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NAME
DTBMV - perform one of the matrix-vector operations x :=
A*x, or x := A'*x,
SYNOPSIS
SUBROUTINE DTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX
)
INTEGER INCX, K, LDA, N
CHARACTER*1 DIAG, TRANS, UPLO
DOUBLE PRECISION A( LDA, * ), X( * )
PURPOSE
DTBMV 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.
PARAMETERS
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 per-
formed as follows:
TRANS = 'N' or 'n' x := A*x.
TRANS = 'T' or 't' x := A'*x.
TRANS = 'C' or 'c' x := 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 triangu-
lar.
DIAG = 'N' or 'n' A is not assumed to be unit tri-
angular.
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 - DOUBLE PRECISION 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 conven-
tional 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 - DOUBLE PRECISION 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 transformed
vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the ele-
ments of X. INCX must not be zero. Unchanged on
exit.
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.