NAME

SYNOPSIS

  SUBROUTINE ZTBSV( UPLO, TRANSA, DIAG, N, NDIAG, A, LDA, Y, INCY)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  DOUBLE COMPLEX A(LDA,*), Y(*)
  INTEGER N, NDIAG, LDA, INCY
 
  SUBROUTINE ZTBSV_64( UPLO, TRANSA, DIAG, N, NDIAG, A, LDA, Y, INCY)
  CHARACTER * 1 UPLO, TRANSA, DIAG
  DOUBLE COMPLEX A(LDA,*), Y(*)
  INTEGER*8 N, NDIAG, LDA, INCY
 

F95 INTERFACE

  SUBROUTINE TBSV( UPLO, [TRANSA], DIAG, [N], NDIAG, A, [LDA], Y, 
 *       [INCY])
  CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
  COMPLEX(8), DIMENSION(:) :: Y
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER :: N, NDIAG, LDA, INCY
 
  SUBROUTINE TBSV_64( UPLO, [TRANSA], DIAG, [N], NDIAG, A, [LDA], Y, 
 *       [INCY])
  CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
  COMPLEX(8), DIMENSION(:) :: Y
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER(8) :: N, NDIAG, LDA, INCY
 

C INTERFACE

void ztbsv(char uplo, char transa, char diag, int n, int ndiag, doublecomplex *a, int lda, doublecomplex *y, int incy);

void ztbsv_64(char uplo, char transa, char diag, long n, long ndiag, doublecomplex *a, long lda, doublecomplex *y, long incy);

PURPOSE

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' conjg( 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 ( 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
 = NDIAG + 1 - J
O 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 ( 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 conventional full matrix storage to band storage:

   DO 20, J = 1, N
 = 1 - J
O 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 >= ( 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.