Mercurial > octave-nkf
comparison libcruft/lapack/dpttrf.f @ 5164:57077d0ddc8e
[project @ 2005-02-25 19:55:24 by jwe]
author | jwe |
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date | Fri, 25 Feb 2005 19:55:28 +0000 |
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children | 68db500cb558 |
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5163:9f3299378193 | 5164:57077d0ddc8e |
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1 SUBROUTINE DPTTRF( N, D, E, INFO ) | |
2 * | |
3 * -- LAPACK routine (version 3.0) -- | |
4 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., | |
5 * Courant Institute, Argonne National Lab, and Rice University | |
6 * June 30, 1999 | |
7 * | |
8 * .. Scalar Arguments .. | |
9 INTEGER INFO, N | |
10 * .. | |
11 * .. Array Arguments .. | |
12 DOUBLE PRECISION D( * ), E( * ) | |
13 * .. | |
14 * | |
15 * Purpose | |
16 * ======= | |
17 * | |
18 * DPTTRF computes the L*D*L' factorization of a real symmetric | |
19 * positive definite tridiagonal matrix A. The factorization may also | |
20 * be regarded as having the form A = U'*D*U. | |
21 * | |
22 * Arguments | |
23 * ========= | |
24 * | |
25 * N (input) INTEGER | |
26 * The order of the matrix A. N >= 0. | |
27 * | |
28 * D (input/output) DOUBLE PRECISION array, dimension (N) | |
29 * On entry, the n diagonal elements of the tridiagonal matrix | |
30 * A. On exit, the n diagonal elements of the diagonal matrix | |
31 * D from the L*D*L' factorization of A. | |
32 * | |
33 * E (input/output) DOUBLE PRECISION array, dimension (N-1) | |
34 * On entry, the (n-1) subdiagonal elements of the tridiagonal | |
35 * matrix A. On exit, the (n-1) subdiagonal elements of the | |
36 * unit bidiagonal factor L from the L*D*L' factorization of A. | |
37 * E can also be regarded as the superdiagonal of the unit | |
38 * bidiagonal factor U from the U'*D*U factorization of A. | |
39 * | |
40 * INFO (output) INTEGER | |
41 * = 0: successful exit | |
42 * < 0: if INFO = -k, the k-th argument had an illegal value | |
43 * > 0: if INFO = k, the leading minor of order k is not | |
44 * positive definite; if k < N, the factorization could not | |
45 * be completed, while if k = N, the factorization was | |
46 * completed, but D(N) = 0. | |
47 * | |
48 * ===================================================================== | |
49 * | |
50 * .. Parameters .. | |
51 DOUBLE PRECISION ZERO | |
52 PARAMETER ( ZERO = 0.0D+0 ) | |
53 * .. | |
54 * .. Local Scalars .. | |
55 INTEGER I, I4 | |
56 DOUBLE PRECISION EI | |
57 * .. | |
58 * .. External Subroutines .. | |
59 EXTERNAL XERBLA | |
60 * .. | |
61 * .. Intrinsic Functions .. | |
62 INTRINSIC MOD | |
63 * .. | |
64 * .. Executable Statements .. | |
65 * | |
66 * Test the input parameters. | |
67 * | |
68 INFO = 0 | |
69 IF( N.LT.0 ) THEN | |
70 INFO = -1 | |
71 CALL XERBLA( 'DPTTRF', -INFO ) | |
72 RETURN | |
73 END IF | |
74 * | |
75 * Quick return if possible | |
76 * | |
77 IF( N.EQ.0 ) | |
78 $ RETURN | |
79 * | |
80 * Compute the L*D*L' (or U'*D*U) factorization of A. | |
81 * | |
82 I4 = MOD( N-1, 4 ) | |
83 DO 10 I = 1, I4 | |
84 IF( D( I ).LE.ZERO ) THEN | |
85 INFO = I | |
86 GO TO 30 | |
87 END IF | |
88 EI = E( I ) | |
89 E( I ) = EI / D( I ) | |
90 D( I+1 ) = D( I+1 ) - E( I )*EI | |
91 10 CONTINUE | |
92 * | |
93 DO 20 I = I4 + 1, N - 4, 4 | |
94 * | |
95 * Drop out of the loop if d(i) <= 0: the matrix is not positive | |
96 * definite. | |
97 * | |
98 IF( D( I ).LE.ZERO ) THEN | |
99 INFO = I | |
100 GO TO 30 | |
101 END IF | |
102 * | |
103 * Solve for e(i) and d(i+1). | |
104 * | |
105 EI = E( I ) | |
106 E( I ) = EI / D( I ) | |
107 D( I+1 ) = D( I+1 ) - E( I )*EI | |
108 * | |
109 IF( D( I+1 ).LE.ZERO ) THEN | |
110 INFO = I + 1 | |
111 GO TO 30 | |
112 END IF | |
113 * | |
114 * Solve for e(i+1) and d(i+2). | |
115 * | |
116 EI = E( I+1 ) | |
117 E( I+1 ) = EI / D( I+1 ) | |
118 D( I+2 ) = D( I+2 ) - E( I+1 )*EI | |
119 * | |
120 IF( D( I+2 ).LE.ZERO ) THEN | |
121 INFO = I + 2 | |
122 GO TO 30 | |
123 END IF | |
124 * | |
125 * Solve for e(i+2) and d(i+3). | |
126 * | |
127 EI = E( I+2 ) | |
128 E( I+2 ) = EI / D( I+2 ) | |
129 D( I+3 ) = D( I+3 ) - E( I+2 )*EI | |
130 * | |
131 IF( D( I+3 ).LE.ZERO ) THEN | |
132 INFO = I + 3 | |
133 GO TO 30 | |
134 END IF | |
135 * | |
136 * Solve for e(i+3) and d(i+4). | |
137 * | |
138 EI = E( I+3 ) | |
139 E( I+3 ) = EI / D( I+3 ) | |
140 D( I+4 ) = D( I+4 ) - E( I+3 )*EI | |
141 20 CONTINUE | |
142 * | |
143 * Check d(n) for positive definiteness. | |
144 * | |
145 IF( D( N ).LE.ZERO ) | |
146 $ INFO = N | |
147 * | |
148 30 CONTINUE | |
149 RETURN | |
150 * | |
151 * End of DPTTRF | |
152 * | |
153 END |