forked from Reference-LAPACK/lapack
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathcla_gbrcond_c.f
341 lines (341 loc) · 9.38 KB
/
cla_gbrcond_c.f
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
*> \brief \b CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CLA_GBRCOND_C + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_gbrcond_c.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_gbrcond_c.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_gbrcond_c.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* REAL FUNCTION CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB,
* LDAFB, IPIV, C, CAPPLY, INFO, WORK,
* RWORK )
*
* .. Scalar Arguments ..
* CHARACTER TRANS
* LOGICAL CAPPLY
* INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
* REAL C( * ), RWORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLA_GBRCOND_C Computes the infinity norm condition number of
*> op(A) * inv(diag(C)) where C is a REAL vector.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> Specifies the form of the system of equations:
*> = 'N': A * X = B (No transpose)
*> = 'T': A**T * X = B (Transpose)
*> = 'C': A**H * X = B (Conjugate Transpose = Transpose)
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of linear equations, i.e., the order of the
*> matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*> KL is INTEGER
*> The number of subdiagonals within the band of A. KL >= 0.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*> KU is INTEGER
*> The number of superdiagonals within the band of A. KU >= 0.
*> \endverbatim
*>
*> \param[in] AB
*> \verbatim
*> AB is COMPLEX array, dimension (LDAB,N)
*> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
*> The j-th column of A is stored in the j-th column of the
*> array AB as follows:
*> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KL+KU+1.
*> \endverbatim
*>
*> \param[in] AFB
*> \verbatim
*> AFB is COMPLEX array, dimension (LDAFB,N)
*> Details of the LU factorization of the band matrix A, as
*> computed by CGBTRF. U is stored as an upper triangular
*> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
*> and the multipliers used during the factorization are stored
*> in rows KL+KU+2 to 2*KL+KU+1.
*> \endverbatim
*>
*> \param[in] LDAFB
*> \verbatim
*> LDAFB is INTEGER
*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> The pivot indices from the factorization A = P*L*U
*> as computed by CGBTRF; row i of the matrix was interchanged
*> with row IPIV(i).
*> \endverbatim
*>
*> \param[in] C
*> \verbatim
*> C is REAL array, dimension (N)
*> The vector C in the formula op(A) * inv(diag(C)).
*> \endverbatim
*>
*> \param[in] CAPPLY
*> \verbatim
*> CAPPLY is LOGICAL
*> If .TRUE. then access the vector C in the formula above.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: Successful exit.
*> i > 0: The ith argument is invalid.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (2*N).
*> Workspace.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexGBcomputational
*
* =====================================================================
REAL FUNCTION CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB,
$ LDAFB, IPIV, C, CAPPLY, INFO, WORK,
$ RWORK )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER TRANS
LOGICAL CAPPLY
INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
REAL C( * ), RWORK( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL NOTRANS
INTEGER KASE, I, J
REAL AINVNM, ANORM, TMP
COMPLEX ZDUM
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CLACN2, CGBTRS, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX
* ..
* .. Statement Functions ..
REAL CABS1
* ..
* .. Statement Function Definitions ..
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
CLA_GBRCOND_C = 0.0E+0
*
INFO = 0
NOTRANS = LSAME( TRANS, 'N' )
IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
$ LSAME( TRANS, 'C' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN
INFO = -3
ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
INFO = -4
ELSE IF( LDAB.LT.KL+KU+1 ) THEN
INFO = -6
ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CLA_GBRCOND_C', -INFO )
RETURN
END IF
*
* Compute norm of op(A)*op2(C).
*
ANORM = 0.0E+0
KD = KU + 1
KE = KL + 1
IF ( NOTRANS ) THEN
DO I = 1, N
TMP = 0.0E+0
IF ( CAPPLY ) THEN
DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
TMP = TMP + CABS1( AB( KD+I-J, J ) ) / C( J )
END DO
ELSE
DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
TMP = TMP + CABS1( AB( KD+I-J, J ) )
END DO
END IF
RWORK( I ) = TMP
ANORM = MAX( ANORM, TMP )
END DO
ELSE
DO I = 1, N
TMP = 0.0E+0
IF ( CAPPLY ) THEN
DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
TMP = TMP + CABS1( AB( KE-I+J, I ) ) / C( J )
END DO
ELSE
DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
TMP = TMP + CABS1( AB( KE-I+J, I ) )
END DO
END IF
RWORK( I ) = TMP
ANORM = MAX( ANORM, TMP )
END DO
END IF
*
* Quick return if possible.
*
IF( N.EQ.0 ) THEN
CLA_GBRCOND_C = 1.0E+0
RETURN
ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
RETURN
END IF
*
* Estimate the norm of inv(op(A)).
*
AINVNM = 0.0E+0
*
KASE = 0
10 CONTINUE
CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( KASE.EQ.2 ) THEN
*
* Multiply by R.
*
DO I = 1, N
WORK( I ) = WORK( I ) * RWORK( I )
END DO
*
IF ( NOTRANS ) THEN
CALL CGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
$ IPIV, WORK, N, INFO )
ELSE
CALL CGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
$ LDAFB, IPIV, WORK, N, INFO )
ENDIF
*
* Multiply by inv(C).
*
IF ( CAPPLY ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) * C( I )
END DO
END IF
ELSE
*
* Multiply by inv(C**H).
*
IF ( CAPPLY ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) * C( I )
END DO
END IF
*
IF ( NOTRANS ) THEN
CALL CGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
$ LDAFB, IPIV, WORK, N, INFO )
ELSE
CALL CGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
$ IPIV, WORK, N, INFO )
END IF
*
* Multiply by R.
*
DO I = 1, N
WORK( I ) = WORK( I ) * RWORK( I )
END DO
END IF
GO TO 10
END IF
*
* Compute the estimate of the reciprocal condition number.
*
IF( AINVNM .NE. 0.0E+0 )
$ CLA_GBRCOND_C = 1.0E+0 / AINVNM
*
RETURN
*
* End of CLA_GBRCOND_C
*
END