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62 * = 'Y': Equilibration was done, i.e., A has been replaced by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