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
|
SUBROUTINE CDTTRF( N, DL, D, DU, INFO )
*
* Written by Andrew J. Cleary, November 1996.
* Modified from CGTTRF:
* -- LAPACK routine (preliminary version) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
*
* .. Scalar Arguments ..
INTEGER INFO, N
* ..
* .. Array Arguments ..
COMPLEX D( * ), DL( * ), DU( * )
* ..
*
* Purpose
* =======
*
* CDTTRF computes an LU factorization of a complex tridiagonal matrix A
* using elimination without partial pivoting.
*
* The factorization has the form
* A = L * U
* where L is a product of unit lower bidiagonal
* matrices and U is upper triangular with nonzeros in only the main
* diagonal and first superdiagonal.
*
* Arguments
* =========
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* DL (input/output) COMPLEX array, dimension (N-1)
* On entry, DL must contain the (n-1) subdiagonal elements of
* A.
* On exit, DL is overwritten by the (n-1) multipliers that
* define the matrix L from the LU factorization of A.
*
* D (input/output) COMPLEX array, dimension (N)
* On entry, D must contain the diagonal elements of A.
* On exit, D is overwritten by the n diagonal elements of the
* upper triangular matrix U from the LU factorization of A.
*
* DU (input/output) COMPLEX array, dimension (N-1)
* On entry, DU must contain the (n-1) superdiagonal elements
* of A.
* On exit, DU is overwritten by the (n-1) elements of the first
* superdiagonal of U.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
* > 0: if INFO = i, U(i,i) is exactly zero. The factorization
* has been completed, but the factor U is exactly
* singular, and division by zero will occur if it is used
* to solve a system of equations.
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I
COMPLEX FACT
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Parameters ..
COMPLEX CZERO
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Executable Statements ..
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
CALL XERBLA( 'CDTTRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
DO 20 I = 1, N - 1
IF( DL( I ).EQ.CZERO ) THEN
*
* Subdiagonal is zero, no elimination is required.
*
IF( D( I ).EQ.CZERO .AND. INFO.EQ.0 )
$ INFO = I
ELSE
*
FACT = DL( I ) / D( I )
DL( I ) = FACT
D( I+1 ) = D( I+1 ) - FACT*DU( I )
END IF
20 CONTINUE
IF( D( N ).EQ.CZERO .AND. INFO.EQ.0 ) THEN
INFO = N
RETURN
END IF
*
RETURN
*
* End of CDTTRF
*
END
|
