sormtr.f

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*> \brief \b SORMTR
*
*  =========== DOCUMENTATION ===========
*
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*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE SORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC,
*                          WORK, LWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          SIDE, TRANS, UPLO
*       INTEGER            INFO, LDA, LDC, LWORK, M, N
*       ..
*       .. Array Arguments ..
*       REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
*      $                   WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SORMTR 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 SSYTRD:
*>
*> 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 triangle of A contains elementary reflectors
*>                 from SSYTRD;
*>          = 'L': Lower triangle of A contains elementary reflectors
*>                 from SSYTRD.
*> \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] A
*> \verbatim
*>          A is REAL array, dimension
*>                               (LDA,M) if SIDE = 'L'
*>                               (LDA,N) if SIDE = 'R'
*>          The vectors which define the elementary reflectors, as
*>          returned by SSYTRD.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.
*>          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is REAL array, dimension
*>                               (M-1) if SIDE = 'L'
*>                               (N-1) if SIDE = 'R'
*>          TAU(i) must contain the scalar factor of the elementary
*>          reflector H(i), as returned by SSYTRD.
*> \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 (MAX(1,LWORK))
*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The dimension of the array WORK.
*>          If SIDE = 'L', LWORK >= max(1,N);
*>          if SIDE = 'R', LWORK >= max(1,M).
*>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
*>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
*>          blocksize.
*>
*>          If LWORK = -1, then a workspace query is assumed; the routine
*>          only calculates the optimal size of the WORK array, returns
*>          this value as the first entry of the WORK array, and no error
*>          message related to LWORK is issued by XERBLA.
*> \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 unmtr
*
*  =====================================================================
      SUBROUTINE sormtr( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C,
     $                   LDC,
     $                   WORK, LWORK, 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, LDA, LDC, LWORK, M, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
     $                   WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            LEFT, LQUERY, UPPER
      INTEGER            I1, I2, IINFO, LWKOPT, MI, NI, NB, NQ, NW
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      REAL               SROUNDUP_LWORK
      EXTERNAL           ilaenv, lsame, sroundup_lwork
*     ..
*     .. External Subroutines ..
      EXTERNAL           sormql, sormqr, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      left = lsame( side, 'L' )
      upper = lsame( uplo, 'U' )
      lquery = ( lwork.EQ.-1 )
*
*     NQ is the order of Q and NW is the minimum dimension of WORK
*
      IF( left ) THEN
         nq = m
         nw = max( 1, n )
      ELSE
         nq = n
         nw = max( 1, m )
      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.lsame( trans, 'N' ) .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( lda.LT.max( 1, nq ) ) THEN
         info = -7
      ELSE IF( ldc.LT.max( 1, m ) ) THEN
         info = -10
      ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
         info = -12
      END IF
*
      IF( info.EQ.0 ) THEN
         IF( upper ) THEN
            IF( left ) THEN
               nb = ilaenv( 1, 'SORMQL', side // trans, m-1, n, m-1,
     $                      -1 )
            ELSE
               nb = ilaenv( 1, 'SORMQL', side // trans, m, n-1, n-1,
     $                      -1 )
            END IF
         ELSE
            IF( left ) THEN
               nb = ilaenv( 1, 'SORMQR', side // trans, m-1, n, m-1,
     $                      -1 )
            ELSE
               nb = ilaenv( 1, 'SORMQR', side // trans, m, n-1, n-1,
     $                      -1 )
            END IF
         END IF
         lwkopt = nw*nb
         work( 1 ) = sroundup_lwork(lwkopt)
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'SORMTR', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 .OR. nq.EQ.1 ) THEN
         work( 1 ) = 1
         RETURN
      END IF
*
      IF( left ) THEN
         mi = m - 1
         ni = n
      ELSE
         mi = m
         ni = n - 1
      END IF
*
      IF( upper ) THEN
*
*        Q was determined by a call to SSYTRD with UPLO = 'U'
*
         CALL sormql( side, trans, mi, ni, nq-1, a( 1, 2 ), lda, tau,
     $                c,
     $                ldc, work, lwork, iinfo )
      ELSE
*
*        Q was determined by a call to SSYTRD with UPLO = 'L'
*
         IF( left ) THEN
            i1 = 2
            i2 = 1
         ELSE
            i1 = 1
            i2 = 2
         END IF
         CALL sormqr( side, trans, mi, ni, nq-1, a( 2, 1 ), lda, tau,
     $                c( i1, i2 ), ldc, work, lwork, iinfo )
      END IF
      work( 1 ) = sroundup_lwork(lwkopt)
      RETURN
*
*     End of SORMTR
*
      SUBROUTINE sormtr( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, …
      END