LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
sla_syrcond.f
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1 *> \brief \b SLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION SLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV, CMODE,
22 * C, INFO, WORK, IWORK )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * INTEGER N, LDA, LDAF, INFO, CMODE
27 * ..
28 * .. Array Arguments
29 * INTEGER IWORK( * ), IPIV( * )
30 * REAL A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> SLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C)
40 *> where op2 is determined by CMODE as follows
41 *> CMODE = 1 op2(C) = C
42 *> CMODE = 0 op2(C) = I
43 *> CMODE = -1 op2(C) = inv(C)
44 *> The Skeel condition number cond(A) = norminf( |inv(A)||A| )
45 *> is computed by computing scaling factors R such that
46 *> diag(R)*A*op2(C) is row equilibrated and computing the standard
47 *> infinity-norm condition number.
48 *> \endverbatim
49 *
50 * Arguments:
51 * ==========
52 *
53 *> \param[in] UPLO
54 *> \verbatim
55 *> UPLO is CHARACTER*1
56 *> = 'U': Upper triangle of A is stored;
57 *> = 'L': Lower triangle of A is stored.
58 *> \endverbatim
59 *>
60 *> \param[in] N
61 *> \verbatim
62 *> N is INTEGER
63 *> The number of linear equations, i.e., the order of the
64 *> matrix A. N >= 0.
65 *> \endverbatim
66 *>
67 *> \param[in] A
68 *> \verbatim
69 *> A is REAL array, dimension (LDA,N)
70 *> On entry, the N-by-N matrix A.
71 *> \endverbatim
72 *>
73 *> \param[in] LDA
74 *> \verbatim
75 *> LDA is INTEGER
76 *> The leading dimension of the array A. LDA >= max(1,N).
77 *> \endverbatim
78 *>
79 *> \param[in] AF
80 *> \verbatim
81 *> AF is REAL array, dimension (LDAF,N)
82 *> The block diagonal matrix D and the multipliers used to
83 *> obtain the factor U or L as computed by SSYTRF.
84 *> \endverbatim
85 *>
86 *> \param[in] LDAF
87 *> \verbatim
88 *> LDAF is INTEGER
89 *> The leading dimension of the array AF. LDAF >= max(1,N).
90 *> \endverbatim
91 *>
92 *> \param[in] IPIV
93 *> \verbatim
94 *> IPIV is INTEGER array, dimension (N)
95 *> Details of the interchanges and the block structure of D
96 *> as determined by SSYTRF.
97 *> \endverbatim
98 *>
99 *> \param[in] CMODE
100 *> \verbatim
101 *> CMODE is INTEGER
102 *> Determines op2(C) in the formula op(A) * op2(C) as follows:
103 *> CMODE = 1 op2(C) = C
104 *> CMODE = 0 op2(C) = I
105 *> CMODE = -1 op2(C) = inv(C)
106 *> \endverbatim
107 *>
108 *> \param[in] C
109 *> \verbatim
110 *> C is REAL array, dimension (N)
111 *> The vector C in the formula op(A) * op2(C).
112 *> \endverbatim
113 *>
114 *> \param[out] INFO
115 *> \verbatim
116 *> INFO is INTEGER
117 *> = 0: Successful exit.
118 *> i > 0: The ith argument is invalid.
119 *> \endverbatim
120 *>
121 *> \param[out] WORK
122 *> \verbatim
123 *> WORK is REAL array, dimension (3*N).
124 *> Workspace.
125 *> \endverbatim
126 *>
127 *> \param[out] IWORK
128 *> \verbatim
129 *> IWORK is INTEGER array, dimension (N).
130 *> Workspace.
131 *> \endverbatim
132 *
133 * Authors:
134 * ========
135 *
136 *> \author Univ. of Tennessee
137 *> \author Univ. of California Berkeley
138 *> \author Univ. of Colorado Denver
139 *> \author NAG Ltd.
140 *
141 *> \ingroup realSYcomputational
142 *
143 * =====================================================================
144  REAL function sla_syrcond( uplo, n, a, lda, af, ldaf, ipiv, cmode,
145  $ c, info, work, iwork )
146 *
147 * -- LAPACK computational routine --
148 * -- LAPACK is a software package provided by Univ. of Tennessee, --
149 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150 *
151 * .. Scalar Arguments ..
152  CHARACTER uplo
153  INTEGER n, lda, ldaf, info, cmode
154 * ..
155 * .. Array Arguments
156  INTEGER iwork( * ), ipiv( * )
157  REAL a( lda, * ), af( ldaf, * ), work( * ), c( * )
158 * ..
159 *
160 * =====================================================================
161 *
162 * .. Local Scalars ..
163  CHARACTER normin
164  INTEGER kase, i, j
165  REAL ainvnm, smlnum, tmp
166  LOGICAL up
167 * ..
168 * .. Local Arrays ..
169  INTEGER isave( 3 )
170 * ..
171 * .. External Functions ..
172  LOGICAL lsame
173  REAL slamch
174  EXTERNAL lsame, slamch
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL slacn2, xerbla, ssytrs
178 * ..
179 * .. Intrinsic Functions ..
180  INTRINSIC abs, max
181 * ..
182 * .. Executable Statements ..
183 *
184  sla_syrcond = 0.0
185 *
186  info = 0
187  IF( n.LT.0 ) THEN
188  info = -2
189  ELSE IF( lda.LT.max( 1, n ) ) THEN
190  info = -4
191  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
192  info = -6
193  END IF
194  IF( info.NE.0 ) THEN
195  CALL xerbla( 'SLA_SYRCOND', -info )
196  RETURN
197  END IF
198  IF( n.EQ.0 ) THEN
199  sla_syrcond = 1.0
200  RETURN
201  END IF
202  up = .false.
203  IF ( lsame( uplo, 'U' ) ) up = .true.
204 *
205 * Compute the equilibration matrix R such that
206 * inv(R)*A*C has unit 1-norm.
207 *
208  IF ( up ) THEN
209  DO i = 1, n
210  tmp = 0.0
211  IF ( cmode .EQ. 1 ) THEN
212  DO j = 1, i
213  tmp = tmp + abs( a( j, i ) * c( j ) )
214  END DO
215  DO j = i+1, n
216  tmp = tmp + abs( a( i, j ) * c( j ) )
217  END DO
218  ELSE IF ( cmode .EQ. 0 ) THEN
219  DO j = 1, i
220  tmp = tmp + abs( a( j, i ) )
221  END DO
222  DO j = i+1, n
223  tmp = tmp + abs( a( i, j ) )
224  END DO
225  ELSE
226  DO j = 1, i
227  tmp = tmp + abs( a( j, i ) / c( j ) )
228  END DO
229  DO j = i+1, n
230  tmp = tmp + abs( a( i, j ) / c( j ) )
231  END DO
232  END IF
233  work( 2*n+i ) = tmp
234  END DO
235  ELSE
236  DO i = 1, n
237  tmp = 0.0
238  IF ( cmode .EQ. 1 ) THEN
239  DO j = 1, i
240  tmp = tmp + abs( a( i, j ) * c( j ) )
241  END DO
242  DO j = i+1, n
243  tmp = tmp + abs( a( j, i ) * c( j ) )
244  END DO
245  ELSE IF ( cmode .EQ. 0 ) THEN
246  DO j = 1, i
247  tmp = tmp + abs( a( i, j ) )
248  END DO
249  DO j = i+1, n
250  tmp = tmp + abs( a( j, i ) )
251  END DO
252  ELSE
253  DO j = 1, i
254  tmp = tmp + abs( a( i, j) / c( j ) )
255  END DO
256  DO j = i+1, n
257  tmp = tmp + abs( a( j, i) / c( j ) )
258  END DO
259  END IF
260  work( 2*n+i ) = tmp
261  END DO
262  ENDIF
263 *
264 * Estimate the norm of inv(op(A)).
265 *
266  smlnum = slamch( 'Safe minimum' )
267  ainvnm = 0.0
268  normin = 'N'
269 
270  kase = 0
271  10 CONTINUE
272  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
273  IF( kase.NE.0 ) THEN
274  IF( kase.EQ.2 ) THEN
275 *
276 * Multiply by R.
277 *
278  DO i = 1, n
279  work( i ) = work( i ) * work( 2*n+i )
280  END DO
281 
282  IF ( up ) THEN
283  CALL ssytrs( 'U', n, 1, af, ldaf, ipiv, work, n, info )
284  ELSE
285  CALL ssytrs( 'L', n, 1, af, ldaf, ipiv, work, n, info )
286  ENDIF
287 *
288 * Multiply by inv(C).
289 *
290  IF ( cmode .EQ. 1 ) THEN
291  DO i = 1, n
292  work( i ) = work( i ) / c( i )
293  END DO
294  ELSE IF ( cmode .EQ. -1 ) THEN
295  DO i = 1, n
296  work( i ) = work( i ) * c( i )
297  END DO
298  END IF
299  ELSE
300 *
301 * Multiply by inv(C**T).
302 *
303  IF ( cmode .EQ. 1 ) THEN
304  DO i = 1, n
305  work( i ) = work( i ) / c( i )
306  END DO
307  ELSE IF ( cmode .EQ. -1 ) THEN
308  DO i = 1, n
309  work( i ) = work( i ) * c( i )
310  END DO
311  END IF
312 
313  IF ( up ) THEN
314  CALL ssytrs( 'U', n, 1, af, ldaf, ipiv, work, n, info )
315  ELSE
316  CALL ssytrs( 'L', n, 1, af, ldaf, ipiv, work, n, info )
317  ENDIF
318 *
319 * Multiply by R.
320 *
321  DO i = 1, n
322  work( i ) = work( i ) * work( 2*n+i )
323  END DO
324  END IF
325 *
326  GO TO 10
327  END IF
328 *
329 * Compute the estimate of the reciprocal condition number.
330 *
331  IF( ainvnm .NE. 0.0 )
332  $ sla_syrcond = ( 1.0 / ainvnm )
333 *
334  RETURN
335 *
336 * End of SLA_SYRCOND
337 *
338  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine slacn2(N, V, X, ISGN, EST, KASE, ISAVE)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: slacn2.f:136
real function sla_syrcond(UPLO, N, A, LDA, AF, LDAF, IPIV, CMODE, C, INFO, WORK, IWORK)
SLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
Definition: sla_syrcond.f:146
subroutine ssytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SSYTRS
Definition: ssytrs.f:120
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68