LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zla_hercond_x.f
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1 *> \brief \b ZLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION ZLA_HERCOND_X( UPLO, N, A, LDA, AF,
22 * LDAF, IPIV, X, INFO,
23 * WORK, RWORK )
24 *
25 * .. Scalar Arguments ..
26 * CHARACTER UPLO
27 * INTEGER N, LDA, LDAF, INFO
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IPIV( * )
31 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
32 * DOUBLE PRECISION RWORK( * )
33 * ..
34 *
35 *
36 *> \par Purpose:
37 * =============
38 *>
39 *> \verbatim
40 *>
41 *> ZLA_HERCOND_X computes the infinity norm condition number of
42 *> op(A) * diag(X) where X is a COMPLEX*16 vector.
43 *> \endverbatim
44 *
45 * Arguments:
46 * ==========
47 *
48 *> \param[in] UPLO
49 *> \verbatim
50 *> UPLO is CHARACTER*1
51 *> = 'U': Upper triangle of A is stored;
52 *> = 'L': Lower triangle of A is stored.
53 *> \endverbatim
54 *>
55 *> \param[in] N
56 *> \verbatim
57 *> N is INTEGER
58 *> The number of linear equations, i.e., the order of the
59 *> matrix A. N >= 0.
60 *> \endverbatim
61 *>
62 *> \param[in] A
63 *> \verbatim
64 *> A is COMPLEX*16 array, dimension (LDA,N)
65 *> On entry, the N-by-N matrix A.
66 *> \endverbatim
67 *>
68 *> \param[in] LDA
69 *> \verbatim
70 *> LDA is INTEGER
71 *> The leading dimension of the array A. LDA >= max(1,N).
72 *> \endverbatim
73 *>
74 *> \param[in] AF
75 *> \verbatim
76 *> AF is COMPLEX*16 array, dimension (LDAF,N)
77 *> The block diagonal matrix D and the multipliers used to
78 *> obtain the factor U or L as computed by ZHETRF.
79 *> \endverbatim
80 *>
81 *> \param[in] LDAF
82 *> \verbatim
83 *> LDAF is INTEGER
84 *> The leading dimension of the array AF. LDAF >= max(1,N).
85 *> \endverbatim
86 *>
87 *> \param[in] IPIV
88 *> \verbatim
89 *> IPIV is INTEGER array, dimension (N)
90 *> Details of the interchanges and the block structure of D
91 *> as determined by CHETRF.
92 *> \endverbatim
93 *>
94 *> \param[in] X
95 *> \verbatim
96 *> X is COMPLEX*16 array, dimension (N)
97 *> The vector X in the formula op(A) * diag(X).
98 *> \endverbatim
99 *>
100 *> \param[out] INFO
101 *> \verbatim
102 *> INFO is INTEGER
103 *> = 0: Successful exit.
104 *> i > 0: The ith argument is invalid.
105 *> \endverbatim
106 *>
107 *> \param[in] WORK
108 *> \verbatim
109 *> WORK is COMPLEX*16 array, dimension (2*N).
110 *> Workspace.
111 *> \endverbatim
112 *>
113 *> \param[in] RWORK
114 *> \verbatim
115 *> RWORK is DOUBLE PRECISION array, dimension (N).
116 *> Workspace.
117 *> \endverbatim
118 *
119 * Authors:
120 * ========
121 *
122 *> \author Univ. of Tennessee
123 *> \author Univ. of California Berkeley
124 *> \author Univ. of Colorado Denver
125 *> \author NAG Ltd.
126 *
127 *> \date September 2012
128 *
129 *> \ingroup complex16HEcomputational
130 *
131 * =====================================================================
132  DOUBLE PRECISION FUNCTION zla_hercond_x( UPLO, N, A, LDA, AF,
133  \$ ldaf, ipiv, x, info,
134  \$ work, rwork )
135 *
136 * -- LAPACK computational routine (version 3.4.2) --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 * September 2012
140 *
141 * .. Scalar Arguments ..
142  CHARACTER UPLO
143  INTEGER N, LDA, LDAF, INFO
144 * ..
145 * .. Array Arguments ..
146  INTEGER IPIV( * )
147  COMPLEX*16 A( lda, * ), AF( ldaf, * ), WORK( * ), X( * )
148  DOUBLE PRECISION RWORK( * )
149 * ..
150 *
151 * =====================================================================
152 *
153 * .. Local Scalars ..
154  INTEGER KASE, I, J
155  DOUBLE PRECISION AINVNM, ANORM, TMP
156  LOGICAL UP, UPPER
157  COMPLEX*16 ZDUM
158 * ..
159 * .. Local Arrays ..
160  INTEGER ISAVE( 3 )
161 * ..
162 * .. External Functions ..
163  LOGICAL LSAME
164  EXTERNAL lsame
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL zlacn2, zhetrs, xerbla
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC abs, max
171 * ..
172 * .. Statement Functions ..
173  DOUBLE PRECISION CABS1
174 * ..
175 * .. Statement Function Definitions ..
176  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
177 * ..
178 * .. Executable Statements ..
179 *
180  zla_hercond_x = 0.0d+0
181 *
182  info = 0
183  upper = lsame( uplo, 'U' )
184  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
185  info = -1
186  ELSE IF ( n.LT.0 ) THEN
187  info = -2
188  ELSE IF( lda.LT.max( 1, n ) ) THEN
189  info = -4
190  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
191  info = -6
192  END IF
193  IF( info.NE.0 ) THEN
194  CALL xerbla( 'ZLA_HERCOND_X', -info )
195  RETURN
196  END IF
197  up = .false.
198  IF ( lsame( uplo, 'U' ) ) up = .true.
199 *
200 * Compute norm of op(A)*op2(C).
201 *
202  anorm = 0.0d+0
203  IF ( up ) THEN
204  DO i = 1, n
205  tmp = 0.0d+0
206  DO j = 1, i
207  tmp = tmp + cabs1( a( j, i ) * x( j ) )
208  END DO
209  DO j = i+1, n
210  tmp = tmp + cabs1( a( i, j ) * x( j ) )
211  END DO
212  rwork( i ) = tmp
213  anorm = max( anorm, tmp )
214  END DO
215  ELSE
216  DO i = 1, n
217  tmp = 0.0d+0
218  DO j = 1, i
219  tmp = tmp + cabs1( a( i, j ) * x( j ) )
220  END DO
221  DO j = i+1, n
222  tmp = tmp + cabs1( a( j, i ) * x( j ) )
223  END DO
224  rwork( i ) = tmp
225  anorm = max( anorm, tmp )
226  END DO
227  END IF
228 *
229 * Quick return if possible.
230 *
231  IF( n.EQ.0 ) THEN
232  zla_hercond_x = 1.0d+0
233  RETURN
234  ELSE IF( anorm .EQ. 0.0d+0 ) THEN
235  RETURN
236  END IF
237 *
238 * Estimate the norm of inv(op(A)).
239 *
240  ainvnm = 0.0d+0
241 *
242  kase = 0
243  10 CONTINUE
244  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
245  IF( kase.NE.0 ) THEN
246  IF( kase.EQ.2 ) THEN
247 *
248 * Multiply by R.
249 *
250  DO i = 1, n
251  work( i ) = work( i ) * rwork( i )
252  END DO
253 *
254  IF ( up ) THEN
255  CALL zhetrs( 'U', n, 1, af, ldaf, ipiv,
256  \$ work, n, info )
257  ELSE
258  CALL zhetrs( 'L', n, 1, af, ldaf, ipiv,
259  \$ work, n, info )
260  ENDIF
261 *
262 * Multiply by inv(X).
263 *
264  DO i = 1, n
265  work( i ) = work( i ) / x( i )
266  END DO
267  ELSE
268 *
269 * Multiply by inv(X**H).
270 *
271  DO i = 1, n
272  work( i ) = work( i ) / x( i )
273  END DO
274 *
275  IF ( up ) THEN
276  CALL zhetrs( 'U', n, 1, af, ldaf, ipiv,
277  \$ work, n, info )
278  ELSE
279  CALL zhetrs( 'L', n, 1, af, ldaf, ipiv,
280  \$ work, n, info )
281  END IF
282 *
283 * Multiply by R.
284 *
285  DO i = 1, n
286  work( i ) = work( i ) * rwork( i )
287  END DO
288  END IF
289  GO TO 10
290  END IF
291 *
292 * Compute the estimate of the reciprocal condition number.
293 *
294  IF( ainvnm .NE. 0.0d+0 )
295  \$ zla_hercond_x = 1.0d+0 / ainvnm
296 *
297  RETURN
298 *
299  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zlacn2(N, V, X, EST, KASE, ISAVE)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: zlacn2.f:135
double precision function zla_hercond_x(UPLO, N, A, LDA, AF, LDAF, IPIV, X, INFO, WORK, RWORK)
ZLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite m...
subroutine zhetrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZHETRS
Definition: zhetrs.f:122