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/* dlaneg.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"
integer dlaneg_(integer *n, doublereal *d__, doublereal *lld, doublereal *
sigma, doublereal *pivmin, integer *r__)
{
/* System generated locals */
integer ret_val, i__1, i__2, i__3, i__4;
/* Local variables */
integer j;
doublereal p, t;
integer bj;
doublereal tmp;
integer neg1, neg2;
doublereal bsav, gamma, dplus;
extern logical disnan_(doublereal *);
integer negcnt;
logical sawnan;
doublereal dminus;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLANEG computes the Sturm count, the number of negative pivots */
/* encountered while factoring tridiagonal T - sigma I = L D L^T. */
/* This implementation works directly on the factors without forming */
/* the tridiagonal matrix T. The Sturm count is also the number of */
/* eigenvalues of T less than sigma. */
/* This routine is called from DLARRB. */
/* The current routine does not use the PIVMIN parameter but rather */
/* requires IEEE-754 propagation of Infinities and NaNs. This */
/* routine also has no input range restrictions but does require */
/* default exception handling such that x/0 produces Inf when x is */
/* non-zero, and Inf/Inf produces NaN. For more information, see: */
/* Marques, Riedy, and Voemel, "Benefits of IEEE-754 Features in */
/* Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on */
/* Scientific Computing, v28, n5, 2006. DOI 10.1137/050641624 */
/* (Tech report version in LAWN 172 with the same title.) */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix. */
/* D (input) DOUBLE PRECISION array, dimension (N) */
/* The N diagonal elements of the diagonal matrix D. */
/* LLD (input) DOUBLE PRECISION array, dimension (N-1) */
/* The (N-1) elements L(i)*L(i)*D(i). */
/* SIGMA (input) DOUBLE PRECISION */
/* Shift amount in T - sigma I = L D L^T. */
/* PIVMIN (input) DOUBLE PRECISION */
/* The minimum pivot in the Sturm sequence. May be used */
/* when zero pivots are encountered on non-IEEE-754 */
/* architectures. */
/* R (input) INTEGER */
/* The twist index for the twisted factorization that is used */
/* for the negcount. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Osni Marques, LBNL/NERSC, USA */
/* Christof Voemel, University of California, Berkeley, USA */
/* Jason Riedy, University of California, Berkeley, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* Some architectures propagate Infinities and NaNs very slowly, so */
/* the code computes counts in BLKLEN chunks. Then a NaN can */
/* propagate at most BLKLEN columns before being detected. This is */
/* not a general tuning parameter; it needs only to be just large */
/* enough that the overhead is tiny in common cases. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--lld;
--d__;
/* Function Body */
negcnt = 0;
/* I) upper part: L D L^T - SIGMA I = L+ D+ L+^T */
t = -(*sigma);
i__1 = *r__ - 1;
for (bj = 1; bj <= i__1; bj += 128) {
neg1 = 0;
bsav = t;
/* Computing MIN */
i__3 = bj + 127, i__4 = *r__ - 1;
i__2 = min(i__3,i__4);
for (j = bj; j <= i__2; ++j) {
dplus = d__[j] + t;
if (dplus < 0.) {
++neg1;
}
tmp = t / dplus;
t = tmp * lld[j] - *sigma;
/* L21: */
}
sawnan = disnan_(&t);
/* Run a slower version of the above loop if a NaN is detected. */
/* A NaN should occur only with a zero pivot after an infinite */
/* pivot. In that case, substituting 1 for T/DPLUS is the */
/* correct limit. */
if (sawnan) {
neg1 = 0;
t = bsav;
/* Computing MIN */
i__3 = bj + 127, i__4 = *r__ - 1;
i__2 = min(i__3,i__4);
for (j = bj; j <= i__2; ++j) {
dplus = d__[j] + t;
if (dplus < 0.) {
++neg1;
}
tmp = t / dplus;
if (disnan_(&tmp)) {
tmp = 1.;
}
t = tmp * lld[j] - *sigma;
/* L22: */
}
}
negcnt += neg1;
/* L210: */
}
/* II) lower part: L D L^T - SIGMA I = U- D- U-^T */
p = d__[*n] - *sigma;
i__1 = *r__;
for (bj = *n - 1; bj >= i__1; bj += -128) {
neg2 = 0;
bsav = p;
/* Computing MAX */
i__3 = bj - 127;
i__2 = max(i__3,*r__);
for (j = bj; j >= i__2; --j) {
dminus = lld[j] + p;
if (dminus < 0.) {
++neg2;
}
tmp = p / dminus;
p = tmp * d__[j] - *sigma;
/* L23: */
}
sawnan = disnan_(&p);
/* As above, run a slower version that substitutes 1 for Inf/Inf. */
if (sawnan) {
neg2 = 0;
p = bsav;
/* Computing MAX */
i__3 = bj - 127;
i__2 = max(i__3,*r__);
for (j = bj; j >= i__2; --j) {
dminus = lld[j] + p;
if (dminus < 0.) {
++neg2;
}
tmp = p / dminus;
if (disnan_(&tmp)) {
tmp = 1.;
}
p = tmp * d__[j] - *sigma;
/* L24: */
}
}
negcnt += neg2;
/* L230: */
}
/* III) Twist index */
/* T was shifted by SIGMA initially. */
gamma = t + *sigma + p;
if (gamma < 0.) {
++negcnt;
}
ret_val = negcnt;
return ret_val;
} /* dlaneg_ */
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