stbmv, dtbmv, ctbmv, ztbmv 

Matrix-vector product for a triangular band matrix

FORMAT

  {S,D,C,Z}TBMV (uplo, trans, diag, n, k, a, lda, x, incx)

Arguments

  uplo                character*1
                      On entry, specifies whether the matrix A is an upper-
                      or lower-triangular matrix:

                      If uplo = 'U' or 'u', A is an upper-triangular matrix.

                      If uplo = 'L' or 'l', A is a lower-triangular matrix.
                      On exit, uplo is unchanged.

  trans               character*1
                      On entry, specifies the operation to be performed:

                      If trans = 'N' or 'n', the operation is y  =  alpha*Ax
                      + beta*y.

                      If trans = 'T' or 't', the operation is y  =
                      alpha*transp(A)*x + beta*y.

                      If trans = 'C' or 'c', the operation is y  =
                      alpha*conjug_transp(A)*x + beta*y.
                      On exit, trans is unchanged.

  diag                character*1
                      On entry, specifies whether the matrix A is unit-
                      triangular:

                      If diag = 'U' or 'u', A is a unit-triangular matrix.

                      If diag = 'N' or 'n', A is not a unit-triangular
                      matrix.
                      On exit, diag is unchanged.

  n                   integer*4
                      On entry, the order of the matrix A; n >= 0.
                      On exit, n is unchanged.

  k                   integer*4
                      On entry, if uplo is equal to 'U' or matrix A.  If uplo
                      is equal to 'L' or 'l', the number of sub-diagonals k
                      of the matrix A; k >= 0.
                      On exit, k is unchanged.

  a                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a two-dimensional array with dimensions lda
                      by n.

  When uplo specifies the upper portion of the matrix, the leading (k + 1) by
  n part of the array must contain the upper-triangular band part of the
  matrix, supplied column by column. The main diagonal of the matrix is
  stored in row (k + 1) of the array, the first super-diagonal is stored in
  row k starting at position 2, and so on.  The bottom left k by k triangle
  of the array A is not referenced.

  When uplo specifies the lower portion of the matrix, the leading (k + 1) by
  n part of the array must contain the lower-triangular band part of the
  matrix, supplied column by column. The main diagonal of the matrix is
  stored in row 1 of the array, the first sub-diagonal is stored in row 2,
  starting at position 1, and so on. The top right k by k triangle of the
  array A is not referenced.

  If diag is equal to 'U' or diagonal elements of the matrix are not
  referenced, but are assumed to be unity.
  On exit, a is unchanged.

  lda                 integer*4
                      On entry, the first dimension of array A; lda >= (k+1).
                      On exit, lda is unchanged.

  x                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a one-dimensional array X of length at least
                      (1+(n-1)*|incx|).  Array X contains the vector x.
                      On exit, x is overwritten with the transformed vector
                      x.

  incx                integer*4
                      On entry, the increment for the elements of X; incx
                      must not equal zero.
                      On exit, incx is unchanged.

Description

  The _TBMV subprograms compute a matrix-vector product for a triangular band
  matrix or its transpose:  x  =  Ax  or
   x  =  transp(A)*x .

  In addition to these operations, the CTBMV and ZTBMV subprograms compute
  the matrix-vector product for the conjugate transpose:
   x  =  conjug_transp(A)*x.

  x is a vector with n elements and A is an n by n band matrix, with (k + 1)
  diagonals. The band matrix is a unit or non-unit, upper- or lower-
  triangular matrix.

Example

  REAL*4 A(5,100), X(100)
  INCX = 1
  LDA = 5
  K = 4
  N = 100
  CALL STBMV('U','N','N',N,K,A,LDA,X,INCX)

  This FORTRAN code computes the product x  =  Ax where A is an upper-
  triangular, non-unit diagonal matrix, with 4 superdiagonals.