CTBTRS 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.

UPLO

          UPLO is CHARACTER*1


          = 'U':  A is upper triangular;


          = 'L':  A is lower triangular.

TRANS

          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

          DIAG is CHARACTER*1


          = 'N':  A is non-unit triangular;


          = 'U':  A is unit triangular.

N

          N is INTEGER


          The order of the matrix A.  N >= 0.

KD

          KD is INTEGER


          The number of superdiagonals or subdiagonals of the


          triangular band matrix A.  KD >= 0.

NRHS

          NRHS is INTEGER


          The number of right hand sides, i.e., the number of columns


          of the matrix B.  NRHS >= 0.

AB

          AB is COMPLEX 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

          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

B

          B is COMPLEX array, dimension (LDB,NRHS)


          On entry, the right hand side matrix B.


          On exit, if INFO = 0, the solution matrix X.

LDB

          LDB is INTEGER


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

INFO

          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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011