forked from Reference-LAPACK/lapack
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathcgbequb.f
347 lines (347 loc) · 9.37 KB
/
cgbequb.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
342
343
344
345
346
347
*> \brief \b CGBEQUB
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CGBEQUB + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgbequb.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgbequb.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgbequb.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, KL, KU, LDAB, M, N
* REAL AMAX, COLCND, ROWCND
* ..
* .. Array Arguments ..
* REAL C( * ), R( * )
* COMPLEX AB( LDAB, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CGBEQUB computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> scale factors and C the column scale factors, chosen to try to make
*> the largest element in each row and column of the matrix B with
*> elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
*> the radix.
*>
*> R(i) and C(j) are restricted to be a power of the radix between
*> SMLNUM = smallest safe number and BIGNUM = largest safe number. Use
*> of these scaling factors is not guaranteed to reduce the condition
*> number of A but works well in practice.
*>
*> This routine differs from CGEEQU by restricting the scaling factors
*> to a power of the radix. Barring over- and underflow, scaling by
*> these factors introduces no additional rounding errors. However, the
*> scaled entries' magnitudes are no longer approximately 1 but lie
*> between sqrt(radix) and 1/sqrt(radix).
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns 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 A. LDAB >= max(1,M).
*> \endverbatim
*>
*> \param[out] R
*> \verbatim
*> R is REAL array, dimension (M)
*> If INFO = 0 or INFO > M, R contains the row scale factors
*> for A.
*> \endverbatim
*>
*> \param[out] C
*> \verbatim
*> C is REAL array, dimension (N)
*> If INFO = 0, C contains the column scale factors for A.
*> \endverbatim
*>
*> \param[out] ROWCND
*> \verbatim
*> ROWCND is REAL
*> If INFO = 0 or INFO > M, ROWCND contains the ratio of the
*> smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
*> AMAX is neither too large nor too small, it is not worth
*> scaling by R.
*> \endverbatim
*>
*> \param[out] COLCND
*> \verbatim
*> COLCND is REAL
*> If INFO = 0, COLCND contains the ratio of the smallest
*> C(i) to the largest C(i). If COLCND >= 0.1, it is not
*> worth scaling by C.
*> \endverbatim
*>
*> \param[out] AMAX
*> \verbatim
*> AMAX is REAL
*> Absolute value of largest matrix element. If AMAX is very
*> close to overflow or very close to underflow, the matrix
*> should be scaled.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, and i is
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexGBcomputational
*
* =====================================================================
SUBROUTINE CGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
$ AMAX, INFO )
*
* -- 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 ..
INTEGER INFO, KL, KU, LDAB, M, N
REAL AMAX, COLCND, ROWCND
* ..
* .. Array Arguments ..
REAL C( * ), R( * )
COMPLEX AB( LDAB, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, J, KD
REAL BIGNUM, RCMAX, RCMIN, SMLNUM, RADIX,
$ LOGRDX
COMPLEX ZDUM
* ..
* .. External Functions ..
REAL SLAMCH
EXTERNAL SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, LOG, REAL, AIMAG
* ..
* .. Statement Functions ..
REAL CABS1
* ..
* .. Statement Function definitions ..
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KL.LT.0 ) THEN
INFO = -3
ELSE IF( KU.LT.0 ) THEN
INFO = -4
ELSE IF( LDAB.LT.KL+KU+1 ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CGBEQUB', -INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( M.EQ.0 .OR. N.EQ.0 ) THEN
ROWCND = ONE
COLCND = ONE
AMAX = ZERO
RETURN
END IF
*
* Get machine constants. Assume SMLNUM is a power of the radix.
*
SMLNUM = SLAMCH( 'S' )
BIGNUM = ONE / SMLNUM
RADIX = SLAMCH( 'B' )
LOGRDX = LOG(RADIX)
*
* Compute row scale factors.
*
DO 10 I = 1, M
R( I ) = ZERO
10 CONTINUE
*
* Find the maximum element in each row.
*
KD = KU + 1
DO 30 J = 1, N
DO 20 I = MAX( J-KU, 1 ), MIN( J+KL, M )
R( I ) = MAX( R( I ), CABS1( AB( KD+I-J, J ) ) )
20 CONTINUE
30 CONTINUE
DO I = 1, M
IF( R( I ).GT.ZERO ) THEN
R( I ) = RADIX**INT( LOG( R( I ) ) / LOGRDX )
END IF
END DO
*
* Find the maximum and minimum scale factors.
*
RCMIN = BIGNUM
RCMAX = ZERO
DO 40 I = 1, M
RCMAX = MAX( RCMAX, R( I ) )
RCMIN = MIN( RCMIN, R( I ) )
40 CONTINUE
AMAX = RCMAX
*
IF( RCMIN.EQ.ZERO ) THEN
*
* Find the first zero scale factor and return an error code.
*
DO 50 I = 1, M
IF( R( I ).EQ.ZERO ) THEN
INFO = I
RETURN
END IF
50 CONTINUE
ELSE
*
* Invert the scale factors.
*
DO 60 I = 1, M
R( I ) = ONE / MIN( MAX( R( I ), SMLNUM ), BIGNUM )
60 CONTINUE
*
* Compute ROWCND = min(R(I)) / max(R(I)).
*
ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
END IF
*
* Compute column scale factors.
*
DO 70 J = 1, N
C( J ) = ZERO
70 CONTINUE
*
* Find the maximum element in each column,
* assuming the row scaling computed above.
*
DO 90 J = 1, N
DO 80 I = MAX( J-KU, 1 ), MIN( J+KL, M )
C( J ) = MAX( C( J ), CABS1( AB( KD+I-J, J ) )*R( I ) )
80 CONTINUE
IF( C( J ).GT.ZERO ) THEN
C( J ) = RADIX**INT( LOG( C( J ) ) / LOGRDX )
END IF
90 CONTINUE
*
* Find the maximum and minimum scale factors.
*
RCMIN = BIGNUM
RCMAX = ZERO
DO 100 J = 1, N
RCMIN = MIN( RCMIN, C( J ) )
RCMAX = MAX( RCMAX, C( J ) )
100 CONTINUE
*
IF( RCMIN.EQ.ZERO ) THEN
*
* Find the first zero scale factor and return an error code.
*
DO 110 J = 1, N
IF( C( J ).EQ.ZERO ) THEN
INFO = M + J
RETURN
END IF
110 CONTINUE
ELSE
*
* Invert the scale factors.
*
DO 120 J = 1, N
C( J ) = ONE / MIN( MAX( C( J ), SMLNUM ), BIGNUM )
120 CONTINUE
*
* Compute COLCND = min(C(J)) / max(C(J)).
*
COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
END IF
*
RETURN
*
* End of CGBEQUB
*
END