LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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slaqsb.f
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1*> \brief \b SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slaqsb.f">
11*> [TGZ]</a>
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaqsb.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
22*
23* .. Scalar Arguments ..
24* CHARACTER EQUED, UPLO
25* INTEGER KD, LDAB, N
26* REAL AMAX, SCOND
27* ..
28* .. Array Arguments ..
29* REAL AB( LDAB, * ), S( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> SLAQSB equilibrates a symmetric band matrix A using the scaling
39*> factors in the vector S.
40*> \endverbatim
41*
42* Arguments:
43* ==========
44*
45*> \param[in] UPLO
46*> \verbatim
47*> UPLO is CHARACTER*1
48*> Specifies whether the upper or lower triangular part of the
49*> symmetric matrix A is stored.
50*> = 'U': Upper triangular
51*> = 'L': Lower triangular
52*> \endverbatim
53*>
54*> \param[in] N
55*> \verbatim
56*> N is INTEGER
57*> The order of the matrix A. N >= 0.
58*> \endverbatim
59*>
60*> \param[in] KD
61*> \verbatim
62*> KD is INTEGER
63*> The number of super-diagonals of the matrix A if UPLO = 'U',
64*> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
65*> \endverbatim
66*>
67*> \param[in,out] AB
68*> \verbatim
69*> AB is REAL array, dimension (LDAB,N)
70*> On entry, the upper or lower triangle of the symmetric band
71*> matrix A, stored in the first KD+1 rows of the array. The
72*> j-th column of A is stored in the j-th column of the array AB
73*> as follows:
74*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
75*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
76*>
77*> On exit, if INFO = 0, the triangular factor U or L from the
78*> Cholesky factorization A = U**T*U or A = L*L**T of the band
79*> matrix A, in the same storage format as A.
80*> \endverbatim
81*>
82*> \param[in] LDAB
83*> \verbatim
84*> LDAB is INTEGER
85*> The leading dimension of the array AB. LDAB >= KD+1.
86*> \endverbatim
87*>
88*> \param[in] S
89*> \verbatim
90*> S is REAL array, dimension (N)
91*> The scale factors for A.
92*> \endverbatim
93*>
94*> \param[in] SCOND
95*> \verbatim
96*> SCOND is REAL
97*> Ratio of the smallest S(i) to the largest S(i).
98*> \endverbatim
99*>
100*> \param[in] AMAX
101*> \verbatim
102*> AMAX is REAL
103*> Absolute value of largest matrix entry.
104*> \endverbatim
105*>
106*> \param[out] EQUED
107*> \verbatim
108*> EQUED is CHARACTER*1
109*> Specifies whether or not equilibration was done.
110*> = 'N': No equilibration.
111*> = 'Y': Equilibration was done, i.e., A has been replaced by
112*> diag(S) * A * diag(S).
113*> \endverbatim
114*
115*> \par Internal Parameters:
116* =========================
117*>
118*> \verbatim
119*> THRESH is a threshold value used to decide if scaling should be done
120*> based on the ratio of the scaling factors. If SCOND < THRESH,
121*> scaling is done.
122*>
123*> LARGE and SMALL are threshold values used to decide if scaling should
124*> be done based on the absolute size of the largest matrix element.
125*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
126*> \endverbatim
127*
128* Authors:
129* ========
130*
131*> \author Univ. of Tennessee
132*> \author Univ. of California Berkeley
133*> \author Univ. of Colorado Denver
134*> \author NAG Ltd.
135*
136*> \ingroup laqhb
137*
138* =====================================================================
139 SUBROUTINE slaqsb( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
140*
141* -- LAPACK auxiliary routine --
142* -- LAPACK is a software package provided by Univ. of Tennessee, --
143* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144*
145* .. Scalar Arguments ..
146 CHARACTER EQUED, UPLO
147 INTEGER KD, LDAB, N
148 REAL AMAX, SCOND
149* ..
150* .. Array Arguments ..
151 REAL AB( LDAB, * ), S( * )
152* ..
153*
154* =====================================================================
155*
156* .. Parameters ..
157 REAL ONE, THRESH
158 parameter( one = 1.0e+0, thresh = 0.1e+0 )
159* ..
160* .. Local Scalars ..
161 INTEGER I, J
162 REAL CJ, LARGE, SMALL
163* ..
164* .. External Functions ..
165 LOGICAL LSAME
166 REAL SLAMCH
167 EXTERNAL lsame, slamch
168* ..
169* .. Intrinsic Functions ..
170 INTRINSIC max, min
171* ..
172* .. Executable Statements ..
173*
174* Quick return if possible
175*
176 IF( n.LE.0 ) THEN
177 equed = 'N'
178 RETURN
179 END IF
180*
181* Initialize LARGE and SMALL.
182*
183 small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
184 large = one / small
185*
186 IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
187*
188* No equilibration
189*
190 equed = 'N'
191 ELSE
192*
193* Replace A by diag(S) * A * diag(S).
194*
195 IF( lsame( uplo, 'U' ) ) THEN
196*
197* Upper triangle of A is stored in band format.
198*
199 DO 20 j = 1, n
200 cj = s( j )
201 DO 10 i = max( 1, j-kd ), j
202 ab( kd+1+i-j, j ) = cj*s( i )*ab( kd+1+i-j, j )
203 10 CONTINUE
204 20 CONTINUE
205 ELSE
206*
207* Lower triangle of A is stored.
208*
209 DO 40 j = 1, n
210 cj = s( j )
211 DO 30 i = j, min( n, j+kd )
212 ab( 1+i-j, j ) = cj*s( i )*ab( 1+i-j, j )
213 30 CONTINUE
214 40 CONTINUE
215 END IF
216 equed = 'Y'
217 END IF
218*
219 RETURN
220*
221* End of SLAQSB
222*
223 END
subroutine slaqsb(uplo, n, kd, ab, ldab, s, scond, amax, equed)
SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
Definition slaqsb.f:140