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# zhbmv

## man page of zhbmv

### zhbmv: perform the matrix-vector operation y := alpha*A*x + beta*y,

```NAME
ZHBMV - perform the matrix-vector operation   y := alpha*A*x + beta*y,

SYNOPSIS
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( * )

PURPOSE
ZHBMV  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 hermitian 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  - COMPLEX*16      .
On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

A      - COMPLEX*16       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  hermitian  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  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

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 hermitian 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  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

Note  that the imaginary parts of the diagonal elements need not
be set and are assumed to be zero.  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      - COMPLEX*16       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   - COMPLEX*16      .
On entry, BETA specifies the scalar beta.  Unchanged on exit.

Y      - COMPLEX*16       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.

ZHBMV(3)
```

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