Refs #247. Included lapack source codes. Avoid downloading tar.gz from netlib.org
Based on 3.4.2 version, apply patch.for_lapack-3.4.2.
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Zhang Xianyi
339
lapack-netlib/SRC/sopmtr.f
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339
lapack-netlib/SRC/sopmtr.f
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*> \brief \b SOPMTR
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SOPMTR + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sopmtr.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sopmtr.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sopmtr.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
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* INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER SIDE, TRANS, UPLO
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* INTEGER INFO, LDC, M, N
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* ..
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* .. Array Arguments ..
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* REAL AP( * ), C( LDC, * ), TAU( * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SOPMTR overwrites the general real M-by-N matrix C with
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*>
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*> SIDE = 'L' SIDE = 'R'
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*> TRANS = 'N': Q * C C * Q
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*> TRANS = 'T': Q**T * C C * Q**T
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*>
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*> where Q is a real orthogonal matrix of order nq, with nq = m if
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*> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
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*> nq-1 elementary reflectors, as returned by SSPTRD using packed
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*> storage:
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*>
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*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
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*>
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*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] SIDE
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*> \verbatim
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*> SIDE is CHARACTER*1
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*> = 'L': apply Q or Q**T from the Left;
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*> = 'R': apply Q or Q**T from the Right.
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*> \endverbatim
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*>
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> = 'U': Upper triangular packed storage used in previous
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*> call to SSPTRD;
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*> = 'L': Lower triangular packed storage used in previous
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*> call to SSPTRD.
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*> \endverbatim
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*>
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> = 'N': No transpose, apply Q;
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*> = 'T': Transpose, apply Q**T.
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix C. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrix C. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] AP
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*> \verbatim
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*> AP is REAL array, dimension
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*> (M*(M+1)/2) if SIDE = 'L'
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*> (N*(N+1)/2) if SIDE = 'R'
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*> The vectors which define the elementary reflectors, as
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*> returned by SSPTRD. AP is modified by the routine but
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*> restored on exit.
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*> \endverbatim
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*>
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*> \param[in] TAU
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*> \verbatim
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*> TAU is REAL array, dimension (M-1) if SIDE = 'L'
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*> or (N-1) if SIDE = 'R'
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*> TAU(i) must contain the scalar factor of the elementary
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*> reflector H(i), as returned by SSPTRD.
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*> \endverbatim
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*>
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*> \param[in,out] C
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*> \verbatim
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*> C is REAL array, dimension (LDC,N)
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*> On entry, the M-by-N matrix C.
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*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
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*> \endverbatim
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*>
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*> \param[in] LDC
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*> \verbatim
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*> LDC is INTEGER
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*> The leading dimension of the array C. LDC >= max(1,M).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension
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*> (N) if SIDE = 'L'
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*> (M) if SIDE = 'R'
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup realOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE SOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
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$ INFO )
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*
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* -- LAPACK computational routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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CHARACTER SIDE, TRANS, UPLO
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INTEGER INFO, LDC, M, N
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* ..
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* .. Array Arguments ..
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REAL AP( * ), C( LDC, * ), TAU( * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE
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PARAMETER ( ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL FORWRD, LEFT, NOTRAN, UPPER
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INTEGER I, I1, I2, I3, IC, II, JC, MI, NI, NQ
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REAL AII
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL SLARF, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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LEFT = LSAME( SIDE, 'L' )
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NOTRAN = LSAME( TRANS, 'N' )
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UPPER = LSAME( UPLO, 'U' )
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*
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* NQ is the order of Q
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*
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IF( LEFT ) THEN
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NQ = M
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ELSE
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NQ = N
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END IF
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IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -2
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ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
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INFO = -3
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ELSE IF( M.LT.0 ) THEN
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INFO = -4
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ELSE IF( N.LT.0 ) THEN
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INFO = -5
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ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
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INFO = -9
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SOPMTR', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( M.EQ.0 .OR. N.EQ.0 )
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$ RETURN
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*
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IF( UPPER ) THEN
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*
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* Q was determined by a call to SSPTRD with UPLO = 'U'
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*
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FORWRD = ( LEFT .AND. NOTRAN ) .OR.
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$ ( .NOT.LEFT .AND. .NOT.NOTRAN )
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*
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IF( FORWRD ) THEN
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I1 = 1
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I2 = NQ - 1
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I3 = 1
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II = 2
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ELSE
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I1 = NQ - 1
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I2 = 1
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I3 = -1
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II = NQ*( NQ+1 ) / 2 - 1
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END IF
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*
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IF( LEFT ) THEN
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NI = N
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ELSE
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MI = M
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END IF
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*
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DO 10 I = I1, I2, I3
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IF( LEFT ) THEN
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*
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* H(i) is applied to C(1:i,1:n)
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*
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MI = I
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ELSE
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*
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* H(i) is applied to C(1:m,1:i)
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*
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NI = I
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END IF
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*
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* Apply H(i)
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*
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AII = AP( II )
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AP( II ) = ONE
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CALL SLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAU( I ), C, LDC,
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$ WORK )
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AP( II ) = AII
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*
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IF( FORWRD ) THEN
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II = II + I + 2
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ELSE
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II = II - I - 1
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END IF
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10 CONTINUE
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ELSE
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*
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* Q was determined by a call to SSPTRD with UPLO = 'L'.
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*
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FORWRD = ( LEFT .AND. .NOT.NOTRAN ) .OR.
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$ ( .NOT.LEFT .AND. NOTRAN )
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*
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IF( FORWRD ) THEN
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I1 = 1
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I2 = NQ - 1
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I3 = 1
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II = 2
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ELSE
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I1 = NQ - 1
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I2 = 1
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I3 = -1
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II = NQ*( NQ+1 ) / 2 - 1
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END IF
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*
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IF( LEFT ) THEN
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NI = N
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JC = 1
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ELSE
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MI = M
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IC = 1
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END IF
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*
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DO 20 I = I1, I2, I3
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AII = AP( II )
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AP( II ) = ONE
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IF( LEFT ) THEN
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*
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* H(i) is applied to C(i+1:m,1:n)
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*
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MI = M - I
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IC = I + 1
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ELSE
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*
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* H(i) is applied to C(1:m,i+1:n)
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*
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NI = N - I
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JC = I + 1
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END IF
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*
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* Apply H(i)
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*
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CALL SLARF( SIDE, MI, NI, AP( II ), 1, TAU( I ),
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$ C( IC, JC ), LDC, WORK )
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AP( II ) = AII
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*
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IF( FORWRD ) THEN
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II = II + NQ - I + 1
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ELSE
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II = II - NQ + I - 2
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END IF
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20 CONTINUE
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END IF
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RETURN
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*
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* End of SOPMTR
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*
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END
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