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
|
*> \brief \b SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SLAQSB + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slaqsb.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slaqsb.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaqsb.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
*
* .. Scalar Arguments ..
* CHARACTER EQUED, UPLO
* INTEGER KD, LDAB, N
* REAL AMAX, SCOND
* ..
* .. Array Arguments ..
* REAL AB( LDAB, * ), S( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SLAQSB equilibrates a symmetric band matrix A using the scaling
*> factors in the vector S.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the upper or lower triangular part of the
*> symmetric matrix A is stored.
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] KD
*> \verbatim
*> KD is INTEGER
*> The number of super-diagonals of the matrix A if UPLO = 'U',
*> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
*> \endverbatim
*>
*> \param[in,out] AB
*> \verbatim
*> AB is REAL array, dimension (LDAB,N)
*> On entry, the upper or lower triangle of the symmetric band
*> matrix A, stored in the first KD+1 rows of the array. The
*> j-th column of A is stored in the j-th column of the array AB
*> as follows:
*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
*>
*> On exit, if INFO = 0, the triangular factor U or L from the
*> Cholesky factorization A = U**T*U or A = L*L**T of the band
*> matrix A, in the same storage format as A.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KD+1.
*> \endverbatim
*>
*> \param[in] S
*> \verbatim
*> S is REAL array, dimension (N)
*> The scale factors for A.
*> \endverbatim
*>
*> \param[in] SCOND
*> \verbatim
*> SCOND is REAL
*> Ratio of the smallest S(i) to the largest S(i).
*> \endverbatim
*>
*> \param[in] AMAX
*> \verbatim
*> AMAX is REAL
*> Absolute value of largest matrix entry.
*> \endverbatim
*>
*> \param[out] EQUED
*> \verbatim
*> EQUED is CHARACTER*1
*> Specifies whether or not equilibration was done.
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
*> \endverbatim
*
*> \par Internal Parameters:
* =========================
*>
*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*>
*> LARGE and SMALL are threshold values used to decide if scaling should
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup realOTHERauxiliary
*
* =====================================================================
SUBROUTINE SLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
*
* -- LAPACK auxiliary routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
CHARACTER EQUED, UPLO
INTEGER KD, LDAB, N
REAL AMAX, SCOND
* ..
* .. Array Arguments ..
REAL AB( LDAB, * ), S( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, THRESH
PARAMETER ( ONE = 1.0E+0, THRESH = 0.1E+0 )
* ..
* .. Local Scalars ..
INTEGER I, J
REAL CJ, LARGE, SMALL
* ..
* .. External Functions ..
LOGICAL LSAME
REAL SLAMCH
EXTERNAL LSAME, SLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.LE.0 ) THEN
EQUED = 'N'
RETURN
END IF
*
* Initialize LARGE and SMALL.
*
SMALL = SLAMCH( 'Safe minimum' ) / SLAMCH( 'Precision' )
LARGE = ONE / SMALL
*
IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
*
* No equilibration
*
EQUED = 'N'
ELSE
*
* Replace A by diag(S) * A * diag(S).
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Upper triangle of A is stored in band format.
*
DO 20 J = 1, N
CJ = S( J )
DO 10 I = MAX( 1, J-KD ), J
AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J )
10 CONTINUE
20 CONTINUE
ELSE
*
* Lower triangle of A is stored.
*
DO 40 J = 1, N
CJ = S( J )
DO 30 I = J, MIN( N, J+KD )
AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J )
30 CONTINUE
40 CONTINUE
END IF
EQUED = 'Y'
END IF
*
RETURN
*
* End of SLAQSB
*
END
|
