sopmtr.f

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*> \brief \b SOPMTR
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  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.
*
*> \ingroup upmtr
*
*  =====================================================================
      SUBROUTINE sopmtr( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC,
     $                   WORK,
     $                   INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE, TRANS, UPLO
      INTEGER            INFO, LDC, M, N
*     ..
*     .. Array Arguments ..
      REAL               AP( * ), C( LDC, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            FORWRD, LEFT, NOTRAN, UPPER
      INTEGER            I, I1, I2, I3, IC, II, JC, MI, NI, NQ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           slarf1f, slarf1l, 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)
*
            CALL slarf1l( side, mi, ni, ap( ii-i+1 ), 1, tau( i ), c,
     $                    ldc, work )
*
            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
            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 slarf1f( side, mi, ni, ap( ii ), 1, tau( i ),
     $                    c( ic, jc ), ldc, work )
*
            IF( forwrd ) THEN
               ii = ii + nq - i + 1
            ELSE
               ii = ii - nq + i - 2
            END IF
   20    CONTINUE
      END IF
      RETURN
*
*     End of SOPMTR
*
      SUBROUTINE sopmtr( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, …
      END