1SLAGTF(1) LAPACK routine (version 3.2) SLAGTF(1)
2
6 SLAGTF - factorizes the matrix (T - lambda*I), where T is an n by n
7 tridiagonal matrix and lambda is a scalar, as T - lambda*I = PLU,
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10 SUBROUTINE SLAGTF( N, A, LAMBDA, B, C, TOL, D, IN, INFO )
11 INTEGER INFO, N
13 REAL LAMBDA, TOL
15 INTEGER IN( * )
17 REAL A( * ), B( * ), C( * ), D( * )
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21 SLAGTF factorizes the matrix (T - lambda*I), where T is an n by n
22 tridiagonal matrix and lambda is a scalar, as where P is a permutation
23 matrix, L is a unit lower tridiagonal matrix with at most one non-zero
24 sub-diagonal elements per column and U is an upper triangular matrix
25 with at most two non-zero super-diagonal elements per column.
26 The factorization is obtained by Gaussian elimination with partial piv‐
27 oting and implicit row scaling.
28 The parameter LAMBDA is included in the routine so that SLAGTF may be
29 used, in conjunction with SLAGTS, to obtain eigenvectors of T by
30 inverse iteration.
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33 N (input) INTEGER
34 The order of the matrix T.
35 A (input/output) REAL array, dimension (N)
37 On entry, A must contain the diagonal elements of T. On exit,
38 A is overwritten by the n diagonal elements of the upper trian‐
39 gular matrix U of the factorization of T.
40 LAMBDA (input) REAL
42 On entry, the scalar lambda.
43 B (input/output) REAL array, dimension (N-1)
45 On entry, B must contain the (n-1) super-diagonal elements of
46 T. On exit, B is overwritten by the (n-1) super-diagonal ele‐
47 ments of the matrix U of the factorization of T.
48 C (input/output) REAL array, dimension (N-1)
50 On entry, C must contain the (n-1) sub-diagonal elements of T.
51 On exit, C is overwritten by the (n-1) sub-diagonal elements of
52 the matrix L of the factorization of T.
53 TOL (input) REAL
55 On entry, a relative tolerance used to indicate whether or not
56 the matrix (T - lambda*I) is nearly singular. TOL should nor‐
57 mally be chose as approximately the largest relative error in
58 the elements of T. For example, if the elements of T are cor‐
59 rect to about 4 significant figures, then TOL should be set to
60 about 5*10**(-4). If TOL is supplied as less than eps, where
61 eps is the relative machine precision, then the value eps is
62 used in place of TOL.
63 D (output) REAL array, dimension (N-2)
65 On exit, D is overwritten by the (n-2) second super-diagonal
66 elements of the matrix U of the factorization of T.
67 IN (output) INTEGER array, dimension (N)
69 On exit, IN contains details of the permutation matrix P. If an
70 interchange occurred at the kth step of the elimination, then
71 IN(k) = 1, otherwise IN(k) = 0. The element IN(n) returns the
72 smallest positive integer j such that abs( u(j,j) ).le. norm(
73 (T - lambda*I)(j) )*TOL, where norm( A(j) ) denotes the sum of
74 the absolute values of the jth row of the matrix A. If no such
75 j exists then IN(n) is returned as zero. If IN(n) is returned
76 as positive, then a diagonal element of U is small, indicating
77 that (T - lambda*I) is singular or nearly singular,
78 INFO (output) INTEGER
80 = 0 : successful exit
81 LAPACK routine (version 3.2) November 2008 SLAGTF(1)