zpbrfs.f - Online Linux Manual Page

Section : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEzpbrfs.f
SYNOPSIS
Functions/Subroutinessubroutine zpbrfs (UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZPBRFS
Function/Subroutine Documentation
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 Purpose: 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.Parameters: UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
N N is INTEGER The order of the matrix A. N >= 0.
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.
NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
AB AB is COMPLEX*16 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 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).
LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.
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).
LDAFB LDAFB is INTEGER The leading dimension of the array AFB. LDAFB >= KD+1.
B B is COMPLEX*16 array, dimension (LDB,NRHS) The right hand side matrix B.
LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
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.
LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
FERR FERR is 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 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).
WORK WORK is COMPLEX*16 array, dimension (2*N)
RWORK RWORK is DOUBLE PRECISION array, dimension (N)
INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal valueInternal Parameters: ITMAX is the maximum number of steps of iterative refinement.Author: Univ​. of Tennessee Univ​. of California Berkeley Univ​. of Colorado Denver NAG Ltd​. Date: June 2016 Definition at line 191 of file zpbrfs​.f​.
AuthorGenerated automatically by Doxygen for LAPACK from the source code​. 0
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