LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zget08.f
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1*> \brief \b ZGET08
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8* Definition:
9* ===========
10*
11* SUBROUTINE ZGET08( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
12* RWORK, RESID )
13*
14* .. Scalar Arguments ..
15* CHARACTER TRANS
16* INTEGER LDA, LDB, LDX, M, N, NRHS
17* DOUBLE PRECISION RESID
18* ..
19* .. Array Arguments ..
20* DOUBLE PRECISION RWORK( * )
21* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
22* ..
23*
24*
25*> \par Purpose:
26* =============
27*>
28*> \verbatim
29*>
30*> ZGET08 computes the residual for a solution of a system of linear
31*> equations A*x = b or A'*x = b:
32*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
33*> where EPS is the machine epsilon.
34*> \endverbatim
35*
36* Arguments:
37* ==========
38*
39*> \param[in] TRANS
40*> \verbatim
41*> TRANS is CHARACTER*1
42*> Specifies the form of the system of equations:
43*> = 'N': A *x = b
44*> = 'T': A^T*x = b, where A^T is the transpose of A
45*> = 'C': A^H*x = b, where A^H is the conjugate transpose of A
46*> \endverbatim
47*>
48*> \param[in] M
49*> \verbatim
50*> M is INTEGER
51*> The number of rows of the matrix A. M >= 0.
52*> \endverbatim
53*>
54*> \param[in] N
55*> \verbatim
56*> N is INTEGER
57*> The number of columns of the matrix A. N >= 0.
58*> \endverbatim
59*>
60*> \param[in] NRHS
61*> \verbatim
62*> NRHS is INTEGER
63*> The number of columns of B, the matrix of right hand sides.
64*> NRHS >= 0.
65*> \endverbatim
66*>
67*> \param[in] A
68*> \verbatim
69*> A is COMPLEX*16 array, dimension (LDA,N)
70*> The original M x N matrix A.
71*> \endverbatim
72*>
73*> \param[in] LDA
74*> \verbatim
75*> LDA is INTEGER
76*> The leading dimension of the array A. LDA >= max(1,M).
77*> \endverbatim
78*>
79*> \param[in] X
80*> \verbatim
81*> X is COMPLEX*16 array, dimension (LDX,NRHS)
82*> The computed solution vectors for the system of linear
83*> equations.
84*> \endverbatim
85*>
86*> \param[in] LDX
87*> \verbatim
88*> LDX is INTEGER
89*> The leading dimension of the array X. If TRANS = 'N',
90*> LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
91*> \endverbatim
92*>
93*> \param[in,out] B
94*> \verbatim
95*> B is COMPLEX*16 array, dimension (LDB,NRHS)
96*> On entry, the right hand side vectors for the system of
97*> linear equations.
98*> On exit, B is overwritten with the difference B - A*X.
99*> \endverbatim
100*>
101*> \param[in] LDB
102*> \verbatim
103*> LDB is INTEGER
104*> The leading dimension of the array B. IF TRANS = 'N',
105*> LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
106*> \endverbatim
107*>
108*> \param[out] RWORK
109*> \verbatim
110*> RWORK is DOUBLE PRECISION array, dimension (M)
111*> \endverbatim
112*>
113*> \param[out] RESID
114*> \verbatim
115*> RESID is DOUBLE PRECISION
116*> The maximum over the number of right hand sides of
117*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
118*> \endverbatim
119*
120* Authors:
121* ========
122*
123*> \author Univ. of Tennessee
124*> \author Univ. of California Berkeley
125*> \author Univ. of Colorado Denver
126*> \author NAG Ltd.
127*
128*> \ingroup complex16_lin
129*
130* =====================================================================
131 SUBROUTINE zget08( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
132 \$ RWORK, RESID )
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 DOUBLE PRECISION RESID
142* ..
143* .. Array Arguments ..
144 DOUBLE PRECISION RWORK( * )
145 COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
146* ..
147*
148* =====================================================================
149*
150* .. Parameters ..
151 DOUBLE PRECISION ZERO, ONE
152 parameter( zero = 0.0d+0, one = 1.0d+0 )
153 COMPLEX*16 CONE
154 parameter( cone = ( 1.0d+0, 0.0d+0 ) )
155* ..
156* .. Local Scalars ..
157 INTEGER J, N1, N2
158 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
159 COMPLEX*16 ZDUM
160* ..
161* .. External Functions ..
162 LOGICAL LSAME
163 INTEGER IZAMAX
164 DOUBLE PRECISION DLAMCH, ZLANGE
165 EXTERNAL lsame, izamax, dlamch, zlange
166* ..
167* .. External Subroutines ..
168 EXTERNAL zgemm
169* ..
170* .. Intrinsic Functions ..
171 INTRINSIC abs, dble, dimag, max
172* ..
173* .. Statement Functions ..
174 DOUBLE PRECISION CABS1
175* ..
176* .. Statement Function definitions ..
177 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
178* ..
179* .. Executable Statements ..
180*
181* Quick exit if M = 0 or N = 0 or NRHS = 0
182*
183 IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.EQ.0 ) THEN
184 resid = zero
185 RETURN
186 END IF
187*
188 IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
189 n1 = n
190 n2 = m
191 ELSE
192 n1 = m
193 n2 = n
194 END IF
195*
196* Exit with RESID = 1/EPS if ANORM = 0.
197*
198 eps = dlamch( 'Epsilon' )
199 anorm = zlange( 'I', n1, n2, a, lda, rwork )
200 IF( anorm.LE.zero ) THEN
201 resid = one / eps
202 RETURN
203 END IF
204*
205* Compute B - A*X (or B - A'*X ) and store in B.
206*
207 CALL zgemm( trans, 'No transpose', n1, nrhs, n2, -cone, a, lda, x,
208 \$ ldx, cone, b, ldb )
209*
210* Compute the maximum over the number of right hand sides of
211* norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
212*
213 resid = zero
214 DO 10 j = 1, nrhs
215 bnorm = cabs1( b( izamax( n1, b( 1, j ), 1 ), j ) )
216 xnorm = cabs1( x( izamax( n2, x( 1, j ), 1 ), j ) )
217 IF( xnorm.LE.zero ) THEN
218 resid = one / eps
219 ELSE
220 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
221 END IF
222 10 CONTINUE
223*
224 RETURN
225*
226* End of ZGET08
227*
228 END
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
subroutine zget08(TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZGET08
Definition: zget08.f:133