/* Copyright (c) 1992-2008 The University of Tennessee.  All rights reserved.
 * See file COPYING in this directory for details. */

#ifdef __cplusplus
extern "C" {
#endif

#include "f2c.h"
#include "hypre_lapack.h"

/* Subroutine */ integer 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 */
    doublereal c_b4 = -1.;
    doublereal c_b5 = 1.;
    integer c__1 = 1;
    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 */
     integer i__;
    extern /* Subroutine */ integer dscal_(integer *, doublereal *, doublereal *,
	    integer *), dgemv_(const 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

#ifdef __cplusplus
}
#endif
