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Tue Dec 21 13:53:31 2010 UTC (13 years, 9 months ago) by
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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
2: *
3: * -- LAPACK auxiliary routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER EQUED, UPLO
10: INTEGER LDA, N
11: DOUBLE PRECISION AMAX, SCOND
12: * ..
13: * .. Array Arguments ..
14: DOUBLE PRECISION A( LDA, * ), S( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * DLAQSY 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N)
51: * The scale factors for A.
52: *
53: * SCOND (input) DOUBLE PRECISION
54: * Ratio of the smallest S(i) to the largest S(i).
55: *
56: * AMAX (input) DOUBLE PRECISION
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62: * = 'Y': Equilibration was done, i.e., A has been replaced by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: DOUBLE PRECISION ONE, THRESH
80: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
81: * ..
82: * .. Local Scalars ..
83: INTEGER I, J
84: DOUBLE PRECISION CJ, LARGE, SMALL
85: * ..
86: * .. External Functions ..
87: LOGICAL LSAME
88: DOUBLE PRECISION DLAMCH
89: EXTERNAL LSAME, DLAMCH
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 = DLAMCH( 'Safe minimum' ) / DLAMCH( '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 DLAQSY
141: *
142: END
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