 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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 ).```

Definition at line 120 of file dppt02.f.

122*
123* -- LAPACK test routine --
124* -- LAPACK is a software package provided by Univ. of Tennessee, --
125* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126*
127* .. Scalar Arguments ..
128 CHARACTER UPLO
129 INTEGER LDB, LDX, N, NRHS
130 DOUBLE PRECISION RESID
131* ..
132* .. Array Arguments ..
133 DOUBLE PRECISION A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
134* ..
135*
136* =====================================================================
137*
138* .. Parameters ..
139 DOUBLE PRECISION ZERO, ONE
140 parameter( zero = 0.0d+0, one = 1.0d+0 )
141* ..
142* .. Local Scalars ..
143 INTEGER J
144 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
145* ..
146* .. External Functions ..
147 DOUBLE PRECISION DASUM, DLAMCH, DLANSP
148 EXTERNAL dasum, dlamch, dlansp
149* ..
150* .. External Subroutines ..
151 EXTERNAL dspmv
152* ..
153* .. Intrinsic Functions ..
154 INTRINSIC max
155* ..
156* .. Executable Statements ..
157*
158* Quick exit if N = 0 or NRHS = 0.
159*
160 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
161 resid = zero
162 RETURN
163 END IF
164*
165* Exit with RESID = 1/EPS if ANORM = 0.
166*
167 eps = dlamch( 'Epsilon' )
168 anorm = dlansp( '1', uplo, n, a, rwork )
169 IF( anorm.LE.zero ) THEN
170 resid = one / eps
171 RETURN
172 END IF
173*
174* Compute B - A*X for the matrix of right hand sides B.
175*
176 DO 10 j = 1, nrhs
177 CALL dspmv( uplo, n, -one, a, x( 1, j ), 1, one, b( 1, j ), 1 )
178 10 CONTINUE
179*
180* Compute the maximum over the number of right hand sides of
181* norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
182*
183 resid = zero
184 DO 20 j = 1, nrhs
185 bnorm = dasum( n, b( 1, j ), 1 )
186 xnorm = dasum( n, x( 1, j ), 1 )
187 IF( xnorm.LE.zero ) THEN
188 resid = one / eps
189 ELSE
190 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
191 END IF
192 20 CONTINUE
193*
194 RETURN
195*
196* End of DPPT02
197*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:71
subroutine dspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
DSPMV
Definition: dspmv.f:147
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,...
Definition: dlansp.f:114
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