ZTBSV  solves one of the systems of equations


    A*x = b,   or   A**T*x = b,   or   A**H*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

          UPLO is CHARACTER*1


           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.

TRANS

          TRANS is CHARACTER*1


           On entry, TRANS specifies the equations to be solved as


           follows:


              TRANS = 'N' or 'n'   A*x = b.


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


              TRANS = 'C' or 'c'   A**H*x = b.

DIAG

          DIAG is CHARACTER*1


           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.

N

          N is INTEGER


           On entry, N specifies the order of the matrix A.


           N must be at least zero.

K

          K is INTEGER


           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 must satisfy  0 .le. K.

A

          A is COMPLEX*16 array, dimension ( LDA, N )


           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


                    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


           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.

LDA

          LDA is INTEGER


           On entry, LDA specifies the first dimension of A as declared


           in the calling (sub) program. LDA must be at least


           ( k + 1 ).

X

          X is COMPLEX*16 array, dimension at least


           ( 1 + ( n - 1 )*abs( INCX ) ).


           Before entry, the incremented array X must contain the n


           element right-hand side vector b. On exit, X is overwritten


           with the solution vector x.

INCX

          INCX is INTEGER


           On entry, INCX specifies the increment for the elements of


           X. INCX must not be zero.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  Level 2 Blas routine.


  -- Written on 22-October-1986.


     Jack Dongarra, Argonne National Lab.


     Jeremy Du Croz, Nag Central Office.


     Sven Hammarling, Nag Central Office.


     Richard Hanson, Sandia National Labs.