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[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 December 2016
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 3.7.0) --
144: * -- LAPACK is a software package provided by Univ. of Tennessee, --
145: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146: * December 2016
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, UPPER
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: UPPER = LSAME( UPLO, 'U' )
192: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
193: INFO = -1
194: ELSE IF( N.LT.0 ) THEN
195: INFO = -2
196: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
197: INFO = -4
198: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
199: INFO = -6
200: END IF
201: IF( INFO.NE.0 ) THEN
202: CALL XERBLA( 'ZLA_HERCOND_C', -INFO )
203: RETURN
204: END IF
205: UP = .FALSE.
206: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
207: *
208: * Compute norm of op(A)*op2(C).
209: *
210: ANORM = 0.0D+0
211: IF ( UP ) THEN
212: DO I = 1, N
213: TMP = 0.0D+0
214: IF ( CAPPLY ) THEN
215: DO J = 1, I
216: TMP = TMP + CABS1( A( J, I ) ) / C( J )
217: END DO
218: DO J = I+1, N
219: TMP = TMP + CABS1( A( I, J ) ) / C( J )
220: END DO
221: ELSE
222: DO J = 1, I
223: TMP = TMP + CABS1( A( J, I ) )
224: END DO
225: DO J = I+1, N
226: TMP = TMP + CABS1( A( I, J ) )
227: END DO
228: END IF
229: RWORK( I ) = TMP
230: ANORM = MAX( ANORM, TMP )
231: END DO
232: ELSE
233: DO I = 1, N
234: TMP = 0.0D+0
235: IF ( CAPPLY ) THEN
236: DO J = 1, I
237: TMP = TMP + CABS1( A( I, J ) ) / C( J )
238: END DO
239: DO J = I+1, N
240: TMP = TMP + CABS1( A( J, I ) ) / C( J )
241: END DO
242: ELSE
243: DO J = 1, I
244: TMP = TMP + CABS1( A( I, J ) )
245: END DO
246: DO J = I+1, N
247: TMP = TMP + CABS1( A( J, I ) )
248: END DO
249: END IF
250: RWORK( I ) = TMP
251: ANORM = MAX( ANORM, TMP )
252: END DO
253: END IF
254: *
255: * Quick return if possible.
256: *
257: IF( N.EQ.0 ) THEN
258: ZLA_HERCOND_C = 1.0D+0
259: RETURN
260: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
261: RETURN
262: END IF
263: *
264: * Estimate the norm of inv(op(A)).
265: *
266: AINVNM = 0.0D+0
267: *
268: KASE = 0
269: 10 CONTINUE
270: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
271: IF( KASE.NE.0 ) THEN
272: IF( KASE.EQ.2 ) THEN
273: *
274: * Multiply by R.
275: *
276: DO I = 1, N
277: WORK( I ) = WORK( I ) * RWORK( I )
278: END DO
279: *
280: IF ( UP ) THEN
281: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
282: $ WORK, N, INFO )
283: ELSE
284: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
285: $ WORK, N, INFO )
286: ENDIF
287: *
288: * Multiply by inv(C).
289: *
290: IF ( CAPPLY ) THEN
291: DO I = 1, N
292: WORK( I ) = WORK( I ) * C( I )
293: END DO
294: END IF
295: ELSE
296: *
297: * Multiply by inv(C**H).
298: *
299: IF ( CAPPLY ) THEN
300: DO I = 1, N
301: WORK( I ) = WORK( I ) * C( I )
302: END DO
303: END IF
304: *
305: IF ( UP ) THEN
306: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
307: $ WORK, N, INFO )
308: ELSE
309: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
310: $ WORK, N, INFO )
311: END IF
312: *
313: * Multiply by R.
314: *
315: DO I = 1, N
316: WORK( I ) = WORK( I ) * RWORK( I )
317: END DO
318: END IF
319: GO TO 10
320: END IF
321: *
322: * Compute the estimate of the reciprocal condition number.
323: *
324: IF( AINVNM .NE. 0.0D+0 )
325: $ ZLA_HERCOND_C = 1.0D+0 / AINVNM
326: *
327: RETURN
328: *
329: END
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