--- rpl/lapack/lapack/dlahrd.f 2011/07/22 07:38:06 1.8
+++ rpl/lapack/lapack/dlahrd.f 2011/11/21 20:42:55 1.9
@@ -1,9 +1,178 @@
+*> \brief \b DLAHRD
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLAHRD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLAHRD( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
+*
+* .. Scalar Arguments ..
+* INTEGER K, LDA, LDT, LDY, N, NB
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( LDA, * ), T( LDT, NB ), TAU( NB ),
+* $ Y( LDY, NB )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLAHRD reduces the first NB columns of a real general n-by-(n-k+1)
+*> matrix A so that elements below the k-th subdiagonal are zero. The
+*> reduction is performed by an orthogonal similarity transformation
+*> Q**T * A * Q. The routine returns the matrices V and T which determine
+*> Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T.
+*>
+*> This is an OBSOLETE auxiliary routine.
+*> This routine will be 'deprecated' in a future release.
+*> Please use the new routine DLAHR2 instead.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A.
+*> \endverbatim
+*>
+*> \param[in] K
+*> \verbatim
+*> K is INTEGER
+*> The offset for the reduction. Elements below the k-th
+*> subdiagonal in the first NB columns are reduced to zero.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*> NB is INTEGER
+*> The number of columns to be reduced.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N-K+1)
+*> On entry, the n-by-(n-k+1) general matrix A.
+*> On exit, the elements on and above the k-th subdiagonal in
+*> the first NB columns are overwritten with the corresponding
+*> elements of the reduced matrix; the elements below the k-th
+*> subdiagonal, with the array TAU, represent the matrix Q as a
+*> product of elementary reflectors. The other columns of A are
+*> unchanged. See Further Details.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*> TAU is DOUBLE PRECISION array, dimension (NB)
+*> The scalar factors of the elementary reflectors. See Further
+*> Details.
+*> \endverbatim
+*>
+*> \param[out] T
+*> \verbatim
+*> T is DOUBLE PRECISION array, dimension (LDT,NB)
+*> The upper triangular matrix T.
+*> \endverbatim
+*>
+*> \param[in] LDT
+*> \verbatim
+*> LDT is INTEGER
+*> The leading dimension of the array T. LDT >= NB.
+*> \endverbatim
+*>
+*> \param[out] Y
+*> \verbatim
+*> Y is DOUBLE PRECISION array, dimension (LDY,NB)
+*> The n-by-nb matrix Y.
+*> \endverbatim
+*>
+*> \param[in] LDY
+*> \verbatim
+*> LDY is INTEGER
+*> The leading dimension of the array Y. LDY >= 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 matrix Q is represented as a product of nb 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+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
+*> A(i+k+1:n,i), and tau in TAU(i).
+*>
+*> The elements of the vectors v together form the (n-k+1)-by-nb matrix
+*> V which is needed, with T and Y, to apply the transformation to the
+*> unreduced part of the matrix, using an update of the form:
+*> A := (I - V*T*V**T) * (A - Y*V**T).
+*>
+*> The contents of A on exit are illustrated by the following example
+*> with n = 7, k = 3 and nb = 2:
+*>
+*> ( a h a a a )
+*> ( a h a a a )
+*> ( a h a a a )
+*> ( h h a a a )
+*> ( v1 h a a a )
+*> ( v1 v2 a a a )
+*> ( v1 v2 a a a )
+*>
+*> where a denotes an element of the original matrix A, h denotes a
+*> modified element of the upper Hessenberg matrix H, and vi denotes an
+*> element of the vector defining H(i).
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DLAHRD( N, K, NB, A, LDA, TAU, T, LDT, 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 K, LDA, LDT, LDY, N, NB
@@ -13,95 +182,6 @@
$ Y( LDY, NB )
* ..
*
-* Purpose
-* =======
-*
-* DLAHRD reduces the first NB columns of a real general n-by-(n-k+1)
-* matrix A so that elements below the k-th subdiagonal are zero. The
-* reduction is performed by an orthogonal similarity transformation
-* Q**T * A * Q. The routine returns the matrices V and T which determine
-* Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T.
-*
-* This is an OBSOLETE auxiliary routine.
-* This routine will be 'deprecated' in a future release.
-* Please use the new routine DLAHR2 instead.
-*
-* Arguments
-* =========
-*
-* N (input) INTEGER
-* The order of the matrix A.
-*
-* K (input) INTEGER
-* The offset for the reduction. Elements below the k-th
-* subdiagonal in the first NB columns are reduced to zero.
-*
-* NB (input) INTEGER
-* The number of columns to be reduced.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA,N-K+1)
-* On entry, the n-by-(n-k+1) general matrix A.
-* On exit, the elements on and above the k-th subdiagonal in
-* the first NB columns are overwritten with the corresponding
-* elements of the reduced matrix; the elements below the k-th
-* subdiagonal, with the array TAU, represent the matrix Q as a
-* product of elementary reflectors. The other columns of A are
-* unchanged. See Further Details.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* TAU (output) DOUBLE PRECISION array, dimension (NB)
-* The scalar factors of the elementary reflectors. See Further
-* Details.
-*
-* T (output) DOUBLE PRECISION array, dimension (LDT,NB)
-* The upper triangular matrix T.
-*
-* LDT (input) INTEGER
-* The leading dimension of the array T. LDT >= NB.
-*
-* Y (output) DOUBLE PRECISION array, dimension (LDY,NB)
-* The n-by-nb matrix Y.
-*
-* LDY (input) INTEGER
-* The leading dimension of the array Y. LDY >= N.
-*
-* Further Details
-* ===============
-*
-* The matrix Q is represented as a product of nb 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+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
-* A(i+k+1:n,i), and tau in TAU(i).
-*
-* The elements of the vectors v together form the (n-k+1)-by-nb matrix
-* V which is needed, with T and Y, to apply the transformation to the
-* unreduced part of the matrix, using an update of the form:
-* A := (I - V*T*V**T) * (A - Y*V**T).
-*
-* The contents of A on exit are illustrated by the following example
-* with n = 7, k = 3 and nb = 2:
-*
-* ( a h a a a )
-* ( a h a a a )
-* ( a h a a a )
-* ( h h a a a )
-* ( v1 h a a a )
-* ( v1 v2 a a a )
-* ( v1 v2 a a a )
-*
-* where a denotes an element of the original matrix A, h denotes a
-* modified element of the upper Hessenberg matrix H, and vi denotes an
-* element of the vector defining H(i).
-*
* =====================================================================
*
* .. Parameters ..