cunmbr.f

          SUBROUTINE CUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
         $                   LDC, WORK, LWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          SIDE, TRANS, VECT
          INTEGER            INFO, K, LDA, LDC, LWORK, M, N
    *     ..
    *     .. Array Arguments ..
          COMPLEX            A( LDA, * ), C( LDC, * ), TAU( * ),
         $                   WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  If VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C
    *  with
    *                  SIDE = 'L'     SIDE = 'R'
    *  TRANS = 'N':      Q * C          C * Q
    *  TRANS = 'C':      Q**H * C       C * Q**H
    *
    *  If VECT = 'P', CUNMBR overwrites the general complex M-by-N matrix C
    *  with
    *                  SIDE = 'L'     SIDE = 'R'
    *  TRANS = 'N':      P * C          C * P
    *  TRANS = 'C':      P**H * C       C * P**H
    *
    *  Here Q and P**H are the unitary matrices determined by CGEBRD when
    *  reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
    *  and P**H are defined as products of elementary reflectors H(i) and
    *  G(i) respectively.
    *
    *  Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
    *  order of the unitary matrix Q or P**H that is applied.
    *
    *  If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
    *  if nq >= k, Q = H(1) H(2) . . . H(k);
    *  if nq < k, Q = H(1) H(2) . . . H(nq-1).
    *
    *  If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
    *  if k < nq, P = G(1) G(2) . . . G(k);
    *  if k >= nq, P = G(1) G(2) . . . G(nq-1).
    *
    *  Arguments
    *  =========
    *
    *  VECT    (input) CHARACTER*1
    *          = 'Q': apply Q or Q**H;
    *          = 'P': apply P or P**H.
    *
    *  SIDE    (input) CHARACTER*1
    *          = 'L': apply Q, Q**H, P or P**H from the Left;
    *          = 'R': apply Q, Q**H, P or P**H from the Right.
    *
    *  TRANS   (input) CHARACTER*1
    *          = 'N':  No transpose, apply Q or P;
    *          = 'C':  Conjugate transpose, apply Q**H or P**H.
    *
    *  M       (input) INTEGER
    *          The number of rows of the matrix C. M >= 0.
    *
    *  N       (input) INTEGER
    *          The number of columns of the matrix C. N >= 0.
    *
    *  K       (input) INTEGER
    *          If VECT = 'Q', the number of columns in the original
    *          matrix reduced by CGEBRD.
    *          If VECT = 'P', the number of rows in the original
    *          matrix reduced by CGEBRD.
    *          K >= 0.
    *
    *  A       (input) COMPLEX array, dimension
    *                                (LDA,min(nq,K)) if VECT = 'Q'
    *                                (LDA,nq)        if VECT = 'P'
    *          The vectors which define the elementary reflectors H(i) and
    *          G(i), whose products determine the matrices Q and P, as
    *          returned by CGEBRD.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.
    *          If VECT = 'Q', LDA >= max(1,nq);
    *          if VECT = 'P', LDA >= max(1,min(nq,K)).
    *
    *  TAU     (input) COMPLEX array, dimension (min(nq,K))
    *          TAU(i) must contain the scalar factor of the elementary
    *          reflector H(i) or G(i) which determines Q or P, as returned
    *          by CGEBRD in the array argument TAUQ or TAUP.
    *
    *  C       (input/output) COMPLEX array, dimension (LDC,N)
    *          On entry, the M-by-N matrix C.
    *          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
    *          or P*C or P**H*C or C*P or C*P**H.
    *
    *  LDC     (input) INTEGER
    *          The leading dimension of the array C. LDC >= max(1,M).
    *
    *  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The dimension of the array WORK.
    *          If SIDE = 'L', LWORK >= max(1,N);
    *          if SIDE = 'R', LWORK >= max(1,M);
    *          if N = 0 or M = 0, LWORK >= 1.
    *          For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
    *          and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
    *          optimal blocksize. (NB = 0 if M = 0 or N = 0.)
    *
    *          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.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *
    *  =====================================================================
    *
    *     .. Local Scalars ..
          LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN
          CHARACTER          TRANST
          INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          EXTERNAL           ILAENV, LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CUNMLQ, CUNMQR, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments
    *
          INFO = 0
          APPLYQ = LSAME( VECT, 'Q' )
          LEFT = LSAME( SIDE, 'L' )
          NOTRAN = LSAME( TRANS, 'N' )
          LQUERY = ( LWORK.EQ.-1 )
    *
    *     NQ is the order of Q or P and NW is the minimum dimension of WORK
    *
          IF( LEFT ) THEN
             NQ = M
             NW = N
          ELSE
             NQ = N
             NW = M
          END IF
          IF( M.EQ.0 .OR. N.EQ.0 ) THEN
             NW = 0
          END IF
          IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
             INFO = -1
          ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
             INFO = -2
          ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
             INFO = -3
          ELSE IF( M.LT.0 ) THEN
             INFO = -4
          ELSE IF( N.LT.0 ) THEN
             INFO = -5
          ELSE IF( K.LT.0 ) THEN
             INFO = -6
          ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
         $         ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
         $          THEN
             INFO = -8
          ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
             INFO = -11
          ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
             INFO = -13
          END IF
    *
          IF( INFO.EQ.0 ) THEN
             IF( NW.GT.0 ) THEN
                IF( APPLYQ ) THEN
                   IF( LEFT ) THEN
                      NB = ILAENV( 1, 'CUNMQR', SIDE // TRANS, M-1, N, M-1,
         $                         -1 )
                   ELSE
                      NB = ILAENV( 1, 'CUNMQR', SIDE // TRANS, M, N-1, N-1,
         $                         -1 )
                   END IF
                ELSE
                   IF( LEFT ) THEN
                      NB = ILAENV( 1, 'CUNMLQ', SIDE // TRANS, M-1, N, M-1,
         $                         -1 )
                   ELSE
                      NB = ILAENV( 1, 'CUNMLQ', SIDE // TRANS, M, N-1, N-1,
         $                         -1 )
                   END IF
                END IF
                LWKOPT = MAX( 1, NW*NB )
             ELSE
                LWKOPT = 1
             END IF
             WORK( 1 ) = LWKOPT
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'CUNMBR', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( M.EQ.0 .OR. N.EQ.0 )
         $   RETURN
    *
          IF( APPLYQ ) THEN
    *
    *        Apply Q
    *
             IF( NQ.GE.K ) THEN
    *
    *           Q was determined by a call to CGEBRD with nq >= k
    *
                CALL CUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
         $                   WORK, LWORK, IINFO )
             ELSE IF( NQ.GT.1 ) THEN
    *
    *           Q was determined by a call to CGEBRD with nq < k
    *
                IF( LEFT ) THEN
                   MI = M - 1
                   NI = N
                   I1 = 2
                   I2 = 1
                ELSE
                   MI = M
                   NI = N - 1
                   I1 = 1
                   I2 = 2
                END IF
                CALL CUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
         $                   C( I1, I2 ), LDC, WORK, LWORK, IINFO )
             END IF
          ELSE
    *
    *        Apply P
    *
             IF( NOTRAN ) THEN
                TRANST = 'C'
             ELSE
                TRANST = 'N'
             END IF
             IF( NQ.GT.K ) THEN
    *
    *           P was determined by a call to CGEBRD with nq > k
    *
                CALL CUNMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
         $                   WORK, LWORK, IINFO )
             ELSE IF( NQ.GT.1 ) THEN
    *
    *           P was determined by a call to CGEBRD with nq <= k
    *
                IF( LEFT ) THEN
                   MI = M - 1
                   NI = N
                   I1 = 2
                   I2 = 1
                ELSE
                   MI = M
                   NI = N - 1
                   I1 = 1
                   I2 = 2
                END IF
                CALL CUNMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
         $                   TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
             END IF
          END IF
          WORK( 1 ) = LWKOPT
          RETURN
    *
    *     End of CUNMBR
    *
          END