ZTBTRS(3)      LAPACK routine of NEC Numeric Library Collection      ZTBTRS(3)



NAME
       ZTBTRS

SYNOPSIS
       SUBROUTINE ZTBTRS (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB,
           INFO)



PURPOSE
            ZTBTRS solves a triangular system of the form

               A * X = B,  A**T * X = B,  or  A**H * X = B,

            where A is a triangular band matrix of order N, and B is an
            N-by-NRHS matrix.  A check is made to verify that A is nonsingular.




ARGUMENTS
           UPLO      (input)
                     UPLO is CHARACTER*1
                     = 'U':  A is upper triangular;
                     = 'L':  A is lower triangular.

           TRANS     (input)
                     TRANS is CHARACTER*1
                     Specifies the form of the system of equations:
                     = 'N':  A * X = B     (No transpose)
                     = 'T':  A**T * X = B  (Transpose)
                     = 'C':  A**H * X = B  (Conjugate transpose)

           DIAG      (input)
                     DIAG is CHARACTER*1
                     = 'N':  A is non-unit triangular;
                     = 'U':  A is unit triangular.

           N         (input)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           KD        (input)
                     KD is INTEGER
                     The number of superdiagonals or subdiagonals of the
                     triangular band matrix A.  KD >= 0.

           NRHS      (input)
                     NRHS is INTEGER
                     The number of right hand sides, i.e., the number of columns
                     of the matrix B.  NRHS >= 0.

           AB        (input)
                     AB is COMPLEX*16 array, dimension (LDAB,N)
                     The upper or lower triangular band matrix A, stored in the
                     first kd+1 rows of AB.  The j-th column of A is stored
                     in the j-th column of the array AB as follows:
                     if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
                     if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
                     If DIAG = 'U', the diagonal elements of A are not referenced
                     and are assumed to be 1.

           LDAB      (input)
                     LDAB is INTEGER
                     The leading dimension of the array AB.  LDAB >= KD+1.

           B         (input/output)
                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     On entry, the right hand side matrix B.
                     On exit, if INFO = 0, the solution matrix X.

           LDB       (input)
                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           INFO      (output)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value
                     > 0:  if INFO = i, the i-th diagonal element of A is zero,
                           indicating that the matrix is singular and the
                           solutions X have not been computed.



LAPACK routine                  31 October 2017                      ZTBTRS(3)