--- rpl/lapack/lapack/dlatrd.f	2011/07/22 07:38:08	1.8
+++ rpl/lapack/lapack/dlatrd.f	2011/11/21 20:42:59	1.9
@@ -1,9 +1,207 @@
+*> \brief \b DLATRD
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLATRD + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlatrd.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlatrd.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlatrd.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            LDA, LDW, N, NB
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   A( LDA, * ), E( * ), TAU( * ), W( LDW, * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLATRD reduces NB rows and columns of a real symmetric matrix A to
+*> symmetric tridiagonal form by an orthogonal similarity
+*> transformation Q**T * A * Q, and returns the matrices V and W which are
+*> needed to apply the transformation to the unreduced part of A.
+*>
+*> If UPLO = 'U', DLATRD reduces the last NB rows and columns of a
+*> matrix, of which the upper triangle is supplied;
+*> if UPLO = 'L', DLATRD reduces the first NB rows and columns of a
+*> matrix, of which the lower triangle is supplied.
+*>
+*> This is an auxiliary routine called by DSYTRD.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the upper or lower triangular part of the
+*>          symmetric matrix A is stored:
+*>          = 'U': Upper triangular
+*>          = 'L': Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*>          NB is INTEGER
+*>          The number of rows and columns to be reduced.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
+*>          n-by-n upper triangular part of A contains the upper
+*>          triangular part of the matrix A, and the strictly lower
+*>          triangular part of A is not referenced.  If UPLO = 'L', the
+*>          leading n-by-n lower triangular part of A contains the lower
+*>          triangular part of the matrix A, and the strictly upper
+*>          triangular part of A is not referenced.
+*>          On exit:
+*>          if UPLO = 'U', the last NB columns have been reduced to
+*>            tridiagonal form, with the diagonal elements overwriting
+*>            the diagonal elements of A; the elements above the diagonal
+*>            with the array TAU, represent the orthogonal matrix Q as a
+*>            product of elementary reflectors;
+*>          if UPLO = 'L', the first NB columns have been reduced to
+*>            tridiagonal form, with the diagonal elements overwriting
+*>            the diagonal elements of A; the elements below the diagonal
+*>            with the array TAU, represent the  orthogonal matrix Q 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 >= (1,N).
+*> \endverbatim
+*>
+*> \param[out] E
+*> \verbatim
+*>          E is DOUBLE PRECISION array, dimension (N-1)
+*>          If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal
+*>          elements of the last NB columns of the reduced matrix;
+*>          if UPLO = 'L', E(1:nb) contains the subdiagonal elements of
+*>          the first NB columns of the reduced matrix.
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*>          TAU is DOUBLE PRECISION array, dimension (N-1)
+*>          The scalar factors of the elementary reflectors, stored in
+*>          TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
+*>          See Further Details.
+*> \endverbatim
+*>
+*> \param[out] W
+*> \verbatim
+*>          W is DOUBLE PRECISION array, dimension (LDW,NB)
+*>          The n-by-nb matrix W required to update the unreduced part
+*>          of A.
+*> \endverbatim
+*>
+*> \param[in] LDW
+*> \verbatim
+*>          LDW is INTEGER
+*>          The leading dimension of the array W. LDW >= 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
+*>
+*>  If UPLO = 'U', the matrix Q is represented as a product of elementary
+*>  reflectors
+*>
+*>     Q = H(n) H(n-1) . . . H(n-nb+1).
+*>
+*>  Each H(i) has the form
+*>
+*>     H(i) = I - tau * v * v**T
+*>
+*>  where tau is a real scalar, and v is a real vector with
+*>  v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
+*>  and tau in TAU(i-1).
+*>
+*>  If UPLO = 'L', the matrix Q is represented as a product of elementary
+*>  reflectors
+*>
+*>     Q = H(1) H(2) . . . H(nb).
+*>
+*>  Each H(i) has the form
+*>
+*>     H(i) = I - tau * v * v**T
+*>
+*>  where tau is a real scalar, and v is a real vector with
+*>  v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
+*>  and tau in TAU(i).
+*>
+*>  The elements of the vectors v together form the n-by-nb matrix V
+*>  which is needed, with W, to apply the transformation to the unreduced
+*>  part of the matrix, using a symmetric rank-2k update of the form:
+*>  A := A - V*W**T - W*V**T.
+*>
+*>  The contents of A on exit are illustrated by the following examples
+*>  with n = 5 and nb = 2:
+*>
+*>  if UPLO = 'U':                       if UPLO = 'L':
+*>
+*>    (  a   a   a   v4  v5 )              (  d                  )
+*>    (      a   a   v4  v5 )              (  1   d              )
+*>    (          a   1   v5 )              (  v1  1   a          )
+*>    (              d   1  )              (  v1  v2  a   a      )
+*>    (                  d  )              (  v1  v2  a   a   a  )
+*>
+*>  where d denotes a diagonal element of the reduced matrix, a denotes
+*>  an element of the original matrix that is unchanged, and vi denotes
+*>  an element of the vector defining H(i).
+*> \endverbatim
+*>
+*  =====================================================================
       SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
 *
-*  -- 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 ..
       CHARACTER          UPLO
@@ -13,127 +211,6 @@
       DOUBLE PRECISION   A( LDA, * ), E( * ), TAU( * ), W( LDW, * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  DLATRD reduces NB rows and columns of a real symmetric matrix A to
-*  symmetric tridiagonal form by an orthogonal similarity
-*  transformation Q**T * A * Q, and returns the matrices V and W which are
-*  needed to apply the transformation to the unreduced part of A.
-*
-*  If UPLO = 'U', DLATRD reduces the last NB rows and columns of a
-*  matrix, of which the upper triangle is supplied;
-*  if UPLO = 'L', DLATRD reduces the first NB rows and columns of a
-*  matrix, of which the lower triangle is supplied.
-*
-*  This is an auxiliary routine called by DSYTRD.
-*
-*  Arguments
-*  =========
-*
-*  UPLO    (input) CHARACTER*1
-*          Specifies whether the upper or lower triangular part of the
-*          symmetric matrix A is stored:
-*          = 'U': Upper triangular
-*          = 'L': Lower triangular
-*
-*  N       (input) INTEGER
-*          The order of the matrix A.
-*
-*  NB      (input) INTEGER
-*          The number of rows and columns to be reduced.
-*
-*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-*          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
-*          n-by-n upper triangular part of A contains the upper
-*          triangular part of the matrix A, and the strictly lower
-*          triangular part of A is not referenced.  If UPLO = 'L', the
-*          leading n-by-n lower triangular part of A contains the lower
-*          triangular part of the matrix A, and the strictly upper
-*          triangular part of A is not referenced.
-*          On exit:
-*          if UPLO = 'U', the last NB columns have been reduced to
-*            tridiagonal form, with the diagonal elements overwriting
-*            the diagonal elements of A; the elements above the diagonal
-*            with the array TAU, represent the orthogonal matrix Q as a
-*            product of elementary reflectors;
-*          if UPLO = 'L', the first NB columns have been reduced to
-*            tridiagonal form, with the diagonal elements overwriting
-*            the diagonal elements of A; the elements below the diagonal
-*            with the array TAU, represent the  orthogonal matrix Q as a
-*            product of elementary reflectors.
-*          See Further Details.
-*
-*  LDA     (input) INTEGER
-*          The leading dimension of the array A.  LDA >= (1,N).
-*
-*  E       (output) DOUBLE PRECISION array, dimension (N-1)
-*          If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal
-*          elements of the last NB columns of the reduced matrix;
-*          if UPLO = 'L', E(1:nb) contains the subdiagonal elements of
-*          the first NB columns of the reduced matrix.
-*
-*  TAU     (output) DOUBLE PRECISION array, dimension (N-1)
-*          The scalar factors of the elementary reflectors, stored in
-*          TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
-*          See Further Details.
-*
-*  W       (output) DOUBLE PRECISION array, dimension (LDW,NB)
-*          The n-by-nb matrix W required to update the unreduced part
-*          of A.
-*
-*  LDW     (input) INTEGER
-*          The leading dimension of the array W. LDW >= max(1,N).
-*
-*  Further Details
-*  ===============
-*
-*  If UPLO = 'U', the matrix Q is represented as a product of elementary
-*  reflectors
-*
-*     Q = H(n) H(n-1) . . . H(n-nb+1).
-*
-*  Each H(i) has the form
-*
-*     H(i) = I - tau * v * v**T
-*
-*  where tau is a real scalar, and v is a real vector with
-*  v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
-*  and tau in TAU(i-1).
-*
-*  If UPLO = 'L', the matrix Q is represented as a product of elementary
-*  reflectors
-*
-*     Q = H(1) H(2) . . . H(nb).
-*
-*  Each H(i) has the form
-*
-*     H(i) = I - tau * v * v**T
-*
-*  where tau is a real scalar, and v is a real vector with
-*  v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
-*  and tau in TAU(i).
-*
-*  The elements of the vectors v together form the n-by-nb matrix V
-*  which is needed, with W, to apply the transformation to the unreduced
-*  part of the matrix, using a symmetric rank-2k update of the form:
-*  A := A - V*W**T - W*V**T.
-*
-*  The contents of A on exit are illustrated by the following examples
-*  with n = 5 and nb = 2:
-*
-*  if UPLO = 'U':                       if UPLO = 'L':
-*
-*    (  a   a   a   v4  v5 )              (  d                  )
-*    (      a   a   v4  v5 )              (  1   d              )
-*    (          a   1   v5 )              (  v1  1   a          )
-*    (              d   1  )              (  v1  v2  a   a      )
-*    (                  d  )              (  v1  v2  a   a   a  )
-*
-*  where d denotes a diagonal element of the reduced matrix, a denotes
-*  an element of the original matrix that is unchanged, and vi denotes
-*  an element of the vector defining H(i).
-*
 *  =====================================================================
 *
 *     .. Parameters ..