sorm22.f

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*> \brief \b SORM22 multiplies a general matrix by a banded orthogonal matrix.
*
*  =========== DOCUMENTATION ===========
*
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*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*     SUBROUTINE SORM22( SIDE, TRANS, M, N, N1, N2, Q, LDQ, C, LDC,
*    $                   WORK, LWORK, INFO )
*
*     .. Scalar Arguments ..
*     CHARACTER          SIDE, TRANS
*     INTEGER            M, N, N1, N2, LDQ, LDC, LWORK, INFO
*     ..
*     .. Array Arguments ..
*     REAL            Q( LDQ, * ), C( LDC, * ), WORK( * )
*     ..
*
*> \par Purpose
*  ============
*>
*> \verbatim
*>
*>
*>  SORM22 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'.
*>  The orthogonal matrix Q processes a 2-by-2 block structure
*>
*>         [  Q11  Q12  ]
*>     Q = [            ]
*>         [  Q21  Q22  ],
*>
*>  where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an
*>  N2-by-N2 upper triangular matrix.
*> \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] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          = 'N':  apply Q (No transpose);
*>          = 'C':  apply Q**T (Conjugate transpose).
*> \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] N1
*> \param[in] N2
*> \verbatim
*>          N1 is INTEGER
*>          N2 is INTEGER
*>          The dimension of Q12 and Q21, respectively. N1, N2 >= 0.
*>          The following requirement must be satisfied:
*>          N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'.
*> \endverbatim
*>
*> \param[in] Q
*> \verbatim
*>          Q is REAL array, dimension
*>                              (LDQ,M) if SIDE = 'L'
*>                              (LDQ,N) if SIDE = 'R'
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*>          LDQ is INTEGER
*>          The leading dimension of the array Q.
*>          LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'.
*> \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 >= M*N.
*>
*>          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 unm22
*
*  =====================================================================
      SUBROUTINE sorm22( SIDE, TRANS, M, N, N1, N2, Q, LDQ, 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..--
*
      IMPLICIT NONE
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE, TRANS
      INTEGER            M, N, N1, N2, LDQ, LDC, LWORK, INFO
*     ..
*     .. Array Arguments ..
      REAL               Q( LDQ, * ), C( LDC, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE
      parameter( one = 1.0e+0 )
*
*     .. Local Scalars ..
      LOGICAL            LEFT, LQUERY, NOTRAN
      INTEGER            I, LDWORK, LEN, LWKOPT, NB, NQ, NW
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SROUNDUP_LWORK
      EXTERNAL           lsame, sroundup_lwork
*     ..
*     .. External Subroutines ..
      EXTERNAL           sgemm, slacpy, strmm, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      left = lsame( side, 'L' )
      notran = lsame( trans, 'N' )
      lquery = ( lwork.EQ.-1 )
*
*     NQ is the order of Q;
*     NW is the minimum dimension of WORK.
*
      IF( left ) THEN
         nq = m
      ELSE
         nq = n
      END IF
      nw = nq
      IF( n1.EQ.0 .OR. n2.EQ.0 ) nw = 1
      IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
         info = -1
      ELSE IF( .NOT.lsame( trans, 'N' ) .AND.
     $         .NOT.lsame( trans, 'T' ) )
     $          THEN
         info = -2
      ELSE IF( m.LT.0 ) THEN
         info = -3
      ELSE IF( n.LT.0 ) THEN
         info = -4
      ELSE IF( n1.LT.0 .OR. n1+n2.NE.nq ) THEN
         info = -5
      ELSE IF( n2.LT.0 ) THEN
         info = -6
      ELSE IF( ldq.LT.max( 1, nq ) ) THEN
         info = -8
      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
         lwkopt = m*n
         work( 1 ) = sroundup_lwork( lwkopt )
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'SORM22', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 ) THEN
         work( 1 ) = 1
         RETURN
      END IF
*
*     Degenerate cases (N1 = 0 or N2 = 0) are handled using STRMM.
*
      IF( n1.EQ.0 ) THEN
         CALL strmm( side, 'Upper', trans, 'Non-Unit', m, n, one,
     $               q, ldq, c, ldc )
         work( 1 ) = one
         RETURN
      ELSE IF( n2.EQ.0 ) THEN
         CALL strmm( side, 'Lower', trans, 'Non-Unit', m, n, one,
     $               q, ldq, c, ldc )
         work( 1 ) = one
         RETURN
      END IF
*
*     Compute the largest chunk size available from the workspace.
*
      nb = max( 1, min( lwork, lwkopt ) / nq )
*
      IF( left ) THEN
         IF( notran ) THEN
            DO i = 1, n, nb
               len = min( nb, n-i+1 )
               ldwork = m
*
*              Multiply bottom part of C by Q12.
*
               CALL slacpy( 'All', n1, len, c( n2+1, i ), ldc, work,
     $                      ldwork )
               CALL strmm( 'Left', 'Lower', 'No Transpose',
     $                     'Non-Unit',
     $                     n1, len, one, q( 1, n2+1 ), ldq, work,
     $                     ldwork )
*
*              Multiply top part of C by Q11.
*
               CALL sgemm( 'No Transpose', 'No Transpose', n1, len,
     $                     n2,
     $                     one, q, ldq, c( 1, i ), ldc, one, work,
     $                     ldwork )
*
*              Multiply top part of C by Q21.
*
               CALL slacpy( 'All', n2, len, c( 1, i ), ldc,
     $                      work( n1+1 ), ldwork )
               CALL strmm( 'Left', 'Upper', 'No Transpose',
     $                     'Non-Unit',
     $                     n2, len, one, q( n1+1, 1 ), ldq,
     $                     work( n1+1 ), ldwork )
*
*              Multiply bottom part of C by Q22.
*
               CALL sgemm( 'No Transpose', 'No Transpose', n2, len,
     $                     n1,
     $                     one, q( n1+1, n2+1 ), ldq, c( n2+1, i ), ldc,
     $                     one, work( n1+1 ), ldwork )
*
*              Copy everything back.
*
               CALL slacpy( 'All', m, len, work, ldwork, c( 1, i ),
     $                      ldc )
            END DO
         ELSE
            DO i = 1, n, nb
               len = min( nb, n-i+1 )
               ldwork = m
*
*              Multiply bottom part of C by Q21**T.
*
               CALL slacpy( 'All', n2, len, c( n1+1, i ), ldc, work,
     $                      ldwork )
               CALL strmm( 'Left', 'Upper', 'Transpose', 'Non-Unit',
     $                     n2, len, one, q( n1+1, 1 ), ldq, work,
     $                     ldwork )
*
*              Multiply top part of C by Q11**T.
*
               CALL sgemm( 'Transpose', 'No Transpose', n2, len, n1,
     $                     one, q, ldq, c( 1, i ), ldc, one, work,
     $                     ldwork )
*
*              Multiply top part of C by Q12**T.
*
               CALL slacpy( 'All', n1, len, c( 1, i ), ldc,
     $                      work( n2+1 ), ldwork )
               CALL strmm( 'Left', 'Lower', 'Transpose', 'Non-Unit',
     $                     n1, len, one, q( 1, n2+1 ), ldq,
     $                     work( n2+1 ), ldwork )
*
*              Multiply bottom part of C by Q22**T.
*
               CALL sgemm( 'Transpose', 'No Transpose', n1, len, n2,
     $                     one, q( n1+1, n2+1 ), ldq, c( n1+1, i ), ldc,
     $                     one, work( n2+1 ), ldwork )
*
*              Copy everything back.
*
               CALL slacpy( 'All', m, len, work, ldwork, c( 1, i ),
     $                      ldc )
            END DO
         END IF
      ELSE
         IF( notran ) THEN
            DO i = 1, m, nb
               len = min( nb, m-i+1 )
               ldwork = len
*
*              Multiply right part of C by Q21.
*
               CALL slacpy( 'All', len, n2, c( i, n1+1 ), ldc, work,
     $                      ldwork )
               CALL strmm( 'Right', 'Upper', 'No Transpose',
     $                     'Non-Unit',
     $                     len, n2, one, q( n1+1, 1 ), ldq, work,
     $                     ldwork )
*
*              Multiply left part of C by Q11.
*
               CALL sgemm( 'No Transpose', 'No Transpose', len, n2,
     $                     n1,
     $                     one, c( i, 1 ), ldc, q, ldq, one, work,
     $                     ldwork )
*
*              Multiply left part of C by Q12.
*
               CALL slacpy( 'All', len, n1, c( i, 1 ), ldc,
     $                      work( 1 + n2*ldwork ), ldwork )
               CALL strmm( 'Right', 'Lower', 'No Transpose',
     $                     'Non-Unit',
     $                     len, n1, one, q( 1, n2+1 ), ldq,
     $                     work( 1 + n2*ldwork ), ldwork )
*
*              Multiply right part of C by Q22.
*
               CALL sgemm( 'No Transpose', 'No Transpose', len, n1,
     $                     n2,
     $                     one, c( i, n1+1 ), ldc, q( n1+1, n2+1 ), ldq,
     $                     one, work( 1 + n2*ldwork ), ldwork )
*
*              Copy everything back.
*
               CALL slacpy( 'All', len, n, work, ldwork, c( i, 1 ),
     $                      ldc )
            END DO
         ELSE
            DO i = 1, m, nb
               len = min( nb, m-i+1 )
               ldwork = len
*
*              Multiply right part of C by Q12**T.
*
               CALL slacpy( 'All', len, n1, c( i, n2+1 ), ldc, work,
     $                      ldwork )
               CALL strmm( 'Right', 'Lower', 'Transpose', 'Non-Unit',
     $                     len, n1, one, q( 1, n2+1 ), ldq, work,
     $                     ldwork )
*
*              Multiply left part of C by Q11**T.
*
               CALL sgemm( 'No Transpose', 'Transpose', len, n1, n2,
     $                     one, c( i, 1 ), ldc, q, ldq, one, work,
     $                     ldwork )
*
*              Multiply left part of C by Q21**T.
*
               CALL slacpy( 'All', len, n2, c( i, 1 ), ldc,
     $                      work( 1 + n1*ldwork ), ldwork )
               CALL strmm( 'Right', 'Upper', 'Transpose', 'Non-Unit',
     $                     len, n2, one, q( n1+1, 1 ), ldq,
     $                     work( 1 + n1*ldwork ), ldwork )
*
*              Multiply right part of C by Q22**T.
*
               CALL sgemm( 'No Transpose', 'Transpose', len, n2, n1,
     $                     one, c( i, n2+1 ), ldc, q( n1+1, n2+1 ), ldq,
     $                     one, work( 1 + n1*ldwork ), ldwork )
*
*              Copy everything back.
*
               CALL slacpy( 'All', len, n, work, ldwork, c( i, 1 ),
     $                      ldc )
            END DO
         END IF
      END IF
*
      work( 1 ) = sroundup_lwork( lwkopt )
      RETURN
*
*     End of SORM22
*
      SUBROUTINE sorm22( SIDE, TRANS, M, N, N1, N2, Q, LDQ, C, LDC, …
      END