LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
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 *> \date December 2016
123 *
124 *> \ingroup complex16_lin
125 *
126 * =====================================================================
127  SUBROUTINE zpot06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
128  $ RWORK, RESID )
129 *
130 * -- LAPACK test routine (version 3.7.0) --
131 * -- LAPACK is a software package provided by Univ. of Tennessee, --
132 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
133 * December 2016
134 *
135 * .. Scalar Arguments ..
136  CHARACTER UPLO
137  INTEGER LDA, LDB, LDX, N, NRHS
138  DOUBLE PRECISION RESID
139 * ..
140 * .. Array Arguments ..
141  DOUBLE PRECISION RWORK( * )
142  COMPLEX*16 A( lda, * ), B( ldb, * ), X( ldx, * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  DOUBLE PRECISION ZERO, ONE
149  parameter( zero = 0.0d+0, one = 1.0d+0 )
150  COMPLEX*16 CONE, NEGCONE
151  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
152  parameter( negcone = ( -1.0d+0, 0.0d+0 ) )
153 * ..
154 * .. Local Scalars ..
155  INTEGER IFAIL, J
156  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
157  COMPLEX*16 ZDUM
158 * ..
159 * .. External Functions ..
160  LOGICAL LSAME
161  INTEGER IZAMAX
162  DOUBLE PRECISION DLAMCH, ZLANSY
163  EXTERNAL lsame, izamax, dlamch, zlansy
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL zhemm
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC abs, dble, dimag, max
170 * ..
171 * .. Statement Functions ..
172  DOUBLE PRECISION CABS1
173 * ..
174 * .. Statement Function definitions ..
175  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
176 * ..
177 * ..
178 * .. Executable Statements ..
179 *
180 * Quick exit if N = 0 or NRHS = 0
181 *
182  IF( n.LE.0 .OR. nrhs.EQ.0 ) THEN
183  resid = zero
184  RETURN
185  END IF
186 *
187 * Exit with RESID = 1/EPS if ANORM = 0.
188 *
189  eps = dlamch( 'Epsilon' )
190  anorm = zlansy( 'I', uplo, n, a, lda, rwork )
191  IF( anorm.LE.zero ) THEN
192  resid = one / eps
193  RETURN
194  END IF
195 *
196 * Compute B - A*X and store in B.
197  ifail=0
198 *
199  CALL zhemm( 'Left', uplo, n, nrhs, negcone, a, lda, x,
200  $ ldx, cone, b, ldb )
201 *
202 * Compute the maximum over the number of right hand sides of
203 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
204 *
205  resid = zero
206  DO 10 j = 1, nrhs
207  bnorm = cabs1(b(izamax( n, b( 1, j ), 1 ),j))
208  xnorm = cabs1(x(izamax( n, x( 1, j ), 1 ),j))
209  IF( xnorm.LE.zero ) THEN
210  resid = one / eps
211  ELSE
212  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
213  END IF
214  10 CONTINUE
215 *
216  RETURN
217 *
218 * End of ZPOT06
219 *
220  END
subroutine zhemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZHEMM
Definition: zhemm.f:193
subroutine zpot06(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZPOT06
Definition: zpot06.f:129