1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
|
SUBROUTINE ZPTTRF( N, D, E, INFO )
*
* -- LAPACK routine (version 3.2) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER INFO, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * )
COMPLEX*16 E( * )
* ..
*
* Purpose
* =======
*
* ZPTTRF computes the L*D*L' factorization of a complex Hermitian
* positive definite tridiagonal matrix A. The factorization may also
* be regarded as having the form A = U'*D*U.
*
* Arguments
* =========
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* D (input/output) DOUBLE PRECISION array, dimension (N)
* On entry, the n diagonal elements of the tridiagonal matrix
* A. On exit, the n diagonal elements of the diagonal matrix
* D from the L*D*L' factorization of A.
*
* E (input/output) COMPLEX*16 array, dimension (N-1)
* On entry, the (n-1) subdiagonal elements of the tridiagonal
* matrix A. On exit, the (n-1) subdiagonal elements of the
* unit bidiagonal factor L from the L*D*L' factorization of A.
* E can also be regarded as the superdiagonal of the unit
* bidiagonal factor U from the U'*D*U factorization of A.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -k, the k-th argument had an illegal value
* > 0: if INFO = k, the leading minor of order k is not
* positive definite; if k < N, the factorization could not
* be completed, while if k = N, the factorization was
* completed, but D(N) <= 0.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, I4
DOUBLE PRECISION EII, EIR, F, G
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCMPLX, DIMAG, MOD
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
CALL XERBLA( 'ZPTTRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Compute the L*D*L' (or U'*D*U) factorization of A.
*
I4 = MOD( N-1, 4 )
DO 10 I = 1, I4
IF( D( I ).LE.ZERO ) THEN
INFO = I
GO TO 30
END IF
EIR = DBLE( E( I ) )
EII = DIMAG( E( I ) )
F = EIR / D( I )
G = EII / D( I )
E( I ) = DCMPLX( F, G )
D( I+1 ) = D( I+1 ) - F*EIR - G*EII
10 CONTINUE
*
DO 20 I = I4 + 1, N - 4, 4
*
* Drop out of the loop if d(i) <= 0: the matrix is not positive
* definite.
*
IF( D( I ).LE.ZERO ) THEN
INFO = I
GO TO 30
END IF
*
* Solve for e(i) and d(i+1).
*
EIR = DBLE( E( I ) )
EII = DIMAG( E( I ) )
F = EIR / D( I )
G = EII / D( I )
E( I ) = DCMPLX( F, G )
D( I+1 ) = D( I+1 ) - F*EIR - G*EII
*
IF( D( I+1 ).LE.ZERO ) THEN
INFO = I + 1
GO TO 30
END IF
*
* Solve for e(i+1) and d(i+2).
*
EIR = DBLE( E( I+1 ) )
EII = DIMAG( E( I+1 ) )
F = EIR / D( I+1 )
G = EII / D( I+1 )
E( I+1 ) = DCMPLX( F, G )
D( I+2 ) = D( I+2 ) - F*EIR - G*EII
*
IF( D( I+2 ).LE.ZERO ) THEN
INFO = I + 2
GO TO 30
END IF
*
* Solve for e(i+2) and d(i+3).
*
EIR = DBLE( E( I+2 ) )
EII = DIMAG( E( I+2 ) )
F = EIR / D( I+2 )
G = EII / D( I+2 )
E( I+2 ) = DCMPLX( F, G )
D( I+3 ) = D( I+3 ) - F*EIR - G*EII
*
IF( D( I+3 ).LE.ZERO ) THEN
INFO = I + 3
GO TO 30
END IF
*
* Solve for e(i+3) and d(i+4).
*
EIR = DBLE( E( I+3 ) )
EII = DIMAG( E( I+3 ) )
F = EIR / D( I+3 )
G = EII / D( I+3 )
E( I+3 ) = DCMPLX( F, G )
D( I+4 ) = D( I+4 ) - F*EIR - G*EII
20 CONTINUE
*
* Check d(n) for positive definiteness.
*
IF( D( N ).LE.ZERO )
$ INFO = N
*
30 CONTINUE
RETURN
*
* End of ZPTTRF
*
END
|
