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SUBROUTINE <a name="DLAGTF.1"></a><a href="dlagtf.f.html#DLAGTF.1">DLAGTF</a>( N, A, LAMBDA, B, C, TOL, D, IN, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> INTEGER INFO, N
DOUBLE PRECISION LAMBDA, TOL
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IN( * )
DOUBLE PRECISION A( * ), B( * ), C( * ), D( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DLAGTF.19"></a><a href="dlagtf.f.html#DLAGTF.1">DLAGTF</a> factorizes the matrix (T - lambda*I), where T is an n by n
</span><span class="comment">*</span><span class="comment"> tridiagonal matrix and lambda is a scalar, as
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> T - lambda*I = PLU,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where P is a permutation matrix, L is a unit lower tridiagonal matrix
</span><span class="comment">*</span><span class="comment"> with at most one non-zero sub-diagonal elements per column and U is
</span><span class="comment">*</span><span class="comment"> an upper triangular matrix with at most two non-zero super-diagonal
</span><span class="comment">*</span><span class="comment"> elements per column.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The factorization is obtained by Gaussian elimination with partial
</span><span class="comment">*</span><span class="comment"> pivoting and implicit row scaling.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The parameter LAMBDA is included in the routine so that <a name="DLAGTF.32"></a><a href="dlagtf.f.html#DLAGTF.1">DLAGTF</a> may
</span><span class="comment">*</span><span class="comment"> be used, in conjunction with <a name="DLAGTS.33"></a><a href="dlagts.f.html#DLAGTS.1">DLAGTS</a>, to obtain eigenvectors of T by
</span><span class="comment">*</span><span class="comment"> inverse iteration.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input/output) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment"> On entry, A must contain the diagonal elements of T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, A is overwritten by the n diagonal elements of the
</span><span class="comment">*</span><span class="comment"> upper triangular matrix U of the factorization of T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LAMBDA (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> On entry, the scalar lambda.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B (input/output) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> On entry, B must contain the (n-1) super-diagonal elements of
</span><span class="comment">*</span><span class="comment"> T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, B is overwritten by the (n-1) super-diagonal
</span><span class="comment">*</span><span class="comment"> elements of the matrix U of the factorization of T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C (input/output) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> On entry, C must contain the (n-1) sub-diagonal elements of
</span><span class="comment">*</span><span class="comment"> T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, C is overwritten by the (n-1) sub-diagonal elements
</span><span class="comment">*</span><span class="comment"> of the matrix L of the factorization of T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TOL (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> On entry, a relative tolerance used to indicate whether or
</span><span class="comment">*</span><span class="comment"> not the matrix (T - lambda*I) is nearly singular. TOL should
</span><span class="comment">*</span><span class="comment"> normally be chose as approximately the largest relative error
</span><span class="comment">*</span><span class="comment"> in the elements of T. For example, if the elements of T are
</span><span class="comment">*</span><span class="comment"> correct to about 4 significant figures, then TOL should be
</span><span class="comment">*</span><span class="comment"> set to about 5*10**(-4). If TOL is supplied as less than eps,
</span><span class="comment">*</span><span class="comment"> where eps is the relative machine precision, then the value
</span><span class="comment">*</span><span class="comment"> eps is used in place of TOL.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> D (output) DOUBLE PRECISION array, dimension (N-2)
</span><span class="comment">*</span><span class="comment"> On exit, D is overwritten by the (n-2) second super-diagonal
</span><span class="comment">*</span><span class="comment"> elements of the matrix U of the factorization of T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IN (output) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment"> On exit, IN contains details of the permutation matrix P. If
</span><span class="comment">*</span><span class="comment"> an interchange occurred at the kth step of the elimination,
</span><span class="comment">*</span><span class="comment"> then IN(k) = 1, otherwise IN(k) = 0. The element IN(n)
</span><span class="comment">*</span><span class="comment"> returns the smallest positive integer j such that
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> abs( u(j,j) ).le. norm( (T - lambda*I)(j) )*TOL,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where norm( A(j) ) denotes the sum of the absolute values of
</span><span class="comment">*</span><span class="comment"> the jth row of the matrix A. If no such j exists then IN(n)
</span><span class="comment">*</span><span class="comment"> is returned as zero. If IN(n) is returned as positive, then a
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