1: *> \brief \b ZLA_HERCOND_C
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
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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[in] WORK
115: *> \verbatim
116: *> WORK is COMPLEX*16 array, dimension (2*N).
117: *> Workspace.
118: *> \endverbatim
119: *>
120: *> \param[in] 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: *> \date November 2011
135: *
136: *> \ingroup complex16HEcomputational
137: *
138: * =====================================================================
139: DOUBLE PRECISION FUNCTION ZLA_HERCOND_C( UPLO, N, A, LDA, AF,
140: $ LDAF, IPIV, C, CAPPLY,
141: $ INFO, WORK, RWORK )
142: *
143: * -- LAPACK computational routine (version 3.4.0) --
144: * -- LAPACK is a software package provided by Univ. of Tennessee, --
145: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146: * November 2011
147: *
148: * .. Scalar Arguments ..
149: CHARACTER UPLO
150: LOGICAL CAPPLY
151: INTEGER N, LDA, LDAF, INFO
152: * ..
153: * .. Array Arguments ..
154: INTEGER IPIV( * )
155: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
156: DOUBLE PRECISION C ( * ), RWORK( * )
157: * ..
158: *
159: * =====================================================================
160: *
161: * .. Local Scalars ..
162: INTEGER KASE, I, J
163: DOUBLE PRECISION AINVNM, ANORM, TMP
164: LOGICAL UP
165: COMPLEX*16 ZDUM
166: * ..
167: * .. Local Arrays ..
168: INTEGER ISAVE( 3 )
169: * ..
170: * .. External Functions ..
171: LOGICAL LSAME
172: EXTERNAL LSAME
173: * ..
174: * .. External Subroutines ..
175: EXTERNAL ZLACN2, ZHETRS, XERBLA
176: * ..
177: * .. Intrinsic Functions ..
178: INTRINSIC ABS, MAX
179: * ..
180: * .. Statement Functions ..
181: DOUBLE PRECISION CABS1
182: * ..
183: * .. Statement Function Definitions ..
184: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
185: * ..
186: * .. Executable Statements ..
187: *
188: ZLA_HERCOND_C = 0.0D+0
189: *
190: INFO = 0
191: IF( N.LT.0 ) THEN
192: INFO = -2
193: END IF
194: IF( INFO.NE.0 ) THEN
195: CALL XERBLA( 'ZLA_HERCOND_C', -INFO )
196: RETURN
197: END IF
198: UP = .FALSE.
199: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
200: *
201: * Compute norm of op(A)*op2(C).
202: *
203: ANORM = 0.0D+0
204: IF ( UP ) THEN
205: DO I = 1, N
206: TMP = 0.0D+0
207: IF ( CAPPLY ) THEN
208: DO J = 1, I
209: TMP = TMP + CABS1( A( J, I ) ) / C( J )
210: END DO
211: DO J = I+1, N
212: TMP = TMP + CABS1( A( I, J ) ) / C( J )
213: END DO
214: ELSE
215: DO J = 1, I
216: TMP = TMP + CABS1( A( J, I ) )
217: END DO
218: DO J = I+1, N
219: TMP = TMP + CABS1( A( I, J ) )
220: END DO
221: END IF
222: RWORK( I ) = TMP
223: ANORM = MAX( ANORM, TMP )
224: END DO
225: ELSE
226: DO I = 1, N
227: TMP = 0.0D+0
228: IF ( CAPPLY ) THEN
229: DO J = 1, I
230: TMP = TMP + CABS1( A( I, J ) ) / C( J )
231: END DO
232: DO J = I+1, N
233: TMP = TMP + CABS1( A( J, I ) ) / C( J )
234: END DO
235: ELSE
236: DO J = 1, I
237: TMP = TMP + CABS1( A( I, J ) )
238: END DO
239: DO J = I+1, N
240: TMP = TMP + CABS1( A( J, I ) )
241: END DO
242: END IF
243: RWORK( I ) = TMP
244: ANORM = MAX( ANORM, TMP )
245: END DO
246: END IF
247: *
248: * Quick return if possible.
249: *
250: IF( N.EQ.0 ) THEN
251: ZLA_HERCOND_C = 1.0D+0
252: RETURN
253: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
254: RETURN
255: END IF
256: *
257: * Estimate the norm of inv(op(A)).
258: *
259: AINVNM = 0.0D+0
260: *
261: KASE = 0
262: 10 CONTINUE
263: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
264: IF( KASE.NE.0 ) THEN
265: IF( KASE.EQ.2 ) THEN
266: *
267: * Multiply by R.
268: *
269: DO I = 1, N
270: WORK( I ) = WORK( I ) * RWORK( I )
271: END DO
272: *
273: IF ( UP ) THEN
274: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
275: $ WORK, N, INFO )
276: ELSE
277: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
278: $ WORK, N, INFO )
279: ENDIF
280: *
281: * Multiply by inv(C).
282: *
283: IF ( CAPPLY ) THEN
284: DO I = 1, N
285: WORK( I ) = WORK( I ) * C( I )
286: END DO
287: END IF
288: ELSE
289: *
290: * Multiply by inv(C**H).
291: *
292: IF ( CAPPLY ) THEN
293: DO I = 1, N
294: WORK( I ) = WORK( I ) * C( I )
295: END DO
296: END IF
297: *
298: IF ( UP ) THEN
299: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
300: $ WORK, N, INFO )
301: ELSE
302: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
303: $ WORK, N, INFO )
304: END IF
305: *
306: * Multiply by R.
307: *
308: DO I = 1, N
309: WORK( I ) = WORK( I ) * RWORK( I )
310: END DO
311: END IF
312: GO TO 10
313: END IF
314: *
315: * Compute the estimate of the reciprocal condition number.
316: *
317: IF( AINVNM .NE. 0.0D+0 )
318: $ ZLA_HERCOND_C = 1.0D+0 / AINVNM
319: *
320: RETURN
321: *
322: END
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