NAME

dtbsv - solve one of the systems of equations A*x = b, or A'*x = b

SYNOPSIS

  SUBROUTINE DTBSV( UPLO, TRANSA, DIAG, N, NDIAG, A, LDA, Y, INCY)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  INTEGER N, NDIAG, LDA, INCY
  DOUBLE PRECISION A(LDA,*), Y(*)

  SUBROUTINE DTBSV_64( UPLO, TRANSA, DIAG, N, NDIAG, A, LDA, Y, INCY)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  INTEGER*8 N, NDIAG, LDA, INCY
  DOUBLE PRECISION A(LDA,*), Y(*)

F95 INTERFACE

  SUBROUTINE TBSV( UPLO, [TRANSA], DIAG, [N], NDIAG, A, [LDA], Y, 
 *       [INCY])
  CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
  INTEGER :: N, NDIAG, LDA, INCY
  REAL(8), DIMENSION(:) :: Y
  REAL(8), DIMENSION(:,:) :: A

  SUBROUTINE TBSV_64( UPLO, [TRANSA], DIAG, [N], NDIAG, A, [LDA], Y, 
 *       [INCY])
  CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
  INTEGER(8) :: N, NDIAG, 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 ndiag, double *a, int lda, double *y, int incy);

void dtbsv_64(char uplo, char transa, char diag, long n, long ndiag, double *a, long lda, double *y, long incy);

PURPOSE

dtbsv 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 ( ndiag + 1 ) diagonals.

No test for singularity or near-singularity is included in this routine. 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 follows:
TRANSA = 'N' or 'n' A*x = b.

TRANSA = 'T' or 't' A'*x = b.

TRANSA = 'C' or 'c' A'*x = b.

Unchanged on exit.
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.
NDIAG (input)
On entry with UPLO = 'U' or 'u', NDIAG specifies the number of super-diagonals of the matrix A. On entry with UPLO = 'L' or 'l', NDIAG specifies the number of sub-diagonals of the matrix A. NDIAG > = 0. Unchanged on exit.
A (input)
Before entry with UPLO = 'U' or 'u', the leading ( ndiag + 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 ( ndiag + 1 ) of the array, the first super-diagonal starting at position 2 in row ndiag, and so on. The top left ndiag by ndiag 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 = NDIAG + 1 - J
      DO 10, I = MAX( 1, J - NDIAG ), J
        A( M + I, J ) = matrix( I, J )
 10   CONTINUE
 20 CONTINUE
```
Before entry with UPLO = 'L' or 'l', the leading ( ndiag + 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 ndiag by ndiag 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 + NDIAG )
        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 > = ( ndiag + 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.