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 tridiagonal, and provides error bounds and backward error  estimates
for the solution

```

#### SYNOPSIS

```       SUBROUTINE SGTRFS( TRANS,  N,  NRHS,  DL,  D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX,
FERR, BERR, WORK, IWORK, INFO )

CHARACTER      TRANS

INTEGER        INFO, LDB, LDX, N, NRHS

INTEGER        IPIV( * ), IWORK( * )

REAL           B( LDB, * ), BERR( * ), D( * ), DF( * ), DL( * ), DLF( * ),  DU(  *  ),
DU2( * ), DUF( * ), FERR( * ), WORK( * ), X( LDX, * )

```

#### PURPOSE

```       SGTRFS 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 = 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) REAL array, dimension (N-1)
The (n-1) subdiagonal elements of A.

D       (input) REAL array, dimension (N)
The diagonal elements of A.

DU      (input) REAL array, dimension (N-1)
The (n-1) superdiagonal elements of A.

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

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

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

DU2     (input) REAL 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 indicates a row interchange was not
required.

B       (input) REAL 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) REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SGTTRS.
On exit, the improved solution matrix X.

LDX     (input) INTEGER
The leading dimension of the array X.  LDX >= max(1,N).

FERR    (output) REAL 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    (output) REAL 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) REAL array, dimension (3*N)

IWORK   (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 refinement.

LAPACK routine (version 3.2)               April 2011                            SGTRFS(3lapack)
```