Contents
dtbmv - perform one of the matrix-vector operations x :=
A*x, or x := A'*x
SUBROUTINE DTBMV(UPLO, TRANSA, DIAG, N, K, A, LDA, Y, INCY)
CHARACTER * 1 UPLO, TRANSA, DIAG
INTEGER N, K, LDA, INCY
DOUBLE PRECISION A(LDA,*), Y(*)
SUBROUTINE DTBMV_64(UPLO, TRANSA, DIAG, N, K, A, LDA, Y, INCY)
CHARACTER * 1 UPLO, TRANSA, DIAG
INTEGER*8 N, K, LDA, INCY
DOUBLE PRECISION A(LDA,*), Y(*)
F95 INTERFACE
SUBROUTINE TBMV(UPLO, [TRANSA], DIAG, [N], K, A, [LDA], Y, [INCY])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
INTEGER :: N, K, LDA, INCY
REAL(8), DIMENSION(:) :: Y
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE TBMV_64(UPLO, [TRANSA], DIAG, [N], K, A, [LDA], Y,
[INCY])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
INTEGER(8) :: N, K, LDA, INCY
REAL(8), DIMENSION(:) :: Y
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dtbmv(char uplo, char transa, char diag, int n, int k,
double *a, int lda, double *y, int incy);
void dtbmv_64(char uplo, char transa, char diag, long n,
long k, double *a, long lda, double *y, long
incy);
dtbmv performs one of the matrix-vector operations x := A*x,
or x := A'*x, 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.
UPLO (input)
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.
TRANSA (input)
On entry, TRANSA specifies the operation to be
performed as follows:
TRANSA = 'N' or 'n' x := A*x.
TRANSA = 'T' or 't' x := A'*x.
TRANSA = 'C' or 'c' x := A'*x.
Unchanged on exit.
TRANSA is defaulted to 'N' for F95 INTERFACE.
DIAG (input)
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit tri-
angular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N (input)
On entry, N specifies the order of the matrix A.
N >= 0. Unchanged on exit.
K (input)
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 >= 0.
Unchanged on exit.
A (input)
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 coef-
ficients, 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 coef-
ficients, 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 (input)
On entry, LDA specifies the first dimension of A
as declared in the calling (sub) program. LDA >= (
k + 1 ). Unchanged on exit.
Y (input/output)
( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the
incremented array Y must contain the n element
vector x. On exit, Y is overwritten with the tran-
formed vector x.
INCY (input)
On entry, INCY specifies the increment for the
elements of Y. INCY <> 0. Unchanged on exit.