LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Go to the source code of this file.
Functions/Subroutines  
subroutine  zpbrfs (UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO) 
ZPBRFS 
subroutine zpbrfs  (  character  UPLO, 
integer  N,  
integer  KD,  
integer  NRHS,  
complex*16, dimension( ldab, * )  AB,  
integer  LDAB,  
complex*16, dimension( ldafb, * )  AFB,  
integer  LDAFB,  
complex*16, dimension( ldb, * )  B,  
integer  LDB,  
complex*16, dimension( ldx, * )  X,  
integer  LDX,  
double precision, dimension( * )  FERR,  
double precision, dimension( * )  BERR,  
complex*16, dimension( * )  WORK,  
double precision, dimension( * )  RWORK,  
integer  INFO  
) 
ZPBRFS
Download ZPBRFS + dependencies [TGZ] [ZIP] [TXT]ZPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian 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 Hermitian 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 COMPLEX*16 array, dimension (LDAFB,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H of the band matrix A as computed by ZPBTRF, 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by ZPBTRS. 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 COMPLEX*16 array, dimension (2*N) 
[out]  RWORK  RWORK is DOUBLE PRECISION 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 zpbrfs.f.