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# zgtrfs

```
NAME
ZGTRFS - improve the computed solution to a system of linear
equations when the coefficient matrix is tridiagonal, and
provides error bounds and backward error estimates for the
solution

SYNOPSIS
SUBROUTINE ZGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF,
DU2, IPIV, B, LDB, X, LDX, FERR, BERR,
WORK, RWORK, INFO )

CHARACTER      TRANS

INTEGER        INFO, LDB, LDX, N, NRHS

INTEGER        IPIV( * )

DOUBLE         PRECISION BERR( * ), FERR( * ), RWORK( *
)

COMPLEX*16     B( LDB, * ), D( * ), DF( * ), DL( * ),
DLF( * ), DU( * ), DU2( * ), DUF( * ),
WORK( * ), X( LDX, * )

PURPOSE
ZGTRFS improves the computed solution to a system of linear
equations when the coefficient matrix is tridiagonal, and
provides error bounds and backward error estimates for the
solution.

ARGUMENTS
TRANS   (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N':  A * X = B     (No transpose)
= 'T':  A**T * X = B  (Transpose)
= 'C':  A**H * X = B  (Conjugate transpose)

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.

DL      (input) COMPLEX*16 array, dimension (N-1)
The (n-1) subdiagonal elements of A.

D       (input) COMPLEX*16 array, dimension (N)
The diagonal elements of A.

DU      (input) COMPLEX*16 array, dimension (N-1)

The (n-1) superdiagonal elements of A.

DLF     (input) COMPLEX*16 array, dimension (N-1)
The (n-1) multipliers that define the matrix L from
the LU factorization of A as computed by ZGTTRF.

DF      (input) COMPLEX*16 array, dimension (N)
The n diagonal elements of the upper triangular
matrix U from the LU factorization of A.

DUF     (input) COMPLEX*16 array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.

DU2     (input) COMPLEX*16 array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.

IPIV    (input) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the
matrix was interchanged with row IPIV(i).  IPIV(i)
will always be either i or i+1; IPIV(i) = i indi-
cates a row interchange was not required.

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
ZGTTRS.  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 estimated forward error bounds for each solution
vector X(j) (the j-th column of the solution matrix
X).  If XTRUE is the true solution, FERR(j) bounds
the magnitude of the largest entry in (X(j) - XTRUE)
divided by the magnitude of the largest entry in
X(j).  The quality of the error bound depends on the
quality of the estimate of norm(inv(A)) computed in
the code; if the estimate of norm(inv(A)) is accu-
rate, the error bound is guaranteed.

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 entry of A or B that makes X(j) an

exact solution).

WORK    (workspace) COMPLEX*16 array, dimension (2*N)

RWORK   (workspace) INTEGER 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 refine-
ment.
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