Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3  -  improves  the  computed  solution  to  a  system of linear equations when the
coefficient matrix is Hermitian positive definite  and  tridiagonal,  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  tridiagonal, 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
factorization:
= '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 factorization 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 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).

BERR    (output) 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    (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 3.3.1)             April 2011                            ZPTRFS(3lapack)
```