---
name: "cgtrfs"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/cgtrfs/3lapack"
---

# cgtrfs(3lapack)

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

## NAME

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

## SYNOPSIS

- SUBROUTINE CGTRFS(

  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( \* )

- REAL

  BERR( \* ), FERR( \* ), RWORK( \* )

- COMPLEX

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

## 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.

## 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 array, dimension (N-1)

  The (n-1) subdiagonal elements of A.

- D (input) COMPLEX array, dimension (N)

  The diagonal elements of A.

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

  The (n-1) superdiagonal elements of A.

- DLF (input) 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 (input) COMPLEX array, dimension (N)

  The n diagonal elements of the upper triangular matrix U from the LU factorization of A.

- DUF (input) COMPLEX array, dimension (N-1)

  The (n-1) elements of the first superdiagonal of U.

- DU2 (input) COMPLEX 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) COMPLEX 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 array, dimension (LDX,NRHS)

  On entry, the solution matrix X, as computed by CGTTRS. 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) COMPLEX array, dimension (2\*N)

  - RWORK (workspace) REAL 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.