1DLAGTF(1) LAPACK routine (version 3.1) DLAGTF(1)
2
6 DLAGTF - the matrix (T - lambda*I), where T is an n by n tridiagonal
7 matrix and lambda is a scalar, as T - lambda*I = PLU,
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10 SUBROUTINE DLAGTF( N, A, LAMBDA, B, C, TOL, D, IN, INFO )
11 INTEGER INFO, N
13 DOUBLE PRECISION LAMBDA, TOL
15 INTEGER IN( * )
17 DOUBLE PRECISION A( * ), B( * ), C( * ), D( * )
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21 DLAGTF factorizes the matrix (T - lambda*I), where T is an n by n
22 tridiagonal matrix and lambda is a scalar, as
23 where P is a permutation matrix, L is a unit lower tridiagonal matrix
25 with at most one non-zero sub-diagonal elements per column and U is an
26 upper triangular matrix with at most two non-zero super-diagonal ele‐
27 ments per column.
28 The factorization is obtained by Gaussian elimination with partial piv‐
30 oting and implicit row scaling.
31 The parameter LAMBDA is included in the routine so that DLAGTF may be
33 used, in conjunction with DLAGTS, to obtain eigenvectors of T by
34 inverse iteration.
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38 N (input) INTEGER
39 The order of the matrix T.
40 A (input/output) DOUBLE PRECISION array, dimension (N)
42 On entry, A must contain the diagonal elements of T.
43 On exit, A is overwritten by the n diagonal elements of the
45 upper triangular matrix U of the factorization of T.
46 LAMBDA (input) DOUBLE PRECISION
48 On entry, the scalar lambda.
49 B (input/output) DOUBLE PRECISION array, dimension (N-1)
51 On entry, B must contain the (n-1) super-diagonal elements of
52 T.
53 On exit, B is overwritten by the (n-1) super-diagonal elements
55 of the matrix U of the factorization of T.
56 C (input/output) DOUBLE PRECISION array, dimension (N-1)
58 On entry, C must contain the (n-1) sub-diagonal elements of T.
59 On exit, C is overwritten by the (n-1) sub-diagonal elements of
61 the matrix L of the factorization of T.
62 TOL (input) DOUBLE PRECISION
64 On entry, a relative tolerance used to indicate whether or not
65 the matrix (T - lambda*I) is nearly singular. TOL should nor‐
66 mally be chose as approximately the largest relative error in
67 the elements of T. For example, if the elements of T are cor‐
68 rect to about 4 significant figures, then TOL should be set to
69 about 5*10**(-4). If TOL is supplied as less than eps, where
70 eps is the relative machine precision, then the value eps is
71 used in place of TOL.
72 D (output) DOUBLE PRECISION array, dimension (N-2)
74 On exit, D is overwritten by the (n-2) second super-diagonal
75 elements of the matrix U of the factorization of T.
76 IN (output) INTEGER array, dimension (N)
78 On exit, IN contains details of the permutation matrix P. If an
79 interchange occurred at the kth step of the elimination, then
80 IN(k) = 1, otherwise IN(k) = 0. The element IN(n) returns the
81 smallest positive integer j such that
82 abs( u(j,j) ).le. norm( (T - lambda*I)(j) )*TOL,
84 where norm( A(j) ) denotes the sum of the absolute values of
86 the jth row of the matrix A. If no such j exists then IN(n) is
87 returned as zero. If IN(n) is returned as positive, then a
88 diagonal element of U is small, indicating that (T - lambda*I)
89 is singular or nearly singular,
90 INFO (output) INTEGER
92 = 0 : successful exit
93 LAPACK routine (version 3.1) November 2006 DLAGTF(1)