dtbsv(3P) Sun Performance Library dtbsv(3P)NAMEdtbsv - solve one of the systems of equations A*x = b, or A'*x = b
SYNOPSIS
SUBROUTINE DTBSV(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 DTBSV_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 TBSV(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 TBSV_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 dtbsv(char uplo, char transa, char diag, int n, int k, double *a,
int lda, double *y, int incy);
void dtbsv_64(char uplo, char transa, char diag, long n, long k, double
*a, long lda, double *y, long incy);
PURPOSEdtbsv solves one of the systems of equations A*x = b, or 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 rou‐
tine. Such tests must be performed before calling this routine.
ARGUMENTS
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 fol‐
lows:
TRANSA = 'N' or 'n' A*x = b.
TRANSA = 'T' or 't' A'*x = b.
TRANSA = 'C' or 'c' 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 triangular.
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 coefficients, supplied column by col‐
umn, 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 conven‐
tional 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 col‐
umn, 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 trans‐
fer 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 overwritten with the solution vector x.
INCY (input)
On entry, INCY specifies the increment for the elements of Y.
INCY <> 0. Unchanged on exit.
6 Mar 2009 dtbsv(3P)
