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[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 complex16SYcomputational
137: *
138: * =====================================================================
139: DOUBLE PRECISION FUNCTION ZLA_SYRCOND_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
163: DOUBLE PRECISION AINVNM, ANORM, TMP
164: INTEGER I, J
165: LOGICAL UP, UPPER
166: COMPLEX*16 ZDUM
167: * ..
168: * .. Local Arrays ..
169: INTEGER ISAVE( 3 )
170: * ..
171: * .. External Functions ..
172: LOGICAL LSAME
173: EXTERNAL LSAME
174: * ..
175: * .. External Subroutines ..
176: EXTERNAL ZLACN2, ZSYTRS, XERBLA
177: * ..
178: * .. Intrinsic Functions ..
179: INTRINSIC ABS, MAX
180: * ..
181: * .. Statement Functions ..
182: DOUBLE PRECISION CABS1
183: * ..
184: * .. Statement Function Definitions ..
185: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
186: * ..
187: * .. Executable Statements ..
188: *
189: ZLA_SYRCOND_C = 0.0D+0
190: *
191: INFO = 0
192: UPPER = LSAME( UPLO, 'U' )
193: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
194: INFO = -1
195: ELSE IF( N.LT.0 ) THEN
196: INFO = -2
197: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
198: INFO = -4
199: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
200: INFO = -6
201: END IF
202: IF( INFO.NE.0 ) THEN
203: CALL XERBLA( 'ZLA_SYRCOND_C', -INFO )
204: RETURN
205: END IF
206: UP = .FALSE.
207: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
208: *
209: * Compute norm of op(A)*op2(C).
210: *
211: ANORM = 0.0D+0
212: IF ( UP ) THEN
213: DO I = 1, N
214: TMP = 0.0D+0
215: IF ( CAPPLY ) THEN
216: DO J = 1, I
217: TMP = TMP + CABS1( A( J, I ) ) / C( J )
218: END DO
219: DO J = I+1, N
220: TMP = TMP + CABS1( A( I, J ) ) / C( J )
221: END DO
222: ELSE
223: DO J = 1, I
224: TMP = TMP + CABS1( A( J, I ) )
225: END DO
226: DO J = I+1, N
227: TMP = TMP + CABS1( A( I, J ) )
228: END DO
229: END IF
230: RWORK( I ) = TMP
231: ANORM = MAX( ANORM, TMP )
232: END DO
233: ELSE
234: DO I = 1, N
235: TMP = 0.0D+0
236: IF ( CAPPLY ) THEN
237: DO J = 1, I
238: TMP = TMP + CABS1( A( I, J ) ) / C( J )
239: END DO
240: DO J = I+1, N
241: TMP = TMP + CABS1( A( J, I ) ) / C( J )
242: END DO
243: ELSE
244: DO J = 1, I
245: TMP = TMP + CABS1( A( I, J ) )
246: END DO
247: DO J = I+1, N
248: TMP = TMP + CABS1( A( J, I ) )
249: END DO
250: END IF
251: RWORK( I ) = TMP
252: ANORM = MAX( ANORM, TMP )
253: END DO
254: END IF
255: *
256: * Quick return if possible.
257: *
258: IF( N.EQ.0 ) THEN
259: ZLA_SYRCOND_C = 1.0D+0
260: RETURN
261: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
262: RETURN
263: END IF
264: *
265: * Estimate the norm of inv(op(A)).
266: *
267: AINVNM = 0.0D+0
268: *
269: KASE = 0
270: 10 CONTINUE
271: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
272: IF( KASE.NE.0 ) THEN
273: IF( KASE.EQ.2 ) THEN
274: *
275: * Multiply by R.
276: *
277: DO I = 1, N
278: WORK( I ) = WORK( I ) * RWORK( I )
279: END DO
280: *
281: IF ( UP ) THEN
282: CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
283: $ WORK, N, INFO )
284: ELSE
285: CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
286: $ WORK, N, INFO )
287: ENDIF
288: *
289: * Multiply by inv(C).
290: *
291: IF ( CAPPLY ) THEN
292: DO I = 1, N
293: WORK( I ) = WORK( I ) * C( I )
294: END DO
295: END IF
296: ELSE
297: *
298: * Multiply by inv(C**T).
299: *
300: IF ( CAPPLY ) THEN
301: DO I = 1, N
302: WORK( I ) = WORK( I ) * C( I )
303: END DO
304: END IF
305: *
306: IF ( UP ) THEN
307: CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
308: $ WORK, N, INFO )
309: ELSE
310: CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
311: $ WORK, N, INFO )
312: END IF
313: *
314: * Multiply by R.
315: *
316: DO I = 1, N
317: WORK( I ) = WORK( I ) * RWORK( I )
318: END DO
319: END IF
320: GO TO 10
321: END IF
322: *
323: * Compute the estimate of the reciprocal condition number.
324: *
325: IF( AINVNM .NE. 0.0D+0 )
326: $ ZLA_SYRCOND_C = 1.0D+0 / AINVNM
327: *
328: RETURN
329: *
330: END
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