text: #include "f2c.h"
  #include "blaswrap.h"
  
  /* Table of constant values */
  
  static integer c__1 = 1;
  static integer c_n1 = -1;
  static integer c__3 = 3;
  static integer c__2 = 2;
  static doublereal c_b21 = -1.;
  static doublereal c_b22 = 1.;
  
  /* Subroutine */ int dgebrd_(integer *m, integer *n, doublereal *a, integer *
  	lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal *
  	taup, doublereal *work, integer *lwork, integer *info)
  {
      /* System generated locals */
      integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
  
      /* Local variables */
      integer i__, j, nb, nx;
      doublereal ws;
      extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
  	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
  	    integer *, doublereal *, doublereal *, integer *);
      integer nbmin, iinfo, minmn;
      extern /* Subroutine */ int dgebd2_(integer *, integer *, doublereal *, 
  	    integer *, doublereal *, doublereal *, doublereal *, doublereal *, 
  	     doublereal *, integer *), dlabrd_(integer *, integer *, integer *
  , doublereal *, integer *, doublereal *, doublereal *, doublereal 
  	    *, doublereal *, doublereal *, integer *, doublereal *, integer *)
  	    , xerbla_(char *, integer *);
      extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
  	    integer *, integer *);
      integer ldwrkx, ldwrky, lwkopt;
      logical lquery;
  
  
  /*  -- LAPACK routine (version 3.1) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  DGEBRD reduces a general real M-by-N matrix A to upper or lower */
  /*  bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. */
  
  /*  If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  M       (input) INTEGER */
  /*          The number of rows in the matrix A.  M >= 0. */
  
  /*  N       (input) INTEGER */
  /*          The number of columns in the matrix A.  N >= 0. */
  
  /*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
  /*          On entry, the M-by-N general matrix to be reduced. */
  /*          On exit, */
  /*          if m >= n, the diagonal and the first superdiagonal are */
  /*            overwritten with the upper bidiagonal matrix B; the */
  /*            elements below the diagonal, with the array TAUQ, represent */
  /*            the orthogonal matrix Q as a product of elementary */
  /*            reflectors, and the elements above the first superdiagonal, */
  /*            with the array TAUP, represent the orthogonal matrix P as */
  /*            a product of elementary reflectors; */
  /*          if m < n, the diagonal and the first subdiagonal are */
  /*            overwritten with the lower bidiagonal matrix B; the */
  /*            elements below the first subdiagonal, with the array TAUQ, */
  /*            represent the orthogonal matrix Q as a product of */
  /*            elementary reflectors, and the elements above the diagonal, */
  /*            with the array TAUP, represent the orthogonal matrix P as */
  /*            a product of elementary reflectors. */
  /*          See Further Details. */
  
  /*  LDA     (input) INTEGER */
  /*          The leading dimension of the array A.  LDA >= max(1,M). */
  
  /*  D       (output) DOUBLE PRECISION array, dimension (min(M,N)) */
  /*          The diagonal elements of the bidiagonal matrix B: */
  /*          D(i) = A(i,i). */
  
  /*  E       (output) DOUBLE PRECISION array, dimension (min(M,N)-1) */
  /*          The off-diagonal elements of the bidiagonal matrix B: */
  /*          if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */
  /*          if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */
  
  /*  TAUQ    (output) DOUBLE PRECISION array dimension (min(M,N)) */
  /*          The scalar factors of the elementary reflectors which */
  /*          represent the orthogonal matrix Q. See Further Details. */
  
  /*  TAUP    (output) DOUBLE PRECISION array, dimension (min(M,N)) */
  /*          The scalar factors of the elementary reflectors which */
  /*          represent the orthogonal matrix P. See Further Details. */
  
  /*  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 length of the array WORK.  LWORK >= max(1,M,N). */
  /*          For optimum performance LWORK >= (M+N)*NB, 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. */
  
  /*  Further Details */
  /*  =============== */
  
  /*  The matrices Q and P are represented as products of elementary */
  /*  reflectors: */
  
  /*  If m >= n, */
  
  /*     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1) */
  
  /*  Each H(i) and G(i) has the form: */
  
  /*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u' */
  
  /*  where tauq and taup are real scalars, and v and u are real vectors; */
  /*  v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); */
  /*  u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); */
  /*  tauq is stored in TAUQ(i) and taup in TAUP(i). */
  
  /*  If m < n, */
  
  /*     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m) */
  
  /*  Each H(i) and G(i) has the form: */
  
  /*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u' */
  
  /*  where tauq and taup are real scalars, and v and u are real vectors; */
  /*  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */
  /*  u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */
  /*  tauq is stored in TAUQ(i) and taup in TAUP(i). */
  
  /*  The contents of A on exit are illustrated by the following examples: */
  
  /*  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n): */
  
  /*    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 ) */
  /*    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 ) */
  /*    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 ) */
  /*    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 ) */
  /*    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 ) */
  /*    (  v1  v2  v3  v4  v5 ) */
  
  /*  where d and e denote diagonal and off-diagonal elements of B, vi */
  /*  denotes an element of the vector defining H(i), and ui an element of */
  /*  the vector defining G(i). */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Test the input parameters */
  
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1;
      a -= a_offset;
      --d__;
      --e;
      --tauq;
      --taup;
      --work;
  
      /* Function Body */
      *info = 0;
  /* Computing MAX */
      i__1 = 1, i__2 = ilaenv_(&c__1, "DGEBRD", " ", m, n, &c_n1, &c_n1);
      nb = max(i__1,i__2);
      lwkopt = (*m + *n) * nb;
      work[1] = (doublereal) lwkopt;
      lquery = *lwork == -1;
      if (*m < 0) {
  	*info = -1;
      } else if (*n < 0) {
  	*info = -2;
      } else if (*lda < max(1,*m)) {
  	*info = -4;
      } else /* if(complicated condition) */ {
  /* Computing MAX */
  	i__1 = max(1,*m);
  	if (*lwork < max(i__1,*n) && ! lquery) {
  	    *info = -10;
  	}
      }
      if (*info < 0) {
  	i__1 = -(*info);
  	xerbla_("DGEBRD", &i__1);
  	return 0;
      } else if (lquery) {
  	return 0;
      }
  
  /*     Quick return if possible */
  
      minmn = min(*m,*n);
      if (minmn == 0) {
  	work[1] = 1.;
  	return 0;
      }
  
      ws = (doublereal) max(*m,*n);
      ldwrkx = *m;
      ldwrky = *n;
  
      if (nb > 1 && nb < minmn) {
  
  /*        Set the crossover point NX. */
  
  /* Computing MAX */
  	i__1 = nb, i__2 = ilaenv_(&c__3, "DGEBRD", " ", m, n, &c_n1, &c_n1);
  	nx = max(i__1,i__2);
  
  /*        Determine when to switch from blocked to unblocked code. */
  
  	if (nx < minmn) {
  	    ws = (doublereal) ((*m + *n) * nb);
  	    if ((doublereal) (*lwork) < ws) {
  
  /*              Not enough work space for the optimal NB, consider using */
  /*              a smaller block size. */
  
  		nbmin = ilaenv_(&c__2, "DGEBRD", " ", m, n, &c_n1, &c_n1);
  		if (*lwork >= (*m + *n) * nbmin) {
  		    nb = *lwork / (*m + *n);
  		} else {
  		    nb = 1;
  		    nx = minmn;
  		}
  	    }
  	}
      } else {
  	nx = minmn;
      }
  
      i__1 = minmn - nx;
      i__2 = nb;
      for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
  
  /*        Reduce rows and columns i:i+nb-1 to bidiagonal form and return */
  /*        the matrices X and Y which are needed to update the unreduced */
  /*        part of the matrix */
  
  	i__3 = *m - i__ + 1;
  	i__4 = *n - i__ + 1;
  	dlabrd_(&i__3, &i__4, &nb, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[
  		i__], &tauq[i__], &taup[i__], &work[1], &ldwrkx, &work[ldwrkx 
  		* nb + 1], &ldwrky);
  
  /*        Update the trailing submatrix A(i+nb:m,i+nb:n), using an update */
  /*        of the form  A := A - V*Y' - X*U' */
  
  	i__3 = *m - i__ - nb + 1;
  	i__4 = *n - i__ - nb + 1;
  	dgemm_("No transpose", "Transpose", &i__3, &i__4, &nb, &c_b21, &a[i__ 
  		+ nb + i__ * a_dim1], lda, &work[ldwrkx * nb + nb + 1], &
  		ldwrky, &c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda);
  	i__3 = *m - i__ - nb + 1;
  	i__4 = *n - i__ - nb + 1;
  	dgemm_("No transpose", "No transpose", &i__3, &i__4, &nb, &c_b21, &
  		work[nb + 1], &ldwrkx, &a[i__ + (i__ + nb) * a_dim1], lda, &
  		c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda);
  
  /*        Copy diagonal and off-diagonal elements of B back into A */
  
  	if (*m >= *n) {
  	    i__3 = i__ + nb - 1;
  	    for (j = i__; j <= i__3; ++j) {
  		a[j + j * a_dim1] = d__[j];
  		a[j + (j + 1) * a_dim1] = e[j];
  /* L10: */
  	    }
  	} else {
  	    i__3 = i__ + nb - 1;
  	    for (j = i__; j <= i__3; ++j) {
  		a[j + j * a_dim1] = d__[j];
  		a[j + 1 + j * a_dim1] = e[j];
  /* L20: */
  	    }
  	}
  /* L30: */
      }
  
  /*     Use unblocked code to reduce the remainder of the matrix */
  
      i__2 = *m - i__ + 1;
      i__1 = *n - i__ + 1;
      dgebd2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], &
  	    tauq[i__], &taup[i__], &work[1], &iinfo);
      work[1] = ws;
      return 0;
  
  /*     End of DGEBRD */
  
  } /* dgebrd_ */
  