1: *> \brief \b ZLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian 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_HERCOND_C + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_hercond_c.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_hercond_c.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_hercond_c.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLA_HERCOND_C( UPLO, N, A, LDA, AF,
22: * LDAF, IPIV, C, CAPPLY,
23: * INFO, WORK, RWORK )
24: *
25: * .. Scalar Arguments ..
26: * CHARACTER UPLO
27: * LOGICAL CAPPLY
28: * INTEGER N, LDA, LDAF, INFO
29: * ..
30: * .. Array Arguments ..
31: * INTEGER IPIV( * )
32: * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
33: * DOUBLE PRECISION C ( * ), RWORK( * )
34: * ..
35: *
36: *
37: *> \par Purpose:
38: * =============
39: *>
40: *> \verbatim
41: *>
42: *> ZLA_HERCOND_C computes the infinity norm condition number of
43: *> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
44: *> \endverbatim
45: *
46: * Arguments:
47: * ==========
48: *
49: *> \param[in] UPLO
50: *> \verbatim
51: *> UPLO is CHARACTER*1
52: *> = 'U': Upper triangle of A is stored;
53: *> = 'L': Lower triangle of A is stored.
54: *> \endverbatim
55: *>
56: *> \param[in] N
57: *> \verbatim
58: *> N is INTEGER
59: *> The number of linear equations, i.e., the order of the
60: *> matrix A. N >= 0.
61: *> \endverbatim
62: *>
63: *> \param[in] A
64: *> \verbatim
65: *> A is COMPLEX*16 array, dimension (LDA,N)
66: *> On entry, the N-by-N matrix A
67: *> \endverbatim
68: *>
69: *> \param[in] LDA
70: *> \verbatim
71: *> LDA is INTEGER
72: *> The leading dimension of the array A. LDA >= max(1,N).
73: *> \endverbatim
74: *>
75: *> \param[in] AF
76: *> \verbatim
77: *> AF is COMPLEX*16 array, dimension (LDAF,N)
78: *> The block diagonal matrix D and the multipliers used to
79: *> obtain the factor U or L as computed by ZHETRF.
80: *> \endverbatim
81: *>
82: *> \param[in] LDAF
83: *> \verbatim
84: *> LDAF is INTEGER
85: *> The leading dimension of the array AF. LDAF >= max(1,N).
86: *> \endverbatim
87: *>
88: *> \param[in] IPIV
89: *> \verbatim
90: *> IPIV is INTEGER array, dimension (N)
91: *> Details of the interchanges and the block structure of D
92: *> as determined by CHETRF.
93: *> \endverbatim
94: *>
95: *> \param[in] C
96: *> \verbatim
97: *> C is DOUBLE PRECISION array, dimension (N)
98: *> The vector C in the formula op(A) * inv(diag(C)).
99: *> \endverbatim
100: *>
101: *> \param[in] CAPPLY
102: *> \verbatim
103: *> CAPPLY is LOGICAL
104: *> If .TRUE. then access the vector C in the formula above.
105: *> \endverbatim
106: *>
107: *> \param[out] INFO
108: *> \verbatim
109: *> INFO is INTEGER
110: *> = 0: Successful exit.
111: *> i > 0: The ith argument is invalid.
112: *> \endverbatim
113: *>
114: *> \param[out] WORK
115: *> \verbatim
116: *> WORK is COMPLEX*16 array, dimension (2*N).
117: *> Workspace.
118: *> \endverbatim
119: *>
120: *> \param[out] RWORK
121: *> \verbatim
122: *> RWORK is DOUBLE PRECISION array, dimension (N).
123: *> Workspace.
124: *> \endverbatim
125: *
126: * Authors:
127: * ========
128: *
129: *> \author Univ. of Tennessee
130: *> \author Univ. of California Berkeley
131: *> \author Univ. of Colorado Denver
132: *> \author NAG Ltd.
133: *
134: *> \ingroup complex16HEcomputational
135: *
136: * =====================================================================
137: DOUBLE PRECISION FUNCTION ZLA_HERCOND_C( UPLO, N, A, LDA, AF,
138: $ LDAF, IPIV, C, CAPPLY,
139: $ INFO, WORK, RWORK )
140: *
141: * -- LAPACK computational routine --
142: * -- LAPACK is a software package provided by Univ. of Tennessee, --
143: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144: *
145: * .. Scalar Arguments ..
146: CHARACTER UPLO
147: LOGICAL CAPPLY
148: INTEGER N, LDA, LDAF, INFO
149: * ..
150: * .. Array Arguments ..
151: INTEGER IPIV( * )
152: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
153: DOUBLE PRECISION C ( * ), RWORK( * )
154: * ..
155: *
156: * =====================================================================
157: *
158: * .. Local Scalars ..
159: INTEGER KASE, I, J
160: DOUBLE PRECISION AINVNM, ANORM, TMP
161: LOGICAL UP, UPPER
162: COMPLEX*16 ZDUM
163: * ..
164: * .. Local Arrays ..
165: INTEGER ISAVE( 3 )
166: * ..
167: * .. External Functions ..
168: LOGICAL LSAME
169: EXTERNAL LSAME
170: * ..
171: * .. External Subroutines ..
172: EXTERNAL ZLACN2, ZHETRS, XERBLA
173: * ..
174: * .. Intrinsic Functions ..
175: INTRINSIC ABS, MAX
176: * ..
177: * .. Statement Functions ..
178: DOUBLE PRECISION CABS1
179: * ..
180: * .. Statement Function Definitions ..
181: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
182: * ..
183: * .. Executable Statements ..
184: *
185: ZLA_HERCOND_C = 0.0D+0
186: *
187: INFO = 0
188: UPPER = LSAME( UPLO, 'U' )
189: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
190: INFO = -1
191: ELSE IF( N.LT.0 ) THEN
192: INFO = -2
193: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
194: INFO = -4
195: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
196: INFO = -6
197: END IF
198: IF( INFO.NE.0 ) THEN
199: CALL XERBLA( 'ZLA_HERCOND_C', -INFO )
200: RETURN
201: END IF
202: UP = .FALSE.
203: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
204: *
205: * Compute norm of op(A)*op2(C).
206: *
207: ANORM = 0.0D+0
208: IF ( UP ) THEN
209: DO I = 1, N
210: TMP = 0.0D+0
211: IF ( CAPPLY ) THEN
212: DO J = 1, I
213: TMP = TMP + CABS1( A( J, I ) ) / C( J )
214: END DO
215: DO J = I+1, N
216: TMP = TMP + CABS1( A( I, J ) ) / C( J )
217: END DO
218: ELSE
219: DO J = 1, I
220: TMP = TMP + CABS1( A( J, I ) )
221: END DO
222: DO J = I+1, N
223: TMP = TMP + CABS1( A( I, J ) )
224: END DO
225: END IF
226: RWORK( I ) = TMP
227: ANORM = MAX( ANORM, TMP )
228: END DO
229: ELSE
230: DO I = 1, N
231: TMP = 0.0D+0
232: IF ( CAPPLY ) THEN
233: DO J = 1, I
234: TMP = TMP + CABS1( A( I, J ) ) / C( J )
235: END DO
236: DO J = I+1, N
237: TMP = TMP + CABS1( A( J, I ) ) / C( J )
238: END DO
239: ELSE
240: DO J = 1, I
241: TMP = TMP + CABS1( A( I, J ) )
242: END DO
243: DO J = I+1, N
244: TMP = TMP + CABS1( A( J, I ) )
245: END DO
246: END IF
247: RWORK( I ) = TMP
248: ANORM = MAX( ANORM, TMP )
249: END DO
250: END IF
251: *
252: * Quick return if possible.
253: *
254: IF( N.EQ.0 ) THEN
255: ZLA_HERCOND_C = 1.0D+0
256: RETURN
257: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
258: RETURN
259: END IF
260: *
261: * Estimate the norm of inv(op(A)).
262: *
263: AINVNM = 0.0D+0
264: *
265: KASE = 0
266: 10 CONTINUE
267: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
268: IF( KASE.NE.0 ) THEN
269: IF( KASE.EQ.2 ) THEN
270: *
271: * Multiply by R.
272: *
273: DO I = 1, N
274: WORK( I ) = WORK( I ) * RWORK( I )
275: END DO
276: *
277: IF ( UP ) THEN
278: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
279: $ WORK, N, INFO )
280: ELSE
281: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
282: $ WORK, N, INFO )
283: ENDIF
284: *
285: * Multiply by inv(C).
286: *
287: IF ( CAPPLY ) THEN
288: DO I = 1, N
289: WORK( I ) = WORK( I ) * C( I )
290: END DO
291: END IF
292: ELSE
293: *
294: * Multiply by inv(C**H).
295: *
296: IF ( CAPPLY ) THEN
297: DO I = 1, N
298: WORK( I ) = WORK( I ) * C( I )
299: END DO
300: END IF
301: *
302: IF ( UP ) THEN
303: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
304: $ WORK, N, INFO )
305: ELSE
306: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
307: $ WORK, N, INFO )
308: END IF
309: *
310: * Multiply by R.
311: *
312: DO I = 1, N
313: WORK( I ) = WORK( I ) * RWORK( I )
314: END DO
315: END IF
316: GO TO 10
317: END IF
318: *
319: * Compute the estimate of the reciprocal condition number.
320: *
321: IF( AINVNM .NE. 0.0D+0 )
322: $ ZLA_HERCOND_C = 1.0D+0 / AINVNM
323: *
324: RETURN
325: *
326: * End of ZLA_HERCOND_C
327: *
328: END
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