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