1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
|
SUBROUTINE ZLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
*
* -- LAPACK auxiliary routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2006
*
* .. Scalar Arguments ..
CHARACTER EQUED, UPLO
INTEGER N
DOUBLE PRECISION AMAX, SCOND
* ..
* .. Array Arguments ..
DOUBLE PRECISION S( * )
COMPLEX*16 AP( * )
* ..
*
* Purpose
* =======
*
* ZLAQSP equilibrates a symmetric matrix A using the scaling factors
* in the vector S.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies whether the upper or lower triangular part of the
* symmetric matrix A is stored.
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
* On entry, the upper or lower triangle of the symmetric matrix
* A, packed columnwise in a linear array. The j-th column of A
* is stored in the array AP as follows:
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
*
* On exit, the equilibrated matrix: diag(S) * A * diag(S), in
* the same storage format as A.
*
* S (input) DOUBLE PRECISION array, dimension (N)
* The scale factors for A.
*
* SCOND (input) DOUBLE PRECISION
* Ratio of the smallest S(i) to the largest S(i).
*
* AMAX (input) DOUBLE PRECISION
* Absolute value of largest matrix entry.
*
* EQUED (output) CHARACTER*1
* Specifies whether or not equilibration was done.
* = 'N': No equilibration.
* = 'Y': Equilibration was done, i.e., A has been replaced by
* diag(S) * A * diag(S).
*
* Internal Parameters
* ===================
*
* THRESH is a threshold value used to decide if scaling should be done
* based on the ratio of the scaling factors. If SCOND < THRESH,
* scaling is done.
*
* LARGE and SMALL are threshold values used to decide if scaling should
* be done based on the absolute size of the largest matrix element.
* If AMAX > LARGE or AMAX < SMALL, scaling is done.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, THRESH
PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J, JC
DOUBLE PRECISION CJ, LARGE, SMALL
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH
EXTERNAL LSAME, DLAMCH
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.LE.0 ) THEN
EQUED = 'N'
RETURN
END IF
*
* Initialize LARGE and SMALL.
*
SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
LARGE = ONE / SMALL
*
IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
*
* No equilibration
*
EQUED = 'N'
ELSE
*
* Replace A by diag(S) * A * diag(S).
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Upper triangle of A is stored.
*
JC = 1
DO 20 J = 1, N
CJ = S( J )
DO 10 I = 1, J
AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 )
10 CONTINUE
JC = JC + J
20 CONTINUE
ELSE
*
* Lower triangle of A is stored.
*
JC = 1
DO 40 J = 1, N
CJ = S( J )
DO 30 I = J, N
AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J )
30 CONTINUE
JC = JC + N - J + 1
40 CONTINUE
END IF
EQUED = 'Y'
END IF
*
RETURN
*
* End of ZLAQSP
*
END
|
