LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zlaqhe.f
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1*> \brief \b ZLAQHE scales a Hermitian matrix.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqhe.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZLAQHE( 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*> ZLAQHE 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*16 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 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 laqhe
131*
132* =====================================================================
133 SUBROUTINE zlaqhe( 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* .. Intrinsic Functions ..
165 INTRINSIC dble
166* ..
167* .. Executable Statements ..
168*
169* Quick return if possible
170*
171 IF( n.LE.0 ) THEN
172 equed = 'N'
173 RETURN
174 END IF
175*
176* Initialize LARGE and SMALL.
177*
178 small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
179 large = one / small
180*
181 IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
182*
183* No equilibration
184*
185 equed = 'N'
186 ELSE
187*
188* Replace A by diag(S) * A * diag(S).
189*
190 IF( lsame( uplo, 'U' ) ) THEN
191*
192* Upper triangle of A is stored.
193*
194 DO 20 j = 1, n
195 cj = s( j )
196 DO 10 i = 1, j - 1
197 a( i, j ) = cj*s( i )*a( i, j )
198 10 CONTINUE
199 a( j, j ) = cj*cj*dble( a( j, j ) )
200 20 CONTINUE
201 ELSE
202*
203* Lower triangle of A is stored.
204*
205 DO 40 j = 1, n
206 cj = s( j )
207 a( j, j ) = cj*cj*dble( a( j, j ) )
208 DO 30 i = j + 1, n
209 a( i, j ) = cj*s( i )*a( i, j )
210 30 CONTINUE
211 40 CONTINUE
212 END IF
213 equed = 'Y'
214 END IF
215*
216 RETURN
217*
218* End of ZLAQHE
219*
220 END
subroutine zlaqhe(uplo, n, a, lda, s, scond, amax, equed)
ZLAQHE scales a Hermitian matrix.
Definition zlaqhe.f:134