man ztbtrs (Fonctions bibliothèques) - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,

NAME

ZTBTRS - solve 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 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.

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.