# sppt05.f - Man Page

TESTING/LIN/sppt05.f

## Synopsis

### Functions/Subroutines

subroutine **sppt05** (uplo, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)**SPPT05**

## Function/Subroutine Documentation

### subroutine sppt05 (character uplo, integer n, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldxact, * ) xact, integer ldxact, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) reslts)

**SPPT05**

**Purpose:**

SPPT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a symmetric matrix in packed storage format. RESLTS(1) = test of the error bound = norm(X - XACT) / ( norm(X) * FERR ) A large value is returned if this ratio is not less than one. RESLTS(2) = residual from the iterative refinement routine = the maximum of BERR / ( (n+1)*EPS + (*) ), where (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

**Parameters***UPLO*UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular

*N*N is INTEGER The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.

*NRHS*NRHS is INTEGER The number of columns of the matrices X, B, and XACT. NRHS >= 0.

*AP*AP is REAL array, dimension (N*(N+1)/2) The upper or lower triangle of the symmetric 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)*(2n-j)/2) = A(i,j) for j<=i<=n.

*B*B is REAL array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.

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

*X*X is REAL array, dimension (LDX,NRHS) The computed solution vectors. Each vector is stored as a column of the matrix X.

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

*XACT*XACT is REAL array, dimension (LDX,NRHS) The exact solution vectors. Each vector is stored as a column of the matrix XACT.

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

*FERR*FERR is REAL array, dimension (NRHS) The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.

*BERR*BERR is REAL array, dimension (NRHS) The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).

*RESLTS*RESLTS is REAL array, dimension (2) The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) RESLTS(2) = BERR / ( (n+1)*EPS + (*) )

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **154** of file **sppt05.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sppt05(3) is an alias of sppt05.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK