--- rpl/lapack/lapack/dormr3.f 2010/04/21 13:45:22 1.2
+++ rpl/lapack/lapack/dormr3.f 2017/06/17 11:06:30 1.17
@@ -1,10 +1,187 @@
+*> \brief \b DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DORMR3 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
+* WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER SIDE, TRANS
+* INTEGER INFO, K, L, LDA, LDC, M, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DORMR3 overwrites the general real m by n matrix C with
+*>
+*> Q * C if SIDE = 'L' and TRANS = 'N', or
+*>
+*> Q**T* C if SIDE = 'L' and TRANS = 'C', or
+*>
+*> C * Q if SIDE = 'R' and TRANS = 'N', or
+*>
+*> C * Q**T if SIDE = 'R' and TRANS = 'C',
+*>
+*> where Q is a real orthogonal matrix defined as the product of k
+*> elementary reflectors
+*>
+*> Q = H(1) H(2) . . . H(k)
+*>
+*> as returned by DTZRZF. Q is of order m if SIDE = 'L' and of order n
+*> if SIDE = 'R'.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] SIDE
+*> \verbatim
+*> SIDE is CHARACTER*1
+*> = 'L': apply Q or Q**T from the Left
+*> = 'R': apply Q or Q**T from the Right
+*> \endverbatim
+*>
+*> \param[in] TRANS
+*> \verbatim
+*> TRANS is CHARACTER*1
+*> = 'N': apply Q (No transpose)
+*> = 'T': apply Q**T (Transpose)
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The number of rows of the matrix C. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of columns of the matrix C. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] K
+*> \verbatim
+*> K is INTEGER
+*> The number of elementary reflectors whose product defines
+*> the matrix Q.
+*> If SIDE = 'L', M >= K >= 0;
+*> if SIDE = 'R', N >= K >= 0.
+*> \endverbatim
+*>
+*> \param[in] L
+*> \verbatim
+*> L is INTEGER
+*> The number of columns of the matrix A containing
+*> the meaningful part of the Householder reflectors.
+*> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension
+*> (LDA,M) if SIDE = 'L',
+*> (LDA,N) if SIDE = 'R'
+*> The i-th row must contain the vector which defines the
+*> elementary reflector H(i), for i = 1,2,...,k, as returned by
+*> DTZRZF in the last k rows of its array argument A.
+*> A is modified by the routine but restored on exit.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,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), as returned by DTZRZF.
+*> \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 Q*C or Q**T*C or C*Q**T or C*Q.
+*> \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
+*> (N) if SIDE = 'L',
+*> (M) if SIDE = 'R'
+*> \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 doubleOTHERcomputational
+*
+*> \par Contributors:
+* ==================
+*>
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
$ WORK, INFO )
*
-* -- 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 SIDE, TRANS
@@ -14,91 +191,6 @@
DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DORMR3 overwrites the general real m by n matrix C with
-*
-* Q * C if SIDE = 'L' and TRANS = 'N', or
-*
-* Q'* C if SIDE = 'L' and TRANS = 'T', or
-*
-* C * Q if SIDE = 'R' and TRANS = 'N', or
-*
-* C * Q' if SIDE = 'R' and TRANS = 'T',
-*
-* where Q is a real orthogonal matrix defined as the product of k
-* elementary reflectors
-*
-* Q = H(1) H(2) . . . H(k)
-*
-* as returned by DTZRZF. Q is of order m if SIDE = 'L' and of order n
-* if SIDE = 'R'.
-*
-* Arguments
-* =========
-*
-* SIDE (input) CHARACTER*1
-* = 'L': apply Q or Q' from the Left
-* = 'R': apply Q or Q' from the Right
-*
-* TRANS (input) CHARACTER*1
-* = 'N': apply Q (No transpose)
-* = 'T': apply Q' (Transpose)
-*
-* M (input) INTEGER
-* The number of rows of the matrix C. M >= 0.
-*
-* N (input) INTEGER
-* The number of columns of the matrix C. N >= 0.
-*
-* K (input) INTEGER
-* The number of elementary reflectors whose product defines
-* the matrix Q.
-* If SIDE = 'L', M >= K >= 0;
-* if SIDE = 'R', N >= K >= 0.
-*
-* L (input) INTEGER
-* The number of columns of the matrix A containing
-* the meaningful part of the Householder reflectors.
-* If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
-*
-* A (input) DOUBLE PRECISION array, dimension
-* (LDA,M) if SIDE = 'L',
-* (LDA,N) if SIDE = 'R'
-* The i-th row must contain the vector which defines the
-* elementary reflector H(i), for i = 1,2,...,k, as returned by
-* DTZRZF in the last k rows of its array argument A.
-* A is modified by the routine but restored on exit.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,K).
-*
-* TAU (input) DOUBLE PRECISION array, dimension (K)
-* TAU(i) must contain the scalar factor of the elementary
-* reflector H(i), as returned by DTZRZF.
-*
-* C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
-* On entry, the m-by-n matrix C.
-* On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
-*
-* LDC (input) INTEGER
-* The leading dimension of the array C. LDC >= max(1,M).
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension
-* (N) if SIDE = 'L',
-* (M) if SIDE = 'R'
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*
* =====================================================================
*
* .. Local Scalars ..
@@ -181,19 +273,19 @@
DO 10 I = I1, I2, I3
IF( LEFT ) THEN
*
-* H(i) or H(i)' is applied to C(i:m,1:n)
+* H(i) or H(i)**T is applied to C(i:m,1:n)
*
MI = M - I + 1
IC = I
ELSE
*
-* H(i) or H(i)' is applied to C(1:m,i:n)
+* H(i) or H(i)**T is applied to C(1:m,i:n)
*
NI = N - I + 1
JC = I
END IF
*
-* Apply H(i) or H(i)'
+* Apply H(i) or H(i)**T
*
CALL DLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAU( I ),
$ C( IC, JC ), LDC, WORK )