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AIX Version 4.3 Base Operating System and Extensions Technical Reference, Volume 2

## SSBMV or DSBMV Subroutine

### Purpose

Performs matrix-vector operations using symmetric band matrix.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

```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(*)```
```SUBROUTINE DSBMV(UPLO, N, K, ALPHA, A, LDA,
X, INCX, BETA, Y, INCY)
DOUBLE PRECISION ALPHA,BETA
INTEGER INCX,INCY,K,LDA,N
CHARACTER*1 UPLO
DOUBLE PRECISION A(LDA,*), X(*), Y(*)```

### Description

The SSBMV or DSBMV subroutine 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.

### Parameters

UPLO 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 On entry, N specifies the order of the matrix A; N must be at least 0; unchanged on exit.
K On entry, K specifies the number of superdiagonals of the matrix A; K must satisfy 0 .le. K; unchanged on exit.
ALPHA On entry, ALPHA specifies the scalar alpha; unchanged on exit.
A An array of dimension ( LDA, N ); on 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 transfers 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```

On 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 transfers 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 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 A vector of dimension at least (1 + (N-1) * abs( INCX ) ); on entry, the incremented array X must contain the vector x; unchanged on exit.
INCX On entry, INCX specifies the increment for the elements of X; INCX must not be 0; unchanged on exit.
BETA On entry, BETA specifies the scalar beta; unchanged on exit.
Y A vector of dimension at least (1 + (N-1) * abs( INCY ) ); on entry, the incremented array Y must contain the vector y; on exit, Y is overwritten by the updated vector y.
INCY On entry, INCY specifies the increment for the elements of Y; INCY must not be 0; unchanged on exit.

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