{S,D}SBMV (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy) {C,Z}HBMV (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
uplo character*1 On entry, specifies whether the upper- or lower- triangular part of the array A is referenced: If uplo = 'U' or 'u', the upper-triangular part of A is referenced. If uplo = 'L' or 'l', the lower-triangular part of A is referenced. On exit, uplo 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 specifies the upper portion of matrix A, k represents the number of super-diagonals of the matrix. If uplo specifies the lower portion, k is the number of subdiagonals; k >= 0. On exit, k is unchanged. alpha real*4 | real*8 | complex*8 | complex*16 On entry, the scalar alpha*. On exit, alpha 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 top 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 bottom right k by k triangle of the array A is not referenced. For CHBMV and ZHBMV routines, the imaginary parts of the diagonal elements are not accessed, need not be set, and are assumed to be zero. 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 unchanged. incx integer*4 On entry, the increment for the elements of X; incx must not equal zero. On exit, incx is unchanged. beta real*4 | real*8 | complex*8 | complex*16 On entry, the scalar beta. On exit, beta is unchanged. y real*4 | real*8 | complex*8 | complex*16 On entry, a one-dimensional array Y of length at least (1+(n-1)*|incy|). If beta= 0, y need not be set. If betais not equal to zero, the incremented array Y must contain the vector y. On exit, y is overwritten by the updated vector y. incy integer*4 On entry, the increment for the elements of Y; incy must not equal zero. On exit, incy is unchanged.
SSBMV and DSBMV compute a matrix-vector product for a real symmetric band matrix. CHBMV and ZHBMV compute a matrix-vector product for a complex Hermitian band matrix. Both products are described by the following operation: y = alpha*Ax + beta*y alphaand betaare scalars, and x and y are vectors with n elements. In the case of SSBMV and DSBMV, A is a symmetric matrix and in the case of CHBMV and ZHBMV, A is a Hermitian matrix.
REAL*8 A(2,10), X(10), Y(10), alpha, beta N = 10 K = 1 alpha = 2.0D0 LDA = 2 INCX = 1 beta = 1.0D0 INCY = 1 CALL DSBMV('U',N,K,alpha,A,LDA,X,INCX,beta,Y,INCY) This FORTRAN code computes the product y = alpha*Ax + y) where A is a symmetric tridiagonal matrix, with A stored in upper-triangular form. COMPLEX*8 A(2,10), X(10), Y(10), alpha, beta N = 10 K = 1 alpha = (2.0, 2.2) LDA = 2 INCX = 1 beta = (1.0, 0.0) This FORTRAN code computes the product y = alpha*Ax + y) where A is a Hermitian tridiagonal matrix, with the upper diagonal of A stored.