1: *> \brief \b DLA_GERCOND estimates the Skeel condition number for a general 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_GERCOND + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gercond.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gercond.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gercond.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION DLA_GERCOND ( TRANS, N, A, LDA, AF,
22: * LDAF, IPIV, CMODE, C,
23: * INFO, WORK, IWORK )
24: *
25: * .. Scalar Arguments ..
26: * CHARACTER TRANS
27: * INTEGER N, LDA, LDAF, INFO, CMODE
28: * ..
29: * .. Array Arguments ..
30: * INTEGER IPIV( * ), IWORK( * )
31: * DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ),
32: * $ C( * )
33: * ..
34: *
35: *
36: *> \par Purpose:
37: * =============
38: *>
39: *> \verbatim
40: *>
41: *> DLA_GERCOND estimates the Skeel condition number of op(A) * op2(C)
42: *> where op2 is determined by CMODE as follows
43: *> CMODE = 1 op2(C) = C
44: *> CMODE = 0 op2(C) = I
45: *> CMODE = -1 op2(C) = inv(C)
46: *> The Skeel condition number cond(A) = norminf( |inv(A)||A| )
47: *> is computed by computing scaling factors R such that
48: *> diag(R)*A*op2(C) is row equilibrated and computing the standard
49: *> infinity-norm condition number.
50: *> \endverbatim
51: *
52: * Arguments:
53: * ==========
54: *
55: *> \param[in] TRANS
56: *> \verbatim
57: *> TRANS is CHARACTER*1
58: *> Specifies the form of the system of equations:
59: *> = 'N': A * X = B (No transpose)
60: *> = 'T': A**T * X = B (Transpose)
61: *> = 'C': A**H * X = B (Conjugate Transpose = Transpose)
62: *> \endverbatim
63: *>
64: *> \param[in] N
65: *> \verbatim
66: *> N is INTEGER
67: *> The number of linear equations, i.e., the order of the
68: *> matrix A. N >= 0.
69: *> \endverbatim
70: *>
71: *> \param[in] A
72: *> \verbatim
73: *> A is DOUBLE PRECISION array, dimension (LDA,N)
74: *> On entry, the N-by-N matrix A.
75: *> \endverbatim
76: *>
77: *> \param[in] LDA
78: *> \verbatim
79: *> LDA is INTEGER
80: *> The leading dimension of the array A. LDA >= max(1,N).
81: *> \endverbatim
82: *>
83: *> \param[in] AF
84: *> \verbatim
85: *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
86: *> The factors L and U from the factorization
87: *> A = P*L*U as computed by DGETRF.
88: *> \endverbatim
89: *>
90: *> \param[in] LDAF
91: *> \verbatim
92: *> LDAF is INTEGER
93: *> The leading dimension of the array AF. LDAF >= max(1,N).
94: *> \endverbatim
95: *>
96: *> \param[in] IPIV
97: *> \verbatim
98: *> IPIV is INTEGER array, dimension (N)
99: *> The pivot indices from the factorization A = P*L*U
100: *> as computed by DGETRF; row i of the matrix was interchanged
101: *> with row IPIV(i).
102: *> \endverbatim
103: *>
104: *> \param[in] CMODE
105: *> \verbatim
106: *> CMODE is INTEGER
107: *> Determines op2(C) in the formula op(A) * op2(C) as follows:
108: *> CMODE = 1 op2(C) = C
109: *> CMODE = 0 op2(C) = I
110: *> CMODE = -1 op2(C) = inv(C)
111: *> \endverbatim
112: *>
113: *> \param[in] C
114: *> \verbatim
115: *> C is DOUBLE PRECISION array, dimension (N)
116: *> The vector C in the formula op(A) * op2(C).
117: *> \endverbatim
118: *>
119: *> \param[out] INFO
120: *> \verbatim
121: *> INFO is INTEGER
122: *> = 0: Successful exit.
123: *> i > 0: The ith argument is invalid.
124: *> \endverbatim
125: *>
126: *> \param[out] WORK
127: *> \verbatim
128: *> WORK is DOUBLE PRECISION array, dimension (3*N).
129: *> Workspace.
130: *> \endverbatim
131: *>
132: *> \param[out] IWORK
133: *> \verbatim
134: *> IWORK is INTEGER array, dimension (N).
135: *> Workspace.
136: *> \endverbatim
137: *
138: * Authors:
139: * ========
140: *
141: *> \author Univ. of Tennessee
142: *> \author Univ. of California Berkeley
143: *> \author Univ. of Colorado Denver
144: *> \author NAG Ltd.
145: *
146: *> \date December 2016
147: *
148: *> \ingroup doubleGEcomputational
149: *
150: * =====================================================================
151: DOUBLE PRECISION FUNCTION DLA_GERCOND ( TRANS, N, A, LDA, AF,
152: $ LDAF, IPIV, CMODE, C,
153: $ INFO, WORK, IWORK )
154: *
155: * -- LAPACK computational routine (version 3.7.0) --
156: * -- LAPACK is a software package provided by Univ. of Tennessee, --
157: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158: * December 2016
159: *
160: * .. Scalar Arguments ..
161: CHARACTER TRANS
162: INTEGER N, LDA, LDAF, INFO, CMODE
163: * ..
164: * .. Array Arguments ..
165: INTEGER IPIV( * ), IWORK( * )
166: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ),
167: $ C( * )
168: * ..
169: *
170: * =====================================================================
171: *
172: * .. Local Scalars ..
173: LOGICAL NOTRANS
174: INTEGER KASE, I, J
175: DOUBLE PRECISION AINVNM, TMP
176: * ..
177: * .. Local Arrays ..
178: INTEGER ISAVE( 3 )
179: * ..
180: * .. External Functions ..
181: LOGICAL LSAME
182: EXTERNAL LSAME
183: * ..
184: * .. External Subroutines ..
185: EXTERNAL DLACN2, DGETRS, XERBLA
186: * ..
187: * .. Intrinsic Functions ..
188: INTRINSIC ABS, MAX
189: * ..
190: * .. Executable Statements ..
191: *
192: DLA_GERCOND = 0.0D+0
193: *
194: INFO = 0
195: NOTRANS = LSAME( TRANS, 'N' )
196: IF ( .NOT. NOTRANS .AND. .NOT. LSAME(TRANS, 'T')
197: $ .AND. .NOT. LSAME(TRANS, 'C') ) THEN
198: INFO = -1
199: ELSE IF( N.LT.0 ) THEN
200: INFO = -2
201: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
202: INFO = -4
203: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
204: INFO = -6
205: END IF
206: IF( INFO.NE.0 ) THEN
207: CALL XERBLA( 'DLA_GERCOND', -INFO )
208: RETURN
209: END IF
210: IF( N.EQ.0 ) THEN
211: DLA_GERCOND = 1.0D+0
212: RETURN
213: END IF
214: *
215: * Compute the equilibration matrix R such that
216: * inv(R)*A*C has unit 1-norm.
217: *
218: IF (NOTRANS) THEN
219: DO I = 1, N
220: TMP = 0.0D+0
221: IF ( CMODE .EQ. 1 ) THEN
222: DO J = 1, N
223: TMP = TMP + ABS( A( I, J ) * C( J ) )
224: END DO
225: ELSE IF ( CMODE .EQ. 0 ) THEN
226: DO J = 1, N
227: TMP = TMP + ABS( A( I, J ) )
228: END DO
229: ELSE
230: DO J = 1, N
231: TMP = TMP + ABS( A( I, J ) / C( J ) )
232: END DO
233: END IF
234: WORK( 2*N+I ) = TMP
235: END DO
236: ELSE
237: DO I = 1, N
238: TMP = 0.0D+0
239: IF ( CMODE .EQ. 1 ) THEN
240: DO J = 1, N
241: TMP = TMP + ABS( A( J, I ) * C( J ) )
242: END DO
243: ELSE IF ( CMODE .EQ. 0 ) THEN
244: DO J = 1, N
245: TMP = TMP + ABS( A( J, I ) )
246: END DO
247: ELSE
248: DO J = 1, N
249: TMP = TMP + ABS( A( J, I ) / C( J ) )
250: END DO
251: END IF
252: WORK( 2*N+I ) = TMP
253: END DO
254: END IF
255: *
256: * Estimate the norm of inv(op(A)).
257: *
258: AINVNM = 0.0D+0
259:
260: KASE = 0
261: 10 CONTINUE
262: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
263: IF( KASE.NE.0 ) THEN
264: IF( KASE.EQ.2 ) THEN
265: *
266: * Multiply by R.
267: *
268: DO I = 1, N
269: WORK(I) = WORK(I) * WORK(2*N+I)
270: END DO
271:
272: IF (NOTRANS) THEN
273: CALL DGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
274: $ WORK, N, INFO )
275: ELSE
276: CALL DGETRS( 'Transpose', N, 1, AF, LDAF, IPIV,
277: $ WORK, N, INFO )
278: END IF
279: *
280: * Multiply by inv(C).
281: *
282: IF ( CMODE .EQ. 1 ) THEN
283: DO I = 1, N
284: WORK( I ) = WORK( I ) / C( I )
285: END DO
286: ELSE IF ( CMODE .EQ. -1 ) THEN
287: DO I = 1, N
288: WORK( I ) = WORK( I ) * C( I )
289: END DO
290: END IF
291: ELSE
292: *
293: * Multiply by inv(C**T).
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:
305: IF (NOTRANS) THEN
306: CALL DGETRS( 'Transpose', N, 1, AF, LDAF, IPIV,
307: $ WORK, N, INFO )
308: ELSE
309: CALL DGETRS( 'No transpose', 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 ) * WORK( 2*N+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: $ DLA_GERCOND = ( 1.0D+0 / AINVNM )
326: *
327: RETURN
328: *
329: END
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