# cgbmv.f - Man Page

BLAS/SRC/cgbmv.f

## Synopsis

### Functions/Subroutines

subroutine cgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)
CGBMV

## Function/Subroutine Documentation

### subroutine cgbmv (character trans, integer m, integer n, integer kl, integer ku, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(*) x, integer incx, complex beta, complex, dimension(*) y, integer incy)

CGBMV

Purpose:

``` CGBMV  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
On entry, ALPHA specifies the scalar alpha.```

A

```          A is COMPLEX array, 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 array, 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
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 array, 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.
If either m or n is zero, then Y not referenced and the function
performs a quick return.```

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.

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 cgbmv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cgbmv(3) is an alias of cgbmv.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK