LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
zlaqsy.f
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1 *> \brief \b ZLAQSY 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 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER EQUED, UPLO
25 * INTEGER LDA, N
26 * DOUBLE PRECISION AMAX, SCOND
27 * ..
28 * .. Array Arguments ..
29 * DOUBLE PRECISION S( * )
30 * COMPLEX*16 A( LDA, * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> ZLAQSY equilibrates a symmetric matrix A using the scaling factors
40 *> in the vector S.
41 *> \endverbatim
42 *
43 * Arguments:
44 * ==========
45 *
46 *> \param[in] UPLO
47 *> \verbatim
48 *> UPLO is CHARACTER*1
49 *> Specifies whether the upper or lower triangular part of the
50 *> symmetric matrix A is stored.
51 *> = 'U': Upper triangular
52 *> = 'L': Lower triangular
53 *> \endverbatim
54 *>
55 *> \param[in] N
56 *> \verbatim
57 *> N is INTEGER
58 *> The order of the matrix A. N >= 0.
59 *> \endverbatim
60 *>
61 *> \param[in,out] A
62 *> \verbatim
63 *> A is COMPLEX*16 array, dimension (LDA,N)
64 *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
65 *> n by n upper triangular part of A contains the upper
66 *> triangular part of the matrix A, and the strictly lower
67 *> triangular part of A is not referenced. If UPLO = 'L', the
68 *> leading n by n lower triangular part of A contains the lower
69 *> triangular part of the matrix A, and the strictly upper
70 *> triangular part of A is not referenced.
71 *>
72 *> On exit, if EQUED = 'Y', the equilibrated matrix:
73 *> diag(S) * A * diag(S).
74 *> \endverbatim
75 *>
76 *> \param[in] LDA
77 *> \verbatim
78 *> LDA is INTEGER
79 *> The leading dimension of the array A. LDA >= max(N,1).
80 *> \endverbatim
81 *>
82 *> \param[in] S
83 *> \verbatim
84 *> S is DOUBLE PRECISION array, dimension (N)
85 *> The scale factors for A.
86 *> \endverbatim
87 *>
88 *> \param[in] SCOND
89 *> \verbatim
90 *> SCOND is DOUBLE PRECISION
91 *> Ratio of the smallest S(i) to the largest S(i).
92 *> \endverbatim
93 *>
94 *> \param[in] AMAX
95 *> \verbatim
96 *> AMAX is DOUBLE PRECISION
97 *> Absolute value of largest matrix entry.
98 *> \endverbatim
99 *>
100 *> \param[out] EQUED
101 *> \verbatim
102 *> EQUED is CHARACTER*1
103 *> Specifies whether or not equilibration was done.
104 *> = 'N': No equilibration.
105 *> = 'Y': Equilibration was done, i.e., A has been replaced by
106 *> diag(S) * A * diag(S).
107 *> \endverbatim
108 *
109 *> \par Internal Parameters:
110 * =========================
111 *>
112 *> \verbatim
113 *> THRESH is a threshold value used to decide if scaling should be done
114 *> based on the ratio of the scaling factors. If SCOND < THRESH,
115 *> scaling is done.
116 *>
117 *> LARGE and SMALL are threshold values used to decide if scaling should
118 *> be done based on the absolute size of the largest matrix element.
119 *> If AMAX > LARGE or AMAX < SMALL, scaling is done.
120 *> \endverbatim
121 *
122 * Authors:
123 * ========
124 *
125 *> \author Univ. of Tennessee
126 *> \author Univ. of California Berkeley
127 *> \author Univ. of Colorado Denver
128 *> \author NAG Ltd.
129 *
130 *> \ingroup complex16SYauxiliary
131 *
132 * =====================================================================
133  SUBROUTINE zlaqsy( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
134 *
135 * -- LAPACK auxiliary routine --
136 * -- LAPACK is a software package provided by Univ. of Tennessee, --
137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138 *
139 * .. Scalar Arguments ..
140  CHARACTER EQUED, UPLO
141  INTEGER LDA, N
142  DOUBLE PRECISION AMAX, SCOND
143 * ..
144 * .. Array Arguments ..
145  DOUBLE PRECISION S( * )
146  COMPLEX*16 A( LDA, * )
147 * ..
148 *
149 * =====================================================================
150 *
151 * .. Parameters ..
152  DOUBLE PRECISION ONE, THRESH
153  parameter( one = 1.0d+0, thresh = 0.1d+0 )
154 * ..
155 * .. Local Scalars ..
156  INTEGER I, J
157  DOUBLE PRECISION CJ, LARGE, SMALL
158 * ..
159 * .. External Functions ..
160  LOGICAL LSAME
161  DOUBLE PRECISION DLAMCH
162  EXTERNAL lsame, dlamch
163 * ..
164 * .. Executable Statements ..
165 *
166 * Quick return if possible
167 *
168  IF( n.LE.0 ) THEN
169  equed = 'N'
170  RETURN
171  END IF
172 *
173 * Initialize LARGE and SMALL.
174 *
175  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
176  large = one / small
177 *
178  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
179 *
180 * No equilibration
181 *
182  equed = 'N'
183  ELSE
184 *
185 * Replace A by diag(S) * A * diag(S).
186 *
187  IF( lsame( uplo, 'U' ) ) THEN
188 *
189 * Upper triangle of A is stored.
190 *
191  DO 20 j = 1, n
192  cj = s( j )
193  DO 10 i = 1, j
194  a( i, j ) = cj*s( i )*a( i, j )
195  10 CONTINUE
196  20 CONTINUE
197  ELSE
198 *
199 * Lower triangle of A is stored.
200 *
201  DO 40 j = 1, n
202  cj = s( j )
203  DO 30 i = j, n
204  a( i, j ) = cj*s( i )*a( i, j )
205  30 CONTINUE
206  40 CONTINUE
207  END IF
208  equed = 'Y'
209  END IF
210 *
211  RETURN
212 *
213 * End of ZLAQSY
214 *
215  END
subroutine zlaqsy(UPLO, N, A, LDA, S, SCOND, AMAX, EQUED)
ZLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
Definition: zlaqsy.f:134