LAPACK  3.6.1 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[in] WORK
123 *> \verbatim
124 *> WORK is DOUBLE PRECISION array, dimension (3*N).
125 *> Workspace.
126 *> \endverbatim
127 *>
128 *> \param[in] 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 *> \date September 2012
143 *
144 *> \ingroup doubleSYcomputational
145 *
146 * =====================================================================
147  DOUBLE PRECISION FUNCTION dla_syrcond( UPLO, N, A, LDA, AF, LDAF,
148  \$ ipiv, cmode, c, info, work,
149  \$ iwork )
150 *
151 * -- LAPACK computational routine (version 3.4.2) --
152 * -- LAPACK is a software package provided by Univ. of Tennessee, --
153 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154 * September 2012
155 *
156 * .. Scalar Arguments ..
157  CHARACTER UPLO
158  INTEGER N, LDA, LDAF, INFO, CMODE
159 * ..
160 * .. Array Arguments
161  INTEGER IWORK( * ), IPIV( * )
162  DOUBLE PRECISION A( lda, * ), AF( ldaf, * ), WORK( * ), C( * )
163 * ..
164 *
165 * =====================================================================
166 *
167 * .. Local Scalars ..
168  CHARACTER NORMIN
169  INTEGER KASE, I, J
170  DOUBLE PRECISION AINVNM, SMLNUM, TMP
171  LOGICAL UP
172 * ..
173 * .. Local Arrays ..
174  INTEGER ISAVE( 3 )
175 * ..
176 * .. External Functions ..
177  LOGICAL LSAME
178  INTEGER IDAMAX
179  DOUBLE PRECISION DLAMCH
180  EXTERNAL lsame, idamax, dlamch
181 * ..
182 * .. External Subroutines ..
183  EXTERNAL dlacn2, dlatrs, drscl, xerbla, dsytrs
184 * ..
185 * .. Intrinsic Functions ..
186  INTRINSIC abs, max
187 * ..
188 * .. Executable Statements ..
189 *
190  dla_syrcond = 0.0d+0
191 *
192  info = 0
193  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( 'DLA_SYRCOND', -info )
202  RETURN
203  END IF
204  IF( n.EQ.0 ) THEN
205  dla_syrcond = 1.0d+0
206  RETURN
207  END IF
208  up = .false.
209  IF ( lsame( uplo, 'U' ) ) up = .true.
210 *
211 * Compute the equilibration matrix R such that
212 * inv(R)*A*C has unit 1-norm.
213 *
214  IF ( up ) THEN
215  DO i = 1, n
216  tmp = 0.0d+0
217  IF ( cmode .EQ. 1 ) THEN
218  DO j = 1, i
219  tmp = tmp + abs( a( j, i ) * c( j ) )
220  END DO
221  DO j = i+1, n
222  tmp = tmp + abs( a( i, j ) * c( j ) )
223  END DO
224  ELSE IF ( cmode .EQ. 0 ) THEN
225  DO j = 1, i
226  tmp = tmp + abs( a( j, i ) )
227  END DO
228  DO j = i+1, n
229  tmp = tmp + abs( a( i, j ) )
230  END DO
231  ELSE
232  DO j = 1, i
233  tmp = tmp + abs( a( j, i ) / c( j ) )
234  END DO
235  DO j = i+1, n
236  tmp = tmp + abs( a( i, j ) / c( j ) )
237  END DO
238  END IF
239  work( 2*n+i ) = tmp
240  END DO
241  ELSE
242  DO i = 1, n
243  tmp = 0.0d+0
244  IF ( cmode .EQ. 1 ) THEN
245  DO j = 1, i
246  tmp = tmp + abs( a( i, j ) * c( j ) )
247  END DO
248  DO j = i+1, n
249  tmp = tmp + abs( a( j, i ) * c( j ) )
250  END DO
251  ELSE IF ( cmode .EQ. 0 ) THEN
252  DO j = 1, i
253  tmp = tmp + abs( a( i, j ) )
254  END DO
255  DO j = i+1, n
256  tmp = tmp + abs( a( j, i ) )
257  END DO
258  ELSE
259  DO j = 1, i
260  tmp = tmp + abs( a( i, j) / c( j ) )
261  END DO
262  DO j = i+1, n
263  tmp = tmp + abs( a( j, i) / c( j ) )
264  END DO
265  END IF
266  work( 2*n+i ) = tmp
267  END DO
268  ENDIF
269 *
270 * Estimate the norm of inv(op(A)).
271 *
272  smlnum = dlamch( 'Safe minimum' )
273  ainvnm = 0.0d+0
274  normin = 'N'
275
276  kase = 0
277  10 CONTINUE
278  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
279  IF( kase.NE.0 ) THEN
280  IF( kase.EQ.2 ) THEN
281 *
282 * Multiply by R.
283 *
284  DO i = 1, n
285  work( i ) = work( i ) * work( 2*n+i )
286  END DO
287
288  IF ( up ) THEN
289  CALL dsytrs( 'U', n, 1, af, ldaf, ipiv, work, n, info )
290  ELSE
291  CALL dsytrs( 'L', n, 1, af, ldaf, ipiv, work, n, info )
292  ENDIF
293 *
294 * Multiply by inv(C).
295 *
296  IF ( cmode .EQ. 1 ) THEN
297  DO i = 1, n
298  work( i ) = work( i ) / c( i )
299  END DO
300  ELSE IF ( cmode .EQ. -1 ) THEN
301  DO i = 1, n
302  work( i ) = work( i ) * c( i )
303  END DO
304  END IF
305  ELSE
306 *
307 * Multiply by inv(C**T).
308 *
309  IF ( cmode .EQ. 1 ) THEN
310  DO i = 1, n
311  work( i ) = work( i ) / c( i )
312  END DO
313  ELSE IF ( cmode .EQ. -1 ) THEN
314  DO i = 1, n
315  work( i ) = work( i ) * c( i )
316  END DO
317  END IF
318
319  IF ( up ) THEN
320  CALL dsytrs( 'U', n, 1, af, ldaf, ipiv, work, n, info )
321  ELSE
322  CALL dsytrs( 'L', n, 1, af, ldaf, ipiv, work, n, info )
323  ENDIF
324 *
325 * Multiply by R.
326 *
327  DO i = 1, n
328  work( i ) = work( i ) * work( 2*n+i )
329  END DO
330  END IF
331 *
332  GO TO 10
333  END IF
334 *
335 * Compute the estimate of the reciprocal condition number.
336 *
337  IF( ainvnm .NE. 0.0d+0 )
338  \$ dla_syrcond = ( 1.0d+0 / ainvnm )
339 *
340  RETURN
341 *
342  END
subroutine dlatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
DLATRS solves a triangular system of equations with the scale factor set to prevent overflow...
Definition: dlatrs.f:240
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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:150
subroutine drscl(N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: drscl.f:86
subroutine dsytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DSYTRS
Definition: dsytrs.f:122
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:138