 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dpot06()

 subroutine dpot06 ( character UPLO, integer N, integer NRHS, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) RWORK, double precision RESID )

DPOT06

Purpose:
``` DPOT06 computes the residual for a solution of a system of linear
equations  A*x = b :
RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
where EPS is the machine epsilon.```
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 (LDA,N) The original M x N matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [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. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', 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. IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', 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 125 of file dpot06.f.

127*
128* -- LAPACK test routine --
129* -- LAPACK is a software package provided by Univ. of Tennessee, --
130* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131*
132* .. Scalar Arguments ..
133 CHARACTER UPLO
134 INTEGER LDA, LDB, LDX, N, NRHS
135 DOUBLE PRECISION RESID
136* ..
137* .. Array Arguments ..
138 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ),
139 \$ X( LDX, * )
140* ..
141*
142* =====================================================================
143*
144* .. Parameters ..
145 DOUBLE PRECISION ZERO, ONE, NEGONE
146 parameter( zero = 0.0d+0, one = 1.0d+0 )
147 parameter( negone = -1.0d+0 )
148* ..
149* .. Local Scalars ..
150 INTEGER IFAIL, J
151 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
152* ..
153* .. External Functions ..
154 INTEGER IDAMAX
155 DOUBLE PRECISION DLAMCH, DLANSY
156 EXTERNAL idamax, dlamch, dlansy
157* ..
158* .. External Subroutines ..
159 EXTERNAL dsymm
160* ..
161* .. Intrinsic Functions ..
162 INTRINSIC max, abs
163* ..
164* .. Executable Statements ..
165*
166* Quick exit if N = 0 or NRHS = 0
167*
168 IF( n.LE.0 .OR. nrhs.EQ.0 ) THEN
169 resid = zero
170 RETURN
171 END IF
172*
173* Exit with RESID = 1/EPS if ANORM = 0.
174*
175 eps = dlamch( 'Epsilon' )
176 anorm = dlansy( 'I', uplo, n, a, lda, rwork )
177 IF( anorm.LE.zero ) THEN
178 resid = one / eps
179 RETURN
180 END IF
181*
182* Compute B - A*X and store in B.
183 ifail=0
184*
185 CALL dsymm( 'Left', uplo, n, nrhs, negone, a, lda, x,
186 \$ ldx, one, b, ldb )
187*
188* Compute the maximum over the number of right hand sides of
189* norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
190*
191 resid = zero
192 DO 10 j = 1, nrhs
193 bnorm = abs(b(idamax( n, b( 1, j ), 1 ),j))
194 xnorm = abs(x(idamax( n, x( 1, j ), 1 ),j))
195 IF( xnorm.LE.zero ) THEN
196 resid = one / eps
197 ELSE
198 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
199 END IF
200 10 CONTINUE
201*
202 RETURN
203*
204* End of DPOT06
205*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:71
subroutine dsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYMM
Definition: dsymm.f:189
double precision function dlansy(NORM, UPLO, N, A, LDA, WORK)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlansy.f:122
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