C Library Functions - ssbmv (3)

NAME

ssbmv(3f) - [BLAS:SINGLE_BLAS_LEVEL2] SY:=alpha*A*SX+beta*SY, A a symmetric band matrix.

Synopsis
Definition
Options
Y
Authors
Further Details
See Also

SYNOPSIS

subroutine ssbmv(uplo,n,k,alpha,a,lda,x,incx,beta,y,incy)

      .. Scalar Arguments ..
      real,intent(in)      :: alpha,beta
      integer,intent(in)   :: incx,incy,k,lda,n
      character,intent(in) :: uplo
      ..
      .. Array Arguments ..
      real,intent(in)      :: a(lda,*),x(*)
      real,intent(inout)   :: y(*)
      ..

DEFINITION

SSBMV 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.

OPTIONS

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.

N

N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero.

K

K is INTEGER On entry, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K.

ALPHA

ALPHA is REAL On entry, ALPHA specifies the scalar alpha.

A

A is REAL array, 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

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 ).

X

X is REAL array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x.

INCX

INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.

BETA

BETA is REAL On entry, BETA specifies the scalar beta.

Y

Y is REAL array, 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

INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.

AUTHORS

o Univ. of Tennessee

o Univ. of California Berkeley

o Univ. of Colorado Denver

o NAG Ltd.
 date:December 2016

FURTHER DETAILS

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.