ZTBTRS(3f)

NAME
ZTBTRS - a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,

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.