LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zla_porcond_x.f
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1 *> \brief \b ZLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION ZLA_PORCOND_X( UPLO, N, A, LDA, AF,
22 * LDAF, X, INFO, WORK,
23 * RWORK )
24 *
25 * .. Scalar Arguments ..
26 * CHARACTER UPLO
27 * INTEGER N, LDA, LDAF, INFO
28 * ..
29 * .. Array Arguments ..
30 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
31 * DOUBLE PRECISION RWORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> ZLA_PORCOND_X Computes the infinity norm condition number of
41 *> op(A) * diag(X) where X is a COMPLEX*16 vector.
42 *> \endverbatim
43 *
44 * Arguments:
45 * ==========
46 *
47 *> \param[in] UPLO
48 *> \verbatim
49 *> UPLO is CHARACTER*1
50 *> = 'U': Upper triangle of A is stored;
51 *> = 'L': Lower triangle of A is stored.
52 *> \endverbatim
53 *>
54 *> \param[in] N
55 *> \verbatim
56 *> N is INTEGER
57 *> The number of linear equations, i.e., the order of the
58 *> matrix A. N >= 0.
59 *> \endverbatim
60 *>
61 *> \param[in] A
62 *> \verbatim
63 *> A is COMPLEX*16 array, dimension (LDA,N)
64 *> On entry, the N-by-N matrix A.
65 *> \endverbatim
66 *>
67 *> \param[in] LDA
68 *> \verbatim
69 *> LDA is INTEGER
70 *> The leading dimension of the array A. LDA >= max(1,N).
71 *> \endverbatim
72 *>
73 *> \param[in] AF
74 *> \verbatim
75 *> AF is COMPLEX*16 array, dimension (LDAF,N)
76 *> The triangular factor U or L from the Cholesky factorization
77 *> A = U**H*U or A = L*L**H, as computed by ZPOTRF.
78 *> \endverbatim
79 *>
80 *> \param[in] LDAF
81 *> \verbatim
82 *> LDAF is INTEGER
83 *> The leading dimension of the array AF. LDAF >= max(1,N).
84 *> \endverbatim
85 *>
86 *> \param[in] X
87 *> \verbatim
88 *> X is COMPLEX*16 array, dimension (N)
89 *> The vector X in the formula op(A) * diag(X).
90 *> \endverbatim
91 *>
92 *> \param[out] INFO
93 *> \verbatim
94 *> INFO is INTEGER
95 *> = 0: Successful exit.
96 *> i > 0: The ith argument is invalid.
97 *> \endverbatim
98 *>
99 *> \param[out] WORK
100 *> \verbatim
101 *> WORK is COMPLEX*16 array, dimension (2*N).
102 *> Workspace.
103 *> \endverbatim
104 *>
105 *> \param[out] RWORK
106 *> \verbatim
107 *> RWORK is DOUBLE PRECISION array, dimension (N).
108 *> Workspace.
109 *> \endverbatim
110 *
111 * Authors:
112 * ========
113 *
114 *> \author Univ. of Tennessee
115 *> \author Univ. of California Berkeley
116 *> \author Univ. of Colorado Denver
117 *> \author NAG Ltd.
118 *
119 *> \ingroup complex16POcomputational
120 *
121 * =====================================================================
122  DOUBLE PRECISION FUNCTION zla_porcond_x( UPLO, N, A, LDA, AF,
123  \$ LDAF, X, INFO, WORK,
124  \$ RWORK )
125 *
126 * -- LAPACK computational routine --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 *
130 * .. Scalar Arguments ..
131  CHARACTER uplo
132  INTEGER n, lda, ldaf, info
133 * ..
134 * .. Array Arguments ..
135  COMPLEX*16 a( lda, * ), af( ldaf, * ), work( * ), x( * )
136  DOUBLE PRECISION rwork( * )
137 * ..
138 *
139 * =====================================================================
140 *
141 * .. Local Scalars ..
142  INTEGER kase, i, j
143  DOUBLE PRECISION ainvnm, anorm, tmp
144  LOGICAL up, upper
145  COMPLEX*16 zdum
146 * ..
147 * .. Local Arrays ..
148  INTEGER isave( 3 )
149 * ..
150 * .. External Functions ..
151  LOGICAL lsame
152  EXTERNAL lsame
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL zlacn2, zpotrs, xerbla
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC abs, max, real, dimag
159 * ..
160 * .. Statement Functions ..
161  DOUBLE PRECISION cabs1
162 * ..
163 * .. Statement Function Definitions ..
164  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
165 * ..
166 * .. Executable Statements ..
167 *
168  zla_porcond_x = 0.0d+0
169 *
170  info = 0
171  upper = lsame( uplo, 'U' )
172  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
173  info = -1
174  ELSE IF ( n.LT.0 ) THEN
175  info = -2
176  ELSE IF( lda.LT.max( 1, n ) ) THEN
177  info = -4
178  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
179  info = -6
180  END IF
181  IF( info.NE.0 ) THEN
182  CALL xerbla( 'ZLA_PORCOND_X', -info )
183  RETURN
184  END IF
185  up = .false.
186  IF ( lsame( uplo, 'U' ) ) up = .true.
187 *
188 * Compute norm of op(A)*op2(C).
189 *
190  anorm = 0.0d+0
191  IF ( up ) THEN
192  DO i = 1, n
193  tmp = 0.0d+0
194  DO j = 1, i
195  tmp = tmp + cabs1( a( j, i ) * x( j ) )
196  END DO
197  DO j = i+1, n
198  tmp = tmp + cabs1( a( i, j ) * x( j ) )
199  END DO
200  rwork( i ) = tmp
201  anorm = max( anorm, tmp )
202  END DO
203  ELSE
204  DO i = 1, n
205  tmp = 0.0d+0
206  DO j = 1, i
207  tmp = tmp + cabs1( a( i, j ) * x( j ) )
208  END DO
209  DO j = i+1, n
210  tmp = tmp + cabs1( a( j, i ) * x( j ) )
211  END DO
212  rwork( i ) = tmp
213  anorm = max( anorm, tmp )
214  END DO
215  END IF
216 *
217 * Quick return if possible.
218 *
219  IF( n.EQ.0 ) THEN
220  zla_porcond_x = 1.0d+0
221  RETURN
222  ELSE IF( anorm .EQ. 0.0d+0 ) THEN
223  RETURN
224  END IF
225 *
226 * Estimate the norm of inv(op(A)).
227 *
228  ainvnm = 0.0d+0
229 *
230  kase = 0
231  10 CONTINUE
232  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
233  IF( kase.NE.0 ) THEN
234  IF( kase.EQ.2 ) THEN
235 *
236 * Multiply by R.
237 *
238  DO i = 1, n
239  work( i ) = work( i ) * rwork( i )
240  END DO
241 *
242  IF ( up ) THEN
243  CALL zpotrs( 'U', n, 1, af, ldaf,
244  \$ work, n, info )
245  ELSE
246  CALL zpotrs( 'L', n, 1, af, ldaf,
247  \$ work, n, info )
248  ENDIF
249 *
250 * Multiply by inv(X).
251 *
252  DO i = 1, n
253  work( i ) = work( i ) / x( i )
254  END DO
255  ELSE
256 *
257 * Multiply by inv(X**H).
258 *
259  DO i = 1, n
260  work( i ) = work( i ) / x( i )
261  END DO
262 *
263  IF ( up ) THEN
264  CALL zpotrs( 'U', n, 1, af, ldaf,
265  \$ work, n, info )
266  ELSE
267  CALL zpotrs( 'L', n, 1, af, ldaf,
268  \$ work, n, info )
269  END IF
270 *
271 * Multiply by R.
272 *
273  DO i = 1, n
274  work( i ) = work( i ) * rwork( i )
275  END DO
276  END IF
277  GO TO 10
278  END IF
279 *
280 * Compute the estimate of the reciprocal condition number.
281 *
282  IF( ainvnm .NE. 0.0d+0 )
283  \$ zla_porcond_x = 1.0d+0 / ainvnm
284 *
285  RETURN
286 *
287 * End of ZLA_PORCOND_X
288 *
289  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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:133
subroutine zpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
ZPOTRS
Definition: zpotrs.f:110
double precision function zla_porcond_x(UPLO, N, A, LDA, AF, LDAF, X, INFO, WORK, RWORK)
ZLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-def...