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63 * = 'Y': Equilibration was done, i.e., A has been replaced by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
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