# ctbmv

```CTBMV(1)                         BLAS routine                         CTBMV(1)

NAME
CTBMV - performs one of the matrix-vector operations   x := A*x, or x
:= A'*x, or x := conjg( A' )*x,

SYNOPSIS
SUBROUTINE CTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)

INTEGER                                        INCX,K,LDA,N

CHARACTER                                      DIAG,TRANS,UPLO

COMPLEX                                        A(LDA,*),X(*)

PURPOSE
CTBMV  performs one of the matrix-vector operations

where x is an n element vector and  A is an n by n unit, or non-unit,
upper or lower triangular band matrix, with ( k + 1 ) diagonals.

ARGUMENTS
UPLO   - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or lower
triangular matrix as follows:

UPLO = 'U' or 'u'   A is an upper triangular matrix.

UPLO = 'L' or 'l'   A is a lower triangular matrix.

Unchanged on exit.

TRANS  - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:

TRANS = 'N' or 'n'   x := A*x.

TRANS = 'T' or 't'   x := A'*x.

TRANS = 'C' or 'c'   x := conjg( A' )*x.

Unchanged on exit.

DIAG   - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular as
follows:

DIAG = 'U' or 'u'   A is assumed to be unit triangular.

DIAG = 'N' or 'n'   A is not assumed to be unit triangular.

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 with UPLO = 'U' or 'u', K specifies the number of
super-diagonals of the matrix A.  On entry with UPLO = 'L' or
'l', K specifies the number of sub-diagonals of the matrix A.  K
must satisfy  0 .le. K.  Unchanged on exit.

A      - COMPLEX          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 matrix of coefficients, 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 an
upper triangular 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 matrix of coefficients, 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 a lower
triangular 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 when DIAG = 'U' or 'u' the elements of the array A
corresponding to the diagonal elements of the matrix are not
referenced, but are assumed to be unity.  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 of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).  Before entry, the incremented
array X must contain the n element vector x. On exit, X is
overwritten with the tranformed vector x.

INCX   - INTEGER.
On entry, INCX specifies the increment for the elements of X.
INCX must not be zero.  Unchanged on exit.

FURTHER DETAILS
Level 2 Blas routine.

-- 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.

BLAS routine                     November 2008                        CTBMV(1)```