Contents
ztbsv - solve one of the systems of equations A*x = b, or
A'*x = b, or conjg( A' )*x = b
SUBROUTINE ZTBSV(UPLO, TRANSA, DIAG, N, K, A, LDA, Y, INCY)
CHARACTER * 1 UPLO, TRANSA, DIAG
DOUBLE COMPLEX A(LDA,*), Y(*)
INTEGER N, K, LDA, INCY
SUBROUTINE ZTBSV_64(UPLO, TRANSA, DIAG, N, K, A, LDA, Y, INCY)
CHARACTER * 1 UPLO, TRANSA, DIAG
DOUBLE COMPLEX A(LDA,*), Y(*)
INTEGER*8 N, K, LDA, INCY
F95 INTERFACE
SUBROUTINE TBSV(UPLO, [TRANSA], DIAG, [N], K, A, [LDA], Y, [INCY])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
COMPLEX(8), DIMENSION(:) :: Y
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: N, K, LDA, INCY
SUBROUTINE TBSV_64(UPLO, [TRANSA], DIAG, [N], K, A, [LDA], Y,
[INCY])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
COMPLEX(8), DIMENSION(:) :: Y
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: N, K, LDA, INCY
C INTERFACE
#include <sunperf.h>
void ztbsv(char uplo, char transa, char diag, int n, int k,
doublecomplex *a, int lda, doublecomplex *y, int
incy);
void ztbsv_64(char uplo, char transa, char diag, long n,
long k, doublecomplex *a, long lda, doublecomplex
*y, long incy);
ztbsv solves one of the systems of equations A*x = b, or
A'*x = b, or conjg( A' )*x = b where b and x are n element
vectors and A is an n by n unit, or non-unit, upper or lower
triangular band matrix, with ( k + 1 ) diagonals.
No test for singularity or near-singularity is included in
this routine. Such tests must be performed before calling
this routine.
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 equations to be
solved as follows:
TRANSA = 'N' or 'n' A*x = b.
TRANSA = 'T' or 't' A'*x = b.
TRANSA = 'C' or 'c' conjg( A' )*x = b.
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
right-hand side vector b. On exit, Y is overwrit-
ten with the solution vector x.
INCY (input)
On entry, INCY specifies the increment for the
elements of Y. INCY <> 0. Unchanged on exit.