PLASMA  2.4.5
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claqsy.f
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1  SUBROUTINE claqsy( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
2 *
3 * -- LAPACK auxiliary routine (version 3.2) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8  CHARACTER equed, uplo
9  INTEGER lda, n
10  REAL amax, scond
11 * ..
12 * .. Array Arguments ..
13  REAL s( * )
14  COMPLEX a( lda, * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * CLAQSY equilibrates a symmetric matrix A using the scaling factors
21 * in the vector S.
22 *
23 * Arguments
24 * =========
25 *
26 * UPLO (input) CHARACTER*1
27 * Specifies whether the upper or lower triangular part of the
28 * symmetric matrix A is stored.
29 * = 'U': Upper triangular
30 * = 'L': Lower triangular
31 *
32 * N (input) INTEGER
33 * The order of the matrix A. N >= 0.
34 *
35 * A (input/output) COMPLEX array, dimension (LDA,N)
36 * On entry, the symmetric matrix A. If UPLO = 'U', the leading
37 * n by n upper triangular part of A contains the upper
38 * triangular part of the matrix A, and the strictly lower
39 * triangular part of A is not referenced. If UPLO = 'L', the
40 * leading n by n lower triangular part of A contains the lower
41 * triangular part of the matrix A, and the strictly upper
42 * triangular part of A is not referenced.
43 *
44 * On exit, if EQUED = 'Y', the equilibrated matrix:
45 * diag(S) * A * diag(S).
46 *
47 * LDA (input) INTEGER
48 * The leading dimension of the array A. LDA >= max(N,1).
49 *
50 * S (input) REAL array, dimension (N)
51 * The scale factors for A.
52 *
53 * SCOND (input) REAL
54 * Ratio of the smallest S(i) to the largest S(i).
55 *
56 * AMAX (input) REAL
57 * Absolute value of largest matrix entry.
58 *
59 * EQUED (output) CHARACTER*1
60 * Specifies whether or not equilibration was done.
61 * = 'N': No equilibration.
62 * = 'Y': Equilibration was done, i.e., A has been replaced by
63 * diag(S) * A * diag(S).
64 *
65 * Internal Parameters
66 * ===================
67 *
68 * THRESH is a threshold value used to decide if scaling should be done
69 * based on the ratio of the scaling factors. If SCOND < THRESH,
70 * scaling is done.
71 *
72 * LARGE and SMALL are threshold values used to decide if scaling should
73 * be done based on the absolute size of the largest matrix element.
74 * If AMAX > LARGE or AMAX < SMALL, scaling is done.
75 *
76 * =====================================================================
77 *
78 * .. Parameters ..
79  REAL one, thresh
80  parameter( one = 1.0e+0, thresh = 0.1e+0 )
81 * ..
82 * .. Local Scalars ..
83  INTEGER i, j
84  REAL cj, large, small
85 * ..
86 * .. External Functions ..
87  LOGICAL lsame
88  REAL slamch
89  EXTERNAL lsame, slamch
90 * ..
91 * .. Executable Statements ..
92 *
93 * Quick return if possible
94 *
95  IF( n.LE.0 ) THEN
96  equed = 'N'
97  return
98  END IF
99 *
100 * Initialize LARGE and SMALL.
101 *
102  small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
103  large = one / small
104 *
105  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
106 *
107 * No equilibration
108 *
109  equed = 'N'
110  ELSE
111 *
112 * Replace A by diag(S) * A * diag(S).
113 *
114  IF( lsame( uplo, 'U' ) ) THEN
115 *
116 * Upper triangle of A is stored.
117 *
118  DO 20 j = 1, n
119  cj = s( j )
120  DO 10 i = 1, j
121  a( i, j ) = cj*s( i )*a( i, j )
122  10 continue
123  20 continue
124  ELSE
125 *
126 * Lower triangle of A is stored.
127 *
128  DO 40 j = 1, n
129  cj = s( j )
130  DO 30 i = j, n
131  a( i, j ) = cj*s( i )*a( i, j )
132  30 continue
133  40 continue
134  END IF
135  equed = 'Y'
136  END IF
137 *
138  return
139 *
140 * End of CLAQSY
141 *
142  END