LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
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 *
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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 *> \date September 2012
130 *
131 *> \ingroup realSYauxiliary
132 *
133 * =====================================================================
134  SUBROUTINE slaqsy( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
135 *
136 * -- LAPACK auxiliary routine (version 3.4.2) --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 * September 2012
140 *
141 * .. Scalar Arguments ..
142  CHARACTER EQUED, UPLO
143  INTEGER LDA, N
144  REAL AMAX, SCOND
145 * ..
146 * .. Array Arguments ..
147  REAL A( lda, * ), S( * )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  REAL ONE, THRESH
154  parameter ( one = 1.0e+0, thresh = 0.1e+0 )
155 * ..
156 * .. Local Scalars ..
157  INTEGER I, J
158  REAL CJ, LARGE, SMALL
159 * ..
160 * .. External Functions ..
161  LOGICAL LSAME
162  REAL SLAMCH
163  EXTERNAL lsame, slamch
164 * ..
165 * .. Executable Statements ..
166 *
167 * Quick return if possible
168 *
169  IF( n.LE.0 ) THEN
170  equed = 'N'
171  RETURN
172  END IF
173 *
174 * Initialize LARGE and SMALL.
175 *
176  small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
177  large = one / small
178 *
179  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
180 *
181 * No equilibration
182 *
183  equed = 'N'
184  ELSE
185 *
186 * Replace A by diag(S) * A * diag(S).
187 *
188  IF( lsame( uplo, 'U' ) ) THEN
189 *
190 * Upper triangle of A is stored.
191 *
192  DO 20 j = 1, n
193  cj = s( j )
194  DO 10 i = 1, j
195  a( i, j ) = cj*s( i )*a( i, j )
196  10 CONTINUE
197  20 CONTINUE
198  ELSE
199 *
200 * Lower triangle of A is stored.
201 *
202  DO 40 j = 1, n
203  cj = s( j )
204  DO 30 i = j, n
205  a( i, j ) = cj*s( i )*a( i, j )
206  30 CONTINUE
207  40 CONTINUE
208  END IF
209  equed = 'Y'
210  END IF
211 *
212  RETURN
213 *
214 * End of SLAQSY
215 *
216  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:135