LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Go to the source code of this file.
Functions/Subroutines  
subroutine  dtbrfs (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO) 
DTBRFS 
subroutine dtbrfs  (  character  UPLO, 
character  TRANS,  
character  DIAG,  
integer  N,  
integer  KD,  
integer  NRHS,  
double precision, dimension( ldab, * )  AB,  
integer  LDAB,  
double precision, dimension( ldb, * )  B,  
integer  LDB,  
double precision, dimension( ldx, * )  X,  
integer  LDX,  
double precision, dimension( * )  FERR,  
double precision, dimension( * )  BERR,  
double precision, dimension( * )  WORK,  
integer, dimension( * )  IWORK,  
integer  INFO  
) 
DTBRFS
Download DTBRFS + dependencies [TGZ] [ZIP] [TXT]DTBRFS 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 DTBTRS or some other means before entering this routine. DTBRFS does not do iterative refinement because doing so cannot improve the backward error.
[in]  UPLO  UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. 
[in]  TRANS  TRANS is 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 = Transpose) 
[in]  DIAG  DIAG is CHARACTER*1 = 'N': A is nonunit triangular; = 'U': A is unit triangular. 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. 
[in]  KD  KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. 
[in]  NRHS  NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. 
[in]  AB  AB is DOUBLE PRECISION array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The jth column of A is stored in the jth column of the array AB as follows: if UPLO = 'U', AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j; if UPLO = 'L', AB(1+ij,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. 
[in]  LDAB  LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. 
[in]  B  B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side matrix B. 
[in]  LDB  LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). 
[in]  X  X is DOUBLE PRECISION array, dimension (LDX,NRHS) The solution matrix X. 
[in]  LDX  LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N). 
[out]  FERR  FERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bound for each solution vector X(j) (the jth 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. 
[out]  BERR  BERR is 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). 
[out]  WORK  WORK is DOUBLE PRECISION array, dimension (3*N) 
[out]  IWORK  IWORK is INTEGER array, dimension (N) 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value 
Definition at line 188 of file dtbrfs.f.