man ztbrfs (Fonctions bibliothèques) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
NAME
ZTBRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
SYNOPSIS
- SUBROUTINE ZTBRFS(
- UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
- CHARACTER DIAG, TRANS, UPLO
- INTEGER INFO, KD, LDAB, LDB, LDX, N, NRHS
- DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
- COMPLEX*16 AB( LDAB, * ), B( LDB, * ), WORK( * ), X( LDX, * )
PURPOSE
ZTBRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. The solution matrix X must be computed by ZTBTRS or some other means before entering this routine. ZTBRFS does not do iterative refinement because doing so cannot improve the backward error.
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 matrices B and X. 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 the array. 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) COMPLEX*16 array, dimension (LDB,NRHS)
- The right hand side matrix B.
- LDB (input) INTEGER
- The leading dimension of the array B. LDB >= max(1,N).
- X (input) COMPLEX*16 array, dimension (LDX,NRHS)
- The solution matrix X.
- LDX (input) INTEGER
- The leading dimension of the array X. LDX >= max(1,N).
- FERR (output) DOUBLE PRECISION array, dimension (NRHS)
- The estimated forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error.
- BERR (output) DOUBLE PRECISION array, dimension (NRHS)
- The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).
- WORK (workspace) COMPLEX*16 array, dimension (2*N)
- RWORK (workspace) DOUBLE PRECISION array, dimension (N)
- INFO (output) INTEGER
- = 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value