1DLAGTS(1) LAPACK auxiliary routine (version 3.1) DLAGTS(1)
2
6 DLAGTS - 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
22 where T is an n by n tridiagonal matrix, for x, following the factor‐
24 ization of (T - lambda*I) as
25 (T - lambda*I) = P*L*U ,
27 by routine DLAGTF. The choice of equation to be solved is controlled by
29 the argument JOB, and in each case there is an option to perturb zero
30 or very small diagonal elements of U, this option being intended for
31 use in applications such as inverse iteration.
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35 JOB (input) INTEGER
36 Specifies the job to be performed by DLAGTS as follows:
37 = 1: The equations (T - lambda*I)x = y are to be solved, but
38 diagonal elements of U are not to be perturbed. = -1: The
39 equations (T - lambda*I)x = y are to be solved and, if over‐
40 flow would otherwise occur, the diagonal elements of U are to
41 be perturbed. See argument TOL below. = 2: The equations (T
42 - lambda*I)'x = y are to be solved, but diagonal elements of U
43 are not to be perturbed. = -2: The equations (T - lambda*I)'x
44 = y are to be solved and, if overflow would otherwise occur,
45 the diagonal elements of U are to be perturbed. See argument
46 TOL below.
47 N (input) INTEGER
49 The order of the matrix T.
50 A (input) DOUBLE PRECISION array, dimension (N)
52 On entry, A must contain the diagonal elements of U as returned
53 from DLAGTF.
54 B (input) DOUBLE PRECISION array, dimension (N-1)
56 On entry, B must contain the first super-diagonal elements of U
57 as returned from DLAGTF.
58 C (input) DOUBLE PRECISION array, dimension (N-1)
60 On entry, C must contain the sub-diagonal elements of L as
61 returned from DLAGTF.
62 D (input) DOUBLE PRECISION array, dimension (N-2)
64 On entry, D must contain the second super-diagonal elements of
65 U as returned from DLAGTF.
66 IN (input) INTEGER array, dimension (N)
68 On entry, IN must contain details of the matrix P as returned
69 from DLAGTF.
70 Y (input/output) DOUBLE PRECISION array, dimension (N)
72 On entry, the right hand side vector y. On exit, Y is over‐
73 written by the solution vector x.
74 TOL (input/output) DOUBLE PRECISION
76 On entry, with JOB .lt. 0, TOL should be the minimum perturba‐
77 tion to be made to very small diagonal elements of U. TOL
78 should normally be chosen as about eps*norm(U), where eps is
79 the relative machine precision, but if TOL is supplied as non-
80 positive, then it is reset to eps*max( abs( u(i,j) ) ). If
81 JOB .gt. 0 then TOL is not referenced.
82 On exit, TOL is changed as described above, only if TOL is non-
84 positive on entry. Otherwise TOL is unchanged.
85 INFO (output) INTEGER
87 = 0 : successful exit
88 element of the solution vector x. This can only occur when JOB
89 is supplied as positive and either means that a diagonal ele‐
90 ment of U is very small, or that the elements of the right-hand
91 side vector y are very large.
92 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006 DLAGTS(1)