ctbmv (l)  Linux Manuals
ctbmv: performs one of the matrixvector operations x := A*x, or x := Aaq*x, or x := conjg( Aaq )*x,
NAME
CTBMV  performs one of the matrixvector operations x := A*x, or x := Aaq*x, or x := conjg( Aaq )*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 matrixvector operationswhere x is an n element vector and A is an n by n unit, or nonunit, 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 = aqUaq or aquaq A is an upper triangular matrix.
UPLO = aqLaq or aqlaq A is a lower triangular matrix.
Unchanged on exit.
 TRANS  CHARACTER*1.

On entry, TRANS specifies the operation to be performed as
follows:
TRANS = aqNaq or aqnaq x := A*x.
TRANS = aqTaq or aqtaq x := Aaq*x.
TRANS = aqCaq or aqcaq x := conjg( Aaq )*x.
Unchanged on exit.
 DIAG  CHARACTER*1.

On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = aqUaq or aquaq A is assumed to be unit triangular.
DIAG = aqNaq or aqnaq 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 = aqUaq or aquaq, K specifies the number of superdiagonals of the matrix A. On entry with UPLO = aqLaq or aqlaq, K specifies the number of subdiagonals of the matrix A. K must satisfy 0 .le. K. Unchanged on exit.
 A  COMPLEX array of DIMENSION ( LDA, n ).

Before entry with UPLO = aqUaq or aquaq, 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 superdiagonal 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 = aqLaq or aqlaq, 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 subdiagonal 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 = aqUaq or aquaq 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 22October1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.