--- rpl/lapack/lapack/dlarzt.f 2010/01/26 15:22:46 1.1.1.1
+++ rpl/lapack/lapack/dlarzt.f 2023/08/07 08:38:58 1.19
@@ -1,9 +1,191 @@
+*> \brief \b DLARZT forms the triangular factor T of a block reflector H = I - vtvH.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLARZT + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
+*
+* .. Scalar Arguments ..
+* CHARACTER DIRECT, STOREV
+* INTEGER K, LDT, LDV, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLARZT forms the triangular factor T of a real block reflector
+*> H of order > n, which is defined as a product of k elementary
+*> reflectors.
+*>
+*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
+*>
+*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
+*>
+*> If STOREV = 'C', the vector which defines the elementary reflector
+*> H(i) is stored in the i-th column of the array V, and
+*>
+*> H = I - V * T * V**T
+*>
+*> If STOREV = 'R', the vector which defines the elementary reflector
+*> H(i) is stored in the i-th row of the array V, and
+*>
+*> H = I - V**T * T * V
+*>
+*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] DIRECT
+*> \verbatim
+*> DIRECT is CHARACTER*1
+*> Specifies the order in which the elementary reflectors are
+*> multiplied to form the block reflector:
+*> = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
+*> = 'B': H = H(k) . . . H(2) H(1) (Backward)
+*> \endverbatim
+*>
+*> \param[in] STOREV
+*> \verbatim
+*> STOREV is CHARACTER*1
+*> Specifies how the vectors which define the elementary
+*> reflectors are stored (see also Further Details):
+*> = 'C': columnwise (not supported yet)
+*> = 'R': rowwise
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the block reflector H. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] K
+*> \verbatim
+*> K is INTEGER
+*> The order of the triangular factor T (= the number of
+*> elementary reflectors). K >= 1.
+*> \endverbatim
+*>
+*> \param[in,out] V
+*> \verbatim
+*> V is DOUBLE PRECISION array, dimension
+*> (LDV,K) if STOREV = 'C'
+*> (LDV,N) if STOREV = 'R'
+*> The matrix V. See further details.
+*> \endverbatim
+*>
+*> \param[in] LDV
+*> \verbatim
+*> LDV is INTEGER
+*> The leading dimension of the array V.
+*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
+*> \endverbatim
+*>
+*> \param[in] TAU
+*> \verbatim
+*> TAU is DOUBLE PRECISION array, dimension (K)
+*> TAU(i) must contain the scalar factor of the elementary
+*> reflector H(i).
+*> \endverbatim
+*>
+*> \param[out] T
+*> \verbatim
+*> T is DOUBLE PRECISION array, dimension (LDT,K)
+*> The k by k triangular factor T of the block reflector.
+*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
+*> lower triangular. The rest of the array is not used.
+*> \endverbatim
+*>
+*> \param[in] LDT
+*> \verbatim
+*> LDT is INTEGER
+*> The leading dimension of the array T. LDT >= K.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Contributors:
+* ==================
+*>
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> The shape of the matrix V and the storage of the vectors which define
+*> the H(i) is best illustrated by the following example with n = 5 and
+*> k = 3. The elements equal to 1 are not stored; the corresponding
+*> array elements are modified but restored on exit. The rest of the
+*> array is not used.
+*>
+*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
+*>
+*> ______V_____
+*> ( v1 v2 v3 ) / \
+*> ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 )
+*> V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 )
+*> ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 )
+*> ( v1 v2 v3 )
+*> . . .
+*> . . .
+*> 1 . .
+*> 1 .
+*> 1
+*>
+*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
+*>
+*> ______V_____
+*> 1 / \
+*> . 1 ( 1 . . . . v1 v1 v1 v1 v1 )
+*> . . 1 ( . 1 . . . v2 v2 v2 v2 v2 )
+*> . . . ( . . 1 . . v3 v3 v3 v3 v3 )
+*> . . .
+*> ( v1 v2 v3 )
+*> ( v1 v2 v3 )
+*> V = ( v1 v2 v3 )
+*> ( v1 v2 v3 )
+*> ( v1 v2 v3 )
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
*
* .. Scalar Arguments ..
CHARACTER DIRECT, STOREV
@@ -13,112 +195,6 @@
DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
-*
-* DLARZT forms the triangular factor T of a real block reflector
-* H of order > n, which is defined as a product of k elementary
-* reflectors.
-*
-* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
-*
-* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
-*
-* If STOREV = 'C', the vector which defines the elementary reflector
-* H(i) is stored in the i-th column of the array V, and
-*
-* H = I - V * T * V'
-*
-* If STOREV = 'R', the vector which defines the elementary reflector
-* H(i) is stored in the i-th row of the array V, and
-*
-* H = I - V' * T * V
-*
-* Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
-*
-* Arguments
-* =========
-*
-* DIRECT (input) CHARACTER*1
-* Specifies the order in which the elementary reflectors are
-* multiplied to form the block reflector:
-* = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
-* = 'B': H = H(k) . . . H(2) H(1) (Backward)
-*
-* STOREV (input) CHARACTER*1
-* Specifies how the vectors which define the elementary
-* reflectors are stored (see also Further Details):
-* = 'C': columnwise (not supported yet)
-* = 'R': rowwise
-*
-* N (input) INTEGER
-* The order of the block reflector H. N >= 0.
-*
-* K (input) INTEGER
-* The order of the triangular factor T (= the number of
-* elementary reflectors). K >= 1.
-*
-* V (input/output) DOUBLE PRECISION array, dimension
-* (LDV,K) if STOREV = 'C'
-* (LDV,N) if STOREV = 'R'
-* The matrix V. See further details.
-*
-* LDV (input) INTEGER
-* The leading dimension of the array V.
-* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
-*
-* TAU (input) DOUBLE PRECISION array, dimension (K)
-* TAU(i) must contain the scalar factor of the elementary
-* reflector H(i).
-*
-* T (output) DOUBLE PRECISION array, dimension (LDT,K)
-* The k by k triangular factor T of the block reflector.
-* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
-* lower triangular. The rest of the array is not used.
-*
-* LDT (input) INTEGER
-* The leading dimension of the array T. LDT >= K.
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*
-* The shape of the matrix V and the storage of the vectors which define
-* the H(i) is best illustrated by the following example with n = 5 and
-* k = 3. The elements equal to 1 are not stored; the corresponding
-* array elements are modified but restored on exit. The rest of the
-* array is not used.
-*
-* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
-*
-* ______V_____
-* ( v1 v2 v3 ) / \
-* ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 )
-* V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 )
-* ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 )
-* ( v1 v2 v3 )
-* . . .
-* . . .
-* 1 . .
-* 1 .
-* 1
-*
-* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
-*
-* ______V_____
-* 1 / \
-* . 1 ( 1 . . . . v1 v1 v1 v1 v1 )
-* . . 1 ( . 1 . . . v2 v2 v2 v2 v2 )
-* . . . ( . . 1 . . v3 v3 v3 v3 v3 )
-* . . .
-* ( v1 v2 v3 )
-* ( v1 v2 v3 )
-* V = ( v1 v2 v3 )
-* ( v1 v2 v3 )
-* ( v1 v2 v3 )
-*
* =====================================================================
*
* .. Parameters ..
@@ -164,7 +240,7 @@
*
IF( I.LT.K ) THEN
*
-* T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)'
+* T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)**T
*
CALL DGEMV( 'No transpose', K-I, N, -TAU( I ),
$ V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,