LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ cqrt16()

 subroutine cqrt16 ( character trans, integer m, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldx, * ) x, integer ldx, complex, dimension( ldb, * ) b, integer ldb, real, dimension( * ) rwork, real resid )

CQRT16

Purpose:
``` CQRT16 computes the residual for a solution of a system of linear
equations  A*x = b  or  A'*x = b:
RESID = norm(B - A*X) / ( max(m,n) * 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^T*x = b, where A^T is the transpose of A = 'C': A^H*x = b, where A^H is the conjugate 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 COMPLEX 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 COMPLEX 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 COMPLEX 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) / ( max(m,n) * norm(A) * norm(X) * EPS ).```

Definition at line 131 of file cqrt16.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 REAL RESID
142* ..
143* .. Array Arguments ..
144 REAL RWORK( * )
145 COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
146* ..
147*
148* =====================================================================
149*
150* .. Parameters ..
151 REAL ZERO, ONE
152 parameter( zero = 0.0e+0, one = 1.0e+0 )
153 COMPLEX CONE
154 parameter( cone = ( 1.0e+0, 0.0e+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 CLANGE, SCASUM, SLAMCH
163 EXTERNAL lsame, clange, scasum, slamch
164* ..
165* .. External Subroutines ..
166 EXTERNAL cgemm
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 anorm = clange( 'I', m, n, a, lda, rwork )
182 n1 = n
183 n2 = m
184 ELSE
185 anorm = clange( '1', m, n, a, lda, rwork )
186 n1 = m
187 n2 = n
188 END IF
189*
190 eps = slamch( 'Epsilon' )
191*
192* Compute B - A*X (or B - A'*X ) and store in B.
193*
194 CALL cgemm( trans, 'No transpose', n1, nrhs, n2, -cone, a, lda, x,
195 \$ ldx, cone, b, ldb )
196*
197* Compute the maximum over the number of right hand sides of
198* norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ) .
199*
200 resid = zero
201 DO 10 j = 1, nrhs
202 bnorm = scasum( n1, b( 1, j ), 1 )
203 xnorm = scasum( n2, x( 1, j ), 1 )
204 IF( anorm.EQ.zero .AND. bnorm.EQ.zero ) THEN
205 resid = zero
206 ELSE IF( anorm.LE.zero .OR. xnorm.LE.zero ) THEN
207 resid = one / eps
208 ELSE
209 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) /
210 \$ ( max( m, n )*eps ) )
211 END IF
212 10 CONTINUE
213*
214 RETURN
215*
216* End of CQRT16
217*
real function scasum(n, cx, incx)
SCASUM
Definition scasum.f:72
subroutine cgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CGEMM
Definition cgemm.f:188
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function clange(norm, m, n, a, lda, work)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition clange.f:115
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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