--- rpl/lapack/lapack/dgehrd.f 2010/01/26 15:22:46 1.1
+++ rpl/lapack/lapack/dgehrd.f 2017/06/17 11:06:15 1.17
@@ -1,9 +1,176 @@
+*> \brief \b DGEHRD
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGEHRD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER IHI, ILO, INFO, LDA, LWORK, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DGEHRD reduces a real general matrix A to upper Hessenberg form H by
+*> an orthogonal similarity transformation: Q**T * 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 DGEBAL; 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 DOUBLE PRECISION 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 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 >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*> TAU is DOUBLE PRECISION 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 DOUBLE PRECISION 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 good performance, LWORK should generally be larger.
+*>
+*> 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 December 2016
+*
+*> \ingroup doubleGEcomputational
+*
+*> \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**T
+*>
+*> where tau is a real scalar, and v is a real 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 DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
*
-* -- LAPACK routine (version 3.2.1) --
+* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* -- April 2009 --
+* December 2016
*
* .. Scalar Arguments ..
INTEGER IHI, ILO, INFO, LDA, LWORK, N
@@ -12,114 +179,22 @@
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DGEHRD reduces a real general matrix A to upper Hessenberg form H by
-* an orthogonal similarity transformation: Q' * 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 DGEBAL; 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) DOUBLE PRECISION 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 orthogonal 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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'
-*
-* where tau is a real scalar, and v is a real 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 ..
- INTEGER NBMAX, LDT
- PARAMETER ( NBMAX = 64, LDT = NBMAX+1 )
+ INTEGER NBMAX, LDT, TSIZE
+ PARAMETER ( NBMAX = 64, LDT = NBMAX+1,
+ $ TSIZE = LDT*NBMAX )
DOUBLE PRECISION ZERO, ONE
- PARAMETER ( ZERO = 0.0D+0,
+ PARAMETER ( ZERO = 0.0D+0,
$ ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL LQUERY
- INTEGER I, IB, IINFO, IWS, J, LDWORK, LWKOPT, NB,
+ INTEGER I, IB, IINFO, IWT, J, LDWORK, LWKOPT, NB,
$ NBMIN, NH, NX
DOUBLE PRECISION EI
* ..
-* .. Local Arrays ..
- DOUBLE PRECISION T( LDT, NBMAX )
-* ..
* .. External Subroutines ..
EXTERNAL DAXPY, DGEHD2, DGEMM, DLAHR2, DLARFB, DTRMM,
$ XERBLA
@@ -136,9 +211,6 @@
* Test the input parameters
*
INFO = 0
- NB = MIN( NBMAX, ILAENV( 1, 'DGEHRD', ' ', N, ILO, IHI, -1 ) )
- LWKOPT = N*NB
- WORK( 1 ) = LWKOPT
LQUERY = ( LWORK.EQ.-1 )
IF( N.LT.0 ) THEN
INFO = -1
@@ -151,6 +223,16 @@
ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
INFO = -8
END IF
+*
+ IF( INFO.EQ.0 ) THEN
+*
+* Compute the workspace requirements
+*
+ NB = MIN( NBMAX, ILAENV( 1, 'DGEHRD', ' ', N, ILO, IHI, -1 ) )
+ LWKOPT = N*NB + TSIZE
+ WORK( 1 ) = LWKOPT
+ END IF
+*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGEHRD', -INFO )
RETURN
@@ -179,7 +261,6 @@
*
NB = MIN( NBMAX, ILAENV( 1, 'DGEHRD', ' ', N, ILO, IHI, -1 ) )
NBMIN = 2
- IWS = 1
IF( NB.GT.1 .AND. NB.LT.NH ) THEN
*
* Determine when to cross over from blocked to unblocked code
@@ -190,8 +271,7 @@
*
* Determine if workspace is large enough for blocked code
*
- IWS = N*NB
- IF( LWORK.LT.IWS ) THEN
+ IF( LWORK.LT.N*NB+TSIZE ) THEN
*
* Not enough workspace to use optimal NB: determine the
* minimum value of NB, and reduce NB or force use of
@@ -199,8 +279,8 @@
*
NBMIN = MAX( 2, ILAENV( 2, 'DGEHRD', ' ', N, ILO, IHI,
$ -1 ) )
- IF( LWORK.GE.N*NBMIN ) THEN
- NB = LWORK / N
+ IF( LWORK.GE.(N*NBMIN + TSIZE) ) THEN
+ NB = (LWORK-TSIZE) / N
ELSE
NB = 1
END IF
@@ -219,23 +299,24 @@
*
* Use blocked code
*
+ IWT = 1 + N*NB
DO 40 I = ILO, IHI - 1 - NX, NB
IB = MIN( NB, IHI-I )
*
* Reduce columns i:i+ib-1 to Hessenberg form, returning the
-* matrices V and T of the block reflector H = I - V*T*V'
+* matrices V and T of the block reflector H = I - V*T*V**T
* which performs the reduction, and also the matrix Y = A*V*T
*
- CALL DLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), T, LDT,
- $ WORK, LDWORK )
+ CALL DLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ),
+ $ WORK( IWT ), LDT, WORK, LDWORK )
*
* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the
-* right, computing A := A - Y * V'. V(i+ib,ib-1) must be set
+* right, computing A := A - Y * V**T. V(i+ib,ib-1) must be set
* to 1
*
EI = A( I+IB, I+IB-1 )
A( I+IB, I+IB-1 ) = ONE
- CALL DGEMM( 'No transpose', 'Transpose',
+ CALL DGEMM( 'No transpose', 'Transpose',
$ IHI, IHI-I-IB+1,
$ IB, -ONE, WORK, LDWORK, A( I+IB, I ), LDA, ONE,
$ A( 1, I+IB ), LDA )
@@ -257,15 +338,16 @@
*
CALL DLARFB( 'Left', 'Transpose', 'Forward',
$ 'Columnwise',
- $ IHI-I, N-I-IB+1, IB, A( I+1, I ), LDA, T, LDT,
- $ A( I+1, I+IB ), LDA, WORK, LDWORK )
+ $ IHI-I, N-I-IB+1, IB, A( I+1, I ), LDA,
+ $ WORK( IWT ), LDT, A( I+1, I+IB ), LDA,
+ $ WORK, LDWORK )
40 CONTINUE
END IF
*
* Use unblocked code to reduce the rest of the matrix
*
CALL DGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO )
- WORK( 1 ) = IWS
+ WORK( 1 ) = LWKOPT
*
RETURN
*