by details of its QR */
/*                       factorization as returned by DGEQRF; */
/*            if M <  N, A is overwritten by details of its LQ */
/*                       factorization as returned by DGELQF. */

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

/*  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */
/*          On entry, the matrix B of right hand side vectors, stored */
/*          columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS */
/*          if TRANS = 'T'. */
/*          On exit, if INFO = 0, B is overwritten by the solution */
/*          vectors, stored columnwise: */
/*          if TRANS = 'N' and m >= n, rows 1 to n of B contain the least */
/*          squares solution vectors; the residual sum of squares for the */
/*          solution in each column is given by the sum of squares of */
/*          elements N+1 to M in that column; */
/*          if TRANS = 'N' and m < n, rows 1 to N of B contain the */
/*          minimum norm solution vectors; */
/*          if TRANS = 'T' and m >= n, rows 1 to M of B contain the */
/*          minimum norm solution vectors; */
/*          if TRANS = 'T' and m < n, rows 1 to M of B contain the */
/*          least squares solution vectors; the residual sum of squares */
/*          for the solution in each column is given by the sum of */
/*          squares of elements M+1 to N in that column. */

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

/*  WORK    (workspace/output) DOUBLE PRECISION 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, MN + max( MN, NRHS ) ). */
/*          For optimal performance, */
/*          LWORK >= max( 1, MN + max( MN, NRHS )*NB ). */
/*          where MN = min(M,N) and NB is the optimum block size. */

/*          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 */
/*          > 0:  if INFO =  i, the i-th diagonal element of the */
/*                triangular factor of A is zero, so that A does not have */
/*                full rank; the least squares solution could not be */
/*                computed. */

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

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

/*     Test the input arguments. */

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

    /* Function Body */
    *info = 0;
    mn = min(*m,*n);
    lquery = *lwork == -1;
    if (! (lsame_(trans, "N") || lsame_(trans, "T"))) {
	*info = -1;
    } else if (*m < 0) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*nrhs < 0) {
	*info = -4;
    } else if (*lda < max(1,*m)) {
	*info = -6;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = max(1,*m);
	if (*ldb < max(i__1,*n)) {
	    *info = -8;
	} else /* if(complicated condition) */ {
/* Computing MAX */
	    i__1 = 1, i__2 = mn + max(mn,*nrhs);
	    if (*lwork < max(i__1,i__2) && ! lquery) {
		*info = -10;
	    }
	}
    }

/*     Figure out optimal block size */

    if (*info == 0 || *info == -10) {

	tpsd = TRUE_;
	if (lsame_(trans, "N")) {
	    tpsd = FALSE_;
	}

	if (*m >= *n) {
	    nb = ilaenv_(&c__1, "DGEQRF", " ", m, n, &c_n1, &c_n1);
	    if (tpsd) {
/* Computing MAX */
		i__1 = nb, i__2 = ilaenv_(&c__1, "DORMQR", "LN", m, nrhs, n, &
			c_n1);
		nb = max(i__1,i__2);
	    } else {
/* Computing MAX */
		i__1 = nb, i__2 = ilaenv_(&c__1, "DORMQR", "LT", m, nrhs, n, &
			c_n1);
		nb = max(i__1,i__2);
	    }
	} else {
	    nb = ilaenv_(&c__1, "DGELQF", " ", m, n, &c_n1, &c_n1);
	    if (tpsd) {
/* Computing MAX */
		i__1 = nb, i__2 = ilaenv_(&c__1, "DORMLQ", "LT", n, nrhs, m, &
			c_n1);
		nb = max(i__1,i__2);
	    } else {
/* Computing MAX */
		i__1 = nb, i__2 = ilaenv_(&c__1, "DORMLQ", "LN", n, nrhs, m, &
			c_n1);
		nb = max(i__1,i__2);
	    }
	}

/* Computing MAX */
	i__1 = 1, i__2 = mn + max(mn,*nrhs) * nb;
	wsize = max(i__1,i__2);
	work[1] = (doublereal) wsize;

    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DGELS ", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

/* Computing MIN */
    i__1 = min(*m,*n);
    if (min(i__1,*nrhs) == 0) {
	i__1 = max(*m,*n);
	dlaset_("Full", &i__1, nrhs, &c_b33, &c_b33, &b[b_offset], ldb);
	return 0;
    }

/*     Get machine parameters */

    smlnum = dlamch_("S") / dlamch_("P");
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);

/*     Scale A, B if max element outside range [SMLNUM,BIGNUM] */

    anrm = dlange_("M", m, n, &a[a_offset], lda, rwork);
    iascl = 0;
    if (anrm > 0. && anrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */

	dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, 
		info);
	iascl = 1;
    } else if (anrm > bignum) {

/*        Scale matrix norm down to BIGNUM */

	dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
		info);
	iascl = 2;
    } else if (anrm == 0.) {

/*        Matrix all zero. Return zero solution. */

	i__1 = max(*m,*n);
	dlaset_("F", &i__1, nrhs, &c_b33, &c_b33, &b[b_offset], ldb);
	goto L50;
    }

    brow = *m;
    if (tpsd) {
	brow = *n;
    }
    bnrm = dlange_("M", &brow, nrhs, &b[b_offset], ldb, rwork);
    ibscl = 0;
    if (bnrm > 0. && bnrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */

	dlascl_("G", &c__0, &c__0, &bnrm, &smlnum, &brow, nrhs, &b[b_offset], 
		ldb, info);
	ibscl = 1;
    } else if (bnrm > bignum) {

/*        Scale matrix norm down to BIGNUM */

	dlascl_("G", &c__0, &c__0, &bnrm, &bignum, &brow, nrhs, &b[b_offset], 
		ldb, info);
	ibscl = 2;
    }

    if (*m >= *n) {

/*        compute QR factorization of A */

	i__1 = *lwork - mn;
	dgeqrf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
		;

/*        workspace at least N, optimally N*NB */

	if (! tpsd) {

/*           Least-Squares Problem min || A * X - B || */

/*           B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */

	    i__1 = *lwork - mn;
	    dormqr_("Left", "Transpose", m, nrhs, n, &a[a_offset], lda, &work[
		    1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);

/*           workspace at least NRHS, optimally NRHS*NB */

/*           B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) */

	    dtrtrs_("Upper", "No transpose", "Non-unit", n, nrhs, &a[a_offset]
, lda, &b[b_offset], ldb, info);

	    if (*info > 0) {
		return 0;
	    }

	    scllen = *n;

	} else {

/*           Overdetermined system of equations A' * X = B */

/*           B(1:N,1:NRHS) := inv(R') * B(1:N,1:NRHS) */

	    dtrtrs_("Upper", "Transpose", "Non-unit", n, nrhs, &a[a_offset], 
		    lda, &b[b_offset], ldb, info);

	    if (*info > 0) {
		return 0;
	    }

/*           B(N+1:M,1:NRHS) = ZERO */

	    i__1 = *nrhs;
	    for (j = 1; j <= i__1; ++j) {
		i__2 = *m;
		for (i__ = *n + 1; i__ <= i__2; ++i__) {
		    b[i__ + j * b_dim1] = 0.;
/* L10: */
		}
/* L20: */
	    }

/*           B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS) */

	    i__1 = *lwork - mn;
	    dormqr_("Left", "No transpose", m, nrhs, n, &a[a_offset], lda, &
		    work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);

/*           workspace at least NRHS, optimally NRHS*NB */

	    scllen = *m;

	}

    } else {

/*        Compute LQ factorization of A */

	i__1 = *lwork - mn;
	dgelqf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
		;

/*        workspace at least M, optimally M*NB. */

	if (! tpsd) {

/*           underdetermined system of equations A * X = B */

/*           B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) */

	    dtrtrs_("Lower", "No transpose", "Non-unit", m, nrhs, &a[a_offset]
, lda, &b[b_offset], ldb, info);

	    if (*info > 0) {
		return 0;
	    }

/*           B(M+1:N,1:NRHS) = 0 */

	    i__1 = *nrhs;
	    for (j = 1; j <= i__1; ++j) {
		i__2 = *n;
		for (i__ = *m + 1; i__ <= i__2; ++i__) {
		    b[i__ + j * b_dim1] = 0.;
/* L30: */
		}
/* L40: */
	    }

/*           B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS) */

	    i__1 = *lwork - mn;
	    dormlq_("Left", "Transpose", n, nrhs, m, &a[a_offset], lda, &work[
		    1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);

/*           workspace at least NRHS, optimally NRHS*NB */

	    scllen = *n;

	} else {

/*           overdetermined system min || A' * X - B || */

/*           B(1:N,1:NRHS) := Q * B(1:N,1:NRHS) */

	    i__1 = *lwork - mn;
	    dormlq_("Left", "No transpose", n, nrhs, m, &a[a_offset], lda, &
		    work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);

/*           workspace at least NRHS, optimally NRHS*NB */

/*           B(1:M,1:NRHS) := inv(L') * B(1:M,1:NRHS) */

	    dtrtrs_("Lower", "Transpose", "Non-unit", m, nrhs, &a[a_offset], 
		    lda, &b[b_offset], ldb, info);

	    if (*info > 0) {
		return 0;
	    }

	    scllen = *m;

	}

    }

/*     Undo scaling */

    if (iascl == 1) {
	dlascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset]
, ldb, info);
    } else if (iascl == 2) {
	dlascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset]
, ldb, info);
    }
    if (ibscl == 1) {
	dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset]
, ldb, info);
    } else if (ibscl == 2) {
	dlascl_("G", &c__0, &c__0, &bignum, &bnrm, &scllen, nrhs, &b[b_offset]
, ldb, info);
    }

L50:
    work[1] = (doublereal) wsize;

    return 0;

/*     End of DGELS */

} /* dgels_ */
Пример #5
0
/* Subroutine */ int dlqt03_(integer *m, integer *n, integer *k, doublereal *
	af, doublereal *c__, doublereal *cc, doublereal *q, integer *lda, 
	doublereal *tau, doublereal *work, integer *lwork, doublereal *rwork, 
	doublereal *result)
{
    /* Initialized data */

    static integer iseed[4] = { 1988,1989,1990,1991 };

    /* System generated locals */
    integer af_dim1, af_offset, c_dim1, c_offset, cc_dim1, cc_offset, q_dim1, 
	    q_offset, i__1;

    /* Builtin functions */
    /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);

    /* Local variables */
    integer j, mc, nc;
    doublereal eps;
    char side[1];
    integer info;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *);
    integer iside;
    extern logical lsame_(char *, char *);
    doublereal resid, cnorm;
    char trans[1];
    extern doublereal dlamch_(char *), dlange_(char *, integer *, 
	    integer *, doublereal *, integer *, doublereal *);
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *), 
	    dlaset_(char *, integer *, integer *, doublereal *, doublereal *, 
	    doublereal *, integer *), dlarnv_(integer *, integer *, 
	    integer *, doublereal *), dorglq_(integer *, integer *, integer *, 
	     doublereal *, integer *, doublereal *, doublereal *, integer *, 
	    integer *), dormlq_(char *, char *, integer *, integer *, integer 
	    *, doublereal *, integer *, doublereal *, doublereal *, integer *, 
	     doublereal *, integer *, integer *);
    integer itrans;


/*  -- LAPACK test routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  DLQT03 tests DORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'. */

/*  DLQT03 compares the results of a call to DORMLQ with the results of */
/*  forming Q explicitly by a call to DORGLQ and then performing matrix */
/*  multiplication by a call to DGEMM. */

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

/*  M       (input) INTEGER */
/*          The number of rows or columns of the matrix C; C is n-by-m if */
/*          Q is applied from the left, or m-by-n if Q is applied from */
/*          the right.  M >= 0. */

/*  N       (input) INTEGER */
/*          The order of the orthogonal matrix Q.  N >= 0. */

/*  K       (input) INTEGER */
/*          The number of elementary reflectors whose product defines the */
/*          orthogonal matrix Q.  N >= K >= 0. */

/*  AF      (input) DOUBLE PRECISION array, dimension (LDA,N) */
/*          Details of the LQ factorization of an m-by-n matrix, as */
/*          returned by DGELQF. See SGELQF for further details. */

/*  C       (workspace) DOUBLE PRECISION array, dimension (LDA,N) */

/*  CC      (workspace) DOUBLE PRECISION array, dimension (LDA,N) */

/*  Q       (workspace) DOUBLE PRECISION array, dimension (LDA,N) */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the arrays AF, C, CC, and Q. */

/*  TAU     (input) DOUBLE PRECISION array, dimension (min(M,N)) */
/*          The scalar factors of the elementary reflectors corresponding */
/*          to the LQ factorization in AF. */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK) */

/*  LWORK   (input) INTEGER */
/*          The length of WORK.  LWORK must be at least M, and should be */
/*          M*NB, where NB is the blocksize for this environment. */

/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (M) */

/*  RESULT  (output) DOUBLE PRECISION array, dimension (4) */
/*          The test ratios compare two techniques for multiplying a */
/*          random matrix C by an n-by-n orthogonal matrix Q. */
/*          RESULT(1) = norm( Q*C - Q*C )  / ( N * norm(C) * EPS ) */
/*          RESULT(2) = norm( C*Q - C*Q )  / ( N * norm(C) * EPS ) */
/*          RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS ) */
/*          RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS ) */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Scalars in Common .. */
/*     .. */
/*     .. Common blocks .. */
/*     .. */
/*     .. Data statements .. */
    /* Parameter adjustments */
    q_dim1 = *lda;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    cc_dim1 = *lda;
    cc_offset = 1 + cc_dim1;
    cc -= cc_offset;
    c_dim1 = *lda;
    c_offset = 1 + c_dim1;
    c__ -= c_offset;
    af_dim1 = *lda;
    af_offset = 1 + af_dim1;
    af -= af_offset;
    --tau;
    --work;
    --rwork;
    --result;

    /* Function Body */
/*     .. */
/*     .. Executable Statements .. */

    eps = dlamch_("Epsilon");

/*     Copy the first k rows of the factorization to the array Q */

    dlaset_("Full", n, n, &c_b4, &c_b4, &q[q_offset], lda);
    i__1 = *n - 1;
    dlacpy_("Upper", k, &i__1, &af[(af_dim1 << 1) + 1], lda, &q[(q_dim1 << 1) 
	    + 1], lda);

/*     Generate the n-by-n matrix Q */

    s_copy(srnamc_1.srnamt, "DORGLQ", (ftnlen)6, (ftnlen)6);
    dorglq_(n, n, k, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);

    for (iside = 1; iside <= 2; ++iside) {
	if (iside == 1) {
	    *(unsigned char *)side = 'L';
	    mc = *n;
	    nc = *m;
	} else {
	    *(unsigned char *)side = 'R';
	    mc = *m;
	    nc = *n;
	}

/*        Generate MC by NC matrix C */

	i__1 = nc;
	for (j = 1; j <= i__1; ++j) {
	    dlarnv_(&c__2, iseed, &mc, &c__[j * c_dim1 + 1]);
/* L10: */
	}
	cnorm = dlange_("1", &mc, &nc, &c__[c_offset], lda, &rwork[1]);
	if (cnorm == 0.) {
	    cnorm = 1.;
	}

	for (itrans = 1; itrans <= 2; ++itrans) {
	    if (itrans == 1) {
		*(unsigned char *)trans = 'N';
	    } else {
		*(unsigned char *)trans = 'T';
	    }

/*           Copy C */

	    dlacpy_("Full", &mc, &nc, &c__[c_offset], lda, &cc[cc_offset], 
		    lda);

/*           Apply Q or Q' to C */

	    s_copy(srnamc_1.srnamt, "DORMLQ", (ftnlen)6, (ftnlen)6);
	    dormlq_(side, trans, &mc, &nc, k, &af[af_offset], lda, &tau[1], &
		    cc[cc_offset], lda, &work[1], lwork, &info);

/*           Form explicit product and subtract */

	    if (lsame_(side, "L")) {
		dgemm_(trans, "No transpose", &mc, &nc, &mc, &c_b21, &q[
			q_offset], lda, &c__[c_offset], lda, &c_b22, &cc[
			cc_offset], lda);
	    } else {
		dgemm_("No transpose", trans, &mc, &nc, &nc, &c_b21, &c__[
			c_offset], lda, &q[q_offset], lda, &c_b22, &cc[
			cc_offset], lda);
	    }

/*           Compute error in the difference */

	    resid = dlange_("1", &mc, &nc, &cc[cc_offset], lda, &rwork[1]);
	    result[(iside - 1 << 1) + itrans] = resid / ((doublereal) max(1,*
		    n) * cnorm * eps);

/* L20: */
	}
/* L30: */
    }

    return 0;

/*     End of DLQT03 */

} /* dlqt03_ */
Пример #6
0
Файл: dormbr.c Проект: vopl/sp
/* Subroutine */ int dormbr_(char *vect, char *side, char *trans, integer *m, 
	integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, 
	doublereal *c__, integer *ldc, doublereal *work, integer *lwork, 
	integer *info)
{
/*  -- LAPACK routine (version 3.1) --   
       Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..   
       November 2006   


    Purpose   
    =======   

    If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C   
    with   
                    SIDE = 'L'     SIDE = 'R'   
    TRANS = 'N':      Q * C          C * Q   
    TRANS = 'T':      Q**T * C       C * Q**T   

    If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C   
    with   
                    SIDE = 'L'     SIDE = 'R'   
    TRANS = 'N':      P * C          C * P   
    TRANS = 'T':      P**T * C       C * P**T   

    Here Q and P**T are the orthogonal matrices determined by DGEBRD when   
    reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and   
    P**T are defined as products of elementary reflectors H(i) and G(i)   
    respectively.   

    Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the   
    order of the orthogonal matrix Q or P**T that is applied.   

    If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:   
    if nq >= k, Q = H(1) H(2) . . . H(k);   
    if nq < k, Q = H(1) H(2) . . . H(nq-1).   

    If VECT = 'P', A is assumed to have been a K-by-NQ matrix:   
    if k < nq, P = G(1) G(2) . . . G(k);   
    if k >= nq, P = G(1) G(2) . . . G(nq-1).   

    Arguments   
    =========   

    VECT    (input) CHARACTER*1   
            = 'Q': apply Q or Q**T;   
            = 'P': apply P or P**T.   

    SIDE    (input) CHARACTER*1   
            = 'L': apply Q, Q**T, P or P**T from the Left;   
            = 'R': apply Q, Q**T, P or P**T from the Right.   

    TRANS   (input) CHARACTER*1   
            = 'N':  No transpose, apply Q  or P;   
            = 'T':  Transpose, apply Q**T or P**T.   

    M       (input) INTEGER   
            The number of rows of the matrix C. M >= 0.   

    N       (input) INTEGER   
            The number of columns of the matrix C. N >= 0.   

    K       (input) INTEGER   
            If VECT = 'Q', the number of columns in the original   
            matrix reduced by DGEBRD.   
            If VECT = 'P', the number of rows in the original   
            matrix reduced by DGEBRD.   
            K >= 0.   

    A       (input) DOUBLE PRECISION array, dimension   
                                  (LDA,min(nq,K)) if VECT = 'Q'   
                                  (LDA,nq)        if VECT = 'P'   
            The vectors which define the elementary reflectors H(i) and   
            G(i), whose products determine the matrices Q and P, as   
            returned by DGEBRD.   

    LDA     (input) INTEGER   
            The leading dimension of the array A.   
            If VECT = 'Q', LDA >= max(1,nq);   
            if VECT = 'P', LDA >= max(1,min(nq,K)).   

    TAU     (input) DOUBLE PRECISION array, dimension (min(nq,K))   
            TAU(i) must contain the scalar factor of the elementary   
            reflector H(i) or G(i) which determines Q or P, as returned   
            by DGEBRD in the array argument TAUQ or TAUP.   

    C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)   
            On entry, the M-by-N matrix C.   
            On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q   
            or P*C or P**T*C or C*P or C*P**T.   

    LDC     (input) INTEGER   
            The leading dimension of the array C. LDC >= max(1,M).   

    WORK    (workspace/output) DOUBLE PRECISION 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.   
            If SIDE = 'L', LWORK >= max(1,N);   
            if SIDE = 'R', LWORK >= max(1,M).   
            For optimum performance LWORK >= N*NB if SIDE = 'L', and   
            LWORK >= M*NB if SIDE = 'R', where NB is the optimal   
            blocksize.   

            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   

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


       Test the input arguments   

       Parameter adjustments */
    /* Table of constant values */
    static const integer c__1 = 1;
    static const integer c_n1 = -1;
    static const integer c__2 = 2;
    
    /* System generated locals */
    address a__1[2];
    integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2];
    char ch__1[2];
    /* Builtin functions   
       Subroutine */ int s_cat(const char *, char **, const integer *, const integer *, const ftnlen);
    /* Local variables */
    _THREAD_STATIC_ integer i1, i2, nb, mi, ni, nq, nw;
    _THREAD_STATIC_ logical left;
    extern logical lsame_(const char *, const char *);
    _THREAD_STATIC_ integer iinfo;
    extern /* Subroutine */ int xerbla_(const char *, const integer *);
    extern integer ilaenv_(const integer *, const char *, const char *, const integer *, const integer *, 
	    const integer *, const integer *, const ftnlen, const ftnlen);
    extern /* Subroutine */ int dormlq_(const char *, const char *, const integer *, const integer *, 
	    const integer *, const doublereal *, const integer *, const doublereal *, const doublereal *, 
	    const integer *, const doublereal *, const integer *, const integer *);
    _THREAD_STATIC_ logical notran;
    extern /* Subroutine */ int dormqr_(const char *, const char *, const integer *, const integer *, 
	    const integer *, const doublereal *, const integer *, const doublereal *, const doublereal *, 
	    const integer *, const doublereal *, const integer *, const integer *);
    _THREAD_STATIC_ logical applyq;
    _THREAD_STATIC_ char transt[1];
    _THREAD_STATIC_ integer lwkopt;
    _THREAD_STATIC_ logical lquery;


    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --tau;
    c_dim1 = *ldc;
    c_offset = 1 + c_dim1;
    c__ -= c_offset;
    --work;

    /* Function Body */
    *info = 0;
    applyq = lsame_(vect, "Q");
    left = lsame_(side, "L");
    notran = lsame_(trans, "N");
    lquery = *lwork == -1;

/*     NQ is the order of Q or P and NW is the minimum dimension of WORK */

    if (left) {
	nq = *m;
	nw = *n;
    } else {
	nq = *n;
	nw = *m;
    }
    if (! applyq && ! lsame_(vect, "P")) {
	*info = -1;
    } else if (! left && ! lsame_(side, "R")) {
	*info = -2;
    } else if (! notran && ! lsame_(trans, "T")) {
	*info = -3;
    } else if (*m < 0) {
	*info = -4;
    } else if (*n < 0) {
	*info = -5;
    } else if (*k < 0) {
	*info = -6;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = 1, i__2 = min(nq,*k);
	if (applyq && *lda < max(1,nq) || ! applyq && *lda < max(i__1,i__2)) {
	    *info = -8;
	} else if (*ldc < max(1,*m)) {
	    *info = -11;
	} else if (*lwork < max(1,nw) && ! lquery) {
	    *info = -13;
	}
    }

    if (*info == 0) {
	if (applyq) {
	    if (left) {
/* Writing concatenation */
		i__3[0] = 1, a__1[0] = side;
		i__3[1] = 1, a__1[1] = trans;
		s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
		i__1 = *m - 1;
		i__2 = *m - 1;
		nb = ilaenv_(&c__1, "DORMQR", ch__1, &i__1, n, &i__2, &c_n1, (
			ftnlen)6, (ftnlen)2);
	    } else {
/* Writing concatenation */
		i__3[0] = 1, a__1[0] = side;
		i__3[1] = 1, a__1[1] = trans;
		s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
		i__1 = *n - 1;
		i__2 = *n - 1;
		nb = ilaenv_(&c__1, "DORMQR", ch__1, m, &i__1, &i__2, &c_n1, (
			ftnlen)6, (ftnlen)2);
	    }
	} else {
	    if (left) {
/* Writing concatenation */
		i__3[0] = 1, a__1[0] = side;
		i__3[1] = 1, a__1[1] = trans;
		s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
		i__1 = *m - 1;
		i__2 = *m - 1;
		nb = ilaenv_(&c__1, "DORMLQ", ch__1, &i__1, n, &i__2, &c_n1, (
			ftnlen)6, (ftnlen)2);
	    } else {
/* Writing concatenation */
		i__3[0] = 1, a__1[0] = side;
		i__3[1] = 1, a__1[1] = trans;
		s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
		i__1 = *n - 1;
		i__2 = *n - 1;
		nb = ilaenv_(&c__1, "DORMLQ", ch__1, m, &i__1, &i__2, &c_n1, (
			ftnlen)6, (ftnlen)2);
	    }
	}
	lwkopt = max(1,nw) * nb;
	work[1] = (doublereal) lwkopt;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DORMBR", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    work[1] = 1.;
    if (*m == 0 || *n == 0) {
	return 0;
    }

    if (applyq) {

/*        Apply Q */

	if (nq >= *k) {

/*           Q was determined by a call to DGEBRD with nq >= k */

	    dormqr_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
		    c_offset], ldc, &work[1], lwork, &iinfo);
	} else if (nq > 1) {

/*           Q was determined by a call to DGEBRD with nq < k */

	    if (left) {
		mi = *m - 1;
		ni = *n;
		i1 = 2;
		i2 = 1;
	    } else {
		mi = *m;
		ni = *n - 1;
		i1 = 1;
		i2 = 2;
	    }
	    i__1 = nq - 1;
	    dormqr_(side, trans, &mi, &ni, &i__1, &a[a_dim1 + 2], lda, &tau[1]
		    , &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo);
	}
    } else {

/*        Apply P */

	if (notran) {
	    *(unsigned char *)transt = 'T';
	} else {
	    *(unsigned char *)transt = 'N';
	}
	if (nq > *k) {

/*           P was determined by a call to DGEBRD with nq > k */

	    dormlq_(side, transt, m, n, k, &a[a_offset], lda, &tau[1], &c__[
		    c_offset], ldc, &work[1], lwork, &iinfo);
	} else if (nq > 1) {

/*           P was determined by a call to DGEBRD with nq <= k */

	    if (left) {
		mi = *m - 1;
		ni = *n;
		i1 = 2;
		i2 = 1;
	    } else {
		mi = *m;
		ni = *n - 1;
		i1 = 1;
		i2 = 2;
	    }
	    i__1 = nq - 1;
	    dormlq_(side, transt, &mi, &ni, &i__1, &a[(a_dim1 << 1) + 1], lda,
		     &tau[1], &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &
		    iinfo);
	}
    }
    work[1] = (doublereal) lwkopt;
    return 0;

/*     End of DORMBR */

} /* dormbr_ */
Пример #7
0
/* Subroutine */ int dgelss_(integer *m, integer *n, integer *nrhs, 
	doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
	s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork,
	 integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
    doublereal d__1;

    /* Local variables */
    static doublereal anrm, bnrm;
    static integer itau;
    static doublereal vdum[1];
    static integer i__;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *);
    static integer iascl, ibscl;
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *), drscl_(integer *, 
	    doublereal *, doublereal *, integer *);
    static integer chunk;
    static doublereal sfmin;
    static integer minmn;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    static integer maxmn, itaup, itauq, mnthr, iwork;
    extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
    static integer bl, ie, il;
    extern /* Subroutine */ int dgebrd_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, doublereal *, doublereal *,
	     doublereal *, integer *, integer *);
    extern doublereal dlamch_(char *);
    static integer mm;
    extern doublereal dlange_(char *, integer *, integer *, doublereal *, 
	    integer *, doublereal *);
    static integer bdspac;
    extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *, integer *), 
	    dlascl_(char *, integer *, integer *, doublereal *, doublereal *, 
	    integer *, integer *, doublereal *, integer *, integer *),
	     dgeqrf_(integer *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *, integer *), dlacpy_(char *,
	     integer *, integer *, doublereal *, integer *, doublereal *, 
	    integer *), dlaset_(char *, integer *, integer *, 
	    doublereal *, doublereal *, doublereal *, integer *), 
	    xerbla_(char *, integer *), dbdsqr_(char *, integer *, 
	    integer *, integer *, integer *, doublereal *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, integer *), dorgbr_(char *, 
	    integer *, integer *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *, integer *);
    static doublereal bignum;
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *, integer *), dormlq_(char *, char *, integer *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *, integer *);
    static integer ldwork;
    extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *, integer *);
    static integer minwrk, maxwrk;
    static doublereal smlnum;
    static logical lquery;
    static doublereal eps, thr;


#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]


/*  -- LAPACK driver routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       October 31, 1999   


    Purpose   
    =======   

    DGELSS computes the minimum norm solution to a real linear least   
    squares problem:   

    Minimize 2-norm(| b - A*x |).   

    using the singular value decomposition (SVD) of A. A is an M-by-N   
    matrix which may be rank-deficient.   

    Several right hand side vectors b and solution vectors x can be   
    handled in a single call; they are stored as the columns of the   
    M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix   
    X.   

    The effective rank of A is determined by treating as zero those   
    singular values which are less than RCOND times the largest singular   
    value.   

    Arguments   
    =========   

    M       (input) INTEGER   
            The number of rows of the matrix A. M >= 0.   

    N       (input) INTEGER   
            The number of columns of the matrix A. N >= 0.   

    NRHS    (input) INTEGER   
            The number of right hand sides, i.e., the number of columns   
            of the matrices B and X. NRHS >= 0.   

    A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)   
            On entry, the M-by-N matrix A.   
            On exit, the first min(m,n) rows of A are overwritten with   
            its right singular vectors, stored rowwise.   

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

    B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)   
            On entry, the M-by-NRHS right hand side matrix B.   
            On exit, B is overwritten by the N-by-NRHS solution   
            matrix X.  If m >= n and RANK = n, the residual   
            sum-of-squares for the solution in the i-th column is given   
            by the sum of squares of elements n+1:m in that column.   

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

    S       (output) DOUBLE PRECISION array, dimension (min(M,N))   
            The singular values of A in decreasing order.   
            The condition number of A in the 2-norm = S(1)/S(min(m,n)).   

    RCOND   (input) DOUBLE PRECISION   
            RCOND is used to determine the effective rank of A.   
            Singular values S(i) <= RCOND*S(1) are treated as zero.   
            If RCOND < 0, machine precision is used instead.   

    RANK    (output) INTEGER   
            The effective rank of A, i.e., the number of singular values   
            which are greater than RCOND*S(1).   

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

    LWORK   (input) INTEGER   
            The dimension of the array WORK. LWORK >= 1, and also:   
            LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS )   
            For good performance, LWORK should generally be larger.   

            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.   
            > 0:  the algorithm for computing the SVD failed to converge;   
                  if INFO = i, i off-diagonal elements of an intermediate   
                  bidiagonal form did not converge to zero.   

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


       Test the input arguments   

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

    /* Function Body */
    *info = 0;
    minmn = min(*m,*n);
    maxmn = max(*m,*n);
    mnthr = ilaenv_(&c__6, "DGELSS", " ", m, n, nrhs, &c_n1, (ftnlen)6, (
	    ftnlen)1);
    lquery = *lwork == -1;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*nrhs < 0) {
	*info = -3;
    } else if (*lda < max(1,*m)) {
	*info = -5;
    } else if (*ldb < max(1,maxmn)) {
	*info = -7;
    }

/*     Compute workspace   
        (Note: Comments in the code beginning "Workspace:" describe the   
         minimal amount of workspace needed at that point in the code,   
         as well as the preferred amount for good performance.   
         NB refers to the optimal block size for the immediately   
         following subroutine, as returned by ILAENV.) */

    minwrk = 1;
    if (*info == 0 && (*lwork >= 1 || lquery)) {
	maxwrk = 0;
	mm = *m;
	if (*m >= *n && *m >= mnthr) {

/*           Path 1a - overdetermined, with many more rows than columns */

	    mm = *n;
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "DGEQRF", " ", m, 
		    n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, "DORMQR", "LT", 
		    m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2);
	    maxwrk = max(i__1,i__2);
	}
	if (*m >= *n) {

/*           Path 1 - overdetermined or exactly determined   

             Compute workspace needed for DBDSQR   

   Computing MAX */
	    i__1 = 1, i__2 = *n * 5;
	    bdspac = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, "DGEBRD"
		    , " ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, "DORMBR", 
		    "QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, "DORGBR",
		     "P", n, n, n, &c_n1, (ftnlen)6, (ftnlen)1);
	    maxwrk = max(i__1,i__2);
	    maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n * *nrhs;
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,i__2);
	    minwrk = max(i__1,bdspac);
	    maxwrk = max(minwrk,maxwrk);
	}
	if (*n > *m) {

/*           Compute workspace needed for DBDSQR   

   Computing MAX */
	    i__1 = 1, i__2 = *m * 5;
	    bdspac = max(i__1,i__2);
/* Computing MAX */
	    i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = max(i__1,i__2);
	    minwrk = max(i__1,bdspac);
	    if (*n >= mnthr) {

/*              Path 2a - underdetermined, with many more columns   
                than rows */

		maxwrk = *m + *m * ilaenv_(&c__1, "DGELQF", " ", m, n, &c_n1, 
			&c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) * 
			ilaenv_(&c__1, "DGEBRD", " ", m, m, &c_n1, &c_n1, (
			ftnlen)6, (ftnlen)1);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(&
			c__1, "DORMBR", "QLT", m, nrhs, m, &c_n1, (ftnlen)6, (
			ftnlen)3);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) * 
			ilaenv_(&c__1, "DORGBR", "P", m, m, m, &c_n1, (ftnlen)
			6, (ftnlen)1);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * *m + *m + bdspac;
		maxwrk = max(i__1,i__2);
		if (*nrhs > 1) {
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
		    maxwrk = max(i__1,i__2);
		} else {
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * *m + (*m << 1);
		    maxwrk = max(i__1,i__2);
		}
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, "DORMLQ", 
			"LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2);
		maxwrk = max(i__1,i__2);
	    } else {

/*              Path 2 - underdetermined */

		maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, "DGEBRD", " ", m,
			 n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, "DORMBR"
			, "QLT", m, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORGBR", 
			"P", m, n, m, &c_n1, (ftnlen)6, (ftnlen)1);
		maxwrk = max(i__1,i__2);
		maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n * *nrhs;
		maxwrk = max(i__1,i__2);
	    }
	}
	maxwrk = max(minwrk,maxwrk);
	work[1] = (doublereal) maxwrk;
    }

    minwrk = max(minwrk,1);
    if (*lwork < minwrk && ! lquery) {
	*info = -12;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DGELSS", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    if (*m == 0 || *n == 0) {
	*rank = 0;
	return 0;
    }

/*     Get machine parameters */

    eps = dlamch_("P");
    sfmin = dlamch_("S");
    smlnum = sfmin / eps;
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);

/*     Scale A if max element outside range [SMLNUM,BIGNUM] */

    anrm = dlange_("M", m, n, &a[a_offset], lda, &work[1]);
    iascl = 0;
    if (anrm > 0. && anrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */

	dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, 
		info);
	iascl = 1;
    } else if (anrm > bignum) {

/*        Scale matrix norm down to BIGNUM */

	dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
		info);
	iascl = 2;
    } else if (anrm == 0.) {

/*        Matrix all zero. Return zero solution. */

	i__1 = max(*m,*n);
	dlaset_("F", &i__1, nrhs, &c_b74, &c_b74, &b[b_offset], ldb);
	dlaset_("F", &minmn, &c__1, &c_b74, &c_b74, &s[1], &c__1);
	*rank = 0;
	goto L70;
    }

/*     Scale B if max element outside range [SMLNUM,BIGNUM] */

    bnrm = dlange_("M", m, nrhs, &b[b_offset], ldb, &work[1]);
    ibscl = 0;
    if (bnrm > 0. && bnrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */

	dlascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
		 info);
	ibscl = 1;
    } else if (bnrm > bignum) {

/*        Scale matrix norm down to BIGNUM */

	dlascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
		 info);
	ibscl = 2;
    }

/*     Overdetermined case */

    if (*m >= *n) {

/*        Path 1 - overdetermined or exactly determined */

	mm = *m;
	if (*m >= mnthr) {

/*           Path 1a - overdetermined, with many more rows than columns */

	    mm = *n;
	    itau = 1;
	    iwork = itau + *n;

/*           Compute A=Q*R   
             (Workspace: need 2*N, prefer N+N*NB) */

	    i__1 = *lwork - iwork + 1;
	    dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1,
		     info);

/*           Multiply B by transpose(Q)   
             (Workspace: need N+NRHS, prefer N+NRHS*NB) */

	    i__1 = *lwork - iwork + 1;
	    dormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
		    b_offset], ldb, &work[iwork], &i__1, info);

/*           Zero out below R */

	    if (*n > 1) {
		i__1 = *n - 1;
		i__2 = *n - 1;
		dlaset_("L", &i__1, &i__2, &c_b74, &c_b74, &a_ref(2, 1), lda);
	    }
	}

	ie = 1;
	itauq = ie + *n;
	itaup = itauq + *n;
	iwork = itaup + *n;

/*        Bidiagonalize R in A   
          (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */

	i__1 = *lwork - iwork + 1;
	dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
		work[itaup], &work[iwork], &i__1, info);

/*        Multiply B by transpose of left bidiagonalizing vectors of R   
          (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */

	i__1 = *lwork - iwork + 1;
	dormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], 
		&b[b_offset], ldb, &work[iwork], &i__1, info);

/*        Generate right bidiagonalizing vectors of R in A   
          (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */

	i__1 = *lwork - iwork + 1;
	dorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &
		i__1, info);
	iwork = ie + *n;

/*        Perform bidiagonal QR iteration   
            multiply B by transpose of left singular vectors   
            compute right singular vectors in A   
          (Workspace: need BDSPAC) */

	dbdsqr_("U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda, 
		vdum, &c__1, &b[b_offset], ldb, &work[iwork], info)
		;
	if (*info != 0) {
	    goto L70;
	}

/*        Multiply B by reciprocals of singular values   

   Computing MAX */
	d__1 = *rcond * s[1];
	thr = max(d__1,sfmin);
	if (*rcond < 0.) {
/* Computing MAX */
	    d__1 = eps * s[1];
	    thr = max(d__1,sfmin);
	}
	*rank = 0;
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    if (s[i__] > thr) {
		drscl_(nrhs, &s[i__], &b_ref(i__, 1), ldb);
		++(*rank);
	    } else {
		dlaset_("F", &c__1, nrhs, &c_b74, &c_b74, &b_ref(i__, 1), ldb);
	    }
/* L10: */
	}

/*        Multiply B by right singular vectors   
          (Workspace: need N, prefer N*NRHS) */

	if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
	    dgemm_("T", "N", n, nrhs, n, &c_b108, &a[a_offset], lda, &b[
		    b_offset], ldb, &c_b74, &work[1], ldb);
	    dlacpy_("G", n, nrhs, &work[1], ldb, &b[b_offset], ldb)
		    ;
	} else if (*nrhs > 1) {
	    chunk = *lwork / *n;
	    i__1 = *nrhs;
	    i__2 = chunk;
	    for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
		i__3 = *nrhs - i__ + 1;
		bl = min(i__3,chunk);
		dgemm_("T", "N", n, &bl, n, &c_b108, &a[a_offset], lda, &
			b_ref(1, i__), ldb, &c_b74, &work[1], n);
		dlacpy_("G", n, &bl, &work[1], n, &b_ref(1, i__), ldb);
/* L20: */
	    }
	} else {
	    dgemv_("T", n, n, &c_b108, &a[a_offset], lda, &b[b_offset], &c__1,
		     &c_b74, &work[1], &c__1);
	    dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
	}

    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__2 = *m, i__1 = (*m << 1) - 4, i__2 = max(i__2,i__1), i__2 = max(
		i__2,*nrhs), i__1 = *n - *m * 3;
	if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__2,i__1)) {

/*        Path 2a - underdetermined, with many more columns than rows   
          and sufficient workspace for an efficient algorithm */

	    ldwork = *m;
/* Computing MAX   
   Computing MAX */
	    i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = 
		    max(i__3,*nrhs), i__4 = *n - *m * 3;
	    i__2 = (*m << 2) + *m * *lda + max(i__3,i__4), i__1 = *m * *lda + 
		    *m + *m * *nrhs;
	    if (*lwork >= max(i__2,i__1)) {
		ldwork = *lda;
	    }
	    itau = 1;
	    iwork = *m + 1;

/*        Compute A=L*Q   
          (Workspace: need 2*M, prefer M+M*NB) */

	    i__2 = *lwork - iwork + 1;
	    dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2,
		     info);
	    il = iwork;

/*        Copy L to WORK(IL), zeroing out above it */

	    dlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork);
	    i__2 = *m - 1;
	    i__1 = *m - 1;
	    dlaset_("U", &i__2, &i__1, &c_b74, &c_b74, &work[il + ldwork], &
		    ldwork);
	    ie = il + ldwork * *m;
	    itauq = ie + *m;
	    itaup = itauq + *m;
	    iwork = itaup + *m;

/*        Bidiagonalize L in WORK(IL)   
          (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */

	    i__2 = *lwork - iwork + 1;
	    dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], 
		    &work[itaup], &work[iwork], &i__2, info);

/*        Multiply B by transpose of left bidiagonalizing vectors of L   
          (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */

	    i__2 = *lwork - iwork + 1;
	    dormbr_("Q", "L", "T", m, nrhs, m, &work[il], &ldwork, &work[
		    itauq], &b[b_offset], ldb, &work[iwork], &i__2, info);

/*        Generate right bidiagonalizing vectors of R in WORK(IL)   
          (Workspace: need M*M+5*M-1, prefer M*M+4*M+(M-1)*NB) */

	    i__2 = *lwork - iwork + 1;
	    dorgbr_("P", m, m, m, &work[il], &ldwork, &work[itaup], &work[
		    iwork], &i__2, info);
	    iwork = ie + *m;

/*        Perform bidiagonal QR iteration,   
             computing right singular vectors of L in WORK(IL) and   
             multiplying B by transpose of left singular vectors   
          (Workspace: need M*M+M+BDSPAC) */

	    dbdsqr_("U", m, m, &c__0, nrhs, &s[1], &work[ie], &work[il], &
		    ldwork, &a[a_offset], lda, &b[b_offset], ldb, &work[iwork]
		    , info);
	    if (*info != 0) {
		goto L70;
	    }

/*        Multiply B by reciprocals of singular values   

   Computing MAX */
	    d__1 = *rcond * s[1];
	    thr = max(d__1,sfmin);
	    if (*rcond < 0.) {
/* Computing MAX */
		d__1 = eps * s[1];
		thr = max(d__1,sfmin);
	    }
	    *rank = 0;
	    i__2 = *m;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		if (s[i__] > thr) {
		    drscl_(nrhs, &s[i__], &b_ref(i__, 1), ldb);
		    ++(*rank);
		} else {
		    dlaset_("F", &c__1, nrhs, &c_b74, &c_b74, &b_ref(i__, 1), 
			    ldb);
		}
/* L30: */
	    }
	    iwork = ie;

/*        Multiply B by right singular vectors of L in WORK(IL)   
          (Workspace: need M*M+2*M, prefer M*M+M+M*NRHS) */

	    if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) {
		dgemm_("T", "N", m, nrhs, m, &c_b108, &work[il], &ldwork, &b[
			b_offset], ldb, &c_b74, &work[iwork], ldb);
		dlacpy_("G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb);
	    } else if (*nrhs > 1) {
		chunk = (*lwork - iwork + 1) / *m;
		i__2 = *nrhs;
		i__1 = chunk;
		for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += 
			i__1) {
/* Computing MIN */
		    i__3 = *nrhs - i__ + 1;
		    bl = min(i__3,chunk);
		    dgemm_("T", "N", m, &bl, m, &c_b108, &work[il], &ldwork, &
			    b_ref(1, i__), ldb, &c_b74, &work[iwork], n);
		    dlacpy_("G", m, &bl, &work[iwork], n, &b_ref(1, i__), ldb);
/* L40: */
		}
	    } else {
		dgemv_("T", m, m, &c_b108, &work[il], &ldwork, &b_ref(1, 1), &
			c__1, &c_b74, &work[iwork], &c__1);
		dcopy_(m, &work[iwork], &c__1, &b_ref(1, 1), &c__1);
	    }

/*        Zero out below first M rows of B */

	    i__1 = *n - *m;
	    dlaset_("F", &i__1, nrhs, &c_b74, &c_b74, &b_ref(*m + 1, 1), ldb);
	    iwork = itau + *m;

/*        Multiply transpose(Q) by B   
          (Workspace: need M+NRHS, prefer M+NRHS*NB) */

	    i__1 = *lwork - iwork + 1;
	    dormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[
		    b_offset], ldb, &work[iwork], &i__1, info);

	} else {

/*        Path 2 - remaining underdetermined cases */

	    ie = 1;
	    itauq = ie + *m;
	    itaup = itauq + *m;
	    iwork = itaup + *m;

/*        Bidiagonalize A   
          (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */

	    i__1 = *lwork - iwork + 1;
	    dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
		    work[itaup], &work[iwork], &i__1, info);

/*        Multiply B by transpose of left bidiagonalizing vectors   
          (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */

	    i__1 = *lwork - iwork + 1;
	    dormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, &work[itauq]
		    , &b[b_offset], ldb, &work[iwork], &i__1, info);

/*        Generate right bidiagonalizing vectors in A   
          (Workspace: need 4*M, prefer 3*M+M*NB) */

	    i__1 = *lwork - iwork + 1;
	    dorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
		    iwork], &i__1, info);
	    iwork = ie + *m;

/*        Perform bidiagonal QR iteration,   
             computing right singular vectors of A in A and   
             multiplying B by transpose of left singular vectors   
          (Workspace: need BDSPAC) */

	    dbdsqr_("L", m, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], 
		    lda, vdum, &c__1, &b[b_offset], ldb, &work[iwork], info);
	    if (*info != 0) {
		goto L70;
	    }

/*        Multiply B by reciprocals of singular values   

   Computing MAX */
	    d__1 = *rcond * s[1];
	    thr = max(d__1,sfmin);
	    if (*rcond < 0.) {
/* Computing MAX */
		d__1 = eps * s[1];
		thr = max(d__1,sfmin);
	    }
	    *rank = 0;
	    i__1 = *m;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		if (s[i__] > thr) {
		    drscl_(nrhs, &s[i__], &b_ref(i__, 1), ldb);
		    ++(*rank);
		} else {
		    dlaset_("F", &c__1, nrhs, &c_b74, &c_b74, &b_ref(i__, 1), 
			    ldb);
		}
/* L50: */
	    }

/*        Multiply B by right singular vectors of A   
          (Workspace: need N, prefer N*NRHS) */

	    if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
		dgemm_("T", "N", n, nrhs, m, &c_b108, &a[a_offset], lda, &b[
			b_offset], ldb, &c_b74, &work[1], ldb);
		dlacpy_("F", n, nrhs, &work[1], ldb, &b[b_offset], ldb);
	    } else if (*nrhs > 1) {
		chunk = *lwork / *n;
		i__1 = *nrhs;
		i__2 = chunk;
		for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += 
			i__2) {
/* Computing MIN */
		    i__3 = *nrhs - i__ + 1;
		    bl = min(i__3,chunk);
		    dgemm_("T", "N", n, &bl, m, &c_b108, &a[a_offset], lda, &
			    b_ref(1, i__), ldb, &c_b74, &work[1], n);
		    dlacpy_("F", n, &bl, &work[1], n, &b_ref(1, i__), ldb);
/* L60: */
		}
	    } else {
		dgemv_("T", m, n, &c_b108, &a[a_offset], lda, &b[b_offset], &
			c__1, &c_b74, &work[1], &c__1);
		dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
	    }
	}
    }

/*     Undo scaling */

    if (iascl == 1) {
	dlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
		 info);
	dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
		minmn, info);
    } else if (iascl == 2) {
	dlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
		 info);
	dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
		minmn, info);
    }
    if (ibscl == 1) {
	dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
		 info);
    } else if (ibscl == 2) {
	dlascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
		 info);
    }

L70:
    work[1] = (doublereal) maxwrk;
    return 0;

/*     End of DGELSS */

} /* dgelss_ */
Пример #8
0
/* Subroutine */ int dtimlq_(char *line, integer *nm, integer *mval, integer *
	nval, integer *nk, integer *kval, integer *nnb, integer *nbval, 
	integer *nxval, integer *nlda, integer *ldaval, doublereal *timmin, 
	doublereal *a, doublereal *tau, doublereal *b, doublereal *work, 
	doublereal *reslts, integer *ldr1, integer *ldr2, integer *ldr3, 
	integer *nout, ftnlen line_len)
{
    /* Initialized data */

    static char subnam[6*3] = "DGELQF" "DORGLQ" "DORMLQ";
    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 doublereal time;
    static integer isub, muse[12], nuse[12], i__, k, m, n;
    static char cname[6];
    static integer iside;
    extern doublereal dopla_(char *, integer *, integer *, integer *, integer 
	    *, integer *);
    static integer itoff, itran, minmn;
    extern /* Subroutine */ int icopy_(integer *, integer *, integer *, 
	    integer *, integer *);
    static char trans[1];
    static integer k1, i4, m1, n1;
    static doublereal s1, s2;
    extern /* Subroutine */ int dprtb4_(char *, char *, char *, integer *, 
	    integer *, integer *, integer *, integer *, integer *, integer *, 
	    doublereal *, integer *, integer *, integer *, ftnlen, ftnlen, 
	    ftnlen), dprtb5_(char *, char *, char *, integer *, integer *, 
	    integer *, integer *, integer *, integer *, doublereal *, integer 
	    *, integer *, integer *, ftnlen, ftnlen, ftnlen);
    static integer ic, nb, ik, im;
    extern doublereal dsecnd_(void);
    extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *, integer *);
    static integer lw, nx, reseed[4];
    extern /* Subroutine */ int atimck_(integer *, char *, integer *, integer 
	    *, integer *, integer *, integer *, integer *, ftnlen), dlacpy_(
	    char *, integer *, integer *, doublereal *, integer *, doublereal 
	    *, integer *);
    extern doublereal dmflop_(doublereal *, doublereal *, integer *);
    extern /* Subroutine */ int atimin_(char *, char *, integer *, char *, 
	    logical *, integer *, integer *, ftnlen, ftnlen, ftnlen), dtimmg_(
	    integer *, integer *, integer *, doublereal *, integer *, integer 
	    *, integer *), dlatms_(integer *, integer *, char *, integer *, 
	    char *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, integer *, char *, doublereal *, integer *, doublereal 
	    *, integer *), dorglq_(integer *, integer 
	    *, integer *, doublereal *, integer *, doublereal *, doublereal *,
	     integer *, integer *), dormlq_(char *, char *, integer *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *, integer *), xlaenv_(integer *, integer *);
    static doublereal untime;
    static logical timsub[3];
    static integer lda, icl, inb, imx;
    static doublereal 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   
    =======   

    DTIMLQ times the LAPACK routines to perform the LQ factorization of   
    a DOUBLE PRECISION 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 DORMLQ.   

    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) DOUBLE PRECISION array, dimension (LDAMAX*NMAX)   
            where LDAMAX and NMAX are the maximum values of LDA and N.   

    TAU     (workspace) DOUBLE PRECISION array, dimension (min(M,N))   

    B       (workspace) DOUBLE PRECISION array, dimension (LDAMAX*NMAX)   

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

    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 DLATMS 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.   

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

       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, "Double precision", (ftnlen)1, (ftnlen)16);
    s_copy(path + 1, "LQ", (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);
		dlatms_(&m, &n, "Uniform", iseed, "Nonsym", &tau[1], &c__3, &
			c_b24, &c_b25, &m, &n, "No packing", &b[1], &lda, &
			work[1], &info);

		if (timsub[0]) {

/*                 DGELQF:  LQ factorization */

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

/*                 Subtract the time used in DLACPY. */

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

		    time = (time - untime) / (doublereal) ic;
		    ops = dopla_("DGELQF", &m, &n, &c__0, &c__0, &nb);
		    reslts_ref(inb, im, ilda, 1) = dmflop_(&ops, &time, &info)
			    ;
		} else {

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

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

		if (timsub[1]) {

/*                 DORGLQ:  Generate orthogonal matrix Q from the LQ   
                   factorization */

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

/*                 Subtract the time used in DLACPY. */

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

		    time = (time - untime) / (doublereal) ic;
		    ops = dopla_("DORGLQ", &minmn, &n, &minmn, &c__0, &nb);
		    reslts_ref(inb, im, ilda, 2) = dmflop_(&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();
	}
	dprtb4_("(  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 DORMLQ 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: */
	}

/*        DORMLQ:  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 LQ decomposition. */

		dlatms_(&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);
		dgelqf_(&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];
				dtimmg_(&c__0, &m1, &n1, &b[1], &lda, &c__0, &
					c__0);
				ic = 0;
				s1 = dsecnd_();
L110:
				dormlq_(side, trans, &m1, &n1, &k1, &a[1], &
					lda, &tau[1], &b[1], &lda, &work[1], &
					lw, &info);
				s2 = dsecnd_();
				time = s2 - s1;
				++ic;
				if (time < *timmin) {
				    dtimmg_(&c__0, &m1, &n1, &b[1], &lda, &
					    c__0, &c__0);
				    goto L110;
				}

/*                          Subtract the time used in DTIMMG. */

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

				time = (time - untime) / (doublereal) ic;
				i__5 = iside - 1;
				ops = dopla_("DORMLQ", &m1, &n1, &k1, &i__5, &
					nb);
				reslts_ref(inb, im, ilda, i4 + itoff + ik) = 
					dmflop_(&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';
			}
			dprtb5_("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 DTIMLQ */

} /* dtimlq_ */
Пример #9
0
/* Subroutine */ int derrlq_(char *path, integer *nunit)
{
    /* Builtin functions */
    integer s_wsle(cilist *), e_wsle(void);
    /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);

    /* Local variables */
    static integer info;
    static doublereal a[4]	/* was [2][2] */, b[2];
    static integer i__, j;
    static doublereal w[2], x[2];
    extern /* Subroutine */ int dgelq2_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *), dorgl2_(
	    integer *, integer *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *), dorml2_(char *, char *, 
	    integer *, integer *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *);
    static doublereal af[4]	/* was [2][2] */;
    extern /* Subroutine */ int alaesm_(char *, logical *, integer *),
	     dgelqf_(integer *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *, integer *), dgelqs_(
	    integer *, integer *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    integer *), chkxer_(char *, integer *, integer *, logical *, 
	    logical *), dorglq_(integer *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
	    integer *), dormlq_(char *, char *, integer *, integer *, integer 
	    *, doublereal *, integer *, doublereal *, doublereal *, integer *,
	     doublereal *, integer *, integer *);

    /* Fortran I/O blocks */
    static cilist io___1 = { 0, 0, 0, 0, 0 };



#define a_ref(a_1,a_2) a[(a_2)*2 + a_1 - 3]
#define af_ref(a_1,a_2) af[(a_2)*2 + a_1 - 3]


/*  -- LAPACK test routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       February 29, 1992   


    Purpose   
    =======   

    DERRLQ tests the error exits for the DOUBLE PRECISION routines   
    that use the LQ decomposition of a general matrix.   

    Arguments   
    =========   

    PATH    (input) CHARACTER*3   
            The LAPACK path name for the routines to be tested.   

    NUNIT   (input) INTEGER   
            The unit number for output.   

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


    infoc_1.nout = *nunit;
    io___1.ciunit = infoc_1.nout;
    s_wsle(&io___1);
    e_wsle();

/*     Set the variables to innocuous values. */

    for (j = 1; j <= 2; ++j) {
	for (i__ = 1; i__ <= 2; ++i__) {
	    a_ref(i__, j) = 1. / (doublereal) (i__ + j);
	    af_ref(i__, j) = 1. / (doublereal) (i__ + j);
/* L10: */
	}
	b[j - 1] = 0.;
	w[j - 1] = 0.;
	x[j - 1] = 0.;
/* L20: */
    }
    infoc_1.ok = TRUE_;

/*     Error exits for LQ factorization   

       DGELQF */

    s_copy(srnamc_1.srnamt, "DGELQF", (ftnlen)6, (ftnlen)6);
    infoc_1.infot = 1;
    dgelqf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
    chkxer_("DGELQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 2;
    dgelqf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
    chkxer_("DGELQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 4;
    dgelqf_(&c__2, &c__1, a, &c__1, b, w, &c__2, &info);
    chkxer_("DGELQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 7;
    dgelqf_(&c__2, &c__1, a, &c__2, b, w, &c__1, &info);
    chkxer_("DGELQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);

/*     DGELQ2 */

    s_copy(srnamc_1.srnamt, "DGELQ2", (ftnlen)6, (ftnlen)6);
    infoc_1.infot = 1;
    dgelq2_(&c_n1, &c__0, a, &c__1, b, w, &info);
    chkxer_("DGELQ2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 2;
    dgelq2_(&c__0, &c_n1, a, &c__1, b, w, &info);
    chkxer_("DGELQ2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 4;
    dgelq2_(&c__2, &c__1, a, &c__1, b, w, &info);
    chkxer_("DGELQ2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);

/*     DGELQS */

    s_copy(srnamc_1.srnamt, "DGELQS", (ftnlen)6, (ftnlen)6);
    infoc_1.infot = 1;
    dgelqs_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
    chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 2;
    dgelqs_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
    chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 2;
    dgelqs_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
    chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 3;
    dgelqs_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
    chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 5;
    dgelqs_(&c__2, &c__2, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
    chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 8;
    dgelqs_(&c__1, &c__2, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
    chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 10;
    dgelqs_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
    chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);

/*     DORGLQ */

    s_copy(srnamc_1.srnamt, "DORGLQ", (ftnlen)6, (ftnlen)6);
    infoc_1.infot = 1;
    dorglq_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
    chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 2;
    dorglq_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
    chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 2;
    dorglq_(&c__2, &c__1, &c__0, a, &c__2, x, w, &c__2, &info);
    chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 3;
    dorglq_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
    chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 3;
    dorglq_(&c__1, &c__1, &c__2, a, &c__1, x, w, &c__1, &info);
    chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 5;
    dorglq_(&c__2, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
    chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 8;
    dorglq_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
    chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);

/*     DORGL2 */

    s_copy(srnamc_1.srnamt, "DORGL2", (ftnlen)6, (ftnlen)6);
    infoc_1.infot = 1;
    dorgl2_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
    chkxer_("DORGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 2;
    dorgl2_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
    chkxer_("DORGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 2;
    dorgl2_(&c__2, &c__1, &c__0, a, &c__2, x, w, &info);
    chkxer_("DORGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 3;
    dorgl2_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
    chkxer_("DORGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 3;
    dorgl2_(&c__1, &c__1, &c__2, a, &c__1, x, w, &info);
    chkxer_("DORGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 5;
    dorgl2_(&c__2, &c__2, &c__0, a, &c__1, x, w, &info);
    chkxer_("DORGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);

/*     DORMLQ */

    s_copy(srnamc_1.srnamt, "DORMLQ", (ftnlen)6, (ftnlen)6);
    infoc_1.infot = 1;
    dormlq_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
	    info);
    chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 2;
    dormlq_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
	    info);
    chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 3;
    dormlq_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
	    info);
    chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 4;
    dormlq_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
	    info);
    chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 5;
    dormlq_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
	    info);
    chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 5;
    dormlq_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
	    info);
    chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 5;
    dormlq_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
	    info);
    chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 7;
    dormlq_("L", "N", &c__2, &c__0, &c__2, a, &c__1, x, af, &c__2, w, &c__1, &
	    info);
    chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 7;
    dormlq_("R", "N", &c__0, &c__2, &c__2, a, &c__1, x, af, &c__1, w, &c__1, &
	    info);
    chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 10;
    dormlq_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &c__1, &
	    info);
    chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 12;
    dormlq_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
	    info);
    chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 12;
    dormlq_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
	    info);
    chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);

/*     DORML2 */

    s_copy(srnamc_1.srnamt, "DORML2", (ftnlen)6, (ftnlen)6);
    infoc_1.infot = 1;
    dorml2_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
    chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 2;
    dorml2_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
    chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 3;
    dorml2_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
    chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 4;
    dorml2_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
    chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 5;
    dorml2_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
    chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 5;
    dorml2_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
    chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 5;
    dorml2_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
    chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 7;
    dorml2_("L", "N", &c__2, &c__1, &c__2, a, &c__1, x, af, &c__2, w, &info);
    chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 7;
    dorml2_("R", "N", &c__1, &c__2, &c__2, a, &c__1, x, af, &c__1, w, &info);
    chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);
    infoc_1.infot = 10;
    dorml2_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &info);
    chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
	    infoc_1.ok);

/*     Print a summary line. */

    alaesm_(path, &infoc_1.ok, &infoc_1.nout);

    return 0;

/*     End of DERRLQ */

} /* derrlq_ */