# cgtrfs.f man page

cgtrfs.f —

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine cgtrfs (characterTRANS, integerN, integerNRHS, complex, dimension( * )DL, complex, dimension( * )D, complex, dimension( * )DU, complex, dimension( * )DLF, complex, dimension( * )DF, complex, dimension( * )DUF, complex, dimension( * )DU2, integer, dimension( * )IPIV, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

**CGTRFS**

**Purpose:**

```
CGTRFS 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.
```

**Parameters:**

*TRANS*

```
TRANS is 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*

```
N is INTEGER
The order of the matrix A. N >= 0.
```

*NRHS*

```
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
```

*DL*

```
DL is COMPLEX array, dimension (N-1)
The (n-1) subdiagonal elements of A.
```

*D*

```
D is COMPLEX array, dimension (N)
The diagonal elements of A.
```

*DU*

```
DU is COMPLEX array, dimension (N-1)
The (n-1) superdiagonal elements of A.
```

*DLF*

```
DLF is COMPLEX array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A as computed by CGTTRF.
```

*DF*

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

*DUF*

```
DUF is COMPLEX array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.
```

*DU2*

```
DU2 is COMPLEX array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.
```

*IPIV*

```
IPIV is 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*

```
B is COMPLEX 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 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CGTTRS.
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 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*

```
BERR is 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*

`WORK is COMPLEX array, dimension (2*N)`

*RWORK*

`RWORK is REAL array, dimension (N)`

*INFO*

```
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
```

**Internal 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:**

September 2012

Definition at line 209 of file cgtrfs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

cgtrfs(3) is an alias of cgtrfs.f(3).