zppt05.f - Man Page

TESTING/LIN/zppt05.f

Synopsis

Functions/Subroutines

subroutine zppt05 (uplo, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
ZPPT05

Function/Subroutine Documentation

subroutine zppt05 (character uplo, integer n, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( ldxact, * ) xact, integer ldxact, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, double precision, dimension( * ) reslts)

ZPPT05

Purpose:

ZPPT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
Hermitian 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
Hermitian 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 COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangle of the Hermitian 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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

NAG Ltd.

Definition at line 155 of file zppt05.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page zppt05(3) is an alias of zppt05.f(3).

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