NAME¶
SSBMV - perform the matrix-vector operation y := alpha*A*x + beta*y,
SYNOPSIS¶
- SUBROUTINE SSBMV
- ( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
REAL ALPHA, BETA INTEGER INCX, INCY, K, LDA, N CHARACTER*1 UPLO REAL A( LDA, *
), X( * ), Y( * )
PURPOSE¶
SSBMV performs the matrix-vector operation
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.
PARAMETERS¶
- UPLO - 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.
Unchanged on exit.
- N - INTEGER.
- On entry, N specifies the order of the matrix A. N must be at least zero.
Unchanged on exit.
- K - INTEGER.
- On entry, K specifies the number of super-diagonals of the matrix A. K
must satisfy 0 .le. K. Unchanged on exit.
- ALPHA - REAL .
- On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
- A - REAL 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
Unchanged on exit.
- LDA - INTEGER.
- On entry, LDA specifies the first dimension of A as declared in the
calling (sub) program. LDA must be at least ( k + 1 ). Unchanged on
exit.
- X - REAL array of DIMENSION at least
- ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must
contain the vector x. Unchanged on exit.
- INCX - INTEGER.
- On entry, INCX specifies the increment for the elements of X. INCX must
not be zero. Unchanged on exit.
- BETA - REAL .
- On entry, BETA specifies the scalar beta. Unchanged on exit.
- Y - REAL 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.
- INCY - INTEGER.
- On entry, INCY specifies the increment for the elements of Y. INCY must
not be zero. Unchanged on exit.
Level 2 Blas routine.
-- 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.