LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  dpbrfs (UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO) 
DPBRFS 
subroutine dpbrfs  (  character  UPLO, 
integer  N,  
integer  KD,  
integer  NRHS,  
double precision, dimension( ldab, * )  AB,  
integer  LDAB,  
double precision, dimension( ldafb, * )  AFB,  
integer  LDAFB,  
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  
) 
DPBRFS
Download DPBRFS + dependencies [TGZ] [ZIP] [TXT]DPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution.
[in]  UPLO  UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. 
[in]  KD  KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. 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 triangle of the symmetric 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). 
[in]  LDAB  LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. 
[in]  AFB  AFB is DOUBLE PRECISION array, dimension (LDAFB,N) The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A as computed by DPBTRF, in the same storage format as A (see AB). 
[in]  LDAFB  LDAFB is INTEGER The leading dimension of the array AFB. LDAFB >= 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,out]  X  X is DOUBLE PRECISION array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by DPBTRS. On exit, the improved 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 
ITMAX is the maximum number of steps of iterative refinement.
Definition at line 189 of file dpbrfs.f.