 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dppt02()

 subroutine dppt02 ( character UPLO, integer N, integer NRHS, double precision, dimension( * ) A, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) RWORK, double precision RESID )

DPPT02

Purpose:
``` DPPT02 computes the residual in the solution of a symmetric system
of linear equations  A*x = b  when packed storage is used for the
coefficient matrix.  The ratio computed is

RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),

where EPS is the machine precision.```
Parameters
 [in] 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``` [in] N ``` N is INTEGER The number of rows and columns of the matrix A. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of columns of B, the matrix of right hand sides. NRHS >= 0.``` [in] A ``` A is DOUBLE PRECISION array, dimension (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.``` [in] X ``` X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).``` [in,out] B ``` B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(B - A*X) / ( norm(A) * norm(X) * EPS ).```
Date
December 2016

Definition at line 124 of file dppt02.f.

124 *
125 * -- LAPACK test routine (version 3.7.0) --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 * December 2016
129 *
130 * .. Scalar Arguments ..
131  CHARACTER uplo
132  INTEGER ldb, ldx, n, nrhs
133  DOUBLE PRECISION resid
134 * ..
135 * .. Array Arguments ..
136  DOUBLE PRECISION a( * ), b( ldb, * ), rwork( * ), x( ldx, * )
137 * ..
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142  DOUBLE PRECISION zero, one
143  parameter( zero = 0.0d+0, one = 1.0d+0 )
144 * ..
145 * .. Local Scalars ..
146  INTEGER j
147  DOUBLE PRECISION anorm, bnorm, eps, xnorm
148 * ..
149 * .. External Functions ..
150  DOUBLE PRECISION dasum, dlamch, dlansp
151  EXTERNAL dasum, dlamch, dlansp
152 * ..
153 * .. External Subroutines ..
154  EXTERNAL dspmv
155 * ..
156 * .. Intrinsic Functions ..
157  INTRINSIC max
158 * ..
159 * .. Executable Statements ..
160 *
161 * Quick exit if N = 0 or NRHS = 0.
162 *
163  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
164  resid = zero
165  RETURN
166  END IF
167 *
168 * Exit with RESID = 1/EPS if ANORM = 0.
169 *
170  eps = dlamch( 'Epsilon' )
171  anorm = dlansp( '1', uplo, n, a, rwork )
172  IF( anorm.LE.zero ) THEN
173  resid = one / eps
174  RETURN
175  END IF
176 *
177 * Compute B - A*X for the matrix of right hand sides B.
178 *
179  DO 10 j = 1, nrhs
180  CALL dspmv( uplo, n, -one, a, x( 1, j ), 1, one, b( 1, j ), 1 )
181  10 CONTINUE
182 *
183 * Compute the maximum over the number of right hand sides of
184 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
185 *
186  resid = zero
187  DO 20 j = 1, nrhs
188  bnorm = dasum( n, b( 1, j ), 1 )
189  xnorm = dasum( n, x( 1, j ), 1 )
190  IF( xnorm.LE.zero ) THEN
191  resid = one / eps
192  ELSE
193  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
194  END IF
195  20 CONTINUE
196 *
197  RETURN
198 *
199 * End of DPPT02
200 *
subroutine dspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
DSPMV
Definition: dspmv.f:149
double precision function dlansp(NORM, UPLO, N, AP, WORK)
DLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.
Definition: dlansp.f:116
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:73
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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