LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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slaqsy.f
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1*> \brief \b SLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaqsy.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
22*
23* .. Scalar Arguments ..
24* CHARACTER EQUED, UPLO
25* INTEGER LDA, N
26* REAL AMAX, SCOND
27* ..
28* .. Array Arguments ..
29* REAL A( LDA, * ), S( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> SLAQSY equilibrates a symmetric matrix A using the scaling factors
39*> 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,out] A
61*> \verbatim
62*> A is REAL array, dimension (LDA,N)
63*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
64*> n by n upper triangular part of A contains the upper
65*> triangular part of the matrix A, and the strictly lower
66*> triangular part of A is not referenced. If UPLO = 'L', the
67*> leading n by n lower triangular part of A contains the lower
68*> triangular part of the matrix A, and the strictly upper
69*> triangular part of A is not referenced.
70*>
71*> On exit, if EQUED = 'Y', the equilibrated matrix:
72*> diag(S) * A * diag(S).
73*> \endverbatim
74*>
75*> \param[in] LDA
76*> \verbatim
77*> LDA is INTEGER
78*> The leading dimension of the array A. LDA >= max(N,1).
79*> \endverbatim
80*>
81*> \param[in] S
82*> \verbatim
83*> S is REAL array, dimension (N)
84*> The scale factors for A.
85*> \endverbatim
86*>
87*> \param[in] SCOND
88*> \verbatim
89*> SCOND is REAL
90*> Ratio of the smallest S(i) to the largest S(i).
91*> \endverbatim
92*>
93*> \param[in] AMAX
94*> \verbatim
95*> AMAX is REAL
96*> Absolute value of largest matrix entry.
97*> \endverbatim
98*>
99*> \param[out] EQUED
100*> \verbatim
101*> EQUED is CHARACTER*1
102*> Specifies whether or not equilibration was done.
103*> = 'N': No equilibration.
104*> = 'Y': Equilibration was done, i.e., A has been replaced by
105*> diag(S) * A * diag(S).
106*> \endverbatim
107*
108*> \par Internal Parameters:
109* =========================
110*>
111*> \verbatim
112*> THRESH is a threshold value used to decide if scaling should be done
113*> based on the ratio of the scaling factors. If SCOND < THRESH,
114*> scaling is done.
115*>
116*> LARGE and SMALL are threshold values used to decide if scaling should
117*> be done based on the absolute size of the largest matrix element.
118*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
119*> \endverbatim
120*
121* Authors:
122* ========
123*
124*> \author Univ. of Tennessee
125*> \author Univ. of California Berkeley
126*> \author Univ. of Colorado Denver
127*> \author NAG Ltd.
128*
129*> \ingroup realSYauxiliary
130*
131* =====================================================================
132 SUBROUTINE slaqsy( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
133*
134* -- LAPACK auxiliary routine --
135* -- LAPACK is a software package provided by Univ. of Tennessee, --
136* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137*
138* .. Scalar Arguments ..
139 CHARACTER EQUED, UPLO
140 INTEGER LDA, N
141 REAL AMAX, SCOND
142* ..
143* .. Array Arguments ..
144 REAL A( LDA, * ), S( * )
145* ..
146*
147* =====================================================================
148*
149* .. Parameters ..
150 REAL ONE, THRESH
151 parameter( one = 1.0e+0, thresh = 0.1e+0 )
152* ..
153* .. Local Scalars ..
154 INTEGER I, J
155 REAL CJ, LARGE, SMALL
156* ..
157* .. External Functions ..
158 LOGICAL LSAME
159 REAL SLAMCH
160 EXTERNAL lsame, slamch
161* ..
162* .. Executable Statements ..
163*
164* Quick return if possible
165*
166 IF( n.LE.0 ) THEN
167 equed = 'N'
168 RETURN
169 END IF
170*
171* Initialize LARGE and SMALL.
172*
173 small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
174 large = one / small
175*
176 IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
177*
178* No equilibration
179*
180 equed = 'N'
181 ELSE
182*
183* Replace A by diag(S) * A * diag(S).
184*
185 IF( lsame( uplo, 'U' ) ) THEN
186*
187* Upper triangle of A is stored.
188*
189 DO 20 j = 1, n
190 cj = s( j )
191 DO 10 i = 1, j
192 a( i, j ) = cj*s( i )*a( i, j )
193 10 CONTINUE
194 20 CONTINUE
195 ELSE
196*
197* Lower triangle of A is stored.
198*
199 DO 40 j = 1, n
200 cj = s( j )
201 DO 30 i = j, n
202 a( i, j ) = cj*s( i )*a( i, j )
203 30 CONTINUE
204 40 CONTINUE
205 END IF
206 equed = 'Y'
207 END IF
208*
209 RETURN
210*
211* End of SLAQSY
212*
213 END
subroutine slaqsy(UPLO, N, A, LDA, S, SCOND, AMAX, EQUED)
SLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
Definition: slaqsy.f:133