 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dget08()

 subroutine dget08 ( character TRANS, integer M, 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 )

DGET08

Purpose:
``` DGET08 computes the residual for a solution of a system of linear
equations  A*x = b  or  A'*x = b:
RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
where EPS is the machine epsilon.```
Parameters
 [in] TRANS ``` TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A *x = b = 'T': A'*x = b, where A' is the transpose of A = 'C': A'*x = b, where A' is the transpose of A``` [in] M ``` M is INTEGER The number of rows of the matrix A. M >= 0.``` [in] N ``` N is INTEGER The number of 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,M).``` [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,M).``` [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 (M)` [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 131 of file dget08.f.

133*
134* -- LAPACK test routine --
135* -- LAPACK is a software package provided by Univ. of Tennessee, --
136* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137*
138* .. Scalar Arguments ..
139 CHARACTER TRANS
140 INTEGER LDA, LDB, LDX, M, N, NRHS
141 DOUBLE PRECISION RESID
142* ..
143* .. Array Arguments ..
144 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ),
145 \$ X( LDX, * )
146* ..
147*
148* =====================================================================
149*
150* .. Parameters ..
151 DOUBLE PRECISION ZERO, ONE
152 parameter( zero = 0.0d+0, one = 1.0d+0 )
153* ..
154* .. Local Scalars ..
155 INTEGER J, N1, N2
156 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
157* ..
158* .. External Functions ..
159 LOGICAL LSAME
160 INTEGER IDAMAX
161 DOUBLE PRECISION DLAMCH, DLANGE
162 EXTERNAL lsame, idamax, dlamch, dlange
163* ..
164* .. External Subroutines ..
165 EXTERNAL dgemm
166* ..
167* .. Intrinsic Functions ..
168 INTRINSIC max, abs
169* ..
170* .. Executable Statements ..
171*
172* Quick exit if M = 0 or N = 0 or NRHS = 0
173*
174 IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.EQ.0 ) THEN
175 resid = zero
176 RETURN
177 END IF
178*
179 IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
180 n1 = n
181 n2 = m
182 ELSE
183 n1 = m
184 n2 = n
185 END IF
186*
187* Exit with RESID = 1/EPS if ANORM = 0.
188*
189 eps = dlamch( 'Epsilon' )
190 anorm = dlange( 'I', n1, n2, a, lda, rwork )
191 IF( anorm.LE.zero ) THEN
192 resid = one / eps
193 RETURN
194 END IF
195*
196* Compute B - A*X (or B - A'*X ) and store in B.
197*
198 CALL dgemm( trans, 'No transpose', n1, nrhs, n2, -one, a, lda, x,
199 \$ ldx, one, b, ldb )
200*
201* Compute the maximum over the number of right hand sides of
202* norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
203*
204 resid = zero
205 DO 10 j = 1, nrhs
206 bnorm = abs(b(idamax( n1, b( 1, j ), 1 ),j))
207 xnorm = abs(x(idamax( n2, x( 1, j ), 1 ),j))
208 IF( xnorm.LE.zero ) THEN
209 resid = one / eps
210 ELSE
211 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
212 END IF
213 10 CONTINUE
214*
215 RETURN
216*
217* End of DGET08
218*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:114
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