LAPACK
3.5.0
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  dsbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
DSBMV More...  
subroutine dsbmv  (  character  UPLO, 
integer  N,  
integer  K,  
double precision  ALPHA,  
double precision, dimension(lda,*)  A,  
integer  LDA,  
double precision, dimension(*)  X,  
integer  INCX,  
double precision  BETA,  
double precision, dimension(*)  Y,  
integer  INCY  
) 
DSBMV
DSBMV performs the matrixvector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric band matrix, with k superdiagonals.
[in]  UPLO  UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the band matrix A is being 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. 
[in]  N  N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. 
[in]  K  K is INTEGER On entry, K specifies the number of superdiagonals of the matrix A. K must satisfy 0 .le. K. 
[in]  ALPHA  ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. 
[in]  A  A is 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, 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 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, 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 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 
[in]  LDA  LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ). 
[in]  X  X is DOUBLE PRECISION array of DIMENSION at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x. 
[in]  INCX  INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 
[in]  BETA  BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta. 
[in,out]  Y  Y is 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. 
[in]  INCY  INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. 
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 185 of file dsbmv.f.