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      SUBROUTINE ZTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
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*     .. Scalar Arguments ..
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      INTEGER INCX,K,LDA,N
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      CHARACTER DIAG,TRANS,UPLO
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*     ..
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*     .. Array Arguments ..
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      DOUBLE COMPLEX A(LDA,*),X(*)
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*     ..
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*
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*  Purpose
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*  =======
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*
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*  ZTBMV  performs one of the matrix-vector operations
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*
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*     x := A*x,   or   x := A'*x,   or   x := conjg( A' )*x,
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*
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*  where x is an n element vector and  A is an n by n unit, or non-unit,
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*  upper or lower triangular band matrix, with ( k + 1 ) diagonals.
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*
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*  Arguments
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*  ==========
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*
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*  UPLO   - CHARACTER*1.
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*           On entry, UPLO specifies whether the matrix is an upper or
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*           lower triangular matrix as follows:
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*
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*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
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*
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*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
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*
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*           Unchanged on exit.
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*
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*  TRANS  - CHARACTER*1.
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*           On entry, TRANS specifies the operation to be performed as
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*           follows:
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*
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*              TRANS = 'N' or 'n'   x := A*x.
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*
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*              TRANS = 'T' or 't'   x := A'*x.
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*
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*              TRANS = 'C' or 'c'   x := conjg( A' )*x.
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*
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*           Unchanged on exit.
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*
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*  DIAG   - CHARACTER*1.
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*           On entry, DIAG specifies whether or not A is unit
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*           triangular as follows:
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*
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*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
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*
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*              DIAG = 'N' or 'n'   A is not assumed to be unit
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*                                  triangular.
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*
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*           Unchanged on exit.
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*
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*  N      - INTEGER.
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*           On entry, N specifies the order of the matrix A.
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*           N must be at least zero.
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*           Unchanged on exit.
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*
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*  K      - INTEGER.
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*           On entry with UPLO = 'U' or 'u', K specifies the number of
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*           super-diagonals of the matrix A.
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*           On entry with UPLO = 'L' or 'l', K specifies the number of
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*           sub-diagonals of the matrix A.
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*           K must satisfy  0 .le. K.
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*           Unchanged on exit.
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*
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*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
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*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
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*           by n part of the array A must contain the upper triangular
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*           band part of the matrix of coefficients, supplied column by
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*           column, with the leading diagonal of the matrix in row
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*           ( k + 1 ) of the array, the first super-diagonal starting at
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*           position 2 in row k, and so on. The top left k by k triangle
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*           of the array A is not referenced.
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*           The following program segment will transfer an upper
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*           triangular band matrix from conventional full matrix storage
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*           to band storage:
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*
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*                 DO 20, J = 1, N
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*                    M = K + 1 - J
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*                    DO 10, I = MAX( 1, J - K ), J
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*                       A( M + I, J ) = matrix( I, J )
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*              10    CONTINUE
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*              20 CONTINUE
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*
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*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
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*           by n part of the array A must contain the lower triangular
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*           band part of the matrix of coefficients, supplied column by
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*           column, with the leading diagonal of the matrix in row 1 of
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*           the array, the first sub-diagonal starting at position 1 in
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*           row 2, and so on. The bottom right k by k triangle of the
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*           array A is not referenced.
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*           The following program segment will transfer a lower
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*           triangular band matrix from conventional full matrix storage
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*           to band storage:
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*
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*                 DO 20, J = 1, N
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*                    M = 1 - J
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*                    DO 10, I = J, MIN( N, J + K )
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*                       A( M + I, J ) = matrix( I, J )
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*              10    CONTINUE
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*              20 CONTINUE
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*
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*           Note that when DIAG = 'U' or 'u' the elements of the array A
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*           corresponding to the diagonal elements of the matrix are not
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*           referenced, but are assumed to be unity.
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*           Unchanged on exit.
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*
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*  LDA    - INTEGER.
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*           On entry, LDA specifies the first dimension of A as declared
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*           in the calling (sub) program. LDA must be at least
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*           ( k + 1 ).
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*           Unchanged on exit.
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*
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*  X      - COMPLEX*16       array of dimension at least
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*           ( 1 + ( n - 1 )*abs( INCX ) ).
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*           Before entry, the incremented array X must contain the n
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*           element vector x. On exit, X is overwritten with the
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*           tranformed vector x.
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*
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*  INCX   - INTEGER.
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*           On entry, INCX specifies the increment for the elements of
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*           X. INCX must not be zero.
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*           Unchanged on exit.
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*
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*
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*  Level 2 Blas routine.
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*
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*  -- Written on 22-October-1986.
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*     Jack Dongarra, Argonne National Lab.
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*     Jeremy Du Croz, Nag Central Office.
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*     Sven Hammarling, Nag Central Office.
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*     Richard Hanson, Sandia National Labs.
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*
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*
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*     .. Parameters ..
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      DOUBLE COMPLEX ZERO
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      PARAMETER (ZERO= (0.0D+0,0.0D+0))
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*     ..
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*     .. Local Scalars ..
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      DOUBLE COMPLEX TEMP
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      INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
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      LOGICAL NOCONJ,NOUNIT
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*     ..
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*     .. External Functions ..
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      LOGICAL LSAME
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      EXTERNAL LSAME
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*     ..
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*     .. External Subroutines ..
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      EXTERNAL XERBLA
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*     ..
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*     .. Intrinsic Functions ..
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      INTRINSIC DCONJG,MAX,MIN
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*     ..
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*
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*     Test the input parameters.
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*
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      INFO = 0
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      IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
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          INFO = 1
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      ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
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     +         .NOT.LSAME(TRANS,'C')) THEN
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          INFO = 2
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      ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
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          INFO = 3
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      ELSE IF (N.LT.0) THEN
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          INFO = 4
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      ELSE IF (K.LT.0) THEN
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          INFO = 5
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      ELSE IF (LDA.LT. (K+1)) THEN
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          INFO = 7
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      ELSE IF (INCX.EQ.0) THEN
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          INFO = 9
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      END IF
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      IF (INFO.NE.0) THEN
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          CALL XERBLA('ZTBMV ',INFO)
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          RETURN
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      END IF
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*
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*     Quick return if possible.
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*
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      IF (N.EQ.0) RETURN
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*
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      NOCONJ = LSAME(TRANS,'T')
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      NOUNIT = LSAME(DIAG,'N')
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*
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*     Set up the start point in X if the increment is not unity. This
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*     will be  ( N - 1 )*INCX   too small for descending loops.
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*
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      IF (INCX.LE.0) THEN
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          KX = 1 - (N-1)*INCX
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      ELSE IF (INCX.NE.1) THEN
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          KX = 1
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      END IF
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*
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*     Start the operations. In this version the elements of A are
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*     accessed sequentially with one pass through A.
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*
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      IF (LSAME(TRANS,'N')) THEN
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*
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*         Form  x := A*x.
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*
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          IF (LSAME(UPLO,'U')) THEN
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              KPLUS1 = K + 1
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              IF (INCX.EQ.1) THEN
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                  DO 20 J = 1,N
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                      IF (X(J).NE.ZERO) THEN
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                          TEMP = X(J)
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                          L = KPLUS1 - J
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                          DO 10 I = MAX(1,J-K),J - 1
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                              X(I) = X(I) + TEMP*A(L+I,J)
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   10                     CONTINUE
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                          IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J)
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                      END IF
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   20             CONTINUE
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              ELSE
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                  JX = KX
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                  DO 40 J = 1,N
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                      IF (X(JX).NE.ZERO) THEN
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                          TEMP = X(JX)
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                          IX = KX
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                          L = KPLUS1 - J
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                          DO 30 I = MAX(1,J-K),J - 1
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                              X(IX) = X(IX) + TEMP*A(L+I,J)
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                              IX = IX + INCX
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   30                     CONTINUE
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                          IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J)
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                      END IF
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                      JX = JX + INCX
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                      IF (J.GT.K) KX = KX + INCX
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   40             CONTINUE
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              END IF
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          ELSE
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              IF (INCX.EQ.1) THEN
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                  DO 60 J = N,1,-1
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                      IF (X(J).NE.ZERO) THEN
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                          TEMP = X(J)
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                          L = 1 - J
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                          DO 50 I = MIN(N,J+K),J + 1,-1
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                              X(I) = X(I) + TEMP*A(L+I,J)
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   50                     CONTINUE
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                          IF (NOUNIT) X(J) = X(J)*A(1,J)
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                      END IF
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   60             CONTINUE
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              ELSE
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                  KX = KX + (N-1)*INCX
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                  JX = KX
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                  DO 80 J = N,1,-1
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                      IF (X(JX).NE.ZERO) THEN
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                          TEMP = X(JX)
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                          IX = KX
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                          L = 1 - J
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                          DO 70 I = MIN(N,J+K),J + 1,-1
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                              X(IX) = X(IX) + TEMP*A(L+I,J)
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                              IX = IX - INCX
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   70                     CONTINUE
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                          IF (NOUNIT) X(JX) = X(JX)*A(1,J)
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                      END IF
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                      JX = JX - INCX
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                      IF ((N-J).GE.K) KX = KX - INCX
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   80             CONTINUE
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              END IF
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          END IF
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      ELSE
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*
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*        Form  x := A'*x  or  x := conjg( A' )*x.
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*
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          IF (LSAME(UPLO,'U')) THEN
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              KPLUS1 = K + 1
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              IF (INCX.EQ.1) THEN
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                  DO 110 J = N,1,-1
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                      TEMP = X(J)
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                      L = KPLUS1 - J
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                      IF (NOCONJ) THEN
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                          IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
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                          DO 90 I = J - 1,MAX(1,J-K),-1
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                              TEMP = TEMP + A(L+I,J)*X(I)
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   90                     CONTINUE
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                      ELSE
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                          IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J))
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                          DO 100 I = J - 1,MAX(1,J-K),-1
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                              TEMP = TEMP + DCONJG(A(L+I,J))*X(I)
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  100                     CONTINUE
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                      END IF
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                      X(J) = TEMP
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  110             CONTINUE
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              ELSE
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                  KX = KX + (N-1)*INCX
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                  JX = KX
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                  DO 140 J = N,1,-1
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                      TEMP = X(JX)
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                      KX = KX - INCX
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                      IX = KX
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                      L = KPLUS1 - J
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                      IF (NOCONJ) THEN
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                          IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
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                          DO 120 I = J - 1,MAX(1,J-K),-1
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                              TEMP = TEMP + A(L+I,J)*X(IX)
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                              IX = IX - INCX
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  120                     CONTINUE
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                      ELSE
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                          IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J))
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                          DO 130 I = J - 1,MAX(1,J-K),-1
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                              TEMP = TEMP + DCONJG(A(L+I,J))*X(IX)
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                              IX = IX - INCX
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  130                     CONTINUE
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                      END IF
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                      X(JX) = TEMP
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                      JX = JX - INCX
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  140             CONTINUE
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              END IF
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          ELSE
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              IF (INCX.EQ.1) THEN
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                  DO 170 J = 1,N
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                      TEMP = X(J)
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                      L = 1 - J
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                      IF (NOCONJ) THEN
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                          IF (NOUNIT) TEMP = TEMP*A(1,J)
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                          DO 150 I = J + 1,MIN(N,J+K)
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                              TEMP = TEMP + A(L+I,J)*X(I)
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  150                     CONTINUE
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                      ELSE
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                          IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J))
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                          DO 160 I = J + 1,MIN(N,J+K)
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                              TEMP = TEMP + DCONJG(A(L+I,J))*X(I)
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  160                     CONTINUE
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                      END IF
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                      X(J) = TEMP
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  170             CONTINUE
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              ELSE
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                  JX = KX
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                  DO 200 J = 1,N
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                      TEMP = X(JX)
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                      KX = KX + INCX
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                      IX = KX
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                      L = 1 - J
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                      IF (NOCONJ) THEN
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                          IF (NOUNIT) TEMP = TEMP*A(1,J)
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                          DO 180 I = J + 1,MIN(N,J+K)
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                              TEMP = TEMP + A(L+I,J)*X(IX)
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                              IX = IX + INCX
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  180                     CONTINUE
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                      ELSE
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                          IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J))
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                          DO 190 I = J + 1,MIN(N,J+K)
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                              TEMP = TEMP + DCONJG(A(L+I,J))*X(IX)
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                              IX = IX + INCX
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  190                     CONTINUE
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                      END IF
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                      X(JX) = TEMP
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                      JX = JX + INCX
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  200             CONTINUE
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              END IF
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          END IF
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      END IF
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*
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      RETURN
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*
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*     End of ZTBMV .
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*
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      END