cupmtr.f

          SUBROUTINE CUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
         $                   INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          SIDE, TRANS, UPLO
          INTEGER            INFO, LDC, M, N
    *     ..
    *     .. Array Arguments ..
          COMPLEX            AP( * ), C( LDC, * ), TAU( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CUPMTR 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
    *
    *  where Q is a complex unitary 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 CHPTRD 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).
    *
    *  Arguments
    *  =========
    *
    *  SIDE    (input) CHARACTER*1
    *          = 'L': apply Q or Q**H from the Left;
    *          = 'R': apply Q or Q**H from the Right.
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U': Upper triangular packed storage used in previous
    *                 call to CHPTRD;
    *          = 'L': Lower triangular packed storage used in previous
    *                 call to CHPTRD.
    *
    *  TRANS   (input) CHARACTER*1
    *          = 'N':  No transpose, apply Q;
    *          = 'C':  Conjugate transpose, apply Q**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.
    *
    *  AP      (input) COMPLEX 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 CHPTRD.  AP is modified by the routine but
    *          restored on exit.
    *
    *  TAU     (input) COMPLEX 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 CHPTRD.
    *
    *  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.
    *
    *  LDC     (input) INTEGER
    *          The leading dimension of the array C. LDC >= max(1,M).
    *
    *  WORK    (workspace) COMPLEX array, dimension
    *                                   (N) if SIDE = 'L'
    *                                   (M) if SIDE = 'R'
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          COMPLEX            ONE
          PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            FORWRD, LEFT, NOTRAN, UPPER
          INTEGER            I, I1, I2, I3, IC, II, JC, MI, NI, NQ
          COMPLEX            AII, TAUI
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CLARF, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          CONJG, 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, 'C' ) ) 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( 'CUPMTR', -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 CHPTRD 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) or H(i)' is applied to C(1:i,1:n)
    *
                   MI = I
                ELSE
    *
    *              H(i) or H(i)' is applied to C(1:m,1:i)
    *
                   NI = I
                END IF
    *
    *           Apply H(i) or H(i)'
    *
                IF( NOTRAN ) THEN
                   TAUI = TAU( I )
                ELSE
                   TAUI = CONJG( TAU( I ) )
                END IF
                AII = AP( II )
                AP( II ) = ONE
                CALL CLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAUI, 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 CHPTRD 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) or H(i)' is applied to C(i+1:m,1:n)
    *
                   MI = M - I
                   IC = I + 1
                ELSE
    *
    *              H(i) or H(i)' is applied to C(1:m,i+1:n)
    *
                   NI = N - I
                   JC = I + 1
                END IF
    *
    *           Apply H(i) or H(i)'
    *
                IF( NOTRAN ) THEN
                   TAUI = TAU( I )
                ELSE
                   TAUI = CONJG( TAU( I ) )
                END IF
                CALL CLARF( SIDE, MI, NI, AP( II ), 1, TAUI, 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 CUPMTR
    *
          END