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references/igraph-1.0.1/vendor/lapack/dlasq4.c
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/* -- translated by f2c (version 20240504).
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"
/* > \brief \b DLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous
transform. Used by sbdsqr.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DLASQ4 + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq4.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq4.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq4.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN,
DN1, DN2, TAU, TTYPE, G )
INTEGER I0, N0, N0IN, PP, TTYPE
DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU
DOUBLE PRECISION Z( * )
> \par Purpose:
=============
>
> \verbatim
>
> DLASQ4 computes an approximation TAU to the smallest eigenvalue
> using values of d from the previous transform.
> \endverbatim
Arguments:
==========
> \param[in] I0
> \verbatim
> I0 is INTEGER
> First index.
> \endverbatim
>
> \param[in] N0
> \verbatim
> N0 is INTEGER
> Last index.
> \endverbatim
>
> \param[in] Z
> \verbatim
> Z is DOUBLE PRECISION array, dimension ( 4*N )
> Z holds the qd array.
> \endverbatim
>
> \param[in] PP
> \verbatim
> PP is INTEGER
> PP=0 for ping, PP=1 for pong.
> \endverbatim
>
> \param[in] N0IN
> \verbatim
> N0IN is INTEGER
> The value of N0 at start of EIGTEST.
> \endverbatim
>
> \param[in] DMIN
> \verbatim
> DMIN is DOUBLE PRECISION
> Minimum value of d.
> \endverbatim
>
> \param[in] DMIN1
> \verbatim
> DMIN1 is DOUBLE PRECISION
> Minimum value of d, excluding D( N0 ).
> \endverbatim
>
> \param[in] DMIN2
> \verbatim
> DMIN2 is DOUBLE PRECISION
> Minimum value of d, excluding D( N0 ) and D( N0-1 ).
> \endverbatim
>
> \param[in] DN
> \verbatim
> DN is DOUBLE PRECISION
> d(N)
> \endverbatim
>
> \param[in] DN1
> \verbatim
> DN1 is DOUBLE PRECISION
> d(N-1)
> \endverbatim
>
> \param[in] DN2
> \verbatim
> DN2 is DOUBLE PRECISION
> d(N-2)
> \endverbatim
>
> \param[out] TAU
> \verbatim
> TAU is DOUBLE PRECISION
> This is the shift.
> \endverbatim
>
> \param[out] TTYPE
> \verbatim
> TTYPE is INTEGER
> Shift type.
> \endverbatim
>
> \param[in,out] G
> \verbatim
> G is REAL
> G is passed as an argument in order to save its value between
> calls to DLASQ4.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup auxOTHERcomputational
> \par Further Details:
=====================
>
> \verbatim
>
> CNST1 = 9/16
> \endverbatim
>
=====================================================================
Subroutine */ int igraphdlasq4_(integer *i0, integer *n0, doublereal *z__,
integer *pp, integer *n0in, doublereal *dmin__, doublereal *dmin1,
doublereal *dmin2, doublereal *dn, doublereal *dn1, doublereal *dn2,
doublereal *tau, integer *ttype, doublereal *g)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal s, a2, b1, b2;
integer i4, nn, np;
doublereal gam, gap1, gap2;
/* -- LAPACK computational routine (version 3.4.2) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
September 2012
=====================================================================
A negative DMIN forces the shift to take that absolute value
TTYPE records the type of shift.
Parameter adjustments */
--z__;
/* Function Body */
if (*dmin__ <= 0.) {
*tau = -(*dmin__);
*ttype = -1;
return 0;
}
nn = (*n0 << 2) + *pp;
if (*n0in == *n0) {
/* No eigenvalues deflated. */
if (*dmin__ == *dn || *dmin__ == *dn1) {
b1 = sqrt(z__[nn - 3]) * sqrt(z__[nn - 5]);
b2 = sqrt(z__[nn - 7]) * sqrt(z__[nn - 9]);
a2 = z__[nn - 7] + z__[nn - 5];
/* Cases 2 and 3. */
if (*dmin__ == *dn && *dmin1 == *dn1) {
gap2 = *dmin2 - a2 - *dmin2 * .25;
if (gap2 > 0. && gap2 > b2) {
gap1 = a2 - *dn - b2 / gap2 * b2;
} else {
gap1 = a2 - *dn - (b1 + b2);
}
if (gap1 > 0. && gap1 > b1) {
/* Computing MAX */
d__1 = *dn - b1 / gap1 * b1, d__2 = *dmin__ * .5;
s = max(d__1,d__2);
*ttype = -2;
} else {
s = 0.;
if (*dn > b1) {
s = *dn - b1;
}
if (a2 > b1 + b2) {
/* Computing MIN */
d__1 = s, d__2 = a2 - (b1 + b2);
s = min(d__1,d__2);
}
/* Computing MAX */
d__1 = s, d__2 = *dmin__ * .333;
s = max(d__1,d__2);
*ttype = -3;
}
} else {
/* Case 4. */
*ttype = -4;
s = *dmin__ * .25;
if (*dmin__ == *dn) {
gam = *dn;
a2 = 0.;
if (z__[nn - 5] > z__[nn - 7]) {
return 0;
}
b2 = z__[nn - 5] / z__[nn - 7];
np = nn - 9;
} else {
np = nn - (*pp << 1);
b2 = z__[np - 2];
gam = *dn1;
if (z__[np - 4] > z__[np - 2]) {
return 0;
}
a2 = z__[np - 4] / z__[np - 2];
if (z__[nn - 9] > z__[nn - 11]) {
return 0;
}
b2 = z__[nn - 9] / z__[nn - 11];
np = nn - 13;
}
/* Approximate contribution to norm squared from I < NN-1. */
a2 += b2;
i__1 = (*i0 << 2) - 1 + *pp;
for (i4 = np; i4 >= i__1; i4 += -4) {
if (b2 == 0.) {
goto L20;
}
b1 = b2;
if (z__[i4] > z__[i4 - 2]) {
return 0;
}
b2 *= z__[i4] / z__[i4 - 2];
a2 += b2;
if (max(b2,b1) * 100. < a2 || .563 < a2) {
goto L20;
}
/* L10: */
}
L20:
a2 *= 1.05;
/* Rayleigh quotient residual bound. */
if (a2 < .563) {
s = gam * (1. - sqrt(a2)) / (a2 + 1.);
}
}
} else if (*dmin__ == *dn2) {
/* Case 5. */
*ttype = -5;
s = *dmin__ * .25;
/* Compute contribution to norm squared from I > NN-2. */
np = nn - (*pp << 1);
b1 = z__[np - 2];
b2 = z__[np - 6];
gam = *dn2;
if (z__[np - 8] > b2 || z__[np - 4] > b1) {
return 0;
}
a2 = z__[np - 8] / b2 * (z__[np - 4] / b1 + 1.);
/* Approximate contribution to norm squared from I < NN-2. */
if (*n0 - *i0 > 2) {
b2 = z__[nn - 13] / z__[nn - 15];
a2 += b2;
i__1 = (*i0 << 2) - 1 + *pp;
for (i4 = nn - 17; i4 >= i__1; i4 += -4) {
if (b2 == 0.) {
goto L40;
}
b1 = b2;
if (z__[i4] > z__[i4 - 2]) {
return 0;
}
b2 *= z__[i4] / z__[i4 - 2];
a2 += b2;
if (max(b2,b1) * 100. < a2 || .563 < a2) {
goto L40;
}
/* L30: */
}
L40:
a2 *= 1.05;
}
if (a2 < .563) {
s = gam * (1. - sqrt(a2)) / (a2 + 1.);
}
} else {
/* Case 6, no information to guide us. */
if (*ttype == -6) {
*g += (1. - *g) * .333;
} else if (*ttype == -18) {
*g = .083250000000000005;
} else {
*g = .25;
}
s = *g * *dmin__;
*ttype = -6;
}
} else if (*n0in == *n0 + 1) {
/* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. */
if (*dmin1 == *dn1 && *dmin2 == *dn2) {
/* Cases 7 and 8. */
*ttype = -7;
s = *dmin1 * .333;
if (z__[nn - 5] > z__[nn - 7]) {
return 0;
}
b1 = z__[nn - 5] / z__[nn - 7];
b2 = b1;
if (b2 == 0.) {
goto L60;
}
i__1 = (*i0 << 2) - 1 + *pp;
for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {
a2 = b1;
if (z__[i4] > z__[i4 - 2]) {
return 0;
}
b1 *= z__[i4] / z__[i4 - 2];
b2 += b1;
if (max(b1,a2) * 100. < b2) {
goto L60;
}
/* L50: */
}
L60:
b2 = sqrt(b2 * 1.05);
/* Computing 2nd power */
d__1 = b2;
a2 = *dmin1 / (d__1 * d__1 + 1.);
gap2 = *dmin2 * .5 - a2;
if (gap2 > 0. && gap2 > b2 * a2) {
/* Computing MAX */
d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2);
s = max(d__1,d__2);
} else {
/* Computing MAX */
d__1 = s, d__2 = a2 * (1. - b2 * 1.01);
s = max(d__1,d__2);
*ttype = -8;
}
} else {
/* Case 9. */
s = *dmin1 * .25;
if (*dmin1 == *dn1) {
s = *dmin1 * .5;
}
*ttype = -9;
}
} else if (*n0in == *n0 + 2) {
/* Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN.
Cases 10 and 11. */
if (*dmin2 == *dn2 && z__[nn - 5] * 2. < z__[nn - 7]) {
*ttype = -10;
s = *dmin2 * .333;
if (z__[nn - 5] > z__[nn - 7]) {
return 0;
}
b1 = z__[nn - 5] / z__[nn - 7];
b2 = b1;
if (b2 == 0.) {
goto L80;
}
i__1 = (*i0 << 2) - 1 + *pp;
for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {
if (z__[i4] > z__[i4 - 2]) {
return 0;
}
b1 *= z__[i4] / z__[i4 - 2];
b2 += b1;
if (b1 * 100. < b2) {
goto L80;
}
/* L70: */
}
L80:
b2 = sqrt(b2 * 1.05);
/* Computing 2nd power */
d__1 = b2;
a2 = *dmin2 / (d__1 * d__1 + 1.);
gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[
nn - 9]) - a2;
if (gap2 > 0. && gap2 > b2 * a2) {
/* Computing MAX */
d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2);
s = max(d__1,d__2);
} else {
/* Computing MAX */
d__1 = s, d__2 = a2 * (1. - b2 * 1.01);
s = max(d__1,d__2);
}
} else {
s = *dmin2 * .25;
*ttype = -11;
}
} else if (*n0in > *n0 + 2) {
/* Case 12, more than two eigenvalues deflated. No information. */
s = 0.;
*ttype = -12;
}
*tau = s;
return 0;
/* End of DLASQ4 */
} /* igraphdlasq4_ */