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zlaqsp.f
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Tue Dec 21 13:53:51 2010 UTC (13 years, 6 months ago) by
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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZLAQSP( UPLO, N, AP, 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 N
11: DOUBLE PRECISION AMAX, SCOND
12: * ..
13: * .. Array Arguments ..
14: DOUBLE PRECISION S( * )
15: COMPLEX*16 AP( * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * ZLAQSP equilibrates a symmetric matrix A using the scaling factors
22: * in the vector S.
23: *
24: * Arguments
25: * =========
26: *
27: * UPLO (input) CHARACTER*1
28: * Specifies whether the upper or lower triangular part of the
29: * symmetric matrix A is stored.
30: * = 'U': Upper triangular
31: * = 'L': Lower triangular
32: *
33: * N (input) INTEGER
34: * The order of the matrix A. N >= 0.
35: *
36: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
37: * On entry, the upper or lower triangle of the symmetric matrix
38: * A, packed columnwise in a linear array. The j-th column of A
39: * is stored in the array AP as follows:
40: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
41: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
42: *
43: * On exit, the equilibrated matrix: diag(S) * A * diag(S), in
44: * the same storage format as A.
45: *
46: * S (input) DOUBLE PRECISION array, dimension (N)
47: * The scale factors for A.
48: *
49: * SCOND (input) DOUBLE PRECISION
50: * Ratio of the smallest S(i) to the largest S(i).
51: *
52: * AMAX (input) DOUBLE PRECISION
53: * Absolute value of largest matrix entry.
54: *
55: * EQUED (output) CHARACTER*1
56: * Specifies whether or not equilibration was done.
57: * = 'N': No equilibration.
58: * = 'Y': Equilibration was done, i.e., A has been replaced by
59: * diag(S) * A * diag(S).
60: *
61: * Internal Parameters
62: * ===================
63: *
64: * THRESH is a threshold value used to decide if scaling should be done
65: * based on the ratio of the scaling factors. If SCOND < THRESH,
66: * scaling is done.
67: *
68: * LARGE and SMALL are threshold values used to decide if scaling should
69: * be done based on the absolute size of the largest matrix element.
70: * If AMAX > LARGE or AMAX < SMALL, scaling is done.
71: *
72: * =====================================================================
73: *
74: * .. Parameters ..
75: DOUBLE PRECISION ONE, THRESH
76: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
77: * ..
78: * .. Local Scalars ..
79: INTEGER I, J, JC
80: DOUBLE PRECISION CJ, LARGE, SMALL
81: * ..
82: * .. External Functions ..
83: LOGICAL LSAME
84: DOUBLE PRECISION DLAMCH
85: EXTERNAL LSAME, DLAMCH
86: * ..
87: * .. Executable Statements ..
88: *
89: * Quick return if possible
90: *
91: IF( N.LE.0 ) THEN
92: EQUED = 'N'
93: RETURN
94: END IF
95: *
96: * Initialize LARGE and SMALL.
97: *
98: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
99: LARGE = ONE / SMALL
100: *
101: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
102: *
103: * No equilibration
104: *
105: EQUED = 'N'
106: ELSE
107: *
108: * Replace A by diag(S) * A * diag(S).
109: *
110: IF( LSAME( UPLO, 'U' ) ) THEN
111: *
112: * Upper triangle of A is stored.
113: *
114: JC = 1
115: DO 20 J = 1, N
116: CJ = S( J )
117: DO 10 I = 1, J
118: AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 )
119: 10 CONTINUE
120: JC = JC + J
121: 20 CONTINUE
122: ELSE
123: *
124: * Lower triangle of A is stored.
125: *
126: JC = 1
127: DO 40 J = 1, N
128: CJ = S( J )
129: DO 30 I = J, N
130: AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J )
131: 30 CONTINUE
132: JC = JC + N - J + 1
133: 40 CONTINUE
134: END IF
135: EQUED = 'Y'
136: END IF
137: *
138: RETURN
139: *
140: * End of ZLAQSP
141: *
142: END
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