NAME

ztbmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x

SYNOPSIS

  SUBROUTINE ZTBMV( 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 ZTBMV_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 TBMV( 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 TBMV_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

#include <sunperf.h>

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

void ztbmv_64(char uplo, char transa, char diag, long n, long ndiag, doublecomplex *a, long lda, doublecomplex *y, long incy);

PURPOSE

ztbmv performs one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( 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 ( ndiag + 1 ) diagonals.

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 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 : = conjg( A' )*x.

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 vector x. On exit, Y is overwritten with the tranformed vector x.
INCY (input)
On entry, INCY specifies the increment for the elements of Y. INCY < > 0. Unchanged on exit.