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

/* Subroutine */ int dlabrd_(integer *m, integer *n, integer *nb, doublereal *
	a, integer *lda, doublereal *d__, doublereal *e, doublereal *tauq, 
	doublereal *taup, doublereal *x, integer *ldx, doublereal *y, integer 
	*ldy)
{
/*  -- LAPACK auxiliary 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   
    =======   

    DLABRD reduces the first NB rows and columns of a real general   
    m by n matrix A to upper or lower bidiagonal form by an orthogonal   
    transformation Q' * A * P, and returns the matrices X and Y which   
    are needed to apply the transformation to the unreduced part of A.   

    If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower   
    bidiagonal form.   

    This is an auxiliary routine called by DGEBRD   

    Arguments   
    =========   

    M       (input) INTEGER   
            The number of rows in the matrix A.   

    N       (input) INTEGER   
            The number of columns in the matrix A.   

    NB      (input) INTEGER   
            The number of leading rows and columns of A to be reduced.   

    A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)   
            On entry, the m by n general matrix to be reduced.   
            On exit, the first NB rows and columns of the matrix are   
            overwritten; the rest of the array is unchanged.   
            If m >= n, elements on and below the diagonal in the first NB   
              columns, with the array TAUQ, represent the orthogonal   
              matrix Q as a product of elementary reflectors; and   
              elements above the diagonal in the first NB rows, with the   
              array TAUP, represent the orthogonal matrix P as a product   
              of elementary reflectors.   
            If m < n, elements below the diagonal in the first NB   
              columns, with the array TAUQ, represent the orthogonal   
              matrix Q as a product of elementary reflectors, and   
              elements on and above the diagonal in the first NB rows,   
              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 (NB)   
            The diagonal elements of the first NB rows and columns of   
            the reduced matrix.  D(i) = A(i,i).   

    E       (output) DOUBLE PRECISION array, dimension (NB)   
            The off-diagonal elements of the first NB rows and columns of   
            the reduced matrix.   

    TAUQ    (output) DOUBLE PRECISION array dimension (NB)   
            The scalar factors of the elementary reflectors which   
            represent the orthogonal matrix Q. See Further Details.   

    TAUP    (output) DOUBLE PRECISION array, dimension (NB)   
            The scalar factors of the elementary reflectors which   
            represent the orthogonal matrix P. See Further Details.   

    X       (output) DOUBLE PRECISION array, dimension (LDX,NB)   
            The m-by-nb matrix X required to update the unreduced part   
            of A.   

    LDX     (input) INTEGER   
            The leading dimension of the array X. LDX >= M.   

    Y       (output) DOUBLE PRECISION array, dimension (LDY,NB)   
            The n-by-nb matrix Y required to update the unreduced part   
            of A.   

    LDY     (output) INTEGER   
            The leading dimension of the array Y. LDY >= N.   

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

    The matrices Q and P are represented as products of elementary   
    reflectors:   

       Q = H(1) H(2) . . . H(nb)  and  P = G(1) G(2) . . . G(nb)   

    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.   

    If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in   
    A(i:m,i); u(1:i) = 0, u(i+1) = 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).   

    If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in   
    A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in   
    A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).   

    The elements of the vectors v and u together form the m-by-nb matrix   
    V and the nb-by-n matrix U' which are needed, with X and Y, to apply   
    the transformation to the unreduced part of the matrix, using a block   
    update of the form:  A := A - V*Y' - X*U'.   

    The contents of A on exit are illustrated by the following examples   
    with nb = 2:   

    m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):   

      (  1   1   u1  u1  u1 )           (  1   u1  u1  u1  u1  u1 )   
      (  v1  1   1   u2  u2 )           (  1   1   u2  u2  u2  u2 )   
      (  v1  v2  a   a   a  )           (  v1  1   a   a   a   a  )   
      (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  )   
      (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  )   
      (  v1  v2  a   a   a  )   

    where a denotes an element of the original matrix which is unchanged,   
    vi denotes an element of the vector defining H(i), and ui an element   
    of the vector defining G(i).   

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


       Quick return if possible   

       Parameter adjustments */
    /* Table of constant values */
    static doublereal c_b4 = -1.;
    static doublereal c_b5 = 1.;
    static integer c__1 = 1;
    static doublereal c_b16 = 0.;
    
    /* System generated locals */
    integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2, 
	    i__3;
    /* Local variables */
    static integer i__;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
	    integer *), dgemv_(char *, integer *, integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
	    doublereal *, integer *), dlarfg_(integer *, doublereal *,
	     doublereal *, integer *, doublereal *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define x_ref(a_1,a_2) x[(a_2)*x_dim1 + a_1]
#define y_ref(a_1,a_2) y[(a_2)*y_dim1 + a_1]


    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --d__;
    --e;
    --tauq;
    --taup;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1 * 1;
    x -= x_offset;
    y_dim1 = *ldy;
    y_offset = 1 + y_dim1 * 1;
    y -= y_offset;

    /* Function Body */
    if (*m <= 0 || *n <= 0) {
	return 0;
    }

    if (*m >= *n) {

/*        Reduce to upper bidiagonal form */

	i__1 = *nb;
	for (i__ = 1; i__ <= i__1; ++i__) {

/*           Update A(i:m,i) */

	    i__2 = *m - i__ + 1;
	    i__3 = i__ - 1;
	    dgemv_("No transpose", &i__2, &i__3, &c_b4, &a_ref(i__, 1), lda, &
		    y_ref(i__, 1), ldy, &c_b5, &a_ref(i__, i__), &c__1);
	    i__2 = *m - i__ + 1;
	    i__3 = i__ - 1;
	    dgemv_("No transpose", &i__2, &i__3, &c_b4, &x_ref(i__, 1), ldx, &
		    a_ref(1, i__), &c__1, &c_b5, &a_ref(i__, i__), &c__1);

/*           Generate reflection Q(i) to annihilate A(i+1:m,i)   

   Computing MIN */
	    i__2 = i__ + 1;
	    i__3 = *m - i__ + 1;
	    dlarfg_(&i__3, &a_ref(i__, i__), &a_ref(min(i__2,*m), i__), &c__1,
		     &tauq[i__]);
	    d__[i__] = a_ref(i__, i__);
	    if (i__ < *n) {
		a_ref(i__, i__) = 1.;

/*              Compute Y(i+1:n,i) */

		i__2 = *m - i__ + 1;
		i__3 = *n - i__;
		dgemv_("Transpose", &i__2, &i__3, &c_b5, &a_ref(i__, i__ + 1),
			 lda, &a_ref(i__, i__), &c__1, &c_b16, &y_ref(i__ + 1,
			 i__), &c__1);
		i__2 = *m - i__ + 1;
		i__3 = i__ - 1;
		dgemv_("Transpose", &i__2, &i__3, &c_b5, &a_ref(i__, 1), lda, 
			&a_ref(i__, i__), &c__1, &c_b16, &y_ref(1, i__), &
			c__1);
		i__2 = *n - i__;
		i__3 = i__ - 1;
		dgemv_("No transpose", &i__2, &i__3, &c_b4, &y_ref(i__ + 1, 1)
			, ldy, &y_ref(1, i__), &c__1, &c_b5, &y_ref(i__ + 1, 
			i__), &c__1);
		i__2 = *m - i__ + 1;
		i__3 = i__ - 1;
		dgemv_("Transpose", &i__2, &i__3, &c_b5, &x_ref(i__, 1), ldx, 
			&a_ref(i__, i__), &c__1, &c_b16, &y_ref(1, i__), &
			c__1);
		i__2 = i__ - 1;
		i__3 = *n - i__;
		dgemv_("Transpose", &i__2, &i__3, &c_b4, &a_ref(1, i__ + 1), 
			lda, &y_ref(1, i__), &c__1, &c_b5, &y_ref(i__ + 1, 
			i__), &c__1);
		i__2 = *n - i__;
		dscal_(&i__2, &tauq[i__], &y_ref(i__ + 1, i__), &c__1);

/*              Update A(i,i+1:n) */

		i__2 = *n - i__;
		dgemv_("No transpose", &i__2, &i__, &c_b4, &y_ref(i__ + 1, 1),
			 ldy, &a_ref(i__, 1), lda, &c_b5, &a_ref(i__, i__ + 1)
			, lda);
		i__2 = i__ - 1;
		i__3 = *n - i__;
		dgemv_("Transpose", &i__2, &i__3, &c_b4, &a_ref(1, i__ + 1), 
			lda, &x_ref(i__, 1), ldx, &c_b5, &a_ref(i__, i__ + 1),
			 lda);

/*              Generate reflection P(i) to annihilate A(i,i+2:n)   

   Computing MIN */
		i__2 = i__ + 2;
		i__3 = *n - i__;
		dlarfg_(&i__3, &a_ref(i__, i__ + 1), &a_ref(i__, min(i__2,*n))
			, lda, &taup[i__]);
		e[i__] = a_ref(i__, i__ + 1);
		a_ref(i__, i__ + 1) = 1.;

/*              Compute X(i+1:m,i) */

		i__2 = *m - i__;
		i__3 = *n - i__;
		dgemv_("No transpose", &i__2, &i__3, &c_b5, &a_ref(i__ + 1, 
			i__ + 1), lda, &a_ref(i__, i__ + 1), lda, &c_b16, &
			x_ref(i__ + 1, i__), &c__1);
		i__2 = *n - i__;
		dgemv_("Transpose", &i__2, &i__, &c_b5, &y_ref(i__ + 1, 1), 
			ldy, &a_ref(i__, i__ + 1), lda, &c_b16, &x_ref(1, i__)
			, &c__1);
		i__2 = *m - i__;
		dgemv_("No transpose", &i__2, &i__, &c_b4, &a_ref(i__ + 1, 1),
			 lda, &x_ref(1, i__), &c__1, &c_b5, &x_ref(i__ + 1, 
			i__), &c__1);
		i__2 = i__ - 1;
		i__3 = *n - i__;
		dgemv_("No transpose", &i__2, &i__3, &c_b5, &a_ref(1, i__ + 1)
			, lda, &a_ref(i__, i__ + 1), lda, &c_b16, &x_ref(1, 
			i__), &c__1);
		i__2 = *m - i__;
		i__3 = i__ - 1;
		dgemv_("No transpose", &i__2, &i__3, &c_b4, &x_ref(i__ + 1, 1)
			, ldx, &x_ref(1, i__), &c__1, &c_b5, &x_ref(i__ + 1, 
			i__), &c__1);
		i__2 = *m - i__;
		dscal_(&i__2, &taup[i__], &x_ref(i__ + 1, i__), &c__1);
	    }
/* L10: */
	}
    } else {

/*        Reduce to lower bidiagonal form */

	i__1 = *nb;
	for (i__ = 1; i__ <= i__1; ++i__) {

/*           Update A(i,i:n) */

	    i__2 = *n - i__ + 1;
	    i__3 = i__ - 1;
	    dgemv_("No transpose", &i__2, &i__3, &c_b4, &y_ref(i__, 1), ldy, &
		    a_ref(i__, 1), lda, &c_b5, &a_ref(i__, i__), lda);
	    i__2 = i__ - 1;
	    i__3 = *n - i__ + 1;
	    dgemv_("Transpose", &i__2, &i__3, &c_b4, &a_ref(1, i__), lda, &
		    x_ref(i__, 1), ldx, &c_b5, &a_ref(i__, i__), lda);

/*           Generate reflection P(i) to annihilate A(i,i+1:n)   

   Computing MIN */
	    i__2 = i__ + 1;
	    i__3 = *n - i__ + 1;
	    dlarfg_(&i__3, &a_ref(i__, i__), &a_ref(i__, min(i__2,*n)), lda, &
		    taup[i__]);
	    d__[i__] = a_ref(i__, i__);
	    if (i__ < *m) {
		a_ref(i__, i__) = 1.;

/*              Compute X(i+1:m,i) */

		i__2 = *m - i__;
		i__3 = *n - i__ + 1;
		dgemv_("No transpose", &i__2, &i__3, &c_b5, &a_ref(i__ + 1, 
			i__), lda, &a_ref(i__, i__), lda, &c_b16, &x_ref(i__ 
			+ 1, i__), &c__1);
		i__2 = *n - i__ + 1;
		i__3 = i__ - 1;
		dgemv_("Transpose", &i__2, &i__3, &c_b5, &y_ref(i__, 1), ldy, 
			&a_ref(i__, i__), lda, &c_b16, &x_ref(1, i__), &c__1);
		i__2 = *m - i__;
		i__3 = i__ - 1;
		dgemv_("No transpose", &i__2, &i__3, &c_b4, &a_ref(i__ + 1, 1)
			, lda, &x_ref(1, i__), &c__1, &c_b5, &x_ref(i__ + 1, 
			i__), &c__1);
		i__2 = i__ - 1;
		i__3 = *n - i__ + 1;
		dgemv_("No transpose", &i__2, &i__3, &c_b5, &a_ref(1, i__), 
			lda, &a_ref(i__, i__), lda, &c_b16, &x_ref(1, i__), &
			c__1);
		i__2 = *m - i__;
		i__3 = i__ - 1;
		dgemv_("No transpose", &i__2, &i__3, &c_b4, &x_ref(i__ + 1, 1)
			, ldx, &x_ref(1, i__), &c__1, &c_b5, &x_ref(i__ + 1, 
			i__), &c__1);
		i__2 = *m - i__;
		dscal_(&i__2, &taup[i__], &x_ref(i__ + 1, i__), &c__1);

/*              Update A(i+1:m,i) */

		i__2 = *m - i__;
		i__3 = i__ - 1;
		dgemv_("No transpose", &i__2, &i__3, &c_b4, &a_ref(i__ + 1, 1)
			, lda, &y_ref(i__, 1), ldy, &c_b5, &a_ref(i__ + 1, 
			i__), &c__1);
		i__2 = *m - i__;
		dgemv_("No transpose", &i__2, &i__, &c_b4, &x_ref(i__ + 1, 1),
			 ldx, &a_ref(1, i__), &c__1, &c_b5, &a_ref(i__ + 1, 
			i__), &c__1);

/*              Generate reflection Q(i) to annihilate A(i+2:m,i)   

   Computing MIN */
		i__2 = i__ + 2;
		i__3 = *m - i__;
		dlarfg_(&i__3, &a_ref(i__ + 1, i__), &a_ref(min(i__2,*m), i__)
			, &c__1, &tauq[i__]);
		e[i__] = a_ref(i__ + 1, i__);
		a_ref(i__ + 1, i__) = 1.;

/*              Compute Y(i+1:n,i) */

		i__2 = *m - i__;
		i__3 = *n - i__;
		dgemv_("Transpose", &i__2, &i__3, &c_b5, &a_ref(i__ + 1, i__ 
			+ 1), lda, &a_ref(i__ + 1, i__), &c__1, &c_b16, &
			y_ref(i__ + 1, i__), &c__1);
		i__2 = *m - i__;
		i__3 = i__ - 1;
		dgemv_("Transpose", &i__2, &i__3, &c_b5, &a_ref(i__ + 1, 1), 
			lda, &a_ref(i__ + 1, i__), &c__1, &c_b16, &y_ref(1, 
			i__), &c__1);
		i__2 = *n - i__;
		i__3 = i__ - 1;
		dgemv_("No transpose", &i__2, &i__3, &c_b4, &y_ref(i__ + 1, 1)
			, ldy, &y_ref(1, i__), &c__1, &c_b5, &y_ref(i__ + 1, 
			i__), &c__1);
		i__2 = *m - i__;
		dgemv_("Transpose", &i__2, &i__, &c_b5, &x_ref(i__ + 1, 1), 
			ldx, &a_ref(i__ + 1, i__), &c__1, &c_b16, &y_ref(1, 
			i__), &c__1);
		i__2 = *n - i__;
		dgemv_("Transpose", &i__, &i__2, &c_b4, &a_ref(1, i__ + 1), 
			lda, &y_ref(1, i__), &c__1, &c_b5, &y_ref(i__ + 1, 
			i__), &c__1);
		i__2 = *n - i__;
		dscal_(&i__2, &tauq[i__], &y_ref(i__ + 1, i__), &c__1);
	    }
/* L20: */
	}
    }
    return 0;

/*     End of DLABRD */

} /* dlabrd_ */

#undef y_ref
#undef x_ref
#undef a_ref


