.TH ZTBTRS 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME ZTBTRS - a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B, .SH SYNOPSIS .TP 19 SUBROUTINE ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) .TP 19 .ti +4 CHARACTER DIAG, TRANS, UPLO .TP 19 .ti +4 INTEGER INFO, KD, LDAB, LDB, N, NRHS .TP 19 .ti +4 COMPLEX*16 AB( LDAB, * ), B( LDB, * ) .SH 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. .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 = \(aqU\(aq: A is upper triangular; .br = \(aqL\(aq: A is lower triangular. .TP 8 TRANS (input) CHARACTER*1 .br Specifies the form of the system of equations: .br = \(aqN\(aq: A * X = B (No transpose) .br = \(aqT\(aq: A**T * X = B (Transpose) .br = \(aqC\(aq: A**H * X = B (Conjugate transpose) .TP 8 DIAG (input) CHARACTER*1 .br = \(aqN\(aq: A is non-unit triangular; .br = \(aqU\(aq: A is unit triangular. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 KD (input) INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. .TP 8 NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. .TP 8 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 = \(aqU\(aq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = \(aqL\(aq, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = \(aqU\(aq, the diagonal elements of A are not referenced and are assumed to be 1. .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. .TP 8 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. .TP 8 LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br > 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.