1: *> \brief \b ZLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general 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_GERCOND_X + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gercond_x.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gercond_x.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gercond_x.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLA_GERCOND_X( TRANS, N, A, LDA, AF,
22: * LDAF, IPIV, X, INFO,
23: * WORK, RWORK )
24: *
25: * .. Scalar Arguments ..
26: * CHARACTER TRANS
27: * INTEGER N, LDA, LDAF, INFO
28: * ..
29: * .. Array Arguments ..
30: * INTEGER IPIV( * )
31: * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
32: * DOUBLE PRECISION RWORK( * )
33: * ..
34: *
35: *
36: *> \par Purpose:
37: * =============
38: *>
39: *> \verbatim
40: *>
41: *> ZLA_GERCOND_X computes the infinity norm condition number of
42: *> op(A) * diag(X) where X is a COMPLEX*16 vector.
43: *> \endverbatim
44: *
45: * Arguments:
46: * ==========
47: *
48: *> \param[in] TRANS
49: *> \verbatim
50: *> TRANS is CHARACTER*1
51: *> Specifies the form of the system of equations:
52: *> = 'N': A * X = B (No transpose)
53: *> = 'T': A**T * X = B (Transpose)
54: *> = 'C': A**H * X = B (Conjugate Transpose = Transpose)
55: *> \endverbatim
56: *>
57: *> \param[in] N
58: *> \verbatim
59: *> N is INTEGER
60: *> The number of linear equations, i.e., the order of the
61: *> matrix A. N >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in] A
65: *> \verbatim
66: *> A is COMPLEX*16 array, dimension (LDA,N)
67: *> On entry, the N-by-N matrix A.
68: *> \endverbatim
69: *>
70: *> \param[in] LDA
71: *> \verbatim
72: *> LDA is INTEGER
73: *> The leading dimension of the array A. LDA >= max(1,N).
74: *> \endverbatim
75: *>
76: *> \param[in] AF
77: *> \verbatim
78: *> AF is COMPLEX*16 array, dimension (LDAF,N)
79: *> The factors L and U from the factorization
80: *> A = P*L*U as computed by ZGETRF.
81: *> \endverbatim
82: *>
83: *> \param[in] LDAF
84: *> \verbatim
85: *> LDAF is INTEGER
86: *> The leading dimension of the array AF. LDAF >= max(1,N).
87: *> \endverbatim
88: *>
89: *> \param[in] IPIV
90: *> \verbatim
91: *> IPIV is INTEGER array, dimension (N)
92: *> The pivot indices from the factorization A = P*L*U
93: *> as computed by ZGETRF; row i of the matrix was interchanged
94: *> with row IPIV(i).
95: *> \endverbatim
96: *>
97: *> \param[in] X
98: *> \verbatim
99: *> X is COMPLEX*16 array, dimension (N)
100: *> The vector X in the formula op(A) * diag(X).
101: *> \endverbatim
102: *>
103: *> \param[out] INFO
104: *> \verbatim
105: *> INFO is INTEGER
106: *> = 0: Successful exit.
107: *> i > 0: The ith argument is invalid.
108: *> \endverbatim
109: *>
110: *> \param[out] WORK
111: *> \verbatim
112: *> WORK is COMPLEX*16 array, dimension (2*N).
113: *> Workspace.
114: *> \endverbatim
115: *>
116: *> \param[out] RWORK
117: *> \verbatim
118: *> RWORK is DOUBLE PRECISION array, dimension (N).
119: *> Workspace.
120: *> \endverbatim
121: *
122: * Authors:
123: * ========
124: *
125: *> \author Univ. of Tennessee
126: *> \author Univ. of California Berkeley
127: *> \author Univ. of Colorado Denver
128: *> \author NAG Ltd.
129: *
130: *> \ingroup complex16GEcomputational
131: *
132: * =====================================================================
133: DOUBLE PRECISION FUNCTION ZLA_GERCOND_X( TRANS, N, A, LDA, AF,
134: $ LDAF, IPIV, X, INFO,
135: $ WORK, RWORK )
136: *
137: * -- LAPACK computational routine --
138: * -- LAPACK is a software package provided by Univ. of Tennessee, --
139: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140: *
141: * .. Scalar Arguments ..
142: CHARACTER TRANS
143: INTEGER N, LDA, LDAF, INFO
144: * ..
145: * .. Array Arguments ..
146: INTEGER IPIV( * )
147: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
148: DOUBLE PRECISION RWORK( * )
149: * ..
150: *
151: * =====================================================================
152: *
153: * .. Local Scalars ..
154: LOGICAL NOTRANS
155: INTEGER KASE
156: DOUBLE PRECISION AINVNM, ANORM, TMP
157: INTEGER I, J
158: COMPLEX*16 ZDUM
159: * ..
160: * .. Local Arrays ..
161: INTEGER ISAVE( 3 )
162: * ..
163: * .. External Functions ..
164: LOGICAL LSAME
165: EXTERNAL LSAME
166: * ..
167: * .. External Subroutines ..
168: EXTERNAL ZLACN2, ZGETRS, XERBLA
169: * ..
170: * .. Intrinsic Functions ..
171: INTRINSIC ABS, MAX, REAL, DIMAG
172: * ..
173: * .. Statement Functions ..
174: DOUBLE PRECISION CABS1
175: * ..
176: * .. Statement Function Definitions ..
177: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
178: * ..
179: * .. Executable Statements ..
180: *
181: ZLA_GERCOND_X = 0.0D+0
182: *
183: INFO = 0
184: NOTRANS = LSAME( TRANS, 'N' )
185: IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
186: $ LSAME( TRANS, 'C' ) ) THEN
187: INFO = -1
188: ELSE IF( N.LT.0 ) THEN
189: INFO = -2
190: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
191: INFO = -4
192: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
193: INFO = -6
194: END IF
195: IF( INFO.NE.0 ) THEN
196: CALL XERBLA( 'ZLA_GERCOND_X', -INFO )
197: RETURN
198: END IF
199: *
200: * Compute norm of op(A)*op2(C).
201: *
202: ANORM = 0.0D+0
203: IF ( NOTRANS ) THEN
204: DO I = 1, N
205: TMP = 0.0D+0
206: DO J = 1, N
207: TMP = TMP + CABS1( A( I, J ) * X( J ) )
208: END DO
209: RWORK( I ) = TMP
210: ANORM = MAX( ANORM, TMP )
211: END DO
212: ELSE
213: DO I = 1, N
214: TMP = 0.0D+0
215: DO J = 1, N
216: TMP = TMP + CABS1( A( J, I ) * X( J ) )
217: END DO
218: RWORK( I ) = TMP
219: ANORM = MAX( ANORM, TMP )
220: END DO
221: END IF
222: *
223: * Quick return if possible.
224: *
225: IF( N.EQ.0 ) THEN
226: ZLA_GERCOND_X = 1.0D+0
227: RETURN
228: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
229: RETURN
230: END IF
231: *
232: * Estimate the norm of inv(op(A)).
233: *
234: AINVNM = 0.0D+0
235: *
236: KASE = 0
237: 10 CONTINUE
238: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
239: IF( KASE.NE.0 ) THEN
240: IF( KASE.EQ.2 ) THEN
241: * Multiply by R.
242: DO I = 1, N
243: WORK( I ) = WORK( I ) * RWORK( I )
244: END DO
245: *
246: IF ( NOTRANS ) THEN
247: CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
248: $ WORK, N, INFO )
249: ELSE
250: CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
251: $ WORK, N, INFO )
252: ENDIF
253: *
254: * Multiply by inv(X).
255: *
256: DO I = 1, N
257: WORK( I ) = WORK( I ) / X( I )
258: END DO
259: ELSE
260: *
261: * Multiply by inv(X**H).
262: *
263: DO I = 1, N
264: WORK( I ) = WORK( I ) / X( I )
265: END DO
266: *
267: IF ( NOTRANS ) THEN
268: CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
269: $ WORK, N, INFO )
270: ELSE
271: CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
272: $ WORK, N, INFO )
273: END IF
274: *
275: * Multiply by R.
276: *
277: DO I = 1, N
278: WORK( I ) = WORK( I ) * RWORK( I )
279: END DO
280: END IF
281: GO TO 10
282: END IF
283: *
284: * Compute the estimate of the reciprocal condition number.
285: *
286: IF( AINVNM .NE. 0.0D+0 )
287: $ ZLA_GERCOND_X = 1.0D+0 / AINVNM
288: *
289: RETURN
290: *
291: * End of ZLA_GERCOND_X
292: *
293: END
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