1: *> \brief \b DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DLA_SYRCOND + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_syrcond.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF,
22: * IPIV, CMODE, C, INFO, WORK,
23: * IWORK )
24: *
25: * .. Scalar Arguments ..
26: * CHARACTER UPLO
27: * INTEGER N, LDA, LDAF, INFO, CMODE
28: * ..
29: * .. Array Arguments
30: * INTEGER IWORK( * ), IPIV( * )
31: * DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> DLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C)
41: *> where op2 is determined by CMODE as follows
42: *> CMODE = 1 op2(C) = C
43: *> CMODE = 0 op2(C) = I
44: *> CMODE = -1 op2(C) = inv(C)
45: *> The Skeel condition number cond(A) = norminf( |inv(A)||A| )
46: *> is computed by computing scaling factors R such that
47: *> diag(R)*A*op2(C) is row equilibrated and computing the standard
48: *> infinity-norm condition number.
49: *> \endverbatim
50: *
51: * Arguments:
52: * ==========
53: *
54: *> \param[in] UPLO
55: *> \verbatim
56: *> UPLO is CHARACTER*1
57: *> = 'U': Upper triangle of A is stored;
58: *> = 'L': Lower triangle of A is stored.
59: *> \endverbatim
60: *>
61: *> \param[in] N
62: *> \verbatim
63: *> N is INTEGER
64: *> The number of linear equations, i.e., the order of the
65: *> matrix A. N >= 0.
66: *> \endverbatim
67: *>
68: *> \param[in] A
69: *> \verbatim
70: *> A is DOUBLE PRECISION array, dimension (LDA,N)
71: *> On entry, the N-by-N matrix A.
72: *> \endverbatim
73: *>
74: *> \param[in] LDA
75: *> \verbatim
76: *> LDA is INTEGER
77: *> The leading dimension of the array A. LDA >= max(1,N).
78: *> \endverbatim
79: *>
80: *> \param[in] AF
81: *> \verbatim
82: *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
83: *> The block diagonal matrix D and the multipliers used to
84: *> obtain the factor U or L as computed by DSYTRF.
85: *> \endverbatim
86: *>
87: *> \param[in] LDAF
88: *> \verbatim
89: *> LDAF is INTEGER
90: *> The leading dimension of the array AF. LDAF >= max(1,N).
91: *> \endverbatim
92: *>
93: *> \param[in] IPIV
94: *> \verbatim
95: *> IPIV is INTEGER array, dimension (N)
96: *> Details of the interchanges and the block structure of D
97: *> as determined by DSYTRF.
98: *> \endverbatim
99: *>
100: *> \param[in] CMODE
101: *> \verbatim
102: *> CMODE is INTEGER
103: *> Determines op2(C) in the formula op(A) * op2(C) as follows:
104: *> CMODE = 1 op2(C) = C
105: *> CMODE = 0 op2(C) = I
106: *> CMODE = -1 op2(C) = inv(C)
107: *> \endverbatim
108: *>
109: *> \param[in] C
110: *> \verbatim
111: *> C is DOUBLE PRECISION array, dimension (N)
112: *> The vector C in the formula op(A) * op2(C).
113: *> \endverbatim
114: *>
115: *> \param[out] INFO
116: *> \verbatim
117: *> INFO is INTEGER
118: *> = 0: Successful exit.
119: *> i > 0: The ith argument is invalid.
120: *> \endverbatim
121: *>
122: *> \param[in] WORK
123: *> \verbatim
124: *> WORK is DOUBLE PRECISION array, dimension (3*N).
125: *> Workspace.
126: *> \endverbatim
127: *>
128: *> \param[in] IWORK
129: *> \verbatim
130: *> IWORK is INTEGER array, dimension (N).
131: *> Workspace.
132: *> \endverbatim
133: *
134: * Authors:
135: * ========
136: *
137: *> \author Univ. of Tennessee
138: *> \author Univ. of California Berkeley
139: *> \author Univ. of Colorado Denver
140: *> \author NAG Ltd.
141: *
142: *> \date September 2012
143: *
144: *> \ingroup doubleSYcomputational
145: *
146: * =====================================================================
147: DOUBLE PRECISION FUNCTION DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF,
148: $ IPIV, CMODE, C, INFO, WORK,
149: $ IWORK )
150: *
151: * -- LAPACK computational routine (version 3.4.2) --
152: * -- LAPACK is a software package provided by Univ. of Tennessee, --
153: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154: * September 2012
155: *
156: * .. Scalar Arguments ..
157: CHARACTER UPLO
158: INTEGER N, LDA, LDAF, INFO, CMODE
159: * ..
160: * .. Array Arguments
161: INTEGER IWORK( * ), IPIV( * )
162: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
163: * ..
164: *
165: * =====================================================================
166: *
167: * .. Local Scalars ..
168: CHARACTER NORMIN
169: INTEGER KASE, I, J
170: DOUBLE PRECISION AINVNM, SMLNUM, TMP
171: LOGICAL UP
172: * ..
173: * .. Local Arrays ..
174: INTEGER ISAVE( 3 )
175: * ..
176: * .. External Functions ..
177: LOGICAL LSAME
178: INTEGER IDAMAX
179: DOUBLE PRECISION DLAMCH
180: EXTERNAL LSAME, IDAMAX, DLAMCH
181: * ..
182: * .. External Subroutines ..
183: EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA, DSYTRS
184: * ..
185: * .. Intrinsic Functions ..
186: INTRINSIC ABS, MAX
187: * ..
188: * .. Executable Statements ..
189: *
190: DLA_SYRCOND = 0.0D+0
191: *
192: INFO = 0
193: IF( N.LT.0 ) THEN
194: INFO = -2
195: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
196: INFO = -4
197: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
198: INFO = -6
199: END IF
200: IF( INFO.NE.0 ) THEN
201: CALL XERBLA( 'DLA_SYRCOND', -INFO )
202: RETURN
203: END IF
204: IF( N.EQ.0 ) THEN
205: DLA_SYRCOND = 1.0D+0
206: RETURN
207: END IF
208: UP = .FALSE.
209: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
210: *
211: * Compute the equilibration matrix R such that
212: * inv(R)*A*C has unit 1-norm.
213: *
214: IF ( UP ) THEN
215: DO I = 1, N
216: TMP = 0.0D+0
217: IF ( CMODE .EQ. 1 ) THEN
218: DO J = 1, I
219: TMP = TMP + ABS( A( J, I ) * C( J ) )
220: END DO
221: DO J = I+1, N
222: TMP = TMP + ABS( A( I, J ) * C( J ) )
223: END DO
224: ELSE IF ( CMODE .EQ. 0 ) THEN
225: DO J = 1, I
226: TMP = TMP + ABS( A( J, I ) )
227: END DO
228: DO J = I+1, N
229: TMP = TMP + ABS( A( I, J ) )
230: END DO
231: ELSE
232: DO J = 1, I
233: TMP = TMP + ABS( A( J, I ) / C( J ) )
234: END DO
235: DO J = I+1, N
236: TMP = TMP + ABS( A( I, J ) / C( J ) )
237: END DO
238: END IF
239: WORK( 2*N+I ) = TMP
240: END DO
241: ELSE
242: DO I = 1, N
243: TMP = 0.0D+0
244: IF ( CMODE .EQ. 1 ) THEN
245: DO J = 1, I
246: TMP = TMP + ABS( A( I, J ) * C( J ) )
247: END DO
248: DO J = I+1, N
249: TMP = TMP + ABS( A( J, I ) * C( J ) )
250: END DO
251: ELSE IF ( CMODE .EQ. 0 ) THEN
252: DO J = 1, I
253: TMP = TMP + ABS( A( I, J ) )
254: END DO
255: DO J = I+1, N
256: TMP = TMP + ABS( A( J, I ) )
257: END DO
258: ELSE
259: DO J = 1, I
260: TMP = TMP + ABS( A( I, J) / C( J ) )
261: END DO
262: DO J = I+1, N
263: TMP = TMP + ABS( A( J, I) / C( J ) )
264: END DO
265: END IF
266: WORK( 2*N+I ) = TMP
267: END DO
268: ENDIF
269: *
270: * Estimate the norm of inv(op(A)).
271: *
272: SMLNUM = DLAMCH( 'Safe minimum' )
273: AINVNM = 0.0D+0
274: NORMIN = 'N'
275:
276: KASE = 0
277: 10 CONTINUE
278: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
279: IF( KASE.NE.0 ) THEN
280: IF( KASE.EQ.2 ) THEN
281: *
282: * Multiply by R.
283: *
284: DO I = 1, N
285: WORK( I ) = WORK( I ) * WORK( 2*N+I )
286: END DO
287:
288: IF ( UP ) THEN
289: CALL DSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
290: ELSE
291: CALL DSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
292: ENDIF
293: *
294: * Multiply by inv(C).
295: *
296: IF ( CMODE .EQ. 1 ) THEN
297: DO I = 1, N
298: WORK( I ) = WORK( I ) / C( I )
299: END DO
300: ELSE IF ( CMODE .EQ. -1 ) THEN
301: DO I = 1, N
302: WORK( I ) = WORK( I ) * C( I )
303: END DO
304: END IF
305: ELSE
306: *
307: * Multiply by inv(C**T).
308: *
309: IF ( CMODE .EQ. 1 ) THEN
310: DO I = 1, N
311: WORK( I ) = WORK( I ) / C( I )
312: END DO
313: ELSE IF ( CMODE .EQ. -1 ) THEN
314: DO I = 1, N
315: WORK( I ) = WORK( I ) * C( I )
316: END DO
317: END IF
318:
319: IF ( UP ) THEN
320: CALL DSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
321: ELSE
322: CALL DSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
323: ENDIF
324: *
325: * Multiply by R.
326: *
327: DO I = 1, N
328: WORK( I ) = WORK( I ) * WORK( 2*N+I )
329: END DO
330: END IF
331: *
332: GO TO 10
333: END IF
334: *
335: * Compute the estimate of the reciprocal condition number.
336: *
337: IF( AINVNM .NE. 0.0D+0 )
338: $ DLA_SYRCOND = ( 1.0D+0 / AINVNM )
339: *
340: RETURN
341: *
342: END
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