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zhbmv.f -

# SYNOPSIS

## Functions/Subroutines

subroutine zhbmv (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
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

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