LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
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 *
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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 = 'Y': Equilibration was done, i.e., A has been replaced by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 *> \date September 2012
122 *
123 *> \ingroup realOTHERauxiliary
124 *
125 * =====================================================================
126  SUBROUTINE slaqsp( UPLO, N, AP, S, SCOND, AMAX, EQUED )
127 *
128 * -- LAPACK auxiliary routine (version 3.4.2) --
129 * -- LAPACK is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 * September 2012
132 *
133 * .. Scalar Arguments ..
134  CHARACTER EQUED, UPLO
135  INTEGER N
136  REAL AMAX, SCOND
137 * ..
138 * .. Array Arguments ..
139  REAL AP( * ), S( * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  REAL ONE, THRESH
146  parameter ( one = 1.0e+0, thresh = 0.1e+0 )
147 * ..
148 * .. Local Scalars ..
149  INTEGER I, J, JC
150  REAL CJ, LARGE, SMALL
151 * ..
152 * .. External Functions ..
153  LOGICAL LSAME
154  REAL SLAMCH
155  EXTERNAL lsame, slamch
156 * ..
157 * .. Executable Statements ..
158 *
159 * Quick return if possible
160 *
161  IF( n.LE.0 ) THEN
162  equed = 'N'
163  RETURN
164  END IF
165 *
166 * Initialize LARGE and SMALL.
167 *
168  small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
169  large = one / small
170 *
171  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
172 *
173 * No equilibration
174 *
175  equed = 'N'
176  ELSE
177 *
178 * Replace A by diag(S) * A * diag(S).
179 *
180  IF( lsame( uplo, 'U' ) ) THEN
181 *
182 * Upper triangle of A is stored.
183 *
184  jc = 1
185  DO 20 j = 1, n
186  cj = s( j )
187  DO 10 i = 1, j
188  ap( jc+i-1 ) = cj*s( i )*ap( jc+i-1 )
189  10 CONTINUE
190  jc = jc + j
191  20 CONTINUE
192  ELSE
193 *
194 * Lower triangle of A is stored.
195 *
196  jc = 1
197  DO 40 j = 1, n
198  cj = s( j )
199  DO 30 i = j, n
200  ap( jc+i-j ) = cj*s( i )*ap( jc+i-j )
201  30 CONTINUE
202  jc = jc + n - j + 1
203  40 CONTINUE
204  END IF
205  equed = 'Y'
206  END IF
207 *
208  RETURN
209 *
210 * End of SLAQSP
211 *
212  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:127