Annotation of rpl/lapack/lapack/dla_syrcond.f, revision 1.14
1.10 bertrand 1: *> \brief \b DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
1.6 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.14 ! bertrand 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
1.6 bertrand 7: *
8: *> \htmlonly
1.14 ! bertrand 9: *> Download DLA_SYRCOND + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_syrcond.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_syrcond.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_syrcond.f">
1.6 bertrand 15: *> [TXT]</a>
1.14 ! bertrand 16: *> \endhtmlonly
1.6 bertrand 17: *
18: * Definition:
19: * ===========
20: *
1.14 ! bertrand 21: * DOUBLE PRECISION FUNCTION DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF,
1.6 bertrand 22: * IPIV, CMODE, C, INFO, WORK,
23: * IWORK )
1.14 ! bertrand 24: *
1.6 bertrand 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: * ..
1.14 ! bertrand 33: *
1.6 bertrand 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: *
1.14 ! bertrand 137: *> \author Univ. of Tennessee
! 138: *> \author Univ. of California Berkeley
! 139: *> \author Univ. of Colorado Denver
! 140: *> \author NAG Ltd.
1.6 bertrand 141: *
1.14 ! bertrand 142: *> \date December 2016
1.6 bertrand 143: *
144: *> \ingroup doubleSYcomputational
145: *
146: * =====================================================================
1.14 ! bertrand 147: DOUBLE PRECISION FUNCTION DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF,
1.1 bertrand 148: $ IPIV, CMODE, C, INFO, WORK,
149: $ IWORK )
150: *
1.14 ! bertrand 151: * -- LAPACK computational routine (version 3.7.0) --
1.6 bertrand 152: * -- LAPACK is a software package provided by Univ. of Tennessee, --
153: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.14 ! bertrand 154: * December 2016
1.1 bertrand 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: DOUBLE PRECISION DLAMCH
1.14 ! bertrand 179: EXTERNAL LSAME, DLAMCH
1.1 bertrand 180: * ..
181: * .. External Subroutines ..
1.14 ! bertrand 182: EXTERNAL DLACN2, XERBLA, DSYTRS
1.1 bertrand 183: * ..
184: * .. Intrinsic Functions ..
185: INTRINSIC ABS, MAX
186: * ..
187: * .. Executable Statements ..
188: *
189: DLA_SYRCOND = 0.0D+0
190: *
191: INFO = 0
192: IF( N.LT.0 ) THEN
193: INFO = -2
1.8 bertrand 194: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
195: INFO = -4
196: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
197: INFO = -6
1.1 bertrand 198: END IF
199: IF( INFO.NE.0 ) THEN
200: CALL XERBLA( 'DLA_SYRCOND', -INFO )
201: RETURN
202: END IF
203: IF( N.EQ.0 ) THEN
204: DLA_SYRCOND = 1.0D+0
205: RETURN
206: END IF
207: UP = .FALSE.
208: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
209: *
210: * Compute the equilibration matrix R such that
211: * inv(R)*A*C has unit 1-norm.
212: *
213: IF ( UP ) THEN
214: DO I = 1, N
215: TMP = 0.0D+0
216: IF ( CMODE .EQ. 1 ) THEN
217: DO J = 1, I
218: TMP = TMP + ABS( A( J, I ) * C( J ) )
219: END DO
220: DO J = I+1, N
221: TMP = TMP + ABS( A( I, J ) * C( J ) )
222: END DO
223: ELSE IF ( CMODE .EQ. 0 ) THEN
224: DO J = 1, I
225: TMP = TMP + ABS( A( J, I ) )
226: END DO
227: DO J = I+1, N
228: TMP = TMP + ABS( A( I, J ) )
229: END DO
230: ELSE
231: DO J = 1, I
232: TMP = TMP + ABS( A( J, I ) / C( J ) )
233: END DO
234: DO J = I+1, N
235: TMP = TMP + ABS( A( I, J ) / C( J ) )
236: END DO
237: END IF
238: WORK( 2*N+I ) = TMP
239: END DO
240: ELSE
241: DO I = 1, N
242: TMP = 0.0D+0
243: IF ( CMODE .EQ. 1 ) THEN
244: DO J = 1, I
245: TMP = TMP + ABS( A( I, J ) * C( J ) )
246: END DO
247: DO J = I+1, N
248: TMP = TMP + ABS( A( J, I ) * C( J ) )
249: END DO
250: ELSE IF ( CMODE .EQ. 0 ) THEN
251: DO J = 1, I
252: TMP = TMP + ABS( A( I, J ) )
253: END DO
254: DO J = I+1, N
255: TMP = TMP + ABS( A( J, I ) )
256: END DO
257: ELSE
258: DO J = 1, I
259: TMP = TMP + ABS( A( I, J) / C( J ) )
260: END DO
261: DO J = I+1, N
262: TMP = TMP + ABS( A( J, I) / C( J ) )
263: END DO
264: END IF
265: WORK( 2*N+I ) = TMP
266: END DO
267: ENDIF
268: *
269: * Estimate the norm of inv(op(A)).
270: *
271: SMLNUM = DLAMCH( 'Safe minimum' )
272: AINVNM = 0.0D+0
273: NORMIN = 'N'
274:
275: KASE = 0
276: 10 CONTINUE
277: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
278: IF( KASE.NE.0 ) THEN
279: IF( KASE.EQ.2 ) THEN
280: *
281: * Multiply by R.
282: *
283: DO I = 1, N
284: WORK( I ) = WORK( I ) * WORK( 2*N+I )
285: END DO
286:
287: IF ( UP ) THEN
288: CALL DSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
289: ELSE
290: CALL DSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
291: ENDIF
292: *
293: * Multiply by inv(C).
294: *
295: IF ( CMODE .EQ. 1 ) THEN
296: DO I = 1, N
297: WORK( I ) = WORK( I ) / C( I )
298: END DO
299: ELSE IF ( CMODE .EQ. -1 ) THEN
300: DO I = 1, N
301: WORK( I ) = WORK( I ) * C( I )
302: END DO
303: END IF
304: ELSE
305: *
1.5 bertrand 306: * Multiply by inv(C**T).
1.1 bertrand 307: *
308: IF ( CMODE .EQ. 1 ) THEN
309: DO I = 1, N
310: WORK( I ) = WORK( I ) / C( I )
311: END DO
312: ELSE IF ( CMODE .EQ. -1 ) THEN
313: DO I = 1, N
314: WORK( I ) = WORK( I ) * C( I )
315: END DO
316: END IF
317:
318: IF ( UP ) THEN
319: CALL DSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
320: ELSE
321: CALL DSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
322: ENDIF
323: *
324: * Multiply by R.
325: *
326: DO I = 1, N
327: WORK( I ) = WORK( I ) * WORK( 2*N+I )
328: END DO
329: END IF
330: *
331: GO TO 10
332: END IF
333: *
334: * Compute the estimate of the reciprocal condition number.
335: *
336: IF( AINVNM .NE. 0.0D+0 )
337: $ DLA_SYRCOND = ( 1.0D+0 / AINVNM )
338: *
339: RETURN
340: *
341: END
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