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/* dlarrr.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Subroutine */ int dlarrr_(integer *n, doublereal *d__, doublereal *e,
integer *info)
{
/* System generated locals */
integer i__1;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__;
doublereal eps, tmp, tmp2, rmin;
extern doublereal dlamch_(char *);
doublereal offdig, safmin;
logical yesrel;
doublereal smlnum, offdig2;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* Perform tests to decide whether the symmetric tridiagonal matrix T */
/* warrants expensive computations which guarantee high relative accuracy */
/* in the eigenvalues. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix. N > 0. */
/* D (input) DOUBLE PRECISION array, dimension (N) */
/* The N diagonal elements of the tridiagonal matrix T. */
/* E (input/output) DOUBLE PRECISION array, dimension (N) */
/* On entry, the first (N-1) entries contain the subdiagonal */
/* elements of the tridiagonal matrix T; E(N) is set to ZERO. */
/* INFO (output) INTEGER */
/* INFO = 0(default) : the matrix warrants computations preserving */
/* relative accuracy. */
/* INFO = 1 : the matrix warrants computations guaranteeing */
/* only absolute accuracy. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Beresford Parlett, University of California, Berkeley, USA */
/* Jim Demmel, University of California, Berkeley, USA */
/* Inderjit Dhillon, University of Texas, Austin, USA */
/* Osni Marques, LBNL/NERSC, USA */
/* Christof Voemel, University of California, Berkeley, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* As a default, do NOT go for relative-accuracy preserving computations. */
/* Parameter adjustments */
--e;
--d__;
/* Function Body */
*info = 1;
safmin = dlamch_("Safe minimum");
eps = dlamch_("Precision");
smlnum = safmin / eps;
rmin = sqrt(smlnum);
/* Tests for relative accuracy */
/* Test for scaled diagonal dominance */
/* Scale the diagonal entries to one and check whether the sum of the */
/* off-diagonals is less than one */
/* The sdd relative error bounds have a 1/(1- 2*x) factor in them, */
/* x = max(OFFDIG + OFFDIG2), so when x is close to 1/2, no relative */
/* accuracy is promised. In the notation of the code fragment below, */
/* 1/(1 - (OFFDIG + OFFDIG2)) is the condition number. */
/* We don't think it is worth going into "sdd mode" unless the relative */
/* condition number is reasonable, not 1/macheps. */
/* The threshold should be compatible with other thresholds used in the */
/* code. We set OFFDIG + OFFDIG2 <= .999 =: RELCOND, it corresponds */
/* to losing at most 3 decimal digits: 1 / (1 - (OFFDIG + OFFDIG2)) <= 1000 */
/* instead of the current OFFDIG + OFFDIG2 < 1 */
yesrel = TRUE_;
offdig = 0.;
tmp = sqrt((abs(d__[1])));
if (tmp < rmin) {
yesrel = FALSE_;
}
if (! yesrel) {
goto L11;
}
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
tmp2 = sqrt((d__1 = d__[i__], abs(d__1)));
if (tmp2 < rmin) {
yesrel = FALSE_;
}
if (! yesrel) {
goto L11;
}
offdig2 = (d__1 = e[i__ - 1], abs(d__1)) / (tmp * tmp2);
if (offdig + offdig2 >= .999) {
yesrel = FALSE_;
}
if (! yesrel) {
goto L11;
}
tmp = tmp2;
offdig = offdig2;
/* L10: */
}
L11:
if (yesrel) {
*info = 0;
return 0;
} else {
}
/* *** MORE TO BE IMPLEMENTED *** */
/* Test if the lower bidiagonal matrix L from T = L D L^T */
/* (zero shift facto) is well conditioned */
/* Test if the upper bidiagonal matrix U from T = U D U^T */
/* (zero shift facto) is well conditioned. */
/* In this case, the matrix needs to be flipped and, at the end */
/* of the eigenvector computation, the flip needs to be applied */
/* to the computed eigenvectors (and the support) */
return 0;
/* END OF DLARRR */
} /* dlarrr_ */
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