 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
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
real function scasum(N, CX, INCX)
SCASUM
Definition: scasum.f:72
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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