# zhbmv.f man page

zhbmv.f —

## Synopsis

### Functions/Subroutines

subroutinezhbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)ZHBMV

## Function/Subroutine Documentation

### subroutine zhbmv (characterUPLO, integerN, integerK, complex*16ALPHA, complex*16, dimension(lda,*)A, integerLDA, complex*16, dimension(*)X, integerINCX, complex*16BETA, complex*16, dimension(*)Y, integerINCY)

**ZHBMV Purpose:**

```
ZHBMV 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 super-diagonals.
```

**Parameters:**

*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 COMPLEX*16
On entry, ALPHA specifies the scalar alpha.
```

*A*

```
A is 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.
```

*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 COMPLEX*16 array of 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 COMPLEX*16
On entry, BETA specifies the scalar beta.
```

*Y*

```
Y is 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*

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

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

**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.
```

Definition at line 188 of file zhbmv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zhbmv(3) is an alias of zhbmv.f(3).