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zgbmv.f -

# SYNOPSIS

## Functions/Subroutines

subroutine zgbmv (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)

ZGBMV

# Function/Subroutine Documentation

## subroutine zgbmv (characterTRANS, integerM, integerN, integerKL, integerKU, complex*16ALPHA, complex*16, dimension(lda,*)A, integerLDA, complex*16, dimension(*)X, integerINCX, complex*16BETA, complex*16, dimension(*)Y, integerINCY)

ZGBMV Purpose:
``` ZGBMV  performs one of the matrix-vector operations

y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or

y := alpha*A**H*x + beta*y,

where alpha and beta are scalars, x and y are vectors and A is an
m by n band matrix, with kl sub-diagonals and ku super-diagonals.
```
Parameters:
TRANS
```          TRANS is CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows:

TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.

TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.

TRANS = 'C' or 'c'   y := alpha*A**H*x + beta*y.
```
M
```          M is INTEGER
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
```
N
```          N is INTEGER
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
```
KL
```          KL is INTEGER
On entry, KL specifies the number of sub-diagonals of the
matrix A. KL must satisfy  0 .le. KL.
```
KU
```          KU is INTEGER
On entry, KU specifies the number of super-diagonals of the
matrix A. KU must satisfy  0 .le. KU.
```
ALPHA
```          ALPHA is COMPLEX*16
On entry, ALPHA specifies the scalar alpha.
```
A
```          A is COMPLEX*16 array of DIMENSION ( LDA, n ).
Before entry, the leading ( kl + ku + 1 ) by n part of the
array A must contain the matrix of coefficients, supplied
column by column, with the leading diagonal of the matrix in
row ( ku + 1 ) of the array, the first super-diagonal
starting at position 2 in row ku, the first sub-diagonal
starting at position 1 in row ( ku + 2 ), and so on.
Elements in the array A that do not correspond to elements
in the band matrix (such as the top left ku by ku triangle)
are not referenced.
The following program segment will transfer a band matrix
from conventional full matrix storage to band storage:

DO 20, J = 1, N
K = KU + 1 - J
DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
A( K + I, J ) = matrix( I, J )
10    CONTINUE
20 CONTINUE
```
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
( kl + ku + 1 ).
```
X
```          X is COMPLEX*16 array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
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. When BETA is
supplied as zero then Y need not be set on input.
```
Y
```          Y is COMPLEX*16 array of DIMENSION at least
( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
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 zgbmv.f.

# Author

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