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/* slasq4.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 slasq4_(integer *i0, integer *n0, real *z__, integer *pp,
integer *n0in, real *dmin__, real *dmin1, real *dmin2, real *dn,
real *dn1, real *dn2, real *tau, integer *ttype, real *g)
{
/* System generated locals */
integer i__1;
real r__1, r__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
real s, a2, b1, b2;
integer i4, nn, np;
real gam, gap1, gap2;
/* -- LAPACK routine (version 3.2) -- */
/* -- Contributed by Osni Marques of the Lawrence Berkeley National -- */
/* -- Laboratory and Beresford Parlett of the Univ. of California at -- */
/* -- Berkeley -- */
/* -- November 2008 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLASQ4 computes an approximation TAU to the smallest eigenvalue */
/* using values of d from the previous transform. */
/* I0 (input) INTEGER */
/* First index. */
/* N0 (input) INTEGER */
/* Last index. */
/* Z (input) REAL array, dimension ( 4*N ) */
/* Z holds the qd array. */
/* PP (input) INTEGER */
/* PP=0 for ping, PP=1 for pong. */
/* NOIN (input) INTEGER */
/* The value of N0 at start of EIGTEST. */
/* DMIN (input) REAL */
/* Minimum value of d. */
/* DMIN1 (input) REAL */
/* Minimum value of d, excluding D( N0 ). */
/* DMIN2 (input) REAL */
/* Minimum value of d, excluding D( N0 ) and D( N0-1 ). */
/* DN (input) REAL */
/* d(N) */
/* DN1 (input) REAL */
/* d(N-1) */
/* DN2 (input) REAL */
/* d(N-2) */
/* TAU (output) REAL */
/* This is the shift. */
/* TTYPE (output) INTEGER */
/* Shift type. */
/* G (input/output) REAL */
/* G is passed as an argument in order to save its value between */
/* calls to SLASQ4. */
/* Further Details */
/* =============== */
/* CNST1 = 9/16 */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* 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.f) {
*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 * .25f;
if (gap2 > 0.f && gap2 > b2) {
gap1 = a2 - *dn - b2 / gap2 * b2;
} else {
gap1 = a2 - *dn - (b1 + b2);
}
if (gap1 > 0.f && gap1 > b1) {
/* Computing MAX */
r__1 = *dn - b1 / gap1 * b1, r__2 = *dmin__ * .5f;
s = dmax(r__1,r__2);
*ttype = -2;
} else {
s = 0.f;
if (*dn > b1) {
s = *dn - b1;
}
if (a2 > b1 + b2) {
/* Computing MIN */
r__1 = s, r__2 = a2 - (b1 + b2);
s = dmin(r__1,r__2);
}
/* Computing MAX */
r__1 = s, r__2 = *dmin__ * .333f;
s = dmax(r__1,r__2);
*ttype = -3;
}
} else {
/* Case 4. */
*ttype = -4;
s = *dmin__ * .25f;
if (*dmin__ == *dn) {
gam = *dn;
a2 = 0.f;
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.f) {
goto L20;
}
b1 = b2;
if (z__[i4] > z__[i4 - 2]) {
return 0;
}
b2 *= z__[i4] / z__[i4 - 2];
a2 += b2;
if (dmax(b2,b1) * 100.f < a2 || .563f < a2) {
goto L20;
}
/* L10: */
}
L20:
a2 *= 1.05f;
/* Rayleigh quotient residual bound. */
if (a2 < .563f) {
s = gam * (1.f - sqrt(a2)) / (a2 + 1.f);
}
}
} else if (*dmin__ == *dn2) {
/* Case 5. */
*ttype = -5;
s = *dmin__ * .25f;
/* 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.f);
/* 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.f) {
goto L40;
}
b1 = b2;
if (z__[i4] > z__[i4 - 2]) {
return 0;
}
b2 *= z__[i4] / z__[i4 - 2];
a2 += b2;
if (dmax(b2,b1) * 100.f < a2 || .563f < a2) {
goto L40;
}
/* L30: */
}
L40:
a2 *= 1.05f;
}
if (a2 < .563f) {
s = gam * (1.f - sqrt(a2)) / (a2 + 1.f);
}
} else {
/* Case 6, no information to guide us. */
if (*ttype == -6) {
*g += (1.f - *g) * .333f;
} else if (*ttype == -18) {
*g = .083250000000000005f;
} else {
*g = .25f;
}
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 * .333f;
if (z__[nn - 5] > z__[nn - 7]) {
return 0;
}
b1 = z__[nn - 5] / z__[nn - 7];
b2 = b1;
if (b2 == 0.f) {
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 (dmax(b1,a2) * 100.f < b2) {
goto L60;
}
/* L50: */
}
L60:
b2 = sqrt(b2 * 1.05f);
/* Computing 2nd power */
r__1 = b2;
a2 = *dmin1 / (r__1 * r__1 + 1.f);
gap2 = *dmin2 * .5f - a2;
if (gap2 > 0.f && gap2 > b2 * a2) {
/* Computing MAX */
r__1 = s, r__2 = a2 * (1.f - a2 * 1.01f * (b2 / gap2) * b2);
s = dmax(r__1,r__2);
} else {
/* Computing MAX */
r__1 = s, r__2 = a2 * (1.f - b2 * 1.01f);
s = dmax(r__1,r__2);
*ttype = -8;
}
} else {
/* Case 9. */
s = *dmin1 * .25f;
if (*dmin1 == *dn1) {
s = *dmin1 * .5f;
}
*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.f < z__[nn - 7]) {
*ttype = -10;
s = *dmin2 * .333f;
if (z__[nn - 5] > z__[nn - 7]) {
return 0;
}
b1 = z__[nn - 5] / z__[nn - 7];
b2 = b1;
if (b2 == 0.f) {
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.f < b2) {
goto L80;
}
/* L70: */
}
L80:
b2 = sqrt(b2 * 1.05f);
/* Computing 2nd power */
r__1 = b2;
a2 = *dmin2 / (r__1 * r__1 + 1.f);
gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[
nn - 9]) - a2;
if (gap2 > 0.f && gap2 > b2 * a2) {
/* Computing MAX */
r__1 = s, r__2 = a2 * (1.f - a2 * 1.01f * (b2 / gap2) * b2);
s = dmax(r__1,r__2);
} else {
/* Computing MAX */
r__1 = s, r__2 = a2 * (1.f - b2 * 1.01f);
s = dmax(r__1,r__2);
}
} else {
s = *dmin2 * .25f;
*ttype = -11;
}
} else if (*n0in > *n0 + 2) {
/* Case 12, more than two eigenvalues deflated. No information. */
s = 0.f;
*ttype = -12;
}
*tau = s;
return 0;
/* End of SLASQ4 */
} /* slasq4_ */
|
