 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine sget02 ( character TRANS, integer M, integer N, integer NRHS, real, dimension( lda, * ) A, integer LDA, real, dimension( ldx, * ) X, integer LDX, real, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID )

SGET02

Purpose:
``` SGET02 computes the residual for a solution of a system of linear
equations  A*x = b  or  A'*x = b:
RESID = norm(B - A*X) / ( norm(A) * norm(X) * 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (M)` [out] RESID ``` RESID is REAL The maximum over the number of right hand sides of norm(B - A*X) / ( norm(A) * norm(X) * EPS ).```
Date
November 2011

Definition at line 135 of file sget02.f.

135 *
136 * -- LAPACK test routine (version 3.4.0) --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 * November 2011
140 *
141 * .. Scalar Arguments ..
142  CHARACTER trans
143  INTEGER lda, ldb, ldx, m, n, nrhs
144  REAL resid
145 * ..
146 * .. Array Arguments ..
147  REAL a( lda, * ), b( ldb, * ), rwork( * ),
148  \$ x( ldx, * )
149 * ..
150 *
151 * =====================================================================
152 *
153 * .. Parameters ..
154  REAL zero, one
155  parameter ( zero = 0.0e+0, one = 1.0e+0 )
156 * ..
157 * .. Local Scalars ..
158  INTEGER j, n1, n2
159  REAL anorm, bnorm, eps, xnorm
160 * ..
161 * .. External Functions ..
162  LOGICAL lsame
163  REAL sasum, slamch, slange
164  EXTERNAL lsame, sasum, slamch, slange
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL sgemm
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC max
171 * ..
172 * .. Executable Statements ..
173 *
174 * Quick exit if M = 0 or N = 0 or NRHS = 0
175 *
176  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.EQ.0 ) THEN
177  resid = zero
178  RETURN
179  END IF
180 *
181  IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
182  n1 = n
183  n2 = m
184  ELSE
185  n1 = m
186  n2 = n
187  END IF
188 *
189 * Exit with RESID = 1/EPS if ANORM = 0.
190 *
191  eps = slamch( 'Epsilon' )
192  anorm = slange( '1', n1, n2, a, lda, rwork )
193  IF( anorm.LE.zero ) THEN
194  resid = one / eps
195  RETURN
196  END IF
197 *
198 * Compute B - A*X (or B - A'*X ) and store in B.
199 *
200  CALL sgemm( trans, 'No transpose', n1, nrhs, n2, -one, a, lda, x,
201  \$ ldx, one, b, ldb )
202 *
203 * Compute the maximum over the number of right hand sides of
204 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
205 *
206  resid = zero
207  DO 10 j = 1, nrhs
208  bnorm = sasum( n1, b( 1, j ), 1 )
209  xnorm = sasum( n2, x( 1, j ), 1 )
210  IF( xnorm.LE.zero ) THEN
211  resid = one / eps
212  ELSE
213  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
214  END IF
215  10 CONTINUE
216 *
217  RETURN
218 *
219 * End of SGET02
220 *
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:116
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:54
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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