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

# stprfs(3lapack)

provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix

## NAME

STPRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix

## SYNOPSIS

- SUBROUTINE STPRFS(

  UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )

- CHARACTER

  DIAG, TRANS, UPLO

- INTEGER

  INFO, LDB, LDX, N, NRHS

- INTEGER

  IWORK( \* )

- REAL

  AP( \* ), B( LDB, \* ), BERR( \* ), FERR( \* ), WORK( \* ), X( LDX, \* )

## PURPOSE

STPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. The solution matrix X must be computed by STPTRS or some other means before entering this routine.  STPRFS does not do iterative refinement because doing so cannot improve the backward error.

## ARGUMENTS

- UPLO (input) CHARACTER\*1

  \= 'U':  A is upper triangular;\
   \= 'L':  A is lower triangular.

- 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 = Transpose)

- DIAG (input) CHARACTER\*1

  \= 'N':  A is non-unit triangular;\
   \= 'U':  A is unit triangular.

- 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.

- AP (input) REAL array, dimension (N\*(N+1)/2)

  The upper or lower triangular matrix A, packed columnwise in a linear array.  The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)\*j/2) = A(i,j) for 1\<=i\<=j; if UPLO = 'L', AP(i + (j-1)\*(2\*n-j)/2) = A(i,j) for j\<=i\<=n. If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

- 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) REAL array, dimension (LDX,NRHS)

  The 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