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1.6 bertrand 1: *> \brief \b ZLA_HERCOND_X
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLA_HERCOND_X + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_hercond_x.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_hercond_x.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_hercond_x.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLA_HERCOND_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_HERCOND_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 ZHETRF.
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 CHETRF.
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 November 2011
128: *
129: *> \ingroup complex16HEcomputational
130: *
131: * =====================================================================
1.1 bertrand 132: DOUBLE PRECISION FUNCTION ZLA_HERCOND_X( UPLO, N, A, LDA, AF,
133: $ LDAF, IPIV, X, INFO,
134: $ WORK, RWORK )
135: *
1.6 bertrand 136: * -- LAPACK computational routine (version 3.4.0) --
137: * -- LAPACK is a software package provided by Univ. of Tennessee, --
138: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139: * November 2011
1.1 bertrand 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, I, J
155: DOUBLE PRECISION AINVNM, ANORM, TMP
156: LOGICAL UP
157: COMPLEX*16 ZDUM
158: * ..
159: * .. Local Arrays ..
160: INTEGER ISAVE( 3 )
161: * ..
162: * .. External Functions ..
163: LOGICAL LSAME
164: EXTERNAL LSAME
165: * ..
166: * .. External Subroutines ..
167: EXTERNAL ZLACN2, ZHETRS, XERBLA
168: * ..
169: * .. Intrinsic Functions ..
170: INTRINSIC ABS, MAX
171: * ..
172: * .. Statement Functions ..
173: DOUBLE PRECISION CABS1
174: * ..
175: * .. Statement Function Definitions ..
176: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
177: * ..
178: * .. Executable Statements ..
179: *
180: ZLA_HERCOND_X = 0.0D+0
181: *
182: INFO = 0
183: IF( N.LT.0 ) THEN
184: INFO = -2
185: END IF
186: IF( INFO.NE.0 ) THEN
187: CALL XERBLA( 'ZLA_HERCOND_X', -INFO )
188: RETURN
189: END IF
190: UP = .FALSE.
191: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
192: *
193: * Compute norm of op(A)*op2(C).
194: *
195: ANORM = 0.0D+0
196: IF ( UP ) THEN
197: DO I = 1, N
198: TMP = 0.0D+0
199: DO J = 1, I
200: TMP = TMP + CABS1( A( J, I ) * X( J ) )
201: END DO
202: DO J = I+1, N
203: TMP = TMP + CABS1( A( I, J ) * X( J ) )
204: END DO
205: RWORK( I ) = TMP
206: ANORM = MAX( ANORM, TMP )
207: END DO
208: ELSE
209: DO I = 1, N
210: TMP = 0.0D+0
211: DO J = 1, I
212: TMP = TMP + CABS1( A( I, J ) * X( J ) )
213: END DO
214: DO J = I+1, N
215: TMP = TMP + CABS1( A( J, I ) * X( J ) )
216: END DO
217: RWORK( I ) = TMP
218: ANORM = MAX( ANORM, TMP )
219: END DO
220: END IF
221: *
222: * Quick return if possible.
223: *
224: IF( N.EQ.0 ) THEN
225: ZLA_HERCOND_X = 1.0D+0
226: RETURN
227: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
228: RETURN
229: END IF
230: *
231: * Estimate the norm of inv(op(A)).
232: *
233: AINVNM = 0.0D+0
234: *
235: KASE = 0
236: 10 CONTINUE
237: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
238: IF( KASE.NE.0 ) THEN
239: IF( KASE.EQ.2 ) THEN
240: *
241: * Multiply by R.
242: *
243: DO I = 1, N
244: WORK( I ) = WORK( I ) * RWORK( I )
245: END DO
246: *
247: IF ( UP ) THEN
248: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
249: $ WORK, N, INFO )
250: ELSE
251: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
252: $ WORK, N, INFO )
253: ENDIF
254: *
255: * Multiply by inv(X).
256: *
257: DO I = 1, N
258: WORK( I ) = WORK( I ) / X( I )
259: END DO
260: ELSE
261: *
1.5 bertrand 262: * Multiply by inv(X**H).
1.1 bertrand 263: *
264: DO I = 1, N
265: WORK( I ) = WORK( I ) / X( I )
266: END DO
267: *
268: IF ( UP ) THEN
269: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
270: $ WORK, N, INFO )
271: ELSE
272: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
273: $ WORK, N, INFO )
274: END IF
275: *
276: * Multiply by R.
277: *
278: DO I = 1, N
279: WORK( I ) = WORK( I ) * RWORK( I )
280: END DO
281: END IF
282: GO TO 10
283: END IF
284: *
285: * Compute the estimate of the reciprocal condition number.
286: *
287: IF( AINVNM .NE. 0.0D+0 )
288: $ ZLA_HERCOND_X = 1.0D+0 / AINVNM
289: *
290: RETURN
291: *
292: END