![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zla_porcond_x.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack|
Return to zla_porcond_x.f CVS log | Up to [local] / rpl / lapack / lapack |
1.6 bertrand 1: *> \brief \b ZLA_PORCOND_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_PORCOND_X + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_porcond_x.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_porcond_x.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_porcond_x.f">
15: *> [TXT]</a>
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[in] WORK
100: *> \verbatim
101: *> WORK is COMPLEX*16 array, dimension (2*N).
102: *> Workspace.
103: *> \endverbatim
104: *>
105: *> \param[in] 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: *> \date November 2011
120: *
121: *> \ingroup complex16POcomputational
122: *
123: * =====================================================================
1.1 bertrand 124: DOUBLE PRECISION FUNCTION ZLA_PORCOND_X( UPLO, N, A, LDA, AF,
125: $ LDAF, X, INFO, WORK,
126: $ RWORK )
127: *
1.6 bertrand 128: * -- LAPACK computational routine (version 3.4.0) --
129: * -- LAPACK is a software package provided by Univ. of Tennessee, --
130: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131: * November 2011
1.1 bertrand 132: *
133: * .. Scalar Arguments ..
134: CHARACTER UPLO
135: INTEGER N, LDA, LDAF, INFO
136: * ..
137: * .. Array Arguments ..
138: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
139: DOUBLE PRECISION RWORK( * )
140: * ..
141: *
142: * =====================================================================
143: *
144: * .. Local Scalars ..
145: INTEGER KASE, I, J
146: DOUBLE PRECISION AINVNM, ANORM, TMP
147: LOGICAL UP
148: COMPLEX*16 ZDUM
149: * ..
150: * .. Local Arrays ..
151: INTEGER ISAVE( 3 )
152: * ..
153: * .. External Functions ..
154: LOGICAL LSAME
155: EXTERNAL LSAME
156: * ..
157: * .. External Subroutines ..
158: EXTERNAL ZLACN2, ZPOTRS, XERBLA
159: * ..
160: * .. Intrinsic Functions ..
161: INTRINSIC ABS, MAX, REAL, DIMAG
162: * ..
163: * .. Statement Functions ..
164: DOUBLE PRECISION CABS1
165: * ..
166: * .. Statement Function Definitions ..
167: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
168: * ..
169: * .. Executable Statements ..
170: *
171: ZLA_PORCOND_X = 0.0D+0
172: *
173: INFO = 0
174: IF( N.LT.0 ) THEN
175: INFO = -2
176: END IF
177: IF( INFO.NE.0 ) THEN
178: CALL XERBLA( 'ZLA_PORCOND_X', -INFO )
179: RETURN
180: END IF
181: UP = .FALSE.
182: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
183: *
184: * Compute norm of op(A)*op2(C).
185: *
186: ANORM = 0.0D+0
187: IF ( UP ) THEN
188: DO I = 1, N
189: TMP = 0.0D+0
190: DO J = 1, I
191: TMP = TMP + CABS1( A( J, I ) * X( J ) )
192: END DO
193: DO J = I+1, N
194: TMP = TMP + CABS1( A( I, J ) * X( J ) )
195: END DO
196: RWORK( I ) = TMP
197: ANORM = MAX( ANORM, TMP )
198: END DO
199: ELSE
200: DO I = 1, N
201: TMP = 0.0D+0
202: DO J = 1, I
203: TMP = TMP + CABS1( A( I, J ) * X( J ) )
204: END DO
205: DO J = I+1, N
206: TMP = TMP + CABS1( A( J, I ) * X( J ) )
207: END DO
208: RWORK( I ) = TMP
209: ANORM = MAX( ANORM, TMP )
210: END DO
211: END IF
212: *
213: * Quick return if possible.
214: *
215: IF( N.EQ.0 ) THEN
216: ZLA_PORCOND_X = 1.0D+0
217: RETURN
218: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
219: RETURN
220: END IF
221: *
222: * Estimate the norm of inv(op(A)).
223: *
224: AINVNM = 0.0D+0
225: *
226: KASE = 0
227: 10 CONTINUE
228: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
229: IF( KASE.NE.0 ) THEN
230: IF( KASE.EQ.2 ) THEN
231: *
232: * Multiply by R.
233: *
234: DO I = 1, N
235: WORK( I ) = WORK( I ) * RWORK( I )
236: END DO
237: *
238: IF ( UP ) THEN
239: CALL ZPOTRS( 'U', N, 1, AF, LDAF,
240: $ WORK, N, INFO )
241: ELSE
242: CALL ZPOTRS( 'L', N, 1, AF, LDAF,
243: $ WORK, N, INFO )
244: ENDIF
245: *
246: * Multiply by inv(X).
247: *
248: DO I = 1, N
249: WORK( I ) = WORK( I ) / X( I )
250: END DO
251: ELSE
252: *
1.5 bertrand 253: * Multiply by inv(X**H).
1.1 bertrand 254: *
255: DO I = 1, N
256: WORK( I ) = WORK( I ) / X( I )
257: END DO
258: *
259: IF ( UP ) THEN
260: CALL ZPOTRS( 'U', N, 1, AF, LDAF,
261: $ WORK, N, INFO )
262: ELSE
263: CALL ZPOTRS( 'L', N, 1, AF, LDAF,
264: $ WORK, N, INFO )
265: END IF
266: *
267: * Multiply by R.
268: *
269: DO I = 1, N
270: WORK( I ) = WORK( I ) * RWORK( I )
271: END DO
272: END IF
273: GO TO 10
274: END IF
275: *
276: * Compute the estimate of the reciprocal condition number.
277: *
278: IF( AINVNM .NE. 0.0D+0 )
279: $ ZLA_PORCOND_X = 1.0D+0 / AINVNM
280: *
281: RETURN
282: *
283: END