1: SUBROUTINE ZLAQHE( 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 S( * )
15: COMPLEX*16 A( LDA, * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * ZLAQHE equilibrates a Hermitian 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: * Hermitian 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: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
37: * On entry, the Hermitian matrix A. If UPLO = 'U', the leading
38: * n by n upper triangular part of A contains the upper
39: * triangular part of the matrix A, and the strictly lower
40: * triangular part of A is not referenced. If UPLO = 'L', the
41: * leading n by n lower triangular part of A contains the lower
42: * triangular part of the matrix A, and the strictly upper
43: * triangular part of A is not referenced.
44: *
45: * On exit, if EQUED = 'Y', the equilibrated matrix:
46: * diag(S) * A * diag(S).
47: *
48: * LDA (input) INTEGER
49: * The leading dimension of the array A. LDA >= max(N,1).
50: *
51: * S (input) DOUBLE PRECISION array, dimension (N)
52: * The scale factors for A.
53: *
54: * SCOND (input) DOUBLE PRECISION
55: * Ratio of the smallest S(i) to the largest S(i).
56: *
57: * AMAX (input) DOUBLE PRECISION
58: * Absolute value of largest matrix entry.
59: *
60: * EQUED (output) CHARACTER*1
61: * Specifies whether or not equilibration was done.
62: * = 'N': No equilibration.
63: * = 'Y': Equilibration was done, i.e., A has been replaced by
64: * diag(S) * A * diag(S).
65: *
66: * Internal Parameters
67: * ===================
68: *
69: * THRESH is a threshold value used to decide if scaling should be done
70: * based on the ratio of the scaling factors. If SCOND < THRESH,
71: * scaling is done.
72: *
73: * LARGE and SMALL are threshold values used to decide if scaling should
74: * be done based on the absolute size of the largest matrix element.
75: * If AMAX > LARGE or AMAX < SMALL, scaling is done.
76: *
77: * =====================================================================
78: *
79: * .. Parameters ..
80: DOUBLE PRECISION ONE, THRESH
81: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
82: * ..
83: * .. Local Scalars ..
84: INTEGER I, J
85: DOUBLE PRECISION CJ, LARGE, SMALL
86: * ..
87: * .. External Functions ..
88: LOGICAL LSAME
89: DOUBLE PRECISION DLAMCH
90: EXTERNAL LSAME, DLAMCH
91: * ..
92: * .. Intrinsic Functions ..
93: INTRINSIC DBLE
94: * ..
95: * .. Executable Statements ..
96: *
97: * Quick return if possible
98: *
99: IF( N.LE.0 ) THEN
100: EQUED = 'N'
101: RETURN
102: END IF
103: *
104: * Initialize LARGE and SMALL.
105: *
106: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
107: LARGE = ONE / SMALL
108: *
109: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
110: *
111: * No equilibration
112: *
113: EQUED = 'N'
114: ELSE
115: *
116: * Replace A by diag(S) * A * diag(S).
117: *
118: IF( LSAME( UPLO, 'U' ) ) THEN
119: *
120: * Upper triangle of A is stored.
121: *
122: DO 20 J = 1, N
123: CJ = S( J )
124: DO 10 I = 1, J - 1
125: A( I, J ) = CJ*S( I )*A( I, J )
126: 10 CONTINUE
127: A( J, J ) = CJ*CJ*DBLE( A( J, J ) )
128: 20 CONTINUE
129: ELSE
130: *
131: * Lower triangle of A is stored.
132: *
133: DO 40 J = 1, N
134: CJ = S( J )
135: A( J, J ) = CJ*CJ*DBLE( A( J, J ) )
136: DO 30 I = J + 1, N
137: A( I, J ) = CJ*S( I )*A( I, J )
138: 30 CONTINUE
139: 40 CONTINUE
140: END IF
141: EQUED = 'Y'
142: END IF
143: *
144: RETURN
145: *
146: * End of ZLAQHE
147: *
148: END
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