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# Technical Reference: Base Operating System and Extensions , Volume 2

## CHBMV or ZHBMV Subroutine

### Purpose

Performs matrix-vector operations using a Hermitian band matrix.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

SUBROUTINE CHBMV(UPLO, N, K, ALPHA, A, LDA,
X, INCX, BETA, Y, INCY)
COMPLEX ALPHA, BETA
INTEGER INCX, INCY, K, LDA, N
CHARACTER*1 UPLO
COMPLEX A(LDA,*), X(*), Y(*)

```SUBROUTINE ZHBMV(UPLO, N, K, ALPHA, A, LDA,
X, INCX, BETA, Y, INCY)
COMPLEX*16 ALPHA,BETA
INTEGER INCX,INCY,K,LDA,N
CHARACTER*1 UPLO
COMPLEX*16 A(LDA,*), X(*), Y(*)
```

### Description

The CHBMV or ZHBMV 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 Hermitian band matrix with K superdiagonals.

### 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 Hermitian 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 Hermitian 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 ``` Note: 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 Hermitian 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 Hermitian 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 ``` The imaginary parts of the diagonal elements need not be set and are assumed to be 0. 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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