1: *> \brief \b ZLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric 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_SYRCOND_C + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_syrcond_c.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_syrcond_c.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_syrcond_c.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLA_SYRCOND_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_SYRCOND_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 ZSYTRF.
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 ZSYTRF.
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 complex16SYcomputational
135: *
136: * =====================================================================
137: DOUBLE PRECISION FUNCTION ZLA_SYRCOND_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
160: DOUBLE PRECISION AINVNM, ANORM, TMP
161: INTEGER I, J
162: LOGICAL UP, UPPER
163: COMPLEX*16 ZDUM
164: * ..
165: * .. Local Arrays ..
166: INTEGER ISAVE( 3 )
167: * ..
168: * .. External Functions ..
169: LOGICAL LSAME
170: EXTERNAL LSAME
171: * ..
172: * .. External Subroutines ..
173: EXTERNAL ZLACN2, ZSYTRS, XERBLA
174: * ..
175: * .. Intrinsic Functions ..
176: INTRINSIC ABS, MAX
177: * ..
178: * .. Statement Functions ..
179: DOUBLE PRECISION CABS1
180: * ..
181: * .. Statement Function Definitions ..
182: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
183: * ..
184: * .. Executable Statements ..
185: *
186: ZLA_SYRCOND_C = 0.0D+0
187: *
188: INFO = 0
189: UPPER = LSAME( UPLO, 'U' )
190: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
191: INFO = -1
192: ELSE IF( N.LT.0 ) THEN
193: INFO = -2
194: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
195: INFO = -4
196: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
197: INFO = -6
198: END IF
199: IF( INFO.NE.0 ) THEN
200: CALL XERBLA( 'ZLA_SYRCOND_C', -INFO )
201: RETURN
202: END IF
203: UP = .FALSE.
204: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
205: *
206: * Compute norm of op(A)*op2(C).
207: *
208: ANORM = 0.0D+0
209: IF ( UP ) THEN
210: DO I = 1, N
211: TMP = 0.0D+0
212: IF ( CAPPLY ) THEN
213: DO J = 1, I
214: TMP = TMP + CABS1( A( J, I ) ) / C( J )
215: END DO
216: DO J = I+1, N
217: TMP = TMP + CABS1( A( I, J ) ) / C( J )
218: END DO
219: ELSE
220: DO J = 1, I
221: TMP = TMP + CABS1( A( J, I ) )
222: END DO
223: DO J = I+1, N
224: TMP = TMP + CABS1( A( I, J ) )
225: END DO
226: END IF
227: RWORK( I ) = TMP
228: ANORM = MAX( ANORM, TMP )
229: END DO
230: ELSE
231: DO I = 1, N
232: TMP = 0.0D+0
233: IF ( CAPPLY ) THEN
234: DO J = 1, I
235: TMP = TMP + CABS1( A( I, J ) ) / C( J )
236: END DO
237: DO J = I+1, N
238: TMP = TMP + CABS1( A( J, I ) ) / C( J )
239: END DO
240: ELSE
241: DO J = 1, I
242: TMP = TMP + CABS1( A( I, J ) )
243: END DO
244: DO J = I+1, N
245: TMP = TMP + CABS1( A( J, I ) )
246: END DO
247: END IF
248: RWORK( I ) = TMP
249: ANORM = MAX( ANORM, TMP )
250: END DO
251: END IF
252: *
253: * Quick return if possible.
254: *
255: IF( N.EQ.0 ) THEN
256: ZLA_SYRCOND_C = 1.0D+0
257: RETURN
258: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
259: RETURN
260: END IF
261: *
262: * Estimate the norm of inv(op(A)).
263: *
264: AINVNM = 0.0D+0
265: *
266: KASE = 0
267: 10 CONTINUE
268: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
269: IF( KASE.NE.0 ) THEN
270: IF( KASE.EQ.2 ) THEN
271: *
272: * Multiply by R.
273: *
274: DO I = 1, N
275: WORK( I ) = WORK( I ) * RWORK( I )
276: END DO
277: *
278: IF ( UP ) THEN
279: CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
280: $ WORK, N, INFO )
281: ELSE
282: CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
283: $ WORK, N, INFO )
284: ENDIF
285: *
286: * Multiply by inv(C).
287: *
288: IF ( CAPPLY ) THEN
289: DO I = 1, N
290: WORK( I ) = WORK( I ) * C( I )
291: END DO
292: END IF
293: ELSE
294: *
295: * Multiply by inv(C**T).
296: *
297: IF ( CAPPLY ) THEN
298: DO I = 1, N
299: WORK( I ) = WORK( I ) * C( I )
300: END DO
301: END IF
302: *
303: IF ( UP ) THEN
304: CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
305: $ WORK, N, INFO )
306: ELSE
307: CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
308: $ WORK, N, INFO )
309: END IF
310: *
311: * Multiply by R.
312: *
313: DO I = 1, N
314: WORK( I ) = WORK( I ) * RWORK( I )
315: END DO
316: END IF
317: GO TO 10
318: END IF
319: *
320: * Compute the estimate of the reciprocal condition number.
321: *
322: IF( AINVNM .NE. 0.0D+0 )
323: $ ZLA_SYRCOND_C = 1.0D+0 / AINVNM
324: *
325: RETURN
326: *
327: * End of ZLA_SYRCOND_C
328: *
329: END
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