 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sget02()

 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 op(A)*X = B:
RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
where op(A) = A or A**T, depending on TRANS, and EPS is the
machine epsilon.
The norm used is the 1-norm.```
Parameters
 [in] TRANS ``` TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose = Transpose)``` [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 - op(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 - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).```

Definition at line 133 of file sget02.f.

135*
136* -- LAPACK test routine --
137* -- LAPACK is a software package provided by Univ. of Tennessee, --
138* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139*
140* .. Scalar Arguments ..
141 CHARACTER TRANS
142 INTEGER LDA, LDB, LDX, M, N, NRHS
143 REAL RESID
144* ..
145* .. Array Arguments ..
146 REAL A( LDA, * ), B( LDB, * ), RWORK( * ),
147 \$ X( LDX, * )
148* ..
149*
150* =====================================================================
151*
152* .. Parameters ..
153 REAL ZERO, ONE
154 parameter( zero = 0.0e+0, one = 1.0e+0 )
155* ..
156* .. Local Scalars ..
157 INTEGER J, N1, N2
158 REAL ANORM, BNORM, EPS, XNORM
159* ..
160* .. External Functions ..
161 LOGICAL LSAME
162 REAL SASUM, SLAMCH, SLANGE
163 EXTERNAL lsame, sasum, slamch, slange
164* ..
165* .. External Subroutines ..
166 EXTERNAL sgemm
167* ..
168* .. Intrinsic Functions ..
169 INTRINSIC max
170* ..
171* .. Executable Statements ..
172*
173* Quick exit if M = 0 or N = 0 or NRHS = 0
174*
175 IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.EQ.0 ) THEN
176 resid = zero
177 RETURN
178 END IF
179*
180 IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
181 n1 = n
182 n2 = m
183 ELSE
184 n1 = m
185 n2 = n
186 END IF
187*
188* Exit with RESID = 1/EPS if ANORM = 0.
189*
190 eps = slamch( 'Epsilon' )
191 IF( lsame( trans, 'N' ) ) THEN
192 anorm = slange( '1', m, n, a, lda, rwork )
193 ELSE
194 anorm = slange( 'I', m, n, a, lda, rwork )
195 END IF
196 IF( anorm.LE.zero ) THEN
197 resid = one / eps
198 RETURN
199 END IF
200*
201* Compute B - op(A)*X and store in B.
202*
203 CALL sgemm( trans, 'No transpose', n1, nrhs, n2, -one, a, lda, x,
204 \$ ldx, one, b, ldb )
205*
206* Compute the maximum over the number of right hand sides of
207* norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ) .
208*
209 resid = zero
210 DO 10 j = 1, nrhs
211 bnorm = sasum( n1, b( 1, j ), 1 )
212 xnorm = sasum( n2, x( 1, j ), 1 )
213 IF( xnorm.LE.zero ) THEN
214 resid = one / eps
215 ELSE
216 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
217 END IF
218 10 CONTINUE
219*
220 RETURN
221*
222* End of SGET02
223*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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:114
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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