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|
*> \brief \b SOPMTR
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SOPMTR + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sopmtr.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sopmtr.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sopmtr.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
* INFO )
*
* .. Scalar Arguments ..
* CHARACTER SIDE, TRANS, UPLO
* INTEGER INFO, LDC, M, N
* ..
* .. Array Arguments ..
* REAL AP( * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SOPMTR 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 SSPTRD 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 SSPTRD;
*> = 'L': Lower triangular packed storage used in previous
*> call to SSPTRD.
*> \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 REAL 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 SSPTRD. AP is modified by the routine but
*> restored on exit.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is REAL 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 SSPTRD.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is REAL 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 REAL 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 realOTHERcomputational
*
* =====================================================================
SUBROUTINE SOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
$ INFO )
*
* -- 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..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER SIDE, TRANS, UPLO
INTEGER INFO, LDC, M, N
* ..
* .. Array Arguments ..
REAL AP( * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL FORWRD, LEFT, NOTRAN, UPPER
INTEGER I, I1, I2, I3, IC, II, JC, MI, NI, NQ
REAL AII
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL SLARF, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
LEFT = LSAME( SIDE, 'L' )
NOTRAN = LSAME( TRANS, 'N' )
UPPER = LSAME( UPLO, 'U' )
*
* NQ is the order of Q
*
IF( LEFT ) THEN
NQ = M
ELSE
NQ = N
END IF
IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
INFO = -1
ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -2
ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
INFO = -3
ELSE IF( M.LT.0 ) THEN
INFO = -4
ELSE IF( N.LT.0 ) THEN
INFO = -5
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -9
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SOPMTR', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Q was determined by a call to SSPTRD with UPLO = 'U'
*
FORWRD = ( LEFT .AND. NOTRAN ) .OR.
$ ( .NOT.LEFT .AND. .NOT.NOTRAN )
*
IF( FORWRD ) THEN
I1 = 1
I2 = NQ - 1
I3 = 1
II = 2
ELSE
I1 = NQ - 1
I2 = 1
I3 = -1
II = NQ*( NQ+1 ) / 2 - 1
END IF
*
IF( LEFT ) THEN
NI = N
ELSE
MI = M
END IF
*
DO 10 I = I1, I2, I3
IF( LEFT ) THEN
*
* H(i) is applied to C(1:i,1:n)
*
MI = I
ELSE
*
* H(i) is applied to C(1:m,1:i)
*
NI = I
END IF
*
* Apply H(i)
*
AII = AP( II )
AP( II ) = ONE
CALL SLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAU( I ), C, LDC,
$ WORK )
AP( II ) = AII
*
IF( FORWRD ) THEN
II = II + I + 2
ELSE
II = II - I - 1
END IF
10 CONTINUE
ELSE
*
* Q was determined by a call to SSPTRD with UPLO = 'L'.
*
FORWRD = ( LEFT .AND. .NOT.NOTRAN ) .OR.
$ ( .NOT.LEFT .AND. NOTRAN )
*
IF( FORWRD ) THEN
I1 = 1
I2 = NQ - 1
I3 = 1
II = 2
ELSE
I1 = NQ - 1
I2 = 1
I3 = -1
II = NQ*( NQ+1 ) / 2 - 1
END IF
*
IF( LEFT ) THEN
NI = N
JC = 1
ELSE
MI = M
IC = 1
END IF
*
DO 20 I = I1, I2, I3
AII = AP( II )
AP( II ) = ONE
IF( LEFT ) THEN
*
* H(i) is applied to C(i+1:m,1:n)
*
MI = M - I
IC = I + 1
ELSE
*
* H(i) is applied to C(1:m,i+1:n)
*
NI = N - I
JC = I + 1
END IF
*
* Apply H(i)
*
CALL SLARF( SIDE, MI, NI, AP( II ), 1, TAU( I ),
$ C( IC, JC ), LDC, WORK )
AP( II ) = AII
*
IF( FORWRD ) THEN
II = II + NQ - I + 1
ELSE
II = II - NQ + I - 2
END IF
20 CONTINUE
END IF
RETURN
*
* End of SOPMTR
*
END
|
