--- rpl/lapack/lapack/dopmtr.f 2010/12/21 13:53:34 1.7 +++ rpl/lapack/lapack/dopmtr.f 2011/11/21 20:43:00 1.8 @@ -1,10 +1,159 @@ +*> \brief \b DOPMTR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DOPMTR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, +* INFO ) +* +* .. Scalar Arguments .. +* CHARACTER SIDE, TRANS, UPLO +* INTEGER INFO, LDC, M, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION AP( * ), C( LDC, * ), TAU( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DOPMTR overwrites the general real M-by-N matrix C with +*> +*> SIDE = 'L' SIDE = 'R' +*> TRANS = 'N': Q * C C * Q +*> TRANS = 'T': Q**T * C C * Q**T +*> +*> where Q is a real orthogonal matrix of order nq, with nq = m if +*> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of +*> nq-1 elementary reflectors, as returned by DSPTRD using packed +*> storage: +*> +*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); +*> +*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). +*> \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] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangular packed storage used in previous +*> call to DSPTRD; +*> = 'L': Lower triangular packed storage used in previous +*> call to DSPTRD. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> = 'N': No transpose, apply Q; +*> = 'T': Transpose, apply Q**T. +*> \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] AP +*> \verbatim +*> AP is DOUBLE PRECISION array, dimension +*> (M*(M+1)/2) if SIDE = 'L' +*> (N*(N+1)/2) if SIDE = 'R' +*> The vectors which define the elementary reflectors, as +*> returned by DSPTRD. AP is modified by the routine but +*> restored on exit. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L' +*> or (N-1) if SIDE = 'R' +*> TAU(i) must contain the scalar factor of the elementary +*> reflector H(i), as returned by DSPTRD. +*> \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 November 2011 +* +*> \ingroup doubleOTHERcomputational +* +* ===================================================================== SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, $ INFO ) * -* -- LAPACK routine (version 3.2) -- +* -- 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..-- -* November 2006 +* November 2011 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS, UPLO @@ -14,74 +163,6 @@ DOUBLE PRECISION AP( * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DOPMTR overwrites the general real M-by-N matrix C with -* -* SIDE = 'L' SIDE = 'R' -* TRANS = 'N': Q * C C * Q -* TRANS = 'T': Q**T * C C * Q**T -* -* where Q is a real orthogonal matrix of order nq, with nq = m if -* SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of -* nq-1 elementary reflectors, as returned by DSPTRD using packed -* storage: -* -* if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); -* -* if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). -* -* Arguments -* ========= -* -* SIDE (input) CHARACTER*1 -* = 'L': apply Q or Q**T from the Left; -* = 'R': apply Q or Q**T from the Right. -* -* UPLO (input) CHARACTER*1 -* = 'U': Upper triangular packed storage used in previous -* call to DSPTRD; -* = 'L': Lower triangular packed storage used in previous -* call to DSPTRD. -* -* TRANS (input) CHARACTER*1 -* = 'N': No transpose, apply Q; -* = 'T': Transpose, apply Q**T. -* -* 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. -* -* AP (input) DOUBLE PRECISION array, dimension -* (M*(M+1)/2) if SIDE = 'L' -* (N*(N+1)/2) if SIDE = 'R' -* The vectors which define the elementary reflectors, as -* returned by DSPTRD. AP is modified by the routine but -* restored on exit. -* -* TAU (input) DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L' -* or (N-1) if SIDE = 'R' -* TAU(i) must contain the scalar factor of the elementary -* reflector H(i), as returned by DSPTRD. -* -* 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**T*C or C*Q**T 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 -* * ===================================================================== * * .. Parameters ..