ZPTRFS(1) LAPACK routine (version 3.2) ZPTRFS(1)NAME
ZPTRFS - improves the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite and tridiag‐
onal, and provides error bounds and backward error estimates for the
solution
SYNOPSIS
SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,
BERR, WORK, RWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, LDX, N, NRHS
DOUBLE PRECISION BERR( * ), D( * ), DF( * ), FERR( * ),
RWORK( * )
COMPLEX*16 B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )
PURPOSE
ZPTRFS improves the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite and tridiag‐
onal, and provides error bounds and backward error estimates for the
solution.
ARGUMENTS
UPLO (input) CHARACTER*1
Specifies whether the superdiagonal or the subdiagonal of the
tridiagonal matrix A is stored and the form of the factoriza‐
tion:
= 'U': E is the superdiagonal of A, and A = U**H*D*U;
= 'L': E is the subdiagonal of A, and A = L*D*L**H. (The two
forms are equivalent if A is real.)
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrix B. NRHS >= 0.
D (input) DOUBLE PRECISION array, dimension (N)
The n real diagonal elements of the tridiagonal matrix A.
E (input) COMPLEX*16 array, dimension (N-1)
The (n-1) off-diagonal elements of the tridiagonal matrix A
(see UPLO).
DF (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D from the fac‐
torization computed by ZPTTRF.
EF (input) COMPLEX*16 array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal factor U
or L from the factorization computed by ZPTTRF (see UPLO).
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/output) COMPLEX*16 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZPTTRS. On
exit, the improved 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 forward error bound for each solution vector X(j) (the j-th
column of the solution matrix X). If XTRUE is the true solu‐
tion 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).
BERR (output) DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution vec‐
tor 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 (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
PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.
LAPACK routine (version 3.2) November 2008 ZPTRFS(1)
