Annotation of rpl/lapack/lapack/zla_hercond_x.f, revision 1.18
1.10 bertrand 1: *> \brief \b ZLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices.
1.6 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.14 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.6 bertrand 7: *
8: *> \htmlonly
1.14 bertrand 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">
1.6 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.6 bertrand 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 )
1.14 bertrand 24: *
1.6 bertrand 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: * ..
1.14 bertrand 34: *
1.6 bertrand 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: *>
1.17 bertrand 107: *> \param[out] WORK
1.6 bertrand 108: *> \verbatim
109: *> WORK is COMPLEX*16 array, dimension (2*N).
110: *> Workspace.
111: *> \endverbatim
112: *>
1.17 bertrand 113: *> \param[out] RWORK
1.6 bertrand 114: *> \verbatim
115: *> RWORK is DOUBLE PRECISION array, dimension (N).
116: *> Workspace.
117: *> \endverbatim
118: *
119: * Authors:
120: * ========
121: *
1.14 bertrand 122: *> \author Univ. of Tennessee
123: *> \author Univ. of California Berkeley
124: *> \author Univ. of Colorado Denver
125: *> \author NAG Ltd.
1.6 bertrand 126: *
127: *> \ingroup complex16HEcomputational
128: *
129: * =====================================================================
1.1 bertrand 130: DOUBLE PRECISION FUNCTION ZLA_HERCOND_X( UPLO, N, A, LDA, AF,
131: $ LDAF, IPIV, X, INFO,
132: $ WORK, RWORK )
133: *
1.18 ! bertrand 134: * -- LAPACK computational routine --
1.6 bertrand 135: * -- LAPACK is a software package provided by Univ. of Tennessee, --
136: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.1 bertrand 137: *
138: * .. Scalar Arguments ..
139: CHARACTER UPLO
140: INTEGER N, LDA, LDAF, INFO
141: * ..
142: * .. Array Arguments ..
143: INTEGER IPIV( * )
144: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
145: DOUBLE PRECISION RWORK( * )
146: * ..
147: *
148: * =====================================================================
149: *
150: * .. Local Scalars ..
151: INTEGER KASE, I, J
152: DOUBLE PRECISION AINVNM, ANORM, TMP
1.8 bertrand 153: LOGICAL UP, UPPER
1.1 bertrand 154: COMPLEX*16 ZDUM
155: * ..
156: * .. Local Arrays ..
157: INTEGER ISAVE( 3 )
158: * ..
159: * .. External Functions ..
160: LOGICAL LSAME
161: EXTERNAL LSAME
162: * ..
163: * .. External Subroutines ..
164: EXTERNAL ZLACN2, ZHETRS, XERBLA
165: * ..
166: * .. Intrinsic Functions ..
167: INTRINSIC ABS, MAX
168: * ..
169: * .. Statement Functions ..
170: DOUBLE PRECISION CABS1
171: * ..
172: * .. Statement Function Definitions ..
173: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
174: * ..
175: * .. Executable Statements ..
176: *
177: ZLA_HERCOND_X = 0.0D+0
178: *
179: INFO = 0
1.8 bertrand 180: UPPER = LSAME( UPLO, 'U' )
181: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
182: INFO = -1
183: ELSE IF ( N.LT.0 ) THEN
1.1 bertrand 184: INFO = -2
1.8 bertrand 185: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
186: INFO = -4
187: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
188: INFO = -6
1.1 bertrand 189: END IF
190: IF( INFO.NE.0 ) THEN
191: CALL XERBLA( 'ZLA_HERCOND_X', -INFO )
192: RETURN
193: END IF
194: UP = .FALSE.
195: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
196: *
197: * Compute norm of op(A)*op2(C).
198: *
199: ANORM = 0.0D+0
200: IF ( UP ) THEN
201: DO I = 1, N
202: TMP = 0.0D+0
203: DO J = 1, I
204: TMP = TMP + CABS1( A( J, I ) * X( J ) )
205: END DO
206: DO J = I+1, N
207: TMP = TMP + CABS1( A( I, J ) * X( J ) )
208: END DO
209: RWORK( I ) = TMP
210: ANORM = MAX( ANORM, TMP )
211: END DO
212: ELSE
213: DO I = 1, N
214: TMP = 0.0D+0
215: DO J = 1, I
216: TMP = TMP + CABS1( A( I, J ) * X( J ) )
217: END DO
218: DO J = I+1, N
219: TMP = TMP + CABS1( A( J, I ) * X( J ) )
220: END DO
221: RWORK( I ) = TMP
222: ANORM = MAX( ANORM, TMP )
223: END DO
224: END IF
225: *
226: * Quick return if possible.
227: *
228: IF( N.EQ.0 ) THEN
229: ZLA_HERCOND_X = 1.0D+0
230: RETURN
231: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
232: RETURN
233: END IF
234: *
235: * Estimate the norm of inv(op(A)).
236: *
237: AINVNM = 0.0D+0
238: *
239: KASE = 0
240: 10 CONTINUE
241: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
242: IF( KASE.NE.0 ) THEN
243: IF( KASE.EQ.2 ) THEN
244: *
245: * Multiply by R.
246: *
247: DO I = 1, N
248: WORK( I ) = WORK( I ) * RWORK( I )
249: END DO
250: *
251: IF ( UP ) THEN
252: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
253: $ WORK, N, INFO )
254: ELSE
255: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
256: $ WORK, N, INFO )
257: ENDIF
258: *
259: * Multiply by inv(X).
260: *
261: DO I = 1, N
262: WORK( I ) = WORK( I ) / X( I )
263: END DO
264: ELSE
265: *
1.5 bertrand 266: * Multiply by inv(X**H).
1.1 bertrand 267: *
268: DO I = 1, N
269: WORK( I ) = WORK( I ) / X( I )
270: END DO
271: *
272: IF ( UP ) THEN
273: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
274: $ WORK, N, INFO )
275: ELSE
276: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
277: $ WORK, N, INFO )
278: END IF
279: *
280: * Multiply by R.
281: *
282: DO I = 1, N
283: WORK( I ) = WORK( I ) * RWORK( I )
284: END DO
285: END IF
286: GO TO 10
287: END IF
288: *
289: * Compute the estimate of the reciprocal condition number.
290: *
291: IF( AINVNM .NE. 0.0D+0 )
292: $ ZLA_HERCOND_X = 1.0D+0 / AINVNM
293: *
294: RETURN
295: *
1.18 ! bertrand 296: * End of ZLA_HERCOND_X
! 297: *
1.1 bertrand 298: END
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