# csbmv.f - Man Page

TESTING/LIN/csbmv.f

## Synopsis

### Functions/Subroutines

subroutine csbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
CSBMV

## Function/Subroutine Documentation

### subroutine csbmv (character uplo, integer n, integer k, complex alpha, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integer incx, complex beta, complex, dimension( * ) y, integer incy)

CSBMV

Purpose:

``` CSBMV  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 symmetric band matrix, with k super-diagonals.```
```  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
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.

A      - COMPLEX array, 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 symmetric 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 symmetric 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 symmetric 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 symmetric 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

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 array, 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
On entry, BETA specifies the scalar beta.
Unchanged on exit.

Y      - COMPLEX array, 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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 150 of file csbmv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK