LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
cla_hercond_x.f
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1 *> \brief \b CLA_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 * REAL FUNCTION CLA_HERCOND_X( UPLO, N, A, LDA, AF, LDAF, IPIV, X,
22 * INFO, WORK, RWORK )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * INTEGER N, LDA, LDAF, INFO
27 * ..
28 * .. Array Arguments ..
29 * INTEGER IPIV( * )
30 * COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
31 * REAL RWORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> CLA_HERCOND_X computes the infinity norm condition number of
41 *> op(A) * diag(X) where X is a COMPLEX vector.
42 *> \endverbatim
43 *
44 * Arguments:
45 * ==========
46 *
47 *> \param[in] UPLO
48 *> \verbatim
49 *> UPLO is CHARACTER*1
50 *> = 'U': Upper triangle of A is stored;
51 *> = 'L': Lower triangle of A is stored.
52 *> \endverbatim
53 *>
54 *> \param[in] N
55 *> \verbatim
56 *> N is INTEGER
57 *> The number of linear equations, i.e., the order of the
58 *> matrix A. N >= 0.
59 *> \endverbatim
60 *>
61 *> \param[in] A
62 *> \verbatim
63 *> A is COMPLEX array, dimension (LDA,N)
64 *> On entry, the N-by-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] AF
74 *> \verbatim
75 *> AF is COMPLEX array, dimension (LDAF,N)
76 *> The block diagonal matrix D and the multipliers used to
77 *> obtain the factor U or L as computed by CHETRF.
78 *> \endverbatim
79 *>
80 *> \param[in] LDAF
81 *> \verbatim
82 *> LDAF is INTEGER
83 *> The leading dimension of the array AF. LDAF >= max(1,N).
84 *> \endverbatim
85 *>
86 *> \param[in] IPIV
87 *> \verbatim
88 *> IPIV is INTEGER array, dimension (N)
89 *> Details of the interchanges and the block structure of D
90 *> as determined by CHETRF.
91 *> \endverbatim
92 *>
93 *> \param[in] X
94 *> \verbatim
95 *> X is COMPLEX array, dimension (N)
96 *> The vector X in the formula op(A) * diag(X).
97 *> \endverbatim
98 *>
99 *> \param[out] INFO
100 *> \verbatim
101 *> INFO is INTEGER
102 *> = 0: Successful exit.
103 *> i > 0: The ith argument is invalid.
104 *> \endverbatim
105 *>
106 *> \param[out] WORK
107 *> \verbatim
108 *> WORK is COMPLEX array, dimension (2*N).
109 *> Workspace.
110 *> \endverbatim
111 *>
112 *> \param[out] RWORK
113 *> \verbatim
114 *> RWORK is REAL array, dimension (N).
115 *> Workspace.
116 *> \endverbatim
117 *
118 * Authors:
119 * ========
120 *
121 *> \author Univ. of Tennessee
122 *> \author Univ. of California Berkeley
123 *> \author Univ. of Colorado Denver
124 *> \author NAG Ltd.
125 *
126 *> \ingroup complexHEcomputational
127 *
128 * =====================================================================
129  REAL function cla_hercond_x( uplo, n, a, lda, af, ldaf, ipiv, x,
130  \$ info, work, rwork )
131 *
132 * -- LAPACK computational routine --
133 * -- LAPACK is a software package provided by Univ. of Tennessee, --
134 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
135 *
136 * .. Scalar Arguments ..
137  CHARACTER uplo
138  INTEGER n, lda, ldaf, info
139 * ..
140 * .. Array Arguments ..
141  INTEGER ipiv( * )
142  COMPLEX a( lda, * ), af( ldaf, * ), work( * ), x( * )
143  REAL rwork( * )
144 * ..
145 *
146 * =====================================================================
147 *
148 * .. Local Scalars ..
149  INTEGER kase, i, j
150  REAL ainvnm, anorm, tmp
151  LOGICAL up, upper
152  COMPLEX zdum
153 * ..
154 * .. Local Arrays ..
155  INTEGER isave( 3 )
156 * ..
157 * .. External Functions ..
158  LOGICAL lsame
159  EXTERNAL lsame
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL clacn2, chetrs, xerbla
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC abs, max
166 * ..
167 * .. Statement Functions ..
168  REAL cabs1
169 * ..
170 * .. Statement Function Definitions ..
171  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
172 * ..
173 * .. Executable Statements ..
174 *
175  cla_hercond_x = 0.0e+0
176 *
177  info = 0
178  upper = lsame( uplo, 'U' )
179  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
180  info = -1
181  ELSE IF ( n.LT.0 ) THEN
182  info = -2
183  ELSE IF( lda.LT.max( 1, n ) ) THEN
184  info = -4
185  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
186  info = -6
187  END IF
188  IF( info.NE.0 ) THEN
189  CALL xerbla( 'CLA_HERCOND_X', -info )
190  RETURN
191  END IF
192  up = .false.
193  IF ( lsame( uplo, 'U' ) ) up = .true.
194 *
195 * Compute norm of op(A)*op2(C).
196 *
197  anorm = 0.0
198  IF ( up ) THEN
199  DO i = 1, n
200  tmp = 0.0e+0
201  DO j = 1, i
202  tmp = tmp + cabs1( a( j, i ) * x( j ) )
203  END DO
204  DO j = i+1, n
205  tmp = tmp + cabs1( a( i, j ) * x( j ) )
206  END DO
207  rwork( i ) = tmp
208  anorm = max( anorm, tmp )
209  END DO
210  ELSE
211  DO i = 1, n
212  tmp = 0.0e+0
213  DO j = 1, i
214  tmp = tmp + cabs1( a( i, j ) * x( j ) )
215  END DO
216  DO j = i+1, n
217  tmp = tmp + cabs1( a( j, i ) * x( j ) )
218  END DO
219  rwork( i ) = tmp
220  anorm = max( anorm, tmp )
221  END DO
222  END IF
223 *
224 * Quick return if possible.
225 *
226  IF( n.EQ.0 ) THEN
227  cla_hercond_x = 1.0e+0
228  RETURN
229  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
230  RETURN
231  END IF
232 *
233 * Estimate the norm of inv(op(A)).
234 *
235  ainvnm = 0.0e+0
236 *
237  kase = 0
238  10 CONTINUE
239  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
240  IF( kase.NE.0 ) THEN
241  IF( kase.EQ.2 ) THEN
242 *
243 * Multiply by R.
244 *
245  DO i = 1, n
246  work( i ) = work( i ) * rwork( i )
247  END DO
248 *
249  IF ( up ) THEN
250  CALL chetrs( 'U', n, 1, af, ldaf, ipiv,
251  \$ work, n, info )
252  ELSE
253  CALL chetrs( 'L', n, 1, af, ldaf, ipiv,
254  \$ work, n, info )
255  ENDIF
256 *
257 * Multiply by inv(X).
258 *
259  DO i = 1, n
260  work( i ) = work( i ) / x( i )
261  END DO
262  ELSE
263 *
264 * Multiply by inv(X**H).
265 *
266  DO i = 1, n
267  work( i ) = work( i ) / x( i )
268  END DO
269 *
270  IF ( up ) THEN
271  CALL chetrs( 'U', n, 1, af, ldaf, ipiv,
272  \$ work, n, info )
273  ELSE
274  CALL chetrs( 'L', n, 1, af, ldaf, ipiv,
275  \$ work, n, info )
276  END IF
277 *
278 * Multiply by R.
279 *
280  DO i = 1, n
281  work( i ) = work( i ) * rwork( i )
282  END DO
283  END IF
284  GO TO 10
285  END IF
286 *
287 * Compute the estimate of the reciprocal condition number.
288 *
289  IF( ainvnm .NE. 0.0e+0 )
290  \$ cla_hercond_x = 1.0e+0 / ainvnm
291 *
292  RETURN
293 *
294 * End of CLA_HERCOND_X
295 *
296  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine chetrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CHETRS
Definition: chetrs.f:120
real function cla_hercond_x(UPLO, N, A, LDA, AF, LDAF, IPIV, X, INFO, WORK, RWORK)
CLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite m...
subroutine clacn2(N, V, X, EST, KASE, ISAVE)
CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: clacn2.f:133