--- rpl/lapack/lapack/dlabrd.f	2011/07/22 07:38:06	1.8
+++ rpl/lapack/lapack/dlabrd.f	2011/11/21 20:42:54	1.9
@@ -1,10 +1,219 @@
+*> \brief \b DLABRD
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLABRD + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlabrd.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlabrd.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlabrd.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y,
+*                          LDY )
+* 
+*       .. Scalar Arguments ..
+*       INTEGER            LDA, LDX, LDY, M, N, NB
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   A( LDA, * ), D( * ), E( * ), TAUP( * ),
+*      $                   TAUQ( * ), X( LDX, * ), Y( LDY, * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> 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**T * 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
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>          The number of rows in the matrix A.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of columns in the matrix A.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*>          NB is INTEGER
+*>          The number of leading rows and columns of A to be reduced.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is 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.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] D
+*> \verbatim
+*>          D is DOUBLE PRECISION array, dimension (NB)
+*>          The diagonal elements of the first NB rows and columns of
+*>          the reduced matrix.  D(i) = A(i,i).
+*> \endverbatim
+*>
+*> \param[out] E
+*> \verbatim
+*>          E is DOUBLE PRECISION array, dimension (NB)
+*>          The off-diagonal elements of the first NB rows and columns of
+*>          the reduced matrix.
+*> \endverbatim
+*>
+*> \param[out] TAUQ
+*> \verbatim
+*>          TAUQ is DOUBLE PRECISION array dimension (NB)
+*>          The scalar factors of the elementary reflectors which
+*>          represent the orthogonal matrix Q. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] TAUP
+*> \verbatim
+*>          TAUP is DOUBLE PRECISION array, dimension (NB)
+*>          The scalar factors of the elementary reflectors which
+*>          represent the orthogonal matrix P. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*>          X is DOUBLE PRECISION array, dimension (LDX,NB)
+*>          The m-by-nb matrix X required to update the unreduced part
+*>          of A.
+*> \endverbatim
+*>
+*> \param[in] LDX
+*> \verbatim
+*>          LDX is INTEGER
+*>          The leading dimension of the array X. LDX >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] Y
+*> \verbatim
+*>          Y is DOUBLE PRECISION array, dimension (LDY,NB)
+*>          The n-by-nb matrix Y required to update the unreduced part
+*>          of A.
+*> \endverbatim
+*>
+*> \param[in] LDY
+*> \verbatim
+*>          LDY is INTEGER
+*>          The leading dimension of the array Y. LDY >= max(1,N).
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup doubleOTHERauxiliary
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  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**T  and G(i) = I - taup * u * u**T
+*>
+*>  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**T 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**T - X*U**T.
+*>
+*>  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).
+*> \endverbatim
+*>
+*  =====================================================================
       SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y,
      $                   LDY )
 *
-*  -- LAPACK auxiliary routine (version 3.3.1) --
+*  -- LAPACK auxiliary routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*  -- April 2011                                                      --
+*     November 2011
 *
 *     .. Scalar Arguments ..
       INTEGER            LDA, LDX, LDY, M, N, NB
@@ -14,125 +223,6 @@
      $                   TAUQ( * ), X( LDX, * ), Y( LDY, * )
 *     ..
 *
-*  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**T * 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 >= max(1,M).
-*
-*  Y       (output) DOUBLE PRECISION array, dimension (LDY,NB)
-*          The n-by-nb matrix Y required to update the unreduced part
-*          of A.
-*
-*  LDY     (input) INTEGER
-*          The leading dimension of the array Y. LDY >= max(1,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**T  and G(i) = I - taup * u * u**T
-*
-*  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**T 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**T - X*U**T.
-*
-*  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).
-*
 *  =====================================================================
 *
 *     .. Parameters ..