-
Notifications
You must be signed in to change notification settings - Fork 0
/
cgbtf2.f
277 lines (277 loc) · 7.93 KB
/
cgbtf2.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
*> \brief \b CGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CGBTF2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgbtf2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgbtf2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgbtf2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, KL, KU, LDAB, M, N
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* COMPLEX AB( LDAB, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CGBTF2 computes an LU factorization of a complex m-by-n band matrix
*> A using partial pivoting with row interchanges.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
*> \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,out] AB
*> \verbatim
*> AB is COMPLEX array, dimension (LDAB,N)
*> On entry, the matrix A in band storage, in rows KL+1 to
*> 2*KL+KU+1; rows 1 to KL of the array need not be set.
*> The j-th column of A is stored in the j-th column of the
*> array AB as follows:
*> AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
*>
*> On exit, details of the factorization: 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.
*> See below for further details.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
*> \endverbatim
*>
*> \param[out] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (min(M,N))
*> The pivot indices; for 1 <= i <= min(M,N), row i of the
*> matrix was interchanged with row IPIV(i).
*> \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, U(i,i) is exactly zero. The factorization
*> has been completed, but the factor U is exactly
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complexGBcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> M = N = 6, KL = 2, KU = 1:
*>
*> On entry: On exit:
*>
*> * * * + + + * * * u14 u25 u36
*> * * + + + + * * u13 u24 u35 u46
*> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
*> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
*> a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
*> a31 a42 a53 a64 * * m31 m42 m53 m64 * *
*>
*> Array elements marked * are not used by the routine; elements marked
*> + need not be set on entry, but are required by the routine to store
*> elements of U, because of fill-in resulting from the row
*> interchanges.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE CGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER INFO, KL, KU, LDAB, M, N
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX AB( LDAB, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE, ZERO
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
$ ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, J, JP, JU, KM, KV
* ..
* .. External Functions ..
INTEGER ICAMAX
EXTERNAL ICAMAX
* ..
* .. External Subroutines ..
EXTERNAL CGERU, CSCAL, CSWAP, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* KV is the number of superdiagonals in the factor U, allowing for
* fill-in.
*
KV = KU + KL
*
* 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+KV+1 ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CGBTF2', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 )
$ RETURN
*
* Gaussian elimination with partial pivoting
*
* Set fill-in elements in columns KU+2 to KV to zero.
*
DO 20 J = KU + 2, MIN( KV, N )
DO 10 I = KV - J + 2, KL
AB( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
*
* JU is the index of the last column affected by the current stage
* of the factorization.
*
JU = 1
*
DO 40 J = 1, MIN( M, N )
*
* Set fill-in elements in column J+KV to zero.
*
IF( J+KV.LE.N ) THEN
DO 30 I = 1, KL
AB( I, J+KV ) = ZERO
30 CONTINUE
END IF
*
* Find pivot and test for singularity. KM is the number of
* subdiagonal elements in the current column.
*
KM = MIN( KL, M-J )
JP = ICAMAX( KM+1, AB( KV+1, J ), 1 )
IPIV( J ) = JP + J - 1
IF( AB( KV+JP, J ).NE.ZERO ) THEN
JU = MAX( JU, MIN( J+KU+JP-1, N ) )
*
* Apply interchange to columns J to JU.
*
IF( JP.NE.1 )
$ CALL CSWAP( JU-J+1, AB( KV+JP, J ), LDAB-1,
$ AB( KV+1, J ), LDAB-1 )
IF( KM.GT.0 ) THEN
*
* Compute multipliers.
*
CALL CSCAL( KM, ONE / AB( KV+1, J ), AB( KV+2, J ), 1 )
*
* Update trailing submatrix within the band.
*
IF( JU.GT.J )
$ CALL CGERU( KM, JU-J, -ONE, AB( KV+2, J ), 1,
$ AB( KV, J+1 ), LDAB-1, AB( KV+1, J+1 ),
$ LDAB-1 )
END IF
ELSE
*
* If pivot is zero, set INFO to the index of the pivot
* unless a zero pivot has already been found.
*
IF( INFO.EQ.0 )
$ INFO = J
END IF
40 CONTINUE
RETURN
*
* End of CGBTF2
*
END