SYNOPSIS

SUBROUTINE ZTBTRS(

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

    

CHARACTER DIAG, TRANS, UPLO

    

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

    

COMPLEX*16 AB( LDAB, * ), B( LDB, * )

PURPOSE

ZTBTRS solves a triangular system of the form 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) CHARACTER*1

= 'U': A is upper triangular;
= 'L': A is lower triangular.

TRANS (input) 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) 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) 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) INTEGER

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

B (input/output) 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) 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 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.