.TH SSBMV 1 "November 2006" "BLAS routine" "BLAS routine" .SH NAME SSBMV - the matrix-vector operation y := alpha*A*x + beta*y, .SH SYNOPSIS .TP 58 SUBROUTINE SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) .TP 58 .ti +4 REAL ALPHA,BETA .TP 58 .ti +4 INTEGER INCX,INCY,K,LDA,N .TP 58 .ti +4 CHARACTER UPLO .TP 58 .ti +4 REAL A(LDA,*),X(*),Y(*) .SH 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. .SH ARGUMENTS .TP 7 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 = \(aqU\(aq or \(aqu\(aq The upper triangular part of A is being supplied. UPLO = \(aqL\(aq or \(aql\(aq The lower triangular part of A is being supplied. Unchanged on exit. .TP 7 N - INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. .TP 7 K - INTEGER. On entry, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K. Unchanged on exit. .TP 7 ALPHA - REAL . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. .TP 7 A - REAL array of DIMENSION ( LDA, n ). Before entry with UPLO = \(aqU\(aq or \(aqu\(aq, 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 = \(aqL\(aq or \(aql\(aq, 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. .TP 7 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. .TP 7 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. .TP 7 INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. .TP 7 BETA - REAL . On entry, BETA specifies the scalar beta. Unchanged on exit. .TP 7 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. .TP 7 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.