LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
claqhe.f
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1 *> \brief \b CLAQHE scales a Hermitian matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CLAQHE( 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 S( * )
30 * COMPLEX A( LDA, * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> CLAQHE equilibrates a Hermitian 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 *> Hermitian 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 array, dimension (LDA,N)
64 *> On entry, the Hermitian 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 REAL array, dimension (N)
85 *> The scale factors for A.
86 *> \endverbatim
87 *>
88 *> \param[in] SCOND
89 *> \verbatim
90 *> SCOND is REAL
91 *> Ratio of the smallest S(i) to the largest S(i).
92 *> \endverbatim
93 *>
94 *> \param[in] AMAX
95 *> \verbatim
96 *> AMAX is REAL
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 *> \date September 2012
131 *
132 *> \ingroup complexHEauxiliary
133 *
134 * =====================================================================
135  SUBROUTINE claqhe( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
136 *
137 * -- LAPACK auxiliary routine (version 3.4.2) --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 * September 2012
141 *
142 * .. Scalar Arguments ..
143  CHARACTER EQUED, UPLO
144  INTEGER LDA, N
145  REAL AMAX, SCOND
146 * ..
147 * .. Array Arguments ..
148  REAL S( * )
149  COMPLEX A( lda, * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  REAL ONE, THRESH
156  parameter ( one = 1.0e+0, thresh = 0.1e+0 )
157 * ..
158 * .. Local Scalars ..
159  INTEGER I, J
160  REAL CJ, LARGE, SMALL
161 * ..
162 * .. External Functions ..
163  LOGICAL LSAME
164  REAL SLAMCH
165  EXTERNAL lsame, slamch
166 * ..
167 * .. Intrinsic Functions ..
168  INTRINSIC real
169 * ..
170 * .. Executable Statements ..
171 *
172 * Quick return if possible
173 *
174  IF( n.LE.0 ) THEN
175  equed = 'N'
176  RETURN
177  END IF
178 *
179 * Initialize LARGE and SMALL.
180 *
181  small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
182  large = one / small
183 *
184  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
185 *
186 * No equilibration
187 *
188  equed = 'N'
189  ELSE
190 *
191 * Replace A by diag(S) * A * diag(S).
192 *
193  IF( lsame( uplo, 'U' ) ) THEN
194 *
195 * Upper triangle of A is stored.
196 *
197  DO 20 j = 1, n
198  cj = s( j )
199  DO 10 i = 1, j - 1
200  a( i, j ) = cj*s( i )*a( i, j )
201  10 CONTINUE
202  a( j, j ) = cj*cj*REAL( A( J, J ) )
203  20 CONTINUE
204  ELSE
205 *
206 * Lower triangle of A is stored.
207 *
208  DO 40 j = 1, n
209  cj = s( j )
210  a( j, j ) = cj*cj*REAL( A( J, J ) )
211  DO 30 i = j + 1, n
212  a( i, j ) = cj*s( i )*a( i, j )
213  30 CONTINUE
214  40 CONTINUE
215  END IF
216  equed = 'Y'
217  END IF
218 *
219  RETURN
220 *
221 * End of CLAQHE
222 *
223  END
subroutine claqhe(UPLO, N, A, LDA, S, SCOND, AMAX, EQUED)
CLAQHE scales a Hermitian matrix.
Definition: claqhe.f:136