LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
zla_hercond_c.f
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1 *> \brief \b ZLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION ZLA_HERCOND_C( UPLO, N, A, LDA, AF,
22 * LDAF, IPIV, C, CAPPLY,
23 * INFO, WORK, RWORK )
24 *
25 * .. Scalar Arguments ..
26 * CHARACTER UPLO
27 * LOGICAL CAPPLY
28 * INTEGER N, LDA, LDAF, INFO
29 * ..
30 * .. Array Arguments ..
31 * INTEGER IPIV( * )
32 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
33 * DOUBLE PRECISION C ( * ), RWORK( * )
34 * ..
35 *
36 *
37 *> \par Purpose:
38 * =============
39 *>
40 *> \verbatim
41 *>
42 *> ZLA_HERCOND_C computes the infinity norm condition number of
43 *> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
44 *> \endverbatim
45 *
46 * Arguments:
47 * ==========
48 *
49 *> \param[in] UPLO
50 *> \verbatim
51 *> UPLO is CHARACTER*1
52 *> = 'U': Upper triangle of A is stored;
53 *> = 'L': Lower triangle of A is stored.
54 *> \endverbatim
55 *>
56 *> \param[in] N
57 *> \verbatim
58 *> N is INTEGER
59 *> The number of linear equations, i.e., the order of the
60 *> matrix A. N >= 0.
61 *> \endverbatim
62 *>
63 *> \param[in] A
64 *> \verbatim
65 *> A is COMPLEX*16 array, dimension (LDA,N)
66 *> On entry, the N-by-N matrix A
67 *> \endverbatim
68 *>
69 *> \param[in] LDA
70 *> \verbatim
71 *> LDA is INTEGER
72 *> The leading dimension of the array A. LDA >= max(1,N).
73 *> \endverbatim
74 *>
75 *> \param[in] AF
76 *> \verbatim
77 *> AF is COMPLEX*16 array, dimension (LDAF,N)
78 *> The block diagonal matrix D and the multipliers used to
79 *> obtain the factor U or L as computed by ZHETRF.
80 *> \endverbatim
81 *>
82 *> \param[in] LDAF
83 *> \verbatim
84 *> LDAF is INTEGER
85 *> The leading dimension of the array AF. LDAF >= max(1,N).
86 *> \endverbatim
87 *>
88 *> \param[in] IPIV
89 *> \verbatim
90 *> IPIV is INTEGER array, dimension (N)
91 *> Details of the interchanges and the block structure of D
92 *> as determined by CHETRF.
93 *> \endverbatim
94 *>
95 *> \param[in] C
96 *> \verbatim
97 *> C is DOUBLE PRECISION array, dimension (N)
98 *> The vector C in the formula op(A) * inv(diag(C)).
99 *> \endverbatim
100 *>
101 *> \param[in] CAPPLY
102 *> \verbatim
103 *> CAPPLY is LOGICAL
104 *> If .TRUE. then access the vector C in the formula above.
105 *> \endverbatim
106 *>
107 *> \param[out] INFO
108 *> \verbatim
109 *> INFO is INTEGER
110 *> = 0: Successful exit.
111 *> i > 0: The ith argument is invalid.
112 *> \endverbatim
113 *>
114 *> \param[in] WORK
115 *> \verbatim
116 *> WORK is COMPLEX*16 array, dimension (2*N).
117 *> Workspace.
118 *> \endverbatim
119 *>
120 *> \param[in] RWORK
121 *> \verbatim
122 *> RWORK is DOUBLE PRECISION array, dimension (N).
123 *> Workspace.
124 *> \endverbatim
125 *
126 * Authors:
127 * ========
128 *
129 *> \author Univ. of Tennessee
130 *> \author Univ. of California Berkeley
131 *> \author Univ. of Colorado Denver
132 *> \author NAG Ltd.
133 *
134 *> \date December 2016
135 *
136 *> \ingroup complex16HEcomputational
137 *
138 * =====================================================================
139  DOUBLE PRECISION FUNCTION zla_hercond_c( UPLO, N, A, LDA, AF,
140  \$ LDAF, IPIV, C, CAPPLY,
141  \$ INFO, WORK, RWORK )
142 *
143 * -- LAPACK computational routine (version 3.7.0) --
144 * -- LAPACK is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 * December 2016
147 *
148 * .. Scalar Arguments ..
149  CHARACTER UPLO
150  LOGICAL CAPPLY
151  INTEGER N, LDA, LDAF, INFO
152 * ..
153 * .. Array Arguments ..
154  INTEGER IPIV( * )
155  COMPLEX*16 A( lda, * ), AF( ldaf, * ), WORK( * )
156  DOUBLE PRECISION C ( * ), RWORK( * )
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Local Scalars ..
162  INTEGER KASE, I, J
163  DOUBLE PRECISION AINVNM, ANORM, TMP
164  LOGICAL UP, UPPER
165  COMPLEX*16 ZDUM
166 * ..
167 * .. Local Arrays ..
168  INTEGER ISAVE( 3 )
169 * ..
170 * .. External Functions ..
171  LOGICAL LSAME
172  EXTERNAL lsame
173 * ..
174 * .. External Subroutines ..
175  EXTERNAL zlacn2, zhetrs, xerbla
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC abs, max
179 * ..
180 * .. Statement Functions ..
181  DOUBLE PRECISION CABS1
182 * ..
183 * .. Statement Function Definitions ..
184  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
185 * ..
186 * .. Executable Statements ..
187 *
188  zla_hercond_c = 0.0d+0
189 *
190  info = 0
191  upper = lsame( uplo, 'U' )
192  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
193  info = -1
194  ELSE IF( n.LT.0 ) THEN
195  info = -2
196  ELSE IF( lda.LT.max( 1, n ) ) THEN
197  info = -4
198  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
199  info = -6
200  END IF
201  IF( info.NE.0 ) THEN
202  CALL xerbla( 'ZLA_HERCOND_C', -info )
203  RETURN
204  END IF
205  up = .false.
206  IF ( lsame( uplo, 'U' ) ) up = .true.
207 *
208 * Compute norm of op(A)*op2(C).
209 *
210  anorm = 0.0d+0
211  IF ( up ) THEN
212  DO i = 1, n
213  tmp = 0.0d+0
214  IF ( capply ) THEN
215  DO j = 1, i
216  tmp = tmp + cabs1( a( j, i ) ) / c( j )
217  END DO
218  DO j = i+1, n
219  tmp = tmp + cabs1( a( i, j ) ) / c( j )
220  END DO
221  ELSE
222  DO j = 1, i
223  tmp = tmp + cabs1( a( j, i ) )
224  END DO
225  DO j = i+1, n
226  tmp = tmp + cabs1( a( i, j ) )
227  END DO
228  END IF
229  rwork( i ) = tmp
230  anorm = max( anorm, tmp )
231  END DO
232  ELSE
233  DO i = 1, n
234  tmp = 0.0d+0
235  IF ( capply ) THEN
236  DO j = 1, i
237  tmp = tmp + cabs1( a( i, j ) ) / c( j )
238  END DO
239  DO j = i+1, n
240  tmp = tmp + cabs1( a( j, i ) ) / c( j )
241  END DO
242  ELSE
243  DO j = 1, i
244  tmp = tmp + cabs1( a( i, j ) )
245  END DO
246  DO j = i+1, n
247  tmp = tmp + cabs1( a( j, i ) )
248  END DO
249  END IF
250  rwork( i ) = tmp
251  anorm = max( anorm, tmp )
252  END DO
253  END IF
254 *
255 * Quick return if possible.
256 *
257  IF( n.EQ.0 ) THEN
258  zla_hercond_c = 1.0d+0
259  RETURN
260  ELSE IF( anorm .EQ. 0.0d+0 ) THEN
261  RETURN
262  END IF
263 *
264 * Estimate the norm of inv(op(A)).
265 *
266  ainvnm = 0.0d+0
267 *
268  kase = 0
269  10 CONTINUE
270  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
271  IF( kase.NE.0 ) THEN
272  IF( kase.EQ.2 ) THEN
273 *
274 * Multiply by R.
275 *
276  DO i = 1, n
277  work( i ) = work( i ) * rwork( i )
278  END DO
279 *
280  IF ( up ) THEN
281  CALL zhetrs( 'U', n, 1, af, ldaf, ipiv,
282  \$ work, n, info )
283  ELSE
284  CALL zhetrs( 'L', n, 1, af, ldaf, ipiv,
285  \$ work, n, info )
286  ENDIF
287 *
288 * Multiply by inv(C).
289 *
290  IF ( capply ) THEN
291  DO i = 1, n
292  work( i ) = work( i ) * c( i )
293  END DO
294  END IF
295  ELSE
296 *
297 * Multiply by inv(C**H).
298 *
299  IF ( capply ) THEN
300  DO i = 1, n
301  work( i ) = work( i ) * c( i )
302  END DO
303  END IF
304 *
305  IF ( up ) THEN
306  CALL zhetrs( 'U', n, 1, af, ldaf, ipiv,
307  \$ work, n, info )
308  ELSE
309  CALL zhetrs( 'L', n, 1, af, ldaf, ipiv,
310  \$ work, n, info )
311  END IF
312 *
313 * Multiply by R.
314 *
315  DO i = 1, n
316  work( i ) = work( i ) * rwork( i )
317  END DO
318  END IF
319  GO TO 10
320  END IF
321 *
322 * Compute the estimate of the reciprocal condition number.
323 *
324  IF( ainvnm .NE. 0.0d+0 )
325  \$ zla_hercond_c = 1.0d+0 / ainvnm
326 *
327  RETURN
328 *
329  END
subroutine zlacn2(N, V, X, EST, KASE, ISAVE)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: zlacn2.f:135
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
double precision function zla_hercond_c(UPLO, N, A, LDA, AF, LDAF, IPIV, C, CAPPLY, INFO, WORK, RWORK)
ZLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefin...
subroutine zhetrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZHETRS
Definition: zhetrs.f:122