LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zlaqhp.f
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1 *> \brief \b ZLAQHP scales a Hermitian matrix stored in packed form.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZLAQHP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER EQUED, UPLO
25 * INTEGER N
26 * DOUBLE PRECISION AMAX, SCOND
27 * ..
28 * .. Array Arguments ..
29 * DOUBLE PRECISION S( * )
30 * COMPLEX*16 AP( * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> ZLAQHP 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] AP
62 *> \verbatim
63 *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
64 *> On entry, the upper or lower triangle of the Hermitian matrix
65 *> A, packed columnwise in a linear array. The j-th column of A
66 *> is stored in the array AP as follows:
67 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
68 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
69 *>
70 *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in
71 *> the same storage format as A.
72 *> \endverbatim
73 *>
74 *> \param[in] S
75 *> \verbatim
76 *> S is DOUBLE PRECISION array, dimension (N)
77 *> The scale factors for A.
78 *> \endverbatim
79 *>
80 *> \param[in] SCOND
81 *> \verbatim
82 *> SCOND is DOUBLE PRECISION
83 *> Ratio of the smallest S(i) to the largest S(i).
84 *> \endverbatim
85 *>
86 *> \param[in] AMAX
87 *> \verbatim
88 *> AMAX is DOUBLE PRECISION
89 *> Absolute value of largest matrix entry.
90 *> \endverbatim
91 *>
92 *> \param[out] EQUED
93 *> \verbatim
94 *> EQUED is CHARACTER*1
95 *> Specifies whether or not equilibration was done.
96 *> = 'N': No equilibration.
97 *> = 'Y': Equilibration was done, i.e., A has been replaced by
98 *> diag(S) * A * diag(S).
99 *> \endverbatim
100 *
101 *> \par Internal Parameters:
102 * =========================
103 *>
104 *> \verbatim
105 *> THRESH is a threshold value used to decide if scaling should be done
106 *> based on the ratio of the scaling factors. If SCOND < THRESH,
107 *> scaling is done.
108 *>
109 *> LARGE and SMALL are threshold values used to decide if scaling should
110 *> be done based on the absolute size of the largest matrix element.
111 *> If AMAX > LARGE or AMAX < SMALL, scaling is done.
112 *> \endverbatim
113 *
114 * Authors:
115 * ========
116 *
117 *> \author Univ. of Tennessee
118 *> \author Univ. of California Berkeley
119 *> \author Univ. of Colorado Denver
120 *> \author NAG Ltd.
121 *
122 *> \ingroup complex16OTHERauxiliary
123 *
124 * =====================================================================
125  SUBROUTINE zlaqhp( UPLO, N, AP, S, SCOND, AMAX, EQUED )
126 *
127 * -- LAPACK auxiliary routine --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 *
131 * .. Scalar Arguments ..
132  CHARACTER EQUED, UPLO
133  INTEGER N
134  DOUBLE PRECISION AMAX, SCOND
135 * ..
136 * .. Array Arguments ..
137  DOUBLE PRECISION S( * )
138  COMPLEX*16 AP( * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  DOUBLE PRECISION ONE, THRESH
145  parameter( one = 1.0d+0, thresh = 0.1d+0 )
146 * ..
147 * .. Local Scalars ..
148  INTEGER I, J, JC
149  DOUBLE PRECISION CJ, LARGE, SMALL
150 * ..
151 * .. External Functions ..
152  LOGICAL LSAME
153  DOUBLE PRECISION DLAMCH
154  EXTERNAL lsame, dlamch
155 * ..
156 * .. Intrinsic Functions ..
157  INTRINSIC dble
158 * ..
159 * .. Executable Statements ..
160 *
161 * Quick return if possible
162 *
163  IF( n.LE.0 ) THEN
164  equed = 'N'
165  RETURN
166  END IF
167 *
168 * Initialize LARGE and SMALL.
169 *
170  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
171  large = one / small
172 *
173  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
174 *
175 * No equilibration
176 *
177  equed = 'N'
178  ELSE
179 *
180 * Replace A by diag(S) * A * diag(S).
181 *
182  IF( lsame( uplo, 'U' ) ) THEN
183 *
184 * Upper triangle of A is stored.
185 *
186  jc = 1
187  DO 20 j = 1, n
188  cj = s( j )
189  DO 10 i = 1, j - 1
190  ap( jc+i-1 ) = cj*s( i )*ap( jc+i-1 )
191  10 CONTINUE
192  ap( jc+j-1 ) = cj*cj*dble( ap( jc+j-1 ) )
193  jc = jc + j
194  20 CONTINUE
195  ELSE
196 *
197 * Lower triangle of A is stored.
198 *
199  jc = 1
200  DO 40 j = 1, n
201  cj = s( j )
202  ap( jc ) = cj*cj*dble( ap( jc ) )
203  DO 30 i = j + 1, n
204  ap( jc+i-j ) = cj*s( i )*ap( jc+i-j )
205  30 CONTINUE
206  jc = jc + n - j + 1
207  40 CONTINUE
208  END IF
209  equed = 'Y'
210  END IF
211 *
212  RETURN
213 *
214 * End of ZLAQHP
215 *
216  END
subroutine zlaqhp(UPLO, N, AP, S, SCOND, AMAX, EQUED)
ZLAQHP scales a Hermitian matrix stored in packed form.
Definition: zlaqhp.f:126