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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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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 matrix-vector 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 super-diagonals.
[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 super-diagonals 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 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, supplied 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 |
[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 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Definition at line 186 of file dsbmv.f.