1DLAGTS(1) LAPACK auxiliary routine (version 3.2) DLAGTS(1)
2
6 DLAGTS - may be used to solve one of the systems of equations (T -
7 lambda*I)*x = y or (T - lambda*I)'*x = y,
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10 SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )
11 INTEGER INFO, JOB, N
13 DOUBLE PRECISION TOL
15 INTEGER IN( * )
17 DOUBLE PRECISION A( * ), B( * ), C( * ), D( * ), Y( * )
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21 DLAGTS may be used to solve one of the systems of equations where T is
22 an n by n tridiagonal matrix, for x, following the factorization of (T
23 - lambda*I) as
24 (T - lambda*I) = P*L*U ,
25 by routine DLAGTF. The choice of equation to be solved is controlled by
26 the argument JOB, and in each case there is an option to perturb zero
27 or very small diagonal elements of U, this option being intended for
28 use in applications such as inverse iteration.
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31 JOB (input) INTEGER
32 Specifies the job to be performed by DLAGTS as follows:
33 = 1: The equations (T - lambda*I)x = y are to be solved, but
34 diagonal elements of U are not to be perturbed. = -1: The
35 equations (T - lambda*I)x = y are to be solved and, if over‐
36 flow would otherwise occur, the diagonal elements of U are to
37 be perturbed. See argument TOL below. = 2: The equations (T
38 - lambda*I)'x = y are to be solved, but diagonal elements of U
39 are not to be perturbed. = -2: The equations (T - lambda*I)'x
40 = y are to be solved and, if overflow would otherwise occur,
41 the diagonal elements of U are to be perturbed. See argument
42 TOL below.
43 N (input) INTEGER
45 The order of the matrix T.
46 A (input) DOUBLE PRECISION array, dimension (N)
48 On entry, A must contain the diagonal elements of U as returned
49 from DLAGTF.
50 B (input) DOUBLE PRECISION array, dimension (N-1)
52 On entry, B must contain the first super-diagonal elements of U
53 as returned from DLAGTF.
54 C (input) DOUBLE PRECISION array, dimension (N-1)
56 On entry, C must contain the sub-diagonal elements of L as
57 returned from DLAGTF.
58 D (input) DOUBLE PRECISION array, dimension (N-2)
60 On entry, D must contain the second super-diagonal elements of
61 U as returned from DLAGTF.
62 IN (input) INTEGER array, dimension (N)
64 On entry, IN must contain details of the matrix P as returned
65 from DLAGTF.
66 Y (input/output) DOUBLE PRECISION array, dimension (N)
68 On entry, the right hand side vector y. On exit, Y is over‐
69 written by the solution vector x.
70 TOL (input/output) DOUBLE PRECISION
72 On entry, with JOB .lt. 0, TOL should be the minimum perturba‐
73 tion to be made to very small diagonal elements of U. TOL
74 should normally be chosen as about eps*norm(U), where eps is
75 the relative machine precision, but if TOL is supplied as non-
76 positive, then it is reset to eps*max( abs( u(i,j) ) ). If
77 JOB .gt. 0 then TOL is not referenced. On exit, TOL is
78 changed as described above, only if TOL is non-positive on
79 entry. Otherwise TOL is unchanged.
80 INFO (output) INTEGER
82 = 0 : successful exit
83 element of the solution vector x. This can only occur when JOB
84 is supplied as positive and either means that a diagonal ele‐
85 ment of U is very small, or that the elements of the right-hand
86 side vector y are very large.
87 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008 DLAGTS(1)