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 = 'Y': Equilibration was done, i.e., A has been replaced by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