--- rpl/lapack/lapack/dlarzb.f 2010/08/06 15:28:42 1.3
+++ rpl/lapack/lapack/dlarzb.f 2017/06/17 11:06:26 1.17
@@ -1,10 +1,192 @@
+*> \brief \b DLARZB applies a block reflector or its transpose to a general matrix.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLARZB + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
+* LDV, T, LDT, C, LDC, WORK, LDWORK )
+*
+* .. Scalar Arguments ..
+* CHARACTER DIRECT, SIDE, STOREV, TRANS
+* INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ),
+* $ WORK( LDWORK, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLARZB applies a real block reflector H or its transpose H**T to
+*> a real distributed M-by-N C from the left or the right.
+*>
+*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] SIDE
+*> \verbatim
+*> SIDE is CHARACTER*1
+*> = 'L': apply H or H**T from the Left
+*> = 'R': apply H or H**T from the Right
+*> \endverbatim
+*>
+*> \param[in] TRANS
+*> \verbatim
+*> TRANS is CHARACTER*1
+*> = 'N': apply H (No transpose)
+*> = 'C': apply H**T (Transpose)
+*> \endverbatim
+*>
+*> \param[in] DIRECT
+*> \verbatim
+*> DIRECT is CHARACTER*1
+*> Indicates how H is formed from a product of elementary
+*> reflectors
+*> = '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
+*> Indicates how the vectors which define the elementary
+*> reflectors are stored:
+*> = 'C': Columnwise (not supported yet)
+*> = 'R': Rowwise
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The number of rows of the matrix C.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of columns of the matrix C.
+*> \endverbatim
+*>
+*> \param[in] K
+*> \verbatim
+*> K is INTEGER
+*> The order of the matrix T (= the number of elementary
+*> reflectors whose product defines the block reflector).
+*> \endverbatim
+*>
+*> \param[in] L
+*> \verbatim
+*> L is INTEGER
+*> The number of columns of the matrix V containing the
+*> meaningful part of the Householder reflectors.
+*> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
+*> \endverbatim
+*>
+*> \param[in] V
+*> \verbatim
+*> V is DOUBLE PRECISION array, dimension (LDV,NV).
+*> If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
+*> \endverbatim
+*>
+*> \param[in] LDV
+*> \verbatim
+*> LDV is INTEGER
+*> The leading dimension of the array V.
+*> If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.
+*> \endverbatim
+*>
+*> \param[in] T
+*> \verbatim
+*> T is DOUBLE PRECISION array, dimension (LDT,K)
+*> The triangular K-by-K matrix T in the representation of the
+*> block reflector.
+*> \endverbatim
+*>
+*> \param[in] LDT
+*> \verbatim
+*> LDT is INTEGER
+*> The leading dimension of the array T. LDT >= K.
+*> \endverbatim
+*>
+*> \param[in,out] C
+*> \verbatim
+*> C is DOUBLE PRECISION array, dimension (LDC,N)
+*> On entry, the M-by-N matrix C.
+*> On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
+*> \endverbatim
+*>
+*> \param[in] LDC
+*> \verbatim
+*> LDC is INTEGER
+*> The leading dimension of the array C. LDC >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (LDWORK,K)
+*> \endverbatim
+*>
+*> \param[in] LDWORK
+*> \verbatim
+*> LDWORK is INTEGER
+*> The leading dimension of the array WORK.
+*> If SIDE = 'L', LDWORK >= max(1,N);
+*> if SIDE = 'R', LDWORK >= max(1,M).
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date December 2016
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Contributors:
+* ==================
+*>
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
$ LDV, T, LDT, C, LDC, WORK, LDWORK )
*
-* -- LAPACK routine (version 3.2) --
+* -- 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..--
-* November 2006
+* December 2016
*
* .. Scalar Arguments ..
CHARACTER DIRECT, SIDE, STOREV, TRANS
@@ -15,86 +197,6 @@
$ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
-*
-* DLARZB applies a real block reflector H or its transpose H**T to
-* a real distributed M-by-N C from the left or the right.
-*
-* Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
-*
-* Arguments
-* =========
-*
-* SIDE (input) CHARACTER*1
-* = 'L': apply H or H' from the Left
-* = 'R': apply H or H' from the Right
-*
-* TRANS (input) CHARACTER*1
-* = 'N': apply H (No transpose)
-* = 'C': apply H' (Transpose)
-*
-* DIRECT (input) CHARACTER*1
-* Indicates how H is formed from a product of elementary
-* reflectors
-* = '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
-* Indicates how the vectors which define the elementary
-* reflectors are stored:
-* = 'C': Columnwise (not supported yet)
-* = 'R': Rowwise
-*
-* M (input) INTEGER
-* The number of rows of the matrix C.
-*
-* N (input) INTEGER
-* The number of columns of the matrix C.
-*
-* K (input) INTEGER
-* The order of the matrix T (= the number of elementary
-* reflectors whose product defines the block reflector).
-*
-* L (input) INTEGER
-* The number of columns of the matrix V containing the
-* meaningful part of the Householder reflectors.
-* If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
-*
-* V (input) DOUBLE PRECISION array, dimension (LDV,NV).
-* If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
-*
-* LDV (input) INTEGER
-* The leading dimension of the array V.
-* If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.
-*
-* T (input) DOUBLE PRECISION array, dimension (LDT,K)
-* The triangular K-by-K matrix T in the representation of the
-* block reflector.
-*
-* LDT (input) INTEGER
-* The leading dimension of the array T. LDT >= K.
-*
-* C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
-* On entry, the M-by-N matrix C.
-* On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
-*
-* LDC (input) INTEGER
-* The leading dimension of the array C. LDC >= max(1,M).
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (LDWORK,K)
-*
-* LDWORK (input) INTEGER
-* The leading dimension of the array WORK.
-* If SIDE = 'L', LDWORK >= max(1,N);
-* if SIDE = 'R', LDWORK >= max(1,M).
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*
* =====================================================================
*
* .. Parameters ..
@@ -140,27 +242,27 @@
*
IF( LSAME( SIDE, 'L' ) ) THEN
*
-* Form H * C or H' * C
+* Form H * C or H**T * C
*
-* W( 1:n, 1:k ) = C( 1:k, 1:n )'
+* W( 1:n, 1:k ) = C( 1:k, 1:n )**T
*
DO 10 J = 1, K
CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
10 CONTINUE
*
* W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
-* C( m-l+1:m, 1:n )' * V( 1:k, 1:l )'
+* C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T
*
IF( L.GT.0 )
$ CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE,
$ C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK )
*
-* W( 1:n, 1:k ) = W( 1:n, 1:k ) * T' or W( 1:m, 1:k ) * T
+* W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T
*
CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
$ LDT, WORK, LDWORK )
*
-* C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )'
+* C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T
*
DO 30 J = 1, N
DO 20 I = 1, K
@@ -169,7 +271,7 @@
30 CONTINUE
*
* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
-* V( 1:k, 1:l )' * W( 1:n, 1:k )'
+* V( 1:k, 1:l )**T * W( 1:n, 1:k )**T
*
IF( L.GT.0 )
$ CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
@@ -177,7 +279,7 @@
*
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
*
-* Form C * H or C * H'
+* Form C * H or C * H**T
*
* W( 1:m, 1:k ) = C( 1:m, 1:k )
*
@@ -186,13 +288,13 @@
40 CONTINUE
*
* W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
-* C( 1:m, n-l+1:n ) * V( 1:k, 1:l )'
+* C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T
*
IF( L.GT.0 )
$ CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
$ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
*
-* W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T'
+* W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T**T
*
CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
$ LDT, WORK, LDWORK )