Mercurial > octave-nkf
comparison libcruft/lapack/zpttrf.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 |
parents | |
children | 68db500cb558 |
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5163:9f3299378193 | 5164:57077d0ddc8e |
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1 SUBROUTINE ZPTTRF( 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( * ) | |
13 COMPLEX*16 E( * ) | |
14 * .. | |
15 * | |
16 * Purpose | |
17 * ======= | |
18 * | |
19 * ZPTTRF computes the L*D*L' factorization of a complex Hermitian | |
20 * positive definite tridiagonal matrix A. The factorization may also | |
21 * be regarded as having the form A = U'*D*U. | |
22 * | |
23 * Arguments | |
24 * ========= | |
25 * | |
26 * N (input) INTEGER | |
27 * The order of the matrix A. N >= 0. | |
28 * | |
29 * D (input/output) DOUBLE PRECISION array, dimension (N) | |
30 * On entry, the n diagonal elements of the tridiagonal matrix | |
31 * A. On exit, the n diagonal elements of the diagonal matrix | |
32 * D from the L*D*L' factorization of A. | |
33 * | |
34 * E (input/output) COMPLEX*16 array, dimension (N-1) | |
35 * On entry, the (n-1) subdiagonal elements of the tridiagonal | |
36 * matrix A. On exit, the (n-1) subdiagonal elements of the | |
37 * unit bidiagonal factor L from the L*D*L' factorization of A. | |
38 * E can also be regarded as the superdiagonal of the unit | |
39 * bidiagonal factor U from the U'*D*U factorization of A. | |
40 * | |
41 * INFO (output) INTEGER | |
42 * = 0: successful exit | |
43 * < 0: if INFO = -k, the k-th argument had an illegal value | |
44 * > 0: if INFO = k, the leading minor of order k is not | |
45 * positive definite; if k < N, the factorization could not | |
46 * be completed, while if k = N, the factorization was | |
47 * completed, but D(N) = 0. | |
48 * | |
49 * ===================================================================== | |
50 * | |
51 * .. Parameters .. | |
52 DOUBLE PRECISION ZERO | |
53 PARAMETER ( ZERO = 0.0D+0 ) | |
54 * .. | |
55 * .. Local Scalars .. | |
56 INTEGER I, I4 | |
57 DOUBLE PRECISION EII, EIR, F, G | |
58 * .. | |
59 * .. External Subroutines .. | |
60 EXTERNAL XERBLA | |
61 * .. | |
62 * .. Intrinsic Functions .. | |
63 INTRINSIC DBLE, DCMPLX, DIMAG, MOD | |
64 * .. | |
65 * .. Executable Statements .. | |
66 * | |
67 * Test the input parameters. | |
68 * | |
69 INFO = 0 | |
70 IF( N.LT.0 ) THEN | |
71 INFO = -1 | |
72 CALL XERBLA( 'ZPTTRF', -INFO ) | |
73 RETURN | |
74 END IF | |
75 * | |
76 * Quick return if possible | |
77 * | |
78 IF( N.EQ.0 ) | |
79 $ RETURN | |
80 * | |
81 * Compute the L*D*L' (or U'*D*U) factorization of A. | |
82 * | |
83 I4 = MOD( N-1, 4 ) | |
84 DO 10 I = 1, I4 | |
85 IF( D( I ).LE.ZERO ) THEN | |
86 INFO = I | |
87 GO TO 30 | |
88 END IF | |
89 EIR = DBLE( E( I ) ) | |
90 EII = DIMAG( E( I ) ) | |
91 F = EIR / D( I ) | |
92 G = EII / D( I ) | |
93 E( I ) = DCMPLX( F, G ) | |
94 D( I+1 ) = D( I+1 ) - F*EIR - G*EII | |
95 10 CONTINUE | |
96 * | |
97 DO 20 I = I4 + 1, N - 4, 4 | |
98 * | |
99 * Drop out of the loop if d(i) <= 0: the matrix is not positive | |
100 * definite. | |
101 * | |
102 IF( D( I ).LE.ZERO ) THEN | |
103 INFO = I | |
104 GO TO 30 | |
105 END IF | |
106 * | |
107 * Solve for e(i) and d(i+1). | |
108 * | |
109 EIR = DBLE( E( I ) ) | |
110 EII = DIMAG( E( I ) ) | |
111 F = EIR / D( I ) | |
112 G = EII / D( I ) | |
113 E( I ) = DCMPLX( F, G ) | |
114 D( I+1 ) = D( I+1 ) - F*EIR - G*EII | |
115 * | |
116 IF( D( I+1 ).LE.ZERO ) THEN | |
117 INFO = I + 1 | |
118 GO TO 30 | |
119 END IF | |
120 * | |
121 * Solve for e(i+1) and d(i+2). | |
122 * | |
123 EIR = DBLE( E( I+1 ) ) | |
124 EII = DIMAG( E( I+1 ) ) | |
125 F = EIR / D( I+1 ) | |
126 G = EII / D( I+1 ) | |
127 E( I+1 ) = DCMPLX( F, G ) | |
128 D( I+2 ) = D( I+2 ) - F*EIR - G*EII | |
129 * | |
130 IF( D( I+2 ).LE.ZERO ) THEN | |
131 INFO = I + 2 | |
132 GO TO 30 | |
133 END IF | |
134 * | |
135 * Solve for e(i+2) and d(i+3). | |
136 * | |
137 EIR = DBLE( E( I+2 ) ) | |
138 EII = DIMAG( E( I+2 ) ) | |
139 F = EIR / D( I+2 ) | |
140 G = EII / D( I+2 ) | |
141 E( I+2 ) = DCMPLX( F, G ) | |
142 D( I+3 ) = D( I+3 ) - F*EIR - G*EII | |
143 * | |
144 IF( D( I+3 ).LE.ZERO ) THEN | |
145 INFO = I + 3 | |
146 GO TO 30 | |
147 END IF | |
148 * | |
149 * Solve for e(i+3) and d(i+4). | |
150 * | |
151 EIR = DBLE( E( I+3 ) ) | |
152 EII = DIMAG( E( I+3 ) ) | |
153 F = EIR / D( I+3 ) | |
154 G = EII / D( I+3 ) | |
155 E( I+3 ) = DCMPLX( F, G ) | |
156 D( I+4 ) = D( I+4 ) - F*EIR - G*EII | |
157 20 CONTINUE | |
158 * | |
159 * Check d(n) for positive definiteness. | |
160 * | |
161 IF( D( N ).LE.ZERO ) | |
162 $ INFO = N | |
163 * | |
164 30 CONTINUE | |
165 RETURN | |
166 * | |
167 * End of ZPTTRF | |
168 * | |
169 END |