DTBTRS  - solve a triangular system of the form  A * X = B
       or A**T * X = B,


SYNOPSIS

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

           CHARACTER      DIAG, TRANS, UPLO

           INTEGER        INFO, KD, LDAB, LDB, N, NRHS

           DOUBLE         PRECISION AB( LDAB, * ), B( LDB, * )


PURPOSE

       DTBTRS solves a triangular system of the form A * X = B or
       A**T * 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 ver­
       ify that A is nonsingular.


ARGUMENTS

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

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

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

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

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

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

       AB      (input) DOUBLE PRECISION 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',

               DIAG = 'U', the diagonal elements  of  A  are  not
               referenced and are assumed to be 1.

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

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

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

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal 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.


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