LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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zpot06.f
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1*> \brief \b ZPOT06
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 ZPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
12* RWORK, RESID )
13*
14* .. Scalar Arguments ..
15* CHARACTER UPLO
16* INTEGER LDA, LDB, LDX, 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*> ZPOT06 computes the residual for a solution of a system of linear
31*> equations A*x = b :
32*> RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
33*> where EPS is the machine epsilon.
34*> \endverbatim
35*
36* Arguments:
37* ==========
38*
39*> \param[in] UPLO
40*> \verbatim
41*> UPLO is CHARACTER*1
42*> Specifies whether the upper or lower triangular part of the
43*> symmetric matrix A is stored:
44*> = 'U': Upper triangular
45*> = 'L': Lower triangular
46*> \endverbatim
47*>
48*> \param[in] N
49*> \verbatim
50*> N is INTEGER
51*> The number of rows and columns of the matrix A. N >= 0.
52*> \endverbatim
53*>
54*> \param[in] NRHS
55*> \verbatim
56*> NRHS is INTEGER
57*> The number of columns of B, the matrix of right hand sides.
58*> NRHS >= 0.
59*> \endverbatim
60*>
61*> \param[in] A
62*> \verbatim
63*> A is COMPLEX*16 array, dimension (LDA,N)
64*> The original M x N matrix A.
65*> \endverbatim
66*>
67*> \param[in] LDA
68*> \verbatim
69*> LDA is INTEGER
70*> The leading dimension of the array A. LDA >= max(1,N).
71*> \endverbatim
72*>
73*> \param[in] X
74*> \verbatim
75*> X is COMPLEX*16 array, dimension (LDX,NRHS)
76*> The computed solution vectors for the system of linear
77*> equations.
78*> \endverbatim
79*>
80*> \param[in] LDX
81*> \verbatim
82*> LDX is INTEGER
83*> The leading dimension of the array X. If TRANS = 'N',
84*> LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N).
85*> \endverbatim
86*>
87*> \param[in,out] B
88*> \verbatim
89*> B is COMPLEX*16 array, dimension (LDB,NRHS)
90*> On entry, the right hand side vectors for the system of
91*> linear equations.
92*> On exit, B is overwritten with the difference B - A*X.
93*> \endverbatim
94*>
95*> \param[in] LDB
96*> \verbatim
97*> LDB is INTEGER
98*> The leading dimension of the array B. IF TRANS = 'N',
99*> LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
100*> \endverbatim
101*>
102*> \param[out] RWORK
103*> \verbatim
104*> RWORK is DOUBLE PRECISION array, dimension (N)
105*> \endverbatim
106*>
107*> \param[out] RESID
108*> \verbatim
109*> RESID is DOUBLE PRECISION
110*> The maximum over the number of right hand sides of
111*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
112*> \endverbatim
113*
114* Authors:
115* ========
116*
117*> \author Univ. of Tennessee
118*> \author Univ. of California Berkeley
119*> \author Univ. of Colorado Denver
120*> \author NAG Ltd.
121*
122*> \ingroup complex16_lin
123*
124* =====================================================================
125 SUBROUTINE zpot06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
126 $ RWORK, RESID )
127*
128* -- LAPACK test routine --
129* -- LAPACK is a software package provided by Univ. of Tennessee, --
130* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131*
132* .. Scalar Arguments ..
133 CHARACTER UPLO
134 INTEGER LDA, LDB, LDX, N, NRHS
135 DOUBLE PRECISION RESID
136* ..
137* .. Array Arguments ..
138 DOUBLE PRECISION RWORK( * )
139 COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
140* ..
141*
142* =====================================================================
143*
144* .. Parameters ..
145 DOUBLE PRECISION ZERO, ONE
146 parameter( zero = 0.0d+0, one = 1.0d+0 )
147 COMPLEX*16 CONE, NEGCONE
148 parameter( cone = ( 1.0d+0, 0.0d+0 ) )
149 parameter( negcone = ( -1.0d+0, 0.0d+0 ) )
150* ..
151* .. Local Scalars ..
152 INTEGER IFAIL, J
153 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
154 COMPLEX*16 ZDUM
155* ..
156* .. External Functions ..
157 LOGICAL LSAME
158 INTEGER IZAMAX
159 DOUBLE PRECISION DLAMCH, ZLANSY
160 EXTERNAL lsame, izamax, dlamch, zlansy
161* ..
162* .. External Subroutines ..
163 EXTERNAL zhemm
164* ..
165* .. Intrinsic Functions ..
166 INTRINSIC abs, dble, dimag, max
167* ..
168* .. Statement Functions ..
169 DOUBLE PRECISION CABS1
170* ..
171* .. Statement Function definitions ..
172 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
173* ..
174* ..
175* .. Executable Statements ..
176*
177* Quick exit if N = 0 or NRHS = 0
178*
179 IF( n.LE.0 .OR. nrhs.EQ.0 ) THEN
180 resid = zero
181 RETURN
182 END IF
183*
184* Exit with RESID = 1/EPS if ANORM = 0.
185*
186 eps = dlamch( 'Epsilon' )
187 anorm = zlansy( 'I', uplo, n, a, lda, rwork )
188 IF( anorm.LE.zero ) THEN
189 resid = one / eps
190 RETURN
191 END IF
192*
193* Compute B - A*X and store in B.
194 ifail=0
195*
196 CALL zhemm( 'Left', uplo, n, nrhs, negcone, a, lda, x,
197 $ ldx, cone, b, ldb )
198*
199* Compute the maximum over the number of right hand sides of
200* norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
201*
202 resid = zero
203 DO 10 j = 1, nrhs
204 bnorm = cabs1(b(izamax( n, b( 1, j ), 1 ),j))
205 xnorm = cabs1(x(izamax( n, x( 1, j ), 1 ),j))
206 IF( xnorm.LE.zero ) THEN
207 resid = one / eps
208 ELSE
209 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
210 END IF
211 10 CONTINUE
212*
213 RETURN
214*
215* End of ZPOT06
216*
217 END
subroutine zhemm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
ZHEMM
Definition zhemm.f:191
subroutine zpot06(uplo, n, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)
ZPOT06
Definition zpot06.f:127