LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zpot03.f
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1 *> \brief \b ZPOT03
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 ZPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
12 * RWORK, RCOND, RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER UPLO
16 * INTEGER LDA, LDAINV, LDWORK, N
17 * DOUBLE PRECISION RCOND, RESID
18 * ..
19 * .. Array Arguments ..
20 * DOUBLE PRECISION RWORK( * )
21 * COMPLEX*16 A( LDA, * ), AINV( LDAINV, * ),
22 * \$ WORK( LDWORK, * )
23 * ..
24 *
25 *
26 *> \par Purpose:
27 * =============
28 *>
29 *> \verbatim
30 *>
31 *> ZPOT03 computes the residual for a Hermitian matrix times its
32 *> inverse:
33 *> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
34 *> where EPS is the machine epsilon.
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] UPLO
41 *> \verbatim
42 *> UPLO is CHARACTER*1
43 *> Specifies whether the upper or lower triangular part of the
44 *> Hermitian matrix A is stored:
45 *> = 'U': Upper triangular
46 *> = 'L': Lower triangular
47 *> \endverbatim
48 *>
49 *> \param[in] N
50 *> \verbatim
51 *> N is INTEGER
52 *> The number of rows and columns of the matrix A. N >= 0.
53 *> \endverbatim
54 *>
55 *> \param[in] A
56 *> \verbatim
57 *> A is COMPLEX*16 array, dimension (LDA,N)
58 *> The original Hermitian matrix A.
59 *> \endverbatim
60 *>
61 *> \param[in] LDA
62 *> \verbatim
63 *> LDA is INTEGER
64 *> The leading dimension of the array A. LDA >= max(1,N)
65 *> \endverbatim
66 *>
67 *> \param[in,out] AINV
68 *> \verbatim
69 *> AINV is COMPLEX*16 array, dimension (LDAINV,N)
70 *> On entry, the inverse of the matrix A, stored as a Hermitian
71 *> matrix in the same format as A.
72 *> In this version, AINV is expanded into a full matrix and
73 *> multiplied by A, so the opposing triangle of AINV will be
74 *> changed; i.e., if the upper triangular part of AINV is
75 *> stored, the lower triangular part will be used as work space.
76 *> \endverbatim
77 *>
78 *> \param[in] LDAINV
79 *> \verbatim
80 *> LDAINV is INTEGER
81 *> The leading dimension of the array AINV. LDAINV >= max(1,N).
82 *> \endverbatim
83 *>
84 *> \param[out] WORK
85 *> \verbatim
86 *> WORK is COMPLEX*16 array, dimension (LDWORK,N)
87 *> \endverbatim
88 *>
89 *> \param[in] LDWORK
90 *> \verbatim
91 *> LDWORK is INTEGER
92 *> The leading dimension of the array WORK. LDWORK >= max(1,N).
93 *> \endverbatim
94 *>
95 *> \param[out] RWORK
96 *> \verbatim
97 *> RWORK is DOUBLE PRECISION array, dimension (N)
98 *> \endverbatim
99 *>
100 *> \param[out] RCOND
101 *> \verbatim
102 *> RCOND is DOUBLE PRECISION
103 *> The reciprocal of the condition number of A, computed as
104 *> ( 1/norm(A) ) / norm(AINV).
105 *> \endverbatim
106 *>
107 *> \param[out] RESID
108 *> \verbatim
109 *> RESID is DOUBLE PRECISION
110 *> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
111 *> \endverbatim
112 *
113 * Authors:
114 * ========
115 *
116 *> \author Univ. of Tennessee
117 *> \author Univ. of California Berkeley
118 *> \author Univ. of Colorado Denver
119 *> \author NAG Ltd.
120 *
121 *> \date November 2011
122 *
123 *> \ingroup complex16_lin
124 *
125 * =====================================================================
126  SUBROUTINE zpot03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
127  \$ rwork, rcond, resid )
128 *
129 * -- LAPACK test routine (version 3.4.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * November 2011
133 *
134 * .. Scalar Arguments ..
135  CHARACTER UPLO
136  INTEGER LDA, LDAINV, LDWORK, N
137  DOUBLE PRECISION RCOND, RESID
138 * ..
139 * .. Array Arguments ..
140  DOUBLE PRECISION RWORK( * )
141  COMPLEX*16 A( lda, * ), AINV( ldainv, * ),
142  \$ work( ldwork, * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  DOUBLE PRECISION ZERO, ONE
149  parameter ( zero = 0.0d+0, one = 1.0d+0 )
150  COMPLEX*16 CZERO, CONE
151  parameter ( czero = ( 0.0d+0, 0.0d+0 ),
152  \$ cone = ( 1.0d+0, 0.0d+0 ) )
153 * ..
154 * .. Local Scalars ..
155  INTEGER I, J
156  DOUBLE PRECISION AINVNM, ANORM, EPS
157 * ..
158 * .. External Functions ..
159  LOGICAL LSAME
160  DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE
161  EXTERNAL lsame, dlamch, zlange, zlanhe
162 * ..
163 * .. External Subroutines ..
164  EXTERNAL zhemm
165 * ..
166 * .. Intrinsic Functions ..
167  INTRINSIC dble, dconjg
168 * ..
169 * .. Executable Statements ..
170 *
171 * Quick exit if N = 0.
172 *
173  IF( n.LE.0 ) THEN
174  rcond = one
175  resid = zero
176  RETURN
177  END IF
178 *
179 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
180 *
181  eps = dlamch( 'Epsilon' )
182  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
183  ainvnm = zlanhe( '1', uplo, n, ainv, ldainv, rwork )
184  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
185  rcond = zero
186  resid = one / eps
187  RETURN
188  END IF
189  rcond = ( one / anorm ) / ainvnm
190 *
191 * Expand AINV into a full matrix and call ZHEMM to multiply
192 * AINV on the left by A.
193 *
194  IF( lsame( uplo, 'U' ) ) THEN
195  DO 20 j = 1, n
196  DO 10 i = 1, j - 1
197  ainv( j, i ) = dconjg( ainv( i, j ) )
198  10 CONTINUE
199  20 CONTINUE
200  ELSE
201  DO 40 j = 1, n
202  DO 30 i = j + 1, n
203  ainv( j, i ) = dconjg( ainv( i, j ) )
204  30 CONTINUE
205  40 CONTINUE
206  END IF
207  CALL zhemm( 'Left', uplo, n, n, -cone, a, lda, ainv, ldainv,
208  \$ czero, work, ldwork )
209 *
210 * Add the identity matrix to WORK .
211 *
212  DO 50 i = 1, n
213  work( i, i ) = work( i, i ) + cone
214  50 CONTINUE
215 *
216 * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
217 *
218  resid = zlange( '1', n, n, work, ldwork, rwork )
219 *
220  resid = ( ( resid*rcond ) / eps ) / dble( n )
221 *
222  RETURN
223 *
224 * End of ZPOT03
225 *
226  END
subroutine zpot03(UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
ZPOT03
Definition: zpot03.f:128
subroutine zhemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZHEMM
Definition: zhemm.f:193