hbmv(3F)

NAME
     CHBMV, ZHBMV - Multiplies a complex vector by a complex Hermitian band
     matrix

SYNOPSIS
     Complex

        CALL CHBMV (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)

     Double complex

        CALL ZHBMV (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)

IMPLEMENTATION
     IRIX systems

DESCRIPTION
     These routines perform the following operation:

          y <- alpha Ax + beta y

     where alpha and beta are scalars, x and y are n-element vectors, and A
     is an n-by-n Hermitian band matrix.

     These routines have the following arguments:

     uplo      Character*1.  (input)
               Specifies whether the upper or lower triangular part of the
               band matrix A is supplied, as follows:
               uplo= 'U' or 'u': the upper triangular part of A is being
               supplied.
               uplo= 'L' or 'l': the lower triangular part of A is being
               supplied.

     n         Integer.  (input)
               Specifies the order of matrix A.  n >= 0.

     k         Integer.  (input)
               Specifies the number of superdiagonals of matrix A.  k >= 0.

     alpha     Scalar alpha.  (input)
               CHBMV: Complex.
               ZHBMV: Double complex.

     a         Array of dimension (lda,n).  (input)
               CHBMV: Complex array.
               ZHBMV: Double complex array.

               Before entry with uplo = 'U' or 'u', the leading (k+1)-by-n
               part of array a must contain the upper triangular band part
               of the Hermitian matrix, supplied column-by-column, with the
               leading diagonal of the matrix in row k+1 of the array, the
               first superdiagonal starting at position 2 in row k, and so
               on.  The top left k-by-k triangle of array a is not
               referenced.

               Before entry with uplo = 'L' or 'l', the leading (k+1)-by-n
               part of array a must contain the lower triangular band part
               of the Hermitian matrix, supplied column-by-column, with the
               leading diagonal of the matrix in row 1 of the array, the
               first subdiagonal starting at position 1 in row 2, and so
               on.  The bottom right k-by-k triangle of array a is not
               referenced.

               The imaginary parts of the diagonal elements need not be set
               and are assumed to be 0.

               See the NOTES section for examples of Fortran code that
               transfer a band matrix from conventional full matrix storage
               to band storage.

     lda       Integer.  (input)
               Specifies the first dimension of a as declared in the
               calling program.  lda >= (k+1).

     x         Array of dimension 1+(n-1) * |incx|.  (input)
               CHBMV: Complex array.
               ZHBMV: Double complex array.
               Contains vector x.

     incx      Integer.  (input)
               Specifies the increment for the elements of x.  incx must
               not be 0.

     beta      Scalar beta.  (input)
               CHBMV: Complex.
               ZHBMV: Double complex.

     y         Array of dimension 1+(n-1) * |incy|.  (input and output)
               CHBMV: Complex array.
               ZHBMV: Double complex array.
               Contains vector y.  On exit, the updated vector overwrites
               array y.

     incy      Integer.  (input)
               Specifies the increment for the elements of y.  incy must
               not be 0.

NOTES
     The following program segment transfers the upper triangular part of a
     Hermitian band matrix from conventional full matrix storage to band
     storage:

              DO 20, J = 1, N
                 M = K + 1 - J
                 DO 10, I = MAX( 1, J - K ), J
                    A( M + I, J ) = MATRIX( I, J )
          10    CONTINUE
          20 CONTINUE

     The following program segment transfers the lower triangular part of a
     Hermitian band matrix from conventional full matrix storage to band
     storage:

              DO 20, J = 1, N
                 M = 1 - J
                 DO 10, I = J, MIN( N, J + K )
                    A( M + I, J ) = MATRIX( I, J )
          10    CONTINUE
          20 CONTINUE

     These routines are Level 2 Basic Linear Algebra Subprograms (Level 2
     BLAS).

     When working backward (incx < 0 or incy < 0), this routine starts at
     the end of the vector and moves backward, as follows:

          x(1-incx * (n-1)), x(1-incx * (n-2)) , ..., x(1)

          y(1-incy * (n-1)), y(1-incy * (n-2)) , ..., y(1)

SEE ALSO
     SBMV(3F)

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