# sptrfs.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **sptrfs** (**N**, **NRHS**, D, E, DF, EF, B, **LDB**, X, LDX, FERR, BERR, WORK, INFO)**SPTRFS**

## Function/Subroutine Documentation

### subroutine sptrfs (integer N, integer NRHS, real, dimension( * ) D, real, dimension( * ) E, real, dimension( * ) DF, real, dimension( * ) EF, real, dimension( ldb, * ) B, integer LDB, real, dimension( ldx, * ) X, integer LDX, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * ) WORK, integer INFO)

**SPTRFS**

**Purpose:**

SPTRFS 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.

**Parameters:***N*N is INTEGER The order of the matrix A. N >= 0.

*NRHS*NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

*D*D is REAL array, dimension (N) The n diagonal elements of the tridiagonal matrix A.

*E*E is REAL array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.

*DF*DF is REAL array, dimension (N) The n diagonal elements of the diagonal matrix D from the factorization computed by SPTTRF.

*EF*EF is REAL array, dimension (N-1) The (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization computed by SPTTRF.

*B*B is REAL array, dimension (LDB,NRHS) The right hand side matrix B.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

*X*X is REAL array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by SPTTRS. On exit, the improved solution matrix X.

*LDX*LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).

*FERR*FERR is 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*BERR is 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*WORK is REAL array, dimension (2*N)

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Internal Parameters:**

ITMAX is the maximum number of steps of iterative refinement.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 165 of file sptrfs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sptrfs(3) is an alias of sptrfs.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK