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

# dptrfs(3lapack)

improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution

## NAME

DPTRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution

## SYNOPSIS

- SUBROUTINE DPTRFS(

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

- INTEGER

  INFO, LDB, LDX, N, NRHS

- DOUBLE

  PRECISION B( LDB, \* ), BERR( \* ), D( \* ), DF( \* ), E( \* ), EF( \* ), FERR( \* ), WORK( \* ), X( LDX, \* )

## PURPOSE

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

## ARGUMENTS

- 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) DOUBLE PRECISION array, dimension (N)

  The n diagonal elements of the tridiagonal matrix A.

- E (input) DOUBLE PRECISION array, dimension (N-1)

  The (n-1) subdiagonal elements of the tridiagonal matrix A.

- DF (input) DOUBLE PRECISION array, dimension (N)

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

- EF (input) DOUBLE PRECISION array, dimension (N-1)

  The (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization computed by DPTTRF.

- B (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)

  On entry, the solution matrix X, as computed by DPTTRS. 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 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (2\*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.