#include "blaswrap.h"
#include "f2c.h"

/* 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)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    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 (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).   

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


       Test the input parameters   

       Parameter adjustments */
    /* 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.;
    
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
    /* Local variables */
    static integer i__, j;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *);
    static integer nbmin, iinfo, minmn;
    extern /* Subroutine */ int dgebd2_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, doublereal *, doublereal *,
	     doublereal *, integer *);
    static integer nb;
    extern /* Subroutine */ int dlabrd_(integer *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, doublereal *,
	     doublereal *, doublereal *, integer *, doublereal *, integer *);
    static integer nx;
    static doublereal ws;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    static integer ldwrkx, ldwrky, lwkopt;
    static logical lquery;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]


    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    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, (
	    ftnlen)6, (ftnlen)1);
    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, (
		ftnlen)6, (ftnlen)1);
	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, (
			ftnlen)6, (ftnlen)1);
		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_ref(i__, i__), 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_ref(
		i__ + nb, i__), lda, &work[ldwrkx * nb + nb + 1], &ldwrky, &
		c_b22, &a_ref(i__ + nb, i__ + nb), 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_ref(i__, i__ + nb), lda, &c_b22, &
		a_ref(i__ + nb, i__ + nb), 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_ref(j, j) = d__[j];
		a_ref(j, j + 1) = e[j];
/* L10: */
	    }
	} else {
	    i__3 = i__ + nb - 1;
	    for (j = i__; j <= i__3; ++j) {
		a_ref(j, j) = d__[j];
		a_ref(j + 1, j) = 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_ref(i__, i__), lda, &d__[i__], &e[i__], &tauq[
	    i__], &taup[i__], &work[1], &iinfo);
    work[1] = ws;
    return 0;

/*     End of DGEBRD */

} /* dgebrd_ */

#undef a_ref


