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dsbmv examples
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Man Page Details
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 NAME
      DSBMV - perform the matrix-vector operation   y := alpha*A*x
      + beta*y,

 SYNOPSIS
      SUBROUTINE DSBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA,
                       Y, INCY )

          DOUBLE       PRECISION ALPHA, BETA

          INTEGER      INCX, INCY, K, LDA, N

          CHARACTER*1  UPLO

          DOUBLE       PRECISION A( LDA, * ), X( * ), Y( * )

 PURPOSE
      DSBMV  performs the matrix-vector  operation

      where alpha and beta are scalars, x and y are n element vec-
      tors and A is an n by n symmetric band matrix, with k
      super-diagonals.

 PARAMETERS
      UPLO   - CHARACTER*1.
             On entry, UPLO specifies whether the upper or lower
             triangular part of the band matrix A is being sup-
             plied 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.

             Unchanged on exit.

      N      - INTEGER.
             On entry, N specifies the order of the matrix A.  N
             must be at least zero.  Unchanged on exit.

      K      - INTEGER.
             On entry, K specifies the number of super-diagonals
             of the matrix A. K must satisfy  0 .le. K.  Unchanged
             on exit.

      ALPHA  - DOUBLE PRECISION.
             On entry, ALPHA specifies the scalar alpha.
             Unchanged on exit.

      A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).

             Before entry with UPLO = 'U' or 'u', the leading ( k
             + 1 ) by n part of the array A must contain the upper
             triangular band part of the symmetric matrix, sup-
             plied column by column, with the leading diagonal of
             the matrix in row ( k + 1 ) of the array, the first
             super-diagonal starting at position 2 in row k, and
             so on. The top left k by k triangle of the array A is
             not referenced.  The following program segment will
             transfer the upper triangular part of a symmetric
             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

             Before entry with UPLO = 'L' or 'l', the leading ( k
             + 1 ) by n part of the array A must contain the lower
             triangular band part of the symmetric matrix, sup-
             plied column by column, with the leading diagonal of
             the matrix in row 1 of the array, the first sub-
             diagonal starting at position 1 in row 2, and so on.
             The bottom right k by k triangle of the array A is
             not referenced.  The following program segment will
             transfer the lower triangular part of a symmetric
             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

             Unchanged on exit.

      LDA    - INTEGER.
             On entry, LDA specifies the first dimension of A as
             declared in the calling (sub) program. LDA must be at
             least ( k + 1 ).  Unchanged on exit.

      X      - DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ).  Before entry, the
             incremented array X must contain the vector x.
             Unchanged on exit.

      INCX   - INTEGER.
             On entry, INCX specifies the increment for the ele-
             ments of X. INCX must not be zero.  Unchanged on
             exit.

      BETA   - DOUBLE PRECISION.
             On entry, BETA specifies the scalar beta.  Unchanged
             on exit.

      Y      - DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCY ) ).  Before entry, the
             incremented array Y must contain the vector y. On
             exit, Y is overwritten by the updated vector y.

      INCY   - INTEGER.
             On entry, INCY specifies the increment for the ele-
             ments of Y. INCY must not be zero.  Unchanged on
             exit.

