LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zget02()

 subroutine zget02 ( character TRANS, integer M, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) RWORK, double precision RESID )

ZGET02

Purpose:
``` ZGET02 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, A**T, or A**H, depending on TRANS, and EPS is the
machine epsilon.```
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)``` [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*16 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*16 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*16 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 - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).```

Definition at line 132 of file zget02.f.

134 *
135 * -- LAPACK test routine --
136 * -- LAPACK is a software package provided by Univ. of Tennessee, --
137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138 *
139 * .. Scalar Arguments ..
140  CHARACTER TRANS
141  INTEGER LDA, LDB, LDX, M, N, NRHS
142  DOUBLE PRECISION RESID
143 * ..
144 * .. Array Arguments ..
145  DOUBLE PRECISION RWORK( * )
146  COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
147 * ..
148 *
149 * =====================================================================
150 *
151 * .. Parameters ..
152  DOUBLE PRECISION ZERO, ONE
153  parameter( zero = 0.0d+0, one = 1.0d+0 )
154  COMPLEX*16 CONE
155  parameter( cone = ( 1.0d+0, 0.0d+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  DOUBLE PRECISION DLAMCH, DZASUM, ZLANGE
164  EXTERNAL lsame, dlamch, dzasum, zlange
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL zgemm
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 = dlamch( 'Epsilon' )
192  IF( lsame( trans, 'N' ) ) THEN
193  anorm = zlange( '1', m, n, a, lda, rwork )
194  ELSE
195  anorm = zlange( 'I', m, n, a, lda, rwork )
196  END IF
197  IF( anorm.LE.zero ) THEN
198  resid = one / eps
199  RETURN
200  END IF
201 *
202 * Compute B - op(A)*X and store in B.
203 *
204  CALL zgemm( trans, 'No transpose', n1, nrhs, n2, -cone, a, lda, x,
205  \$ ldx, cone, b, ldb )
206 *
207 * Compute the maximum over the number of right hand sides of
208 * norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ) .
209 *
210  resid = zero
211  DO 10 j = 1, nrhs
212  bnorm = dzasum( n1, b( 1, j ), 1 )
213  xnorm = dzasum( n2, x( 1, j ), 1 )
214  IF( xnorm.LE.zero ) THEN
215  resid = one / eps
216  ELSE
217  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
218  END IF
219  10 CONTINUE
220 *
221  RETURN
222 *
223 * End of ZGET02
224 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:115
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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