LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
zsyt03.f
Go to the documentation of this file.
1 *> \brief \b ZSYT03
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 ZSYT03( 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 *> ZSYT03 computes the residual for a complex symmetric matrix times
32 *> its 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 *> complex symmetric 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 complex symmetric 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 symmetric
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 *> RCOND = 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 *> \ingroup complex16_lin
122 *
123 * =====================================================================
124  SUBROUTINE zsyt03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
125  \$ RWORK, RCOND, RESID )
126 *
127 * -- LAPACK test routine --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 *
131 * .. Scalar Arguments ..
132  CHARACTER UPLO
133  INTEGER LDA, LDAINV, LDWORK, N
134  DOUBLE PRECISION RCOND, RESID
135 * ..
136 * .. Array Arguments ..
137  DOUBLE PRECISION RWORK( * )
138  COMPLEX*16 A( LDA, * ), AINV( LDAINV, * ),
139  \$ work( ldwork, * )
140 * ..
141 *
142 * =====================================================================
143 *
144 *
145 * .. Parameters ..
146  DOUBLE PRECISION ZERO, ONE
147  parameter( zero = 0.0d+0, one = 1.0d+0 )
148  COMPLEX*16 CZERO, CONE
149  parameter( czero = ( 0.0d+0, 0.0d+0 ),
150  \$ cone = ( 1.0d+0, 0.0d+0 ) )
151 * ..
152 * .. Local Scalars ..
153  INTEGER I, J
154  DOUBLE PRECISION AINVNM, ANORM, EPS
155 * ..
156 * .. External Functions ..
157  LOGICAL LSAME
158  DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY
159  EXTERNAL lsame, dlamch, zlange, zlansy
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL zsymm
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC dble
166 * ..
167 * .. Executable Statements ..
168 *
169 * Quick exit if N = 0
170 *
171  IF( n.LE.0 ) THEN
172  rcond = one
173  resid = zero
174  RETURN
175  END IF
176 *
177 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
178 *
179  eps = dlamch( 'Epsilon' )
180  anorm = zlansy( '1', uplo, n, a, lda, rwork )
181  ainvnm = zlansy( '1', uplo, n, ainv, ldainv, rwork )
182  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
183  rcond = zero
184  resid = one / eps
185  RETURN
186  END IF
187  rcond = ( one / anorm ) / ainvnm
188 *
189 * Expand AINV into a full matrix and call ZSYMM to multiply
190 * AINV on the left by A (store the result in WORK).
191 *
192  IF( lsame( uplo, 'U' ) ) THEN
193  DO 20 j = 1, n
194  DO 10 i = 1, j - 1
195  ainv( j, i ) = ainv( i, j )
196  10 CONTINUE
197  20 CONTINUE
198  ELSE
199  DO 40 j = 1, n
200  DO 30 i = j + 1, n
201  ainv( j, i ) = ainv( i, j )
202  30 CONTINUE
203  40 CONTINUE
204  END IF
205  CALL zsymm( 'Left', uplo, n, n, -cone, a, lda, ainv, ldainv,
206  \$ czero, work, ldwork )
207 *
208 * Add the identity matrix to WORK .
209 *
210  DO 50 i = 1, n
211  work( i, i ) = work( i, i ) + cone
212  50 CONTINUE
213 *
214 * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
215 *
216  resid = zlange( '1', n, n, work, ldwork, rwork )
217 *
218  resid = ( ( resid*rcond ) / eps ) / dble( n )
219 *
220  RETURN
221 *
222 * End of ZSYT03
223 *
224  END
subroutine zsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZSYMM
Definition: zsymm.f:189
subroutine zsyt03(UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
ZSYT03
Definition: zsyt03.f:126