--- rpl/lapack/lapack/zgehrd.f 2011/07/22 07:38:14 1.8
+++ rpl/lapack/lapack/zgehrd.f 2011/11/21 20:43:09 1.9
@@ -1,9 +1,177 @@
+*> \brief \b ZGEHRD
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZGEHRD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER IHI, ILO, INFO, LDA, LWORK, N
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by
+*> an unitary similarity transformation: Q**H * A * Q = H .
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] ILO
+*> \verbatim
+*> ILO is INTEGER
+*> \endverbatim
+*>
+*> \param[in] IHI
+*> \verbatim
+*> IHI is INTEGER
+*>
+*> It is assumed that A is already upper triangular in rows
+*> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
+*> set by a previous call to ZGEBAL; otherwise they should be
+*> set to 1 and N respectively. See Further Details.
+*> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> On entry, the N-by-N general matrix to be reduced.
+*> On exit, the upper triangle and the first subdiagonal of A
+*> are overwritten with the upper Hessenberg matrix H, and the
+*> elements below the first subdiagonal, with the array TAU,
+*> represent the unitary 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 >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*> TAU is COMPLEX*16 array, dimension (N-1)
+*> The scalar factors of the elementary reflectors (see Further
+*> Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
+*> zero.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (LWORK)
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of the array WORK. LWORK >= max(1,N).
+*> For optimum performance LWORK >= N*NB, where NB is the
+*> optimal blocksize.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16GEcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> The matrix Q is represented as a product of (ihi-ilo) elementary
+*> reflectors
+*>
+*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
+*>
+*> Each H(i) has the form
+*>
+*> H(i) = I - tau * v * v**H
+*>
+*> where tau is a complex scalar, and v is a complex vector with
+*> v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
+*> exit in A(i+2:ihi,i), and tau in TAU(i).
+*>
+*> The contents of A are illustrated by the following example, with
+*> n = 7, ilo = 2 and ihi = 6:
+*>
+*> on entry, on exit,
+*>
+*> ( a a a a a a a ) ( a a h h h h a )
+*> ( a a a a a a ) ( a h h h h a )
+*> ( a a a a a a ) ( h h h h h h )
+*> ( a a a a a a ) ( v2 h h h h h )
+*> ( a a a a a a ) ( v2 v3 h h h h )
+*> ( a a a a a a ) ( v2 v3 v4 h h h )
+*> ( 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).
+*>
+*> This file is a slight modification of LAPACK-3.0's DGEHRD
+*> subroutine incorporating improvements proposed by Quintana-Orti and
+*> Van de Geijn (2006). (See DLAHR2.)
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE ZGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
*
-* -- LAPACK routine (version 3.3.1) --
+* -- LAPACK computational 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 2009 --
+* November 2011
*
* .. Scalar Arguments ..
INTEGER IHI, ILO, INFO, LDA, LWORK, N
@@ -12,96 +180,6 @@
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by
-* an unitary similarity transformation: Q**H * A * Q = H .
-*
-* Arguments
-* =========
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* ILO (input) INTEGER
-* IHI (input) INTEGER
-* It is assumed that A is already upper triangular in rows
-* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
-* set by a previous call to ZGEBAL; otherwise they should be
-* set to 1 and N respectively. See Further Details.
-* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
-*
-* A (input/output) COMPLEX*16 array, dimension (LDA,N)
-* On entry, the N-by-N general matrix to be reduced.
-* On exit, the upper triangle and the first subdiagonal of A
-* are overwritten with the upper Hessenberg matrix H, and the
-* elements below the first subdiagonal, with the array TAU,
-* represent the unitary matrix Q as a product of elementary
-* reflectors. See Further Details.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* TAU (output) COMPLEX*16 array, dimension (N-1)
-* The scalar factors of the elementary reflectors (see Further
-* Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
-* zero.
-*
-* WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
-* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
-*
-* LWORK (input) INTEGER
-* The length of the array WORK. LWORK >= max(1,N).
-* For optimum performance LWORK >= N*NB, where NB is the
-* optimal blocksize.
-*
-* If LWORK = -1, then a workspace query is assumed; the routine
-* only calculates the optimal size of the WORK array, returns
-* this value as the first entry of the WORK array, and no error
-* message related to LWORK is issued by XERBLA.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-*
-* Further Details
-* ===============
-*
-* The matrix Q is represented as a product of (ihi-ilo) elementary
-* reflectors
-*
-* Q = H(ilo) H(ilo+1) . . . H(ihi-1).
-*
-* Each H(i) has the form
-*
-* H(i) = I - tau * v * v**H
-*
-* where tau is a complex scalar, and v is a complex vector with
-* v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
-* exit in A(i+2:ihi,i), and tau in TAU(i).
-*
-* The contents of A are illustrated by the following example, with
-* n = 7, ilo = 2 and ihi = 6:
-*
-* on entry, on exit,
-*
-* ( a a a a a a a ) ( a a h h h h a )
-* ( a a a a a a ) ( a h h h h a )
-* ( a a a a a a ) ( h h h h h h )
-* ( a a a a a a ) ( v2 h h h h h )
-* ( a a a a a a ) ( v2 v3 h h h h )
-* ( a a a a a a ) ( v2 v3 v4 h h h )
-* ( 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).
-*
-* This file is a slight modification of LAPACK-3.0's DGEHRD
-* subroutine incorporating improvements proposed by Quintana-Orti and
-* Van de Geijn (2006). (See DLAHR2.)
-*
* =====================================================================
*
* .. Parameters ..