1: *> \brief \b ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLA_SYRCOND_X + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_syrcond_x.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_syrcond_x.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_syrcond_x.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLA_SYRCOND_X( UPLO, N, A, LDA, AF,
22: * LDAF, IPIV, X, INFO,
23: * WORK, RWORK )
24: *
25: * .. Scalar Arguments ..
26: * CHARACTER UPLO
27: * INTEGER N, LDA, LDAF, INFO
28: * ..
29: * .. Array Arguments ..
30: * INTEGER IPIV( * )
31: * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
32: * DOUBLE PRECISION RWORK( * )
33: * ..
34: *
35: *
36: *> \par Purpose:
37: * =============
38: *>
39: *> \verbatim
40: *>
41: *> ZLA_SYRCOND_X Computes the infinity norm condition number of
42: *> op(A) * diag(X) where X is a COMPLEX*16 vector.
43: *> \endverbatim
44: *
45: * Arguments:
46: * ==========
47: *
48: *> \param[in] UPLO
49: *> \verbatim
50: *> UPLO is CHARACTER*1
51: *> = 'U': Upper triangle of A is stored;
52: *> = 'L': Lower triangle of A is stored.
53: *> \endverbatim
54: *>
55: *> \param[in] N
56: *> \verbatim
57: *> N is INTEGER
58: *> The number of linear equations, i.e., the order of the
59: *> matrix A. N >= 0.
60: *> \endverbatim
61: *>
62: *> \param[in] A
63: *> \verbatim
64: *> A is COMPLEX*16 array, dimension (LDA,N)
65: *> On entry, the N-by-N matrix A.
66: *> \endverbatim
67: *>
68: *> \param[in] LDA
69: *> \verbatim
70: *> LDA is INTEGER
71: *> The leading dimension of the array A. LDA >= max(1,N).
72: *> \endverbatim
73: *>
74: *> \param[in] AF
75: *> \verbatim
76: *> AF is COMPLEX*16 array, dimension (LDAF,N)
77: *> The block diagonal matrix D and the multipliers used to
78: *> obtain the factor U or L as computed by ZSYTRF.
79: *> \endverbatim
80: *>
81: *> \param[in] LDAF
82: *> \verbatim
83: *> LDAF is INTEGER
84: *> The leading dimension of the array AF. LDAF >= max(1,N).
85: *> \endverbatim
86: *>
87: *> \param[in] IPIV
88: *> \verbatim
89: *> IPIV is INTEGER array, dimension (N)
90: *> Details of the interchanges and the block structure of D
91: *> as determined by ZSYTRF.
92: *> \endverbatim
93: *>
94: *> \param[in] X
95: *> \verbatim
96: *> X is COMPLEX*16 array, dimension (N)
97: *> The vector X in the formula op(A) * diag(X).
98: *> \endverbatim
99: *>
100: *> \param[out] INFO
101: *> \verbatim
102: *> INFO is INTEGER
103: *> = 0: Successful exit.
104: *> i > 0: The ith argument is invalid.
105: *> \endverbatim
106: *>
107: *> \param[in] WORK
108: *> \verbatim
109: *> WORK is COMPLEX*16 array, dimension (2*N).
110: *> Workspace.
111: *> \endverbatim
112: *>
113: *> \param[in] RWORK
114: *> \verbatim
115: *> RWORK is DOUBLE PRECISION array, dimension (N).
116: *> Workspace.
117: *> \endverbatim
118: *
119: * Authors:
120: * ========
121: *
122: *> \author Univ. of Tennessee
123: *> \author Univ. of California Berkeley
124: *> \author Univ. of Colorado Denver
125: *> \author NAG Ltd.
126: *
127: *> \date September 2012
128: *
129: *> \ingroup complex16SYcomputational
130: *
131: * =====================================================================
132: DOUBLE PRECISION FUNCTION ZLA_SYRCOND_X( UPLO, N, A, LDA, AF,
133: $ LDAF, IPIV, X, INFO,
134: $ WORK, RWORK )
135: *
136: * -- LAPACK computational routine (version 3.4.2) --
137: * -- LAPACK is a software package provided by Univ. of Tennessee, --
138: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139: * September 2012
140: *
141: * .. Scalar Arguments ..
142: CHARACTER UPLO
143: INTEGER N, LDA, LDAF, INFO
144: * ..
145: * .. Array Arguments ..
146: INTEGER IPIV( * )
147: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
148: DOUBLE PRECISION RWORK( * )
149: * ..
150: *
151: * =====================================================================
152: *
153: * .. Local Scalars ..
154: INTEGER KASE
155: DOUBLE PRECISION AINVNM, ANORM, TMP
156: INTEGER I, J
157: LOGICAL UP, UPPER
158: COMPLEX*16 ZDUM
159: * ..
160: * .. Local Arrays ..
161: INTEGER ISAVE( 3 )
162: * ..
163: * .. External Functions ..
164: LOGICAL LSAME
165: EXTERNAL LSAME
166: * ..
167: * .. External Subroutines ..
168: EXTERNAL ZLACN2, ZSYTRS, XERBLA
169: * ..
170: * .. Intrinsic Functions ..
171: INTRINSIC ABS, MAX
172: * ..
173: * .. Statement Functions ..
174: DOUBLE PRECISION CABS1
175: * ..
176: * .. Statement Function Definitions ..
177: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
178: * ..
179: * .. Executable Statements ..
180: *
181: ZLA_SYRCOND_X = 0.0D+0
182: *
183: INFO = 0
184: UPPER = LSAME( UPLO, 'U' )
185: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
186: INFO = -1
187: ELSE 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( 'ZLA_SYRCOND_X', -INFO )
196: RETURN
197: END IF
198: UP = .FALSE.
199: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
200: *
201: * Compute norm of op(A)*op2(C).
202: *
203: ANORM = 0.0D+0
204: IF ( UP ) THEN
205: DO I = 1, N
206: TMP = 0.0D+0
207: DO J = 1, I
208: TMP = TMP + CABS1( A( J, I ) * X( J ) )
209: END DO
210: DO J = I+1, N
211: TMP = TMP + CABS1( A( I, J ) * X( J ) )
212: END DO
213: RWORK( I ) = TMP
214: ANORM = MAX( ANORM, TMP )
215: END DO
216: ELSE
217: DO I = 1, N
218: TMP = 0.0D+0
219: DO J = 1, I
220: TMP = TMP + CABS1( A( I, J ) * X( J ) )
221: END DO
222: DO J = I+1, N
223: TMP = TMP + CABS1( A( J, I ) * X( J ) )
224: END DO
225: RWORK( I ) = TMP
226: ANORM = MAX( ANORM, TMP )
227: END DO
228: END IF
229: *
230: * Quick return if possible.
231: *
232: IF( N.EQ.0 ) THEN
233: ZLA_SYRCOND_X = 1.0D+0
234: RETURN
235: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
236: RETURN
237: END IF
238: *
239: * Estimate the norm of inv(op(A)).
240: *
241: AINVNM = 0.0D+0
242: *
243: KASE = 0
244: 10 CONTINUE
245: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
246: IF( KASE.NE.0 ) THEN
247: IF( KASE.EQ.2 ) THEN
248: *
249: * Multiply by R.
250: *
251: DO I = 1, N
252: WORK( I ) = WORK( I ) * RWORK( I )
253: END DO
254: *
255: IF ( UP ) THEN
256: CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
257: $ WORK, N, INFO )
258: ELSE
259: CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
260: $ WORK, N, INFO )
261: ENDIF
262: *
263: * Multiply by inv(X).
264: *
265: DO I = 1, N
266: WORK( I ) = WORK( I ) / X( I )
267: END DO
268: ELSE
269: *
270: * Multiply by inv(X**T).
271: *
272: DO I = 1, N
273: WORK( I ) = WORK( I ) / X( I )
274: END DO
275: *
276: IF ( UP ) THEN
277: CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
278: $ WORK, N, INFO )
279: ELSE
280: CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
281: $ WORK, N, INFO )
282: END IF
283: *
284: * Multiply by R.
285: *
286: DO I = 1, N
287: WORK( I ) = WORK( I ) * RWORK( I )
288: END DO
289: END IF
290: GO TO 10
291: END IF
292: *
293: * Compute the estimate of the reciprocal condition number.
294: *
295: IF( AINVNM .NE. 0.0D+0 )
296: $ ZLA_SYRCOND_X = 1.0D+0 / AINVNM
297: *
298: RETURN
299: *
300: END
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