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

# sporfs(3lapack)

improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,

## NAME

SPORFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,

## SYNOPSIS

- SUBROUTINE SPORFS(

  UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )

- CHARACTER

  UPLO

- INTEGER

  INFO, LDA, LDAF, LDB, LDX, N, NRHS

- INTEGER

  IWORK( \* )

- REAL

  A( LDA, \* ), AF( LDAF, \* ), B( LDB, \* ), BERR( \* ), FERR( \* ), WORK( \* ), X( LDX, \* )

## PURPOSE

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

## ARGUMENTS

- UPLO (input) CHARACTER\*1

  \= 'U':  Upper triangle of A is stored;\
   \= 'L':  Lower triangle of A is stored.

- 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 matrices B and X.  NRHS \>= 0.

- A (input) REAL array, dimension (LDA,N)

  The symmetric matrix A.  If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced.  If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

- LDA (input) INTEGER

  The leading dimension of the array A.  LDA \>= max(1,N).

- AF (input) REAL array, dimension (LDAF,N)

  The triangular factor U or L from the Cholesky factorization A = U\*\*T\*U or A = L\*L\*\*T, as computed by SPOTRF.

- LDAF (input) INTEGER

  The leading dimension of the array AF.  LDAF \>= max(1,N).

- 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 SPOTRS. 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.