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ZTBTRS(l)) ZTBTRS(l)NAMEZTBTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,SYNOPSISSUBROUTINE 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, * )PURPOSEZTBTRS 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.ARGUMENTSUPLO (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 =, 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.-iLAPACK version 3.015 June 2000 ZTBTRS(l)

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