LAPACK  3.7.0 LAPACK: Linear Algebra PACKage
cla_syrcond_c.f
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1 *> \brief \b CLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION CLA_SYRCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C,
22 * CAPPLY, INFO, WORK, RWORK )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * LOGICAL CAPPLY
27 * INTEGER N, LDA, LDAF, INFO
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IPIV( * )
31 * COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * )
32 * REAL C( * ), RWORK( * )
33 * ..
34 *
35 *
36 *> \par Purpose:
37 * =============
38 *>
39 *> \verbatim
40 *>
41 *> CLA_SYRCOND_C Computes the infinity norm condition number of
42 *> op(A) * inv(diag(C)) where C is a REAL 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 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 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 CSYTRF.
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 CSYTRF.
92 *> \endverbatim
93 *>
94 *> \param[in] C
95 *> \verbatim
96 *> C is REAL array, dimension (N)
97 *> The vector C in the formula op(A) * inv(diag(C)).
98 *> \endverbatim
99 *>
100 *> \param[in] CAPPLY
101 *> \verbatim
102 *> CAPPLY is LOGICAL
103 *> If .TRUE. then access the vector C in the formula above.
104 *> \endverbatim
105 *>
106 *> \param[out] INFO
107 *> \verbatim
108 *> INFO is INTEGER
109 *> = 0: Successful exit.
110 *> i > 0: The ith argument is invalid.
111 *> \endverbatim
112 *>
113 *> \param[in] WORK
114 *> \verbatim
115 *> WORK is COMPLEX array, dimension (2*N).
116 *> Workspace.
117 *> \endverbatim
118 *>
119 *> \param[in] RWORK
120 *> \verbatim
121 *> RWORK is REAL array, dimension (N).
122 *> Workspace.
123 *> \endverbatim
124 *
125 * Authors:
126 * ========
127 *
128 *> \author Univ. of Tennessee
129 *> \author Univ. of California Berkeley
130 *> \author Univ. of Colorado Denver
131 *> \author NAG Ltd.
132 *
133 *> \date December 2016
134 *
135 *> \ingroup complexSYcomputational
136 *
137 * =====================================================================
138  REAL FUNCTION cla_syrcond_c( UPLO, N, A, LDA, AF, LDAF, IPIV, C,
139  \$ capply, info, work, rwork )
140 *
141 * -- LAPACK computational routine (version 3.7.0) --
142 * -- LAPACK is a software package provided by Univ. of Tennessee, --
143 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144 * December 2016
145 *
146 * .. Scalar Arguments ..
147  CHARACTER UPLO
148  LOGICAL CAPPLY
149  INTEGER N, LDA, LDAF, INFO
150 * ..
151 * .. Array Arguments ..
152  INTEGER IPIV( * )
153  COMPLEX A( lda, * ), AF( ldaf, * ), WORK( * )
154  REAL C( * ), RWORK( * )
155 * ..
156 *
157 * =====================================================================
158 *
159 * .. Local Scalars ..
160  INTEGER KASE
161  REAL AINVNM, ANORM, TMP
162  INTEGER I, J
163  LOGICAL UP, UPPER
164  COMPLEX ZDUM
165 * ..
166 * .. Local Arrays ..
167  INTEGER ISAVE( 3 )
168 * ..
169 * .. External Functions ..
170  LOGICAL LSAME
171  EXTERNAL lsame
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL clacn2, csytrs, xerbla
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC abs, max
178 * ..
179 * .. Statement Functions ..
180  REAL CABS1
181 * ..
182 * .. Statement Function Definitions ..
183  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( AIMAG( zdum ) )
184 * ..
185 * .. Executable Statements ..
186 *
187  cla_syrcond_c = 0.0e+0
188 *
189  info = 0
190  upper = lsame( uplo, 'U' )
191  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
192  info = -1
193  ELSE IF( n.LT.0 ) THEN
194  info = -2
195  ELSE IF( lda.LT.max( 1, n ) ) THEN
196  info = -4
197  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
198  info = -6
199  END IF
200  IF( info.NE.0 ) THEN
201  CALL xerbla( 'CLA_SYRCOND_C', -info )
202  RETURN
203  END IF
204  up = .false.
205  IF ( lsame( uplo, 'U' ) ) up = .true.
206 *
207 * Compute norm of op(A)*op2(C).
208 *
209  anorm = 0.0e+0
210  IF ( up ) THEN
211  DO i = 1, n
212  tmp = 0.0e+0
213  IF ( capply ) THEN
214  DO j = 1, i
215  tmp = tmp + cabs1( a( j, i ) ) / c( j )
216  END DO
217  DO j = i+1, n
218  tmp = tmp + cabs1( a( i, j ) ) / c( j )
219  END DO
220  ELSE
221  DO j = 1, i
222  tmp = tmp + cabs1( a( j, i ) )
223  END DO
224  DO j = i+1, n
225  tmp = tmp + cabs1( a( i, j ) )
226  END DO
227  END IF
228  rwork( i ) = tmp
229  anorm = max( anorm, tmp )
230  END DO
231  ELSE
232  DO i = 1, n
233  tmp = 0.0e+0
234  IF ( capply ) THEN
235  DO j = 1, i
236  tmp = tmp + cabs1( a( i, j ) ) / c( j )
237  END DO
238  DO j = i+1, n
239  tmp = tmp + cabs1( a( j, i ) ) / c( j )
240  END DO
241  ELSE
242  DO j = 1, i
243  tmp = tmp + cabs1( a( i, j ) )
244  END DO
245  DO j = i+1, n
246  tmp = tmp + cabs1( a( j, i ) )
247  END DO
248  END IF
249  rwork( i ) = tmp
250  anorm = max( anorm, tmp )
251  END DO
252  END IF
253 *
254 * Quick return if possible.
255 *
256  IF( n.EQ.0 ) THEN
257  cla_syrcond_c = 1.0e+0
258  RETURN
259  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
260  RETURN
261  END IF
262 *
263 * Estimate the norm of inv(op(A)).
264 *
265  ainvnm = 0.0e+0
266 *
267  kase = 0
268  10 CONTINUE
269  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
270  IF( kase.NE.0 ) THEN
271  IF( kase.EQ.2 ) THEN
272 *
273 * Multiply by R.
274 *
275  DO i = 1, n
276  work( i ) = work( i ) * rwork( i )
277  END DO
278 *
279  IF ( up ) THEN
280  CALL csytrs( 'U', n, 1, af, ldaf, ipiv,
281  \$ work, n, info )
282  ELSE
283  CALL csytrs( 'L', n, 1, af, ldaf, ipiv,
284  \$ work, n, info )
285  ENDIF
286 *
287 * Multiply by inv(C).
288 *
289  IF ( capply ) THEN
290  DO i = 1, n
291  work( i ) = work( i ) * c( i )
292  END DO
293  END IF
294  ELSE
295 *
296 * Multiply by inv(C**T).
297 *
298  IF ( capply ) THEN
299  DO i = 1, n
300  work( i ) = work( i ) * c( i )
301  END DO
302  END IF
303 *
304  IF ( up ) THEN
305  CALL csytrs( 'U', n, 1, af, ldaf, ipiv,
306  \$ work, n, info )
307  ELSE
308  CALL csytrs( 'L', n, 1, af, ldaf, ipiv,
309  \$ work, n, info )
310  END IF
311 *
312 * Multiply by R.
313 *
314  DO i = 1, n
315  work( i ) = work( i ) * rwork( i )
316  END DO
317  END IF
318  GO TO 10
319  END IF
320 *
321 * Compute the estimate of the reciprocal condition number.
322 *
323  IF( ainvnm .NE. 0.0e+0 )
324  \$ cla_syrcond_c = 1.0e+0 / ainvnm
325 *
326  RETURN
327 *
328  END
subroutine csytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CSYTRS
Definition: csytrs.f:122
real function cla_syrcond_c(UPLO, N, A, LDA, AF, LDAF, IPIV, C, CAPPLY, INFO, WORK, RWORK)
CLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefin...
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