LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
zpot02.f
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1 *> \brief \b ZPOT02
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 ZPOT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
12 * 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 *> ZPOT02 computes the residual for the solution of a Hermitian system
31 *> of linear equations A*x = b:
32 *>
33 *> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
34 *>
35 *> where EPS is the machine epsilon.
36 *> \endverbatim
37 *
38 * Arguments:
39 * ==========
40 *
41 *> \param[in] UPLO
42 *> \verbatim
43 *> UPLO is CHARACTER*1
44 *> Specifies whether the upper or lower triangular part of the
45 *> Hermitian matrix A is stored:
46 *> = 'U': Upper triangular
47 *> = 'L': Lower triangular
48 *> \endverbatim
49 *>
50 *> \param[in] N
51 *> \verbatim
52 *> N is INTEGER
53 *> The number of rows and columns of the matrix A. N >= 0.
54 *> \endverbatim
55 *>
56 *> \param[in] NRHS
57 *> \verbatim
58 *> NRHS is INTEGER
59 *> The number of columns of B, the matrix of right hand sides.
60 *> NRHS >= 0.
61 *> \endverbatim
62 *>
63 *> \param[in] A
64 *> \verbatim
65 *> A is COMPLEX*16 array, dimension (LDA,N)
66 *> The original Hermitian matrix A.
67 *> \endverbatim
68 *>
69 *> \param[in] LDA
70 *> \verbatim
71 *> LDA is INTEGER
72 *> The leading dimension of the array A. LDA >= max(1,N)
73 *> \endverbatim
74 *>
75 *> \param[in] X
76 *> \verbatim
77 *> X is COMPLEX*16 array, dimension (LDX,NRHS)
78 *> The computed solution vectors for the system of linear
79 *> equations.
80 *> \endverbatim
81 *>
82 *> \param[in] LDX
83 *> \verbatim
84 *> LDX is INTEGER
85 *> The leading dimension of the array X. LDX >= max(1,N).
86 *> \endverbatim
87 *>
88 *> \param[in,out] B
89 *> \verbatim
90 *> B is COMPLEX*16 array, dimension (LDB,NRHS)
91 *> On entry, the right hand side vectors for the system of
92 *> linear equations.
93 *> On exit, B is overwritten with the difference B - A*X.
94 *> \endverbatim
95 *>
96 *> \param[in] LDB
97 *> \verbatim
98 *> LDB is INTEGER
99 *> The leading dimension of the array B. 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 zpot02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
128  $ 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
151  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
152 * ..
153 * .. Local Scalars ..
154  INTEGER J
155  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
156 * ..
157 * .. External Functions ..
158  DOUBLE PRECISION DLAMCH, DZASUM, ZLANHE
159  EXTERNAL dlamch, dzasum, zlanhe
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL zhemm
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC max
166 * ..
167 * .. Executable Statements ..
168 *
169 * Quick exit if N = 0 or NRHS = 0.
170 *
171  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
172  resid = zero
173  RETURN
174  END IF
175 *
176 * Exit with RESID = 1/EPS if ANORM = 0.
177 *
178  eps = dlamch( 'Epsilon' )
179  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
180  IF( anorm.LE.zero ) THEN
181  resid = one / eps
182  RETURN
183  END IF
184 *
185 * Compute B - A*X
186 *
187  CALL zhemm( 'Left', uplo, n, nrhs, -cone, a, lda, x, ldx, cone, b,
188  $ ldb )
189 *
190 * Compute the maximum over the number of right hand sides of
191 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
192 *
193  resid = zero
194  DO 10 j = 1, nrhs
195  bnorm = dzasum( n, b( 1, j ), 1 )
196  xnorm = dzasum( n, x( 1, j ), 1 )
197  IF( xnorm.LE.zero ) THEN
198  resid = one / eps
199  ELSE
200  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
201  END IF
202  10 CONTINUE
203 *
204  RETURN
205 *
206 * End of ZPOT02
207 *
208  END
subroutine zhemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZHEMM
Definition: zhemm.f:193
subroutine zpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZPOT02
Definition: zpot02.f:129