LAPACK  3.7.0 LAPACK: Linear Algebra PACKage
cla_syrcond_x.f
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1 *> \brief \b CLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION CLA_SYRCOND_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_SYRCOND_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 CSYTRF.
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 CSYTRF.
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[in] WORK
107 *> \verbatim
108 *> WORK is COMPLEX array, dimension (2*N).
109 *> Workspace.
110 *> \endverbatim
111 *>
112 *> \param[in] 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 *> \date December 2016
127 *
128 *> \ingroup complexSYcomputational
129 *
130 * =====================================================================
131  REAL FUNCTION cla_syrcond_x( UPLO, N, A, LDA, AF, LDAF, IPIV, X,
132  \$ info, work, rwork )
133 *
134 * -- LAPACK computational routine (version 3.7.0) --
135 * -- LAPACK is a software package provided by Univ. of Tennessee, --
136 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137 * December 2016
138 *
139 * .. Scalar Arguments ..
140  CHARACTER UPLO
141  INTEGER N, LDA, LDAF, INFO
142 * ..
143 * .. Array Arguments ..
144  INTEGER IPIV( * )
145  COMPLEX A( lda, * ), AF( ldaf, * ), WORK( * ), X( * )
146  REAL RWORK( * )
147 * ..
148 *
149 * =====================================================================
150 *
151 * .. Local Scalars ..
152  INTEGER KASE
153  REAL AINVNM, ANORM, TMP
154  INTEGER I, J
155  LOGICAL UP, UPPER
156  COMPLEX ZDUM
157 * ..
158 * .. Local Arrays ..
159  INTEGER ISAVE( 3 )
160 * ..
161 * .. External Functions ..
162  LOGICAL LSAME
163  EXTERNAL lsame
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL clacn2, csytrs, xerbla
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC abs, max
170 * ..
171 * .. Statement Functions ..
172  REAL CABS1
173 * ..
174 * .. Statement Function Definitions ..
175  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( AIMAG( zdum ) )
176 * ..
177 * .. Executable Statements ..
178 *
179  cla_syrcond_x = 0.0e+0
180 *
181  info = 0
182  upper = lsame( uplo, 'U' )
183  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
184  info = -1
185  ELSE IF ( n.LT.0 ) THEN
186  info = -2
187  ELSE IF( lda.LT.max( 1, n ) ) THEN
188  info = -4
189  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
190  info = -6
191  END IF
192  IF( info.NE.0 ) THEN
193  CALL xerbla( 'CLA_SYRCOND_X', -info )
194  RETURN
195  END IF
196  up = .false.
197  IF ( lsame( uplo, 'U' ) ) up = .true.
198 *
199 * Compute norm of op(A)*op2(C).
200 *
201  anorm = 0.0
202  IF ( up ) THEN
203  DO i = 1, n
204  tmp = 0.0e+0
205  DO j = 1, i
206  tmp = tmp + cabs1( a( j, i ) * x( j ) )
207  END DO
208  DO j = i+1, n
209  tmp = tmp + cabs1( a( i, j ) * x( j ) )
210  END DO
211  rwork( i ) = tmp
212  anorm = max( anorm, tmp )
213  END DO
214  ELSE
215  DO i = 1, n
216  tmp = 0.0e+0
217  DO j = 1, i
218  tmp = tmp + cabs1( a( i, j ) * x( j ) )
219  END DO
220  DO j = i+1, n
221  tmp = tmp + cabs1( a( j, i ) * x( j ) )
222  END DO
223  rwork( i ) = tmp
224  anorm = max( anorm, tmp )
225  END DO
226  END IF
227 *
228 * Quick return if possible.
229 *
230  IF( n.EQ.0 ) THEN
231  cla_syrcond_x = 1.0e+0
232  RETURN
233  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
234  RETURN
235  END IF
236 *
237 * Estimate the norm of inv(op(A)).
238 *
239  ainvnm = 0.0e+0
240 *
241  kase = 0
242  10 CONTINUE
243  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
244  IF( kase.NE.0 ) THEN
245  IF( kase.EQ.2 ) THEN
246 *
247 * Multiply by R.
248 *
249  DO i = 1, n
250  work( i ) = work( i ) * rwork( i )
251  END DO
252 *
253  IF ( up ) THEN
254  CALL csytrs( 'U', n, 1, af, ldaf, ipiv,
255  \$ work, n, info )
256  ELSE
257  CALL csytrs( 'L', n, 1, af, ldaf, ipiv,
258  \$ work, n, info )
259  ENDIF
260 *
261 * Multiply by inv(X).
262 *
263  DO i = 1, n
264  work( i ) = work( i ) / x( i )
265  END DO
266  ELSE
267 *
268 * Multiply by inv(X**T).
269 *
270  DO i = 1, n
271  work( i ) = work( i ) / x( i )
272  END DO
273 *
274  IF ( up ) THEN
275  CALL csytrs( 'U', n, 1, af, ldaf, ipiv,
276  \$ work, n, info )
277  ELSE
278  CALL csytrs( 'L', n, 1, af, ldaf, ipiv,
279  \$ work, n, info )
280  END IF
281 *
282 * Multiply by R.
283 *
284  DO i = 1, n
285  work( i ) = work( i ) * rwork( i )
286  END DO
287  END IF
288  GO TO 10
289  END IF
290 *
291 * Compute the estimate of the reciprocal condition number.
292 *
293  IF( ainvnm .NE. 0.0e+0 )
294  \$ cla_syrcond_x = 1.0e+0 / ainvnm
295 *
296  RETURN
297 *
298  END
real function cla_syrcond_x(UPLO, N, A, LDA, AF, LDAF, IPIV, X, INFO, WORK, RWORK)
CLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite m...
subroutine csytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CSYTRS
Definition: csytrs.f:122
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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:135