 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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 ).```
Date
December 2016

Definition at line 135 of file dget08.f.

135 *
136 * -- LAPACK test routine (version 3.7.0) --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 * December 2016
140 *
141 * .. Scalar Arguments ..
142  CHARACTER trans
143  INTEGER lda, ldb, ldx, m, n, nrhs
144  DOUBLE PRECISION resid
145 * ..
146 * .. Array Arguments ..
147  DOUBLE PRECISION a( lda, * ), b( ldb, * ), rwork( * ),
148  \$ x( ldx, * )
149 * ..
150 *
151 * =====================================================================
152 *
153 * .. Parameters ..
154  DOUBLE PRECISION zero, one
155  parameter( zero = 0.0d+0, one = 1.0d+0 )
156 * ..
157 * .. Local Scalars ..
158  INTEGER j, n1, n2
159  DOUBLE PRECISION anorm, bnorm, eps, xnorm
160 * ..
161 * .. External Functions ..
162  LOGICAL lsame
163  INTEGER idamax
164  DOUBLE PRECISION dlamch, dlange
165  EXTERNAL lsame, idamax, dlamch, dlange
166 * ..
167 * .. External Subroutines ..
168  EXTERNAL dgemm
169 * ..
170 * .. Intrinsic Functions ..
171  INTRINSIC max, abs
172 * ..
173 * .. Executable Statements ..
174 *
175 * Quick exit if M = 0 or N = 0 or NRHS = 0
176 *
177  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.EQ.0 ) THEN
178  resid = zero
179  RETURN
180  END IF
181 *
182  IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
183  n1 = n
184  n2 = m
185  ELSE
186  n1 = m
187  n2 = n
188  END IF
189 *
190 * Exit with RESID = 1/EPS if ANORM = 0.
191 *
192  eps = dlamch( 'Epsilon' )
193  anorm = dlange( 'I', n1, n2, a, lda, rwork )
194  IF( anorm.LE.zero ) THEN
195  resid = one / eps
196  RETURN
197  END IF
198 *
199 * Compute B - A*X (or B - A'*X ) and store in B.
200 *
201  CALL dgemm( trans, 'No transpose', n1, nrhs, n2, -one, a, lda, x,
202  \$ ldx, one, b, ldb )
203 *
204 * Compute the maximum over the number of right hand sides of
205 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
206 *
207  resid = zero
208  DO 10 j = 1, nrhs
209  bnorm = abs(b(idamax( n1, b( 1, j ), 1 ),j))
210  xnorm = abs(x(idamax( n2, x( 1, j ), 1 ),j))
211  IF( xnorm.LE.zero ) THEN
212  resid = one / eps
213  ELSE
214  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
215  END IF
216  10 CONTINUE
217 *
218  RETURN
219 *
220 * End of DGET02
221 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:73
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
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:116
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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