LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
dla_syrcond.f
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1 *> \brief \b DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF,
22 * IPIV, CMODE, C, INFO, WORK,
23 * IWORK )
24 *
25 * .. Scalar Arguments ..
26 * CHARACTER UPLO
27 * INTEGER N, LDA, LDAF, INFO, CMODE
28 * ..
29 * .. Array Arguments
30 * INTEGER IWORK( * ), IPIV( * )
31 * DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> DLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C)
41 *> where op2 is determined by CMODE as follows
42 *> CMODE = 1 op2(C) = C
43 *> CMODE = 0 op2(C) = I
44 *> CMODE = -1 op2(C) = inv(C)
45 *> The Skeel condition number cond(A) = norminf( |inv(A)||A| )
46 *> is computed by computing scaling factors R such that
47 *> diag(R)*A*op2(C) is row equilibrated and computing the standard
48 *> infinity-norm condition number.
49 *> \endverbatim
50 *
51 * Arguments:
52 * ==========
53 *
54 *> \param[in] UPLO
55 *> \verbatim
56 *> UPLO is CHARACTER*1
57 *> = 'U': Upper triangle of A is stored;
58 *> = 'L': Lower triangle of A is stored.
59 *> \endverbatim
60 *>
61 *> \param[in] N
62 *> \verbatim
63 *> N is INTEGER
64 *> The number of linear equations, i.e., the order of the
65 *> matrix A. N >= 0.
66 *> \endverbatim
67 *>
68 *> \param[in] A
69 *> \verbatim
70 *> A is DOUBLE PRECISION array, dimension (LDA,N)
71 *> On entry, the N-by-N matrix A.
72 *> \endverbatim
73 *>
74 *> \param[in] LDA
75 *> \verbatim
76 *> LDA is INTEGER
77 *> The leading dimension of the array A. LDA >= max(1,N).
78 *> \endverbatim
79 *>
80 *> \param[in] AF
81 *> \verbatim
82 *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
83 *> The block diagonal matrix D and the multipliers used to
84 *> obtain the factor U or L as computed by DSYTRF.
85 *> \endverbatim
86 *>
87 *> \param[in] LDAF
88 *> \verbatim
89 *> LDAF is INTEGER
90 *> The leading dimension of the array AF. LDAF >= max(1,N).
91 *> \endverbatim
92 *>
93 *> \param[in] IPIV
94 *> \verbatim
95 *> IPIV is INTEGER array, dimension (N)
96 *> Details of the interchanges and the block structure of D
97 *> as determined by DSYTRF.
98 *> \endverbatim
99 *>
100 *> \param[in] CMODE
101 *> \verbatim
102 *> CMODE is INTEGER
103 *> Determines op2(C) in the formula op(A) * op2(C) as follows:
104 *> CMODE = 1 op2(C) = C
105 *> CMODE = 0 op2(C) = I
106 *> CMODE = -1 op2(C) = inv(C)
107 *> \endverbatim
108 *>
109 *> \param[in] C
110 *> \verbatim
111 *> C is DOUBLE PRECISION array, dimension (N)
112 *> The vector C in the formula op(A) * op2(C).
113 *> \endverbatim
114 *>
115 *> \param[out] INFO
116 *> \verbatim
117 *> INFO is INTEGER
118 *> = 0: Successful exit.
119 *> i > 0: The ith argument is invalid.
120 *> \endverbatim
121 *>
122 *> \param[out] WORK
123 *> \verbatim
124 *> WORK is DOUBLE PRECISION array, dimension (3*N).
125 *> Workspace.
126 *> \endverbatim
127 *>
128 *> \param[out] IWORK
129 *> \verbatim
130 *> IWORK is INTEGER array, dimension (N).
131 *> Workspace.
132 *> \endverbatim
133 *
134 * Authors:
135 * ========
136 *
137 *> \author Univ. of Tennessee
138 *> \author Univ. of California Berkeley
139 *> \author Univ. of Colorado Denver
140 *> \author NAG Ltd.
141 *
142 *> \ingroup doubleSYcomputational
143 *
144 * =====================================================================
145  DOUBLE PRECISION FUNCTION dla_syrcond( UPLO, N, A, LDA, AF, LDAF,
146  \$ IPIV, CMODE, C, INFO, WORK,
147  \$ IWORK )
148 *
149 * -- LAPACK computational routine --
150 * -- LAPACK is a software package provided by Univ. of Tennessee, --
151 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
152 *
153 * .. Scalar Arguments ..
154  CHARACTER uplo
155  INTEGER n, lda, ldaf, info, cmode
156 * ..
157 * .. Array Arguments
158  INTEGER iwork( * ), ipiv( * )
159  DOUBLE PRECISION a( lda, * ), af( ldaf, * ), work( * ), c( * )
160 * ..
161 *
162 * =====================================================================
163 *
164 * .. Local Scalars ..
165  CHARACTER normin
166  INTEGER kase, i, j
167  DOUBLE PRECISION ainvnm, smlnum, tmp
168  LOGICAL up
169 * ..
170 * .. Local Arrays ..
171  INTEGER isave( 3 )
172 * ..
173 * .. External Functions ..
174  LOGICAL lsame
175  DOUBLE PRECISION dlamch
176  EXTERNAL lsame, dlamch
177 * ..
178 * .. External Subroutines ..
179  EXTERNAL dlacn2, xerbla, dsytrs
180 * ..
181 * .. Intrinsic Functions ..
182  INTRINSIC abs, max
183 * ..
184 * .. Executable Statements ..
185 *
186  dla_syrcond = 0.0d+0
187 *
188  info = 0
189  IF( n.LT.0 ) THEN
190  info = -2
191  ELSE IF( lda.LT.max( 1, n ) ) THEN
192  info = -4
193  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
194  info = -6
195  END IF
196  IF( info.NE.0 ) THEN
197  CALL xerbla( 'DLA_SYRCOND', -info )
198  RETURN
199  END IF
200  IF( n.EQ.0 ) THEN
201  dla_syrcond = 1.0d+0
202  RETURN
203  END IF
204  up = .false.
205  IF ( lsame( uplo, 'U' ) ) up = .true.
206 *
207 * Compute the equilibration matrix R such that
208 * inv(R)*A*C has unit 1-norm.
209 *
210  IF ( up ) THEN
211  DO i = 1, n
212  tmp = 0.0d+0
213  IF ( cmode .EQ. 1 ) THEN
214  DO j = 1, i
215  tmp = tmp + abs( a( j, i ) * c( j ) )
216  END DO
217  DO j = i+1, n
218  tmp = tmp + abs( a( i, j ) * c( j ) )
219  END DO
220  ELSE IF ( cmode .EQ. 0 ) THEN
221  DO j = 1, i
222  tmp = tmp + abs( a( j, i ) )
223  END DO
224  DO j = i+1, n
225  tmp = tmp + abs( a( i, j ) )
226  END DO
227  ELSE
228  DO j = 1, i
229  tmp = tmp + abs( a( j, i ) / c( j ) )
230  END DO
231  DO j = i+1, n
232  tmp = tmp + abs( a( i, j ) / c( j ) )
233  END DO
234  END IF
235  work( 2*n+i ) = tmp
236  END DO
237  ELSE
238  DO i = 1, n
239  tmp = 0.0d+0
240  IF ( cmode .EQ. 1 ) THEN
241  DO j = 1, i
242  tmp = tmp + abs( a( i, j ) * c( j ) )
243  END DO
244  DO j = i+1, n
245  tmp = tmp + abs( a( j, i ) * c( j ) )
246  END DO
247  ELSE IF ( cmode .EQ. 0 ) THEN
248  DO j = 1, i
249  tmp = tmp + abs( a( i, j ) )
250  END DO
251  DO j = i+1, n
252  tmp = tmp + abs( a( j, i ) )
253  END DO
254  ELSE
255  DO j = 1, i
256  tmp = tmp + abs( a( i, j) / c( j ) )
257  END DO
258  DO j = i+1, n
259  tmp = tmp + abs( a( j, i) / c( j ) )
260  END DO
261  END IF
262  work( 2*n+i ) = tmp
263  END DO
264  ENDIF
265 *
266 * Estimate the norm of inv(op(A)).
267 *
268  smlnum = dlamch( 'Safe minimum' )
269  ainvnm = 0.0d+0
270  normin = 'N'
271
272  kase = 0
273  10 CONTINUE
274  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
275  IF( kase.NE.0 ) THEN
276  IF( kase.EQ.2 ) THEN
277 *
278 * Multiply by R.
279 *
280  DO i = 1, n
281  work( i ) = work( i ) * work( 2*n+i )
282  END DO
283
284  IF ( up ) THEN
285  CALL dsytrs( 'U', n, 1, af, ldaf, ipiv, work, n, info )
286  ELSE
287  CALL dsytrs( 'L', n, 1, af, ldaf, ipiv, work, n, info )
288  ENDIF
289 *
290 * Multiply by inv(C).
291 *
292  IF ( cmode .EQ. 1 ) THEN
293  DO i = 1, n
294  work( i ) = work( i ) / c( i )
295  END DO
296  ELSE IF ( cmode .EQ. -1 ) THEN
297  DO i = 1, n
298  work( i ) = work( i ) * c( i )
299  END DO
300  END IF
301  ELSE
302 *
303 * Multiply by inv(C**T).
304 *
305  IF ( cmode .EQ. 1 ) THEN
306  DO i = 1, n
307  work( i ) = work( i ) / c( i )
308  END DO
309  ELSE IF ( cmode .EQ. -1 ) THEN
310  DO i = 1, n
311  work( i ) = work( i ) * c( i )
312  END DO
313  END IF
314
315  IF ( up ) THEN
316  CALL dsytrs( 'U', n, 1, af, ldaf, ipiv, work, n, info )
317  ELSE
318  CALL dsytrs( 'L', n, 1, af, ldaf, ipiv, work, n, info )
319  ENDIF
320 *
321 * Multiply by R.
322 *
323  DO i = 1, n
324  work( i ) = work( i ) * work( 2*n+i )
325  END DO
326  END IF
327 *
328  GO TO 10
329  END IF
330 *
331 * Compute the estimate of the reciprocal condition number.
332 *
333  IF( ainvnm .NE. 0.0d+0 )
334  \$ dla_syrcond = ( 1.0d+0 / ainvnm )
335 *
336  RETURN
337 *
338 * End of DLA_SYRCOND
339 *
340  END
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dlacn2(N, V, X, ISGN, EST, KASE, ISAVE)
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: dlacn2.f:136
subroutine dsytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DSYTRS
Definition: dsytrs.f:120
double precision function dla_syrcond(UPLO, N, A, LDA, AF, LDAF, IPIV, CMODE, C, INFO, WORK, IWORK)
DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
Definition: dla_syrcond.f:148