1 SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
2 $ NSPLIT, ISPLIT, INFO )
3 IMPLICIT NONE
4 *
5 * -- LAPACK auxiliary routine (version 3.2.2) --
6 * -- LAPACK is a software package provided by Univ. of Tennessee, --
7 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8 * June 2010
9 *
10 * .. Scalar Arguments ..
11 INTEGER INFO, N, NSPLIT
12 DOUBLE PRECISION SPLTOL, TNRM
13 * ..
14 * .. Array Arguments ..
15 INTEGER ISPLIT( * )
16 DOUBLE PRECISION D( * ), E( * ), E2( * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * Compute the splitting points with threshold SPLTOL.
23 * DLARRA sets any "small" off-diagonal elements to zero.
24 *
25 * Arguments
26 * =========
27 *
28 * N (input) INTEGER
29 * The order of the matrix. N > 0.
30 *
31 * D (input) DOUBLE PRECISION array, dimension (N)
32 * On entry, the N diagonal elements of the tridiagonal
33 * matrix T.
34 *
35 * E (input/output) DOUBLE PRECISION array, dimension (N)
36 * On entry, the first (N-1) entries contain the subdiagonal
37 * elements of the tridiagonal matrix T; E(N) need not be set.
38 * On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
39 * are set to zero, the other entries of E are untouched.
40 *
41 * E2 (input/output) DOUBLE PRECISION array, dimension (N)
42 * On entry, the first (N-1) entries contain the SQUARES of the
43 * subdiagonal elements of the tridiagonal matrix T;
44 * E2(N) need not be set.
45 * On exit, the entries E2( ISPLIT( I ) ),
46 * 1 <= I <= NSPLIT, have been set to zero
47 *
48 * SPLTOL (input) DOUBLE PRECISION
49 * The threshold for splitting. Two criteria can be used:
50 * SPLTOL<0 : criterion based on absolute off-diagonal value
51 * SPLTOL>0 : criterion that preserves relative accuracy
52 *
53 * TNRM (input) DOUBLE PRECISION
54 * The norm of the matrix.
55 *
56 * NSPLIT (output) INTEGER
57 * The number of blocks T splits into. 1 <= NSPLIT <= N.
58 *
59 * ISPLIT (output) INTEGER array, dimension (N)
60 * The splitting points, at which T breaks up into blocks.
61 * The first block consists of rows/columns 1 to ISPLIT(1),
62 * the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
63 * etc., and the NSPLIT-th consists of rows/columns
64 * ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
65 *
66 *
67 * INFO (output) INTEGER
68 * = 0: successful exit
69 *
70 * Further Details
71 * ===============
72 *
73 * Based on contributions by
74 * Beresford Parlett, University of California, Berkeley, USA
75 * Jim Demmel, University of California, Berkeley, USA
76 * Inderjit Dhillon, University of Texas, Austin, USA
77 * Osni Marques, LBNL/NERSC, USA
78 * Christof Voemel, University of California, Berkeley, USA
79 *
80 * =====================================================================
81 *
82 * .. Parameters ..
83 DOUBLE PRECISION ZERO
84 PARAMETER ( ZERO = 0.0D0 )
85 * ..
86 * .. Local Scalars ..
87 INTEGER I
88 DOUBLE PRECISION EABS, TMP1
89
90 * ..
91 * .. Intrinsic Functions ..
92 INTRINSIC ABS
93 * ..
94 * .. Executable Statements ..
95 *
96 INFO = 0
97
98 * Compute splitting points
99 NSPLIT = 1
100 IF(SPLTOL.LT.ZERO) THEN
101 * Criterion based on absolute off-diagonal value
102 TMP1 = ABS(SPLTOL)* TNRM
103 DO 9 I = 1, N-1
104 EABS = ABS( E(I) )
105 IF( EABS .LE. TMP1) THEN
106 E(I) = ZERO
107 E2(I) = ZERO
108 ISPLIT( NSPLIT ) = I
109 NSPLIT = NSPLIT + 1
110 END IF
111 9 CONTINUE
112 ELSE
113 * Criterion that guarantees relative accuracy
114 DO 10 I = 1, N-1
115 EABS = ABS( E(I) )
116 IF( EABS .LE. SPLTOL * SQRT(ABS(D(I)))*SQRT(ABS(D(I+1))) )
117 $ THEN
118 E(I) = ZERO
119 E2(I) = ZERO
120 ISPLIT( NSPLIT ) = I
121 NSPLIT = NSPLIT + 1
122 END IF
123 10 CONTINUE
124 ENDIF
125 ISPLIT( NSPLIT ) = N
126
127 RETURN
128 *
129 * End of DLARRA
130 *
131 END
2 $ NSPLIT, ISPLIT, INFO )
3 IMPLICIT NONE
4 *
5 * -- LAPACK auxiliary routine (version 3.2.2) --
6 * -- LAPACK is a software package provided by Univ. of Tennessee, --
7 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8 * June 2010
9 *
10 * .. Scalar Arguments ..
11 INTEGER INFO, N, NSPLIT
12 DOUBLE PRECISION SPLTOL, TNRM
13 * ..
14 * .. Array Arguments ..
15 INTEGER ISPLIT( * )
16 DOUBLE PRECISION D( * ), E( * ), E2( * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * Compute the splitting points with threshold SPLTOL.
23 * DLARRA sets any "small" off-diagonal elements to zero.
24 *
25 * Arguments
26 * =========
27 *
28 * N (input) INTEGER
29 * The order of the matrix. N > 0.
30 *
31 * D (input) DOUBLE PRECISION array, dimension (N)
32 * On entry, the N diagonal elements of the tridiagonal
33 * matrix T.
34 *
35 * E (input/output) DOUBLE PRECISION array, dimension (N)
36 * On entry, the first (N-1) entries contain the subdiagonal
37 * elements of the tridiagonal matrix T; E(N) need not be set.
38 * On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
39 * are set to zero, the other entries of E are untouched.
40 *
41 * E2 (input/output) DOUBLE PRECISION array, dimension (N)
42 * On entry, the first (N-1) entries contain the SQUARES of the
43 * subdiagonal elements of the tridiagonal matrix T;
44 * E2(N) need not be set.
45 * On exit, the entries E2( ISPLIT( I ) ),
46 * 1 <= I <= NSPLIT, have been set to zero
47 *
48 * SPLTOL (input) DOUBLE PRECISION
49 * The threshold for splitting. Two criteria can be used:
50 * SPLTOL<0 : criterion based on absolute off-diagonal value
51 * SPLTOL>0 : criterion that preserves relative accuracy
52 *
53 * TNRM (input) DOUBLE PRECISION
54 * The norm of the matrix.
55 *
56 * NSPLIT (output) INTEGER
57 * The number of blocks T splits into. 1 <= NSPLIT <= N.
58 *
59 * ISPLIT (output) INTEGER array, dimension (N)
60 * The splitting points, at which T breaks up into blocks.
61 * The first block consists of rows/columns 1 to ISPLIT(1),
62 * the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
63 * etc., and the NSPLIT-th consists of rows/columns
64 * ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
65 *
66 *
67 * INFO (output) INTEGER
68 * = 0: successful exit
69 *
70 * Further Details
71 * ===============
72 *
73 * Based on contributions by
74 * Beresford Parlett, University of California, Berkeley, USA
75 * Jim Demmel, University of California, Berkeley, USA
76 * Inderjit Dhillon, University of Texas, Austin, USA
77 * Osni Marques, LBNL/NERSC, USA
78 * Christof Voemel, University of California, Berkeley, USA
79 *
80 * =====================================================================
81 *
82 * .. Parameters ..
83 DOUBLE PRECISION ZERO
84 PARAMETER ( ZERO = 0.0D0 )
85 * ..
86 * .. Local Scalars ..
87 INTEGER I
88 DOUBLE PRECISION EABS, TMP1
89
90 * ..
91 * .. Intrinsic Functions ..
92 INTRINSIC ABS
93 * ..
94 * .. Executable Statements ..
95 *
96 INFO = 0
97
98 * Compute splitting points
99 NSPLIT = 1
100 IF(SPLTOL.LT.ZERO) THEN
101 * Criterion based on absolute off-diagonal value
102 TMP1 = ABS(SPLTOL)* TNRM
103 DO 9 I = 1, N-1
104 EABS = ABS( E(I) )
105 IF( EABS .LE. TMP1) THEN
106 E(I) = ZERO
107 E2(I) = ZERO
108 ISPLIT( NSPLIT ) = I
109 NSPLIT = NSPLIT + 1
110 END IF
111 9 CONTINUE
112 ELSE
113 * Criterion that guarantees relative accuracy
114 DO 10 I = 1, N-1
115 EABS = ABS( E(I) )
116 IF( EABS .LE. SPLTOL * SQRT(ABS(D(I)))*SQRT(ABS(D(I+1))) )
117 $ THEN
118 E(I) = ZERO
119 E2(I) = ZERO
120 ISPLIT( NSPLIT ) = I
121 NSPLIT = NSPLIT + 1
122 END IF
123 10 CONTINUE
124 ENDIF
125 ISPLIT( NSPLIT ) = N
126
127 RETURN
128 *
129 * End of DLARRA
130 *
131 END