# sptt05.f - Man Page

TESTING/LIN/sptt05.f

## Synopsis

### Functions/Subroutines

subroutine sptt05 (n, nrhs, d, e, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
SPTT05

## Function/Subroutine Documentation

### subroutine sptt05 (integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, 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)

SPTT05

Purpose:

``` SPTT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
symmetric tridiagonal matrix of order n.

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 / ( NZ*EPS + (*) ), where
(*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
and NZ = max. number of nonzeros in any row of A, plus 1```
Parameters

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.```

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.```

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 / ( NZ*EPS + (*) )```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 148 of file sptt05.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sptt05(3) is an alias of sptt05.f(3).

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