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

# cptrfs(3lapack)

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

## NAME

CPTRFS - 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 CPTRFS(

  UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )

- CHARACTER

  UPLO

- INTEGER

  INFO, LDB, LDX, N, NRHS

- REAL

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

- COMPLEX

  B( LDB, \* ), E( \* ), EF( \* ), WORK( \* ), X( LDX, \* )

## PURPOSE

CPTRFS 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) REAL array, dimension (N)

  The n real diagonal elements of the tridiagonal matrix A.

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

  The (n-1) off-diagonal elements of the tridiagonal matrix A (see UPLO).

- DF (input) REAL array, dimension (N)

  The n diagonal elements of the diagonal matrix D from the factorization computed by CPTTRF.

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

  The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by CPTTRF (see UPLO).

- 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 CPTTRS. 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 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) 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 (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.