1: *> \brief \b ZPOCON
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZPOCON + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpocon.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpocon.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpocon.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK,
22: * INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER UPLO
26: * INTEGER INFO, LDA, N
27: * DOUBLE PRECISION ANORM, RCOND
28: * ..
29: * .. Array Arguments ..
30: * DOUBLE PRECISION RWORK( * )
31: * COMPLEX*16 A( LDA, * ), WORK( * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> ZPOCON estimates the reciprocal of the condition number (in the
41: *> 1-norm) of a complex Hermitian positive definite matrix using the
42: *> Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.
43: *>
44: *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
45: *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
46: *> \endverbatim
47: *
48: * Arguments:
49: * ==========
50: *
51: *> \param[in] UPLO
52: *> \verbatim
53: *> UPLO is CHARACTER*1
54: *> = 'U': Upper triangle of A is stored;
55: *> = 'L': Lower triangle of A is stored.
56: *> \endverbatim
57: *>
58: *> \param[in] N
59: *> \verbatim
60: *> N is INTEGER
61: *> The order of the matrix A. N >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in] A
65: *> \verbatim
66: *> A is COMPLEX*16 array, dimension (LDA,N)
67: *> The triangular factor U or L from the Cholesky factorization
68: *> A = U**H*U or A = L*L**H, as computed by ZPOTRF.
69: *> \endverbatim
70: *>
71: *> \param[in] LDA
72: *> \verbatim
73: *> LDA is INTEGER
74: *> The leading dimension of the array A. LDA >= max(1,N).
75: *> \endverbatim
76: *>
77: *> \param[in] ANORM
78: *> \verbatim
79: *> ANORM is DOUBLE PRECISION
80: *> The 1-norm (or infinity-norm) of the Hermitian matrix A.
81: *> \endverbatim
82: *>
83: *> \param[out] RCOND
84: *> \verbatim
85: *> RCOND is DOUBLE PRECISION
86: *> The reciprocal of the condition number of the matrix A,
87: *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
88: *> estimate of the 1-norm of inv(A) computed in this routine.
89: *> \endverbatim
90: *>
91: *> \param[out] WORK
92: *> \verbatim
93: *> WORK is COMPLEX*16 array, dimension (2*N)
94: *> \endverbatim
95: *>
96: *> \param[out] RWORK
97: *> \verbatim
98: *> RWORK is DOUBLE PRECISION array, dimension (N)
99: *> \endverbatim
100: *>
101: *> \param[out] INFO
102: *> \verbatim
103: *> INFO is INTEGER
104: *> = 0: successful exit
105: *> < 0: if INFO = -i, the i-th argument had an illegal value
106: *> \endverbatim
107: *
108: * Authors:
109: * ========
110: *
111: *> \author Univ. of Tennessee
112: *> \author Univ. of California Berkeley
113: *> \author Univ. of Colorado Denver
114: *> \author NAG Ltd.
115: *
116: *> \ingroup complex16POcomputational
117: *
118: * =====================================================================
119: SUBROUTINE ZPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK,
120: $ INFO )
121: *
122: * -- LAPACK computational routine --
123: * -- LAPACK is a software package provided by Univ. of Tennessee, --
124: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125: *
126: * .. Scalar Arguments ..
127: CHARACTER UPLO
128: INTEGER INFO, LDA, N
129: DOUBLE PRECISION ANORM, RCOND
130: * ..
131: * .. Array Arguments ..
132: DOUBLE PRECISION RWORK( * )
133: COMPLEX*16 A( LDA, * ), WORK( * )
134: * ..
135: *
136: * =====================================================================
137: *
138: * .. Parameters ..
139: DOUBLE PRECISION ONE, ZERO
140: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
141: * ..
142: * .. Local Scalars ..
143: LOGICAL UPPER
144: CHARACTER NORMIN
145: INTEGER IX, KASE
146: DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
147: COMPLEX*16 ZDUM
148: * ..
149: * .. Local Arrays ..
150: INTEGER ISAVE( 3 )
151: * ..
152: * .. External Functions ..
153: LOGICAL LSAME
154: INTEGER IZAMAX
155: DOUBLE PRECISION DLAMCH
156: EXTERNAL LSAME, IZAMAX, DLAMCH
157: * ..
158: * .. External Subroutines ..
159: EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATRS
160: * ..
161: * .. Intrinsic Functions ..
162: INTRINSIC ABS, DBLE, DIMAG, MAX
163: * ..
164: * .. Statement Functions ..
165: DOUBLE PRECISION CABS1
166: * ..
167: * .. Statement Function definitions ..
168: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
169: * ..
170: * .. Executable Statements ..
171: *
172: * Test the input parameters.
173: *
174: INFO = 0
175: UPPER = LSAME( UPLO, 'U' )
176: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
177: INFO = -1
178: ELSE IF( N.LT.0 ) THEN
179: INFO = -2
180: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
181: INFO = -4
182: ELSE IF( ANORM.LT.ZERO ) THEN
183: INFO = -5
184: END IF
185: IF( INFO.NE.0 ) THEN
186: CALL XERBLA( 'ZPOCON', -INFO )
187: RETURN
188: END IF
189: *
190: * Quick return if possible
191: *
192: RCOND = ZERO
193: IF( N.EQ.0 ) THEN
194: RCOND = ONE
195: RETURN
196: ELSE IF( ANORM.EQ.ZERO ) THEN
197: RETURN
198: END IF
199: *
200: SMLNUM = DLAMCH( 'Safe minimum' )
201: *
202: * Estimate the 1-norm of inv(A).
203: *
204: KASE = 0
205: NORMIN = 'N'
206: 10 CONTINUE
207: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
208: IF( KASE.NE.0 ) THEN
209: IF( UPPER ) THEN
210: *
211: * Multiply by inv(U**H).
212: *
213: CALL ZLATRS( 'Upper', 'Conjugate transpose', 'Non-unit',
214: $ NORMIN, N, A, LDA, WORK, SCALEL, RWORK, INFO )
215: NORMIN = 'Y'
216: *
217: * Multiply by inv(U).
218: *
219: CALL ZLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
220: $ A, LDA, WORK, SCALEU, RWORK, INFO )
221: ELSE
222: *
223: * Multiply by inv(L).
224: *
225: CALL ZLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
226: $ A, LDA, WORK, SCALEL, RWORK, INFO )
227: NORMIN = 'Y'
228: *
229: * Multiply by inv(L**H).
230: *
231: CALL ZLATRS( 'Lower', 'Conjugate transpose', 'Non-unit',
232: $ NORMIN, N, A, LDA, WORK, SCALEU, RWORK, INFO )
233: END IF
234: *
235: * Multiply by 1/SCALE if doing so will not cause overflow.
236: *
237: SCALE = SCALEL*SCALEU
238: IF( SCALE.NE.ONE ) THEN
239: IX = IZAMAX( N, WORK, 1 )
240: IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
241: $ GO TO 20
242: CALL ZDRSCL( N, SCALE, WORK, 1 )
243: END IF
244: GO TO 10
245: END IF
246: *
247: * Compute the estimate of the reciprocal condition number.
248: *
249: IF( AINVNM.NE.ZERO )
250: $ RCOND = ( ONE / AINVNM ) / ANORM
251: *
252: 20 CONTINUE
253: RETURN
254: *
255: * End of ZPOCON
256: *
257: END
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