/* Subroutine */ int dlasq3_(integer *i0, integer *n0, doublereal *z__,
integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig,
doublereal *qmax, integer *nfail, integer *iter, integer *ndiv,
logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2,
doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *g,
doublereal *tau)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal s, t;
integer j4, nn;
doublereal eps, tol;
integer n0in, ipn4;
doublereal tol2, temp;
extern /* Subroutine */ int dlasq4_(integer *, integer *, doublereal *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *,
doublereal *), dlasq5_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, logical *), dlasq6_(
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *);
extern doublereal dlamch_(char *);
extern logical disnan_(doublereal *);
/* -- 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 */
/* ======= */
/* DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds. */
/* In case of failure it changes shifts, and tries again until output */
/* is positive. */
/* Arguments */
/* ========= */
/* I0 (input) INTEGER */
/* First index. */
/* N0 (input) INTEGER */
/* Last index. */
/* Z (input) DOUBLE PRECISION array, dimension ( 4*N ) */
/* Z holds the qd array. */
/* PP (input/output) INTEGER */
/* PP=0 for ping, PP=1 for pong. */
/* PP=2 indicates that flipping was applied to the Z array */
/* and that the initial tests for deflation should not be */
/* performed. */
/* DMIN (output) DOUBLE PRECISION */
/* Minimum value of d. */
/* SIGMA (output) DOUBLE PRECISION */
/* Sum of shifts used in current segment. */
/* DESIG (input/output) DOUBLE PRECISION */
/* Lower order part of SIGMA */
/* QMAX (input) DOUBLE PRECISION */
/* Maximum value of q. */
/* NFAIL (output) INTEGER */
/* Number of times shift was too big. */
/* ITER (output) INTEGER */
/* Number of iterations. */
/* NDIV (output) INTEGER */
/* Number of divisions. */
/* IEEE (input) LOGICAL */
/* Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). */
/* TTYPE (input/output) INTEGER */
/* Shift type. */
/* DMIN1, DMIN2, DN, DN1, DN2, G, TAU (input/output) DOUBLE PRECISION */
/* These are passed as arguments in order to save their values */
/* between calls to DLASQ3. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Function .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--z__;
/* Function Body */
n0in = *n0;
eps = dlamch_("Precision");
tol = eps * 100.;
/* Computing 2nd power */
d__1 = tol;
tol2 = d__1 * d__1;
/* Check for deflation. */
L10:
if (*n0 < *i0) {
return 0;
}
if (*n0 == *i0) {
goto L20;
}
nn = (*n0 << 2) + *pp;
if (*n0 == *i0 + 1) {
goto L40;
}
/* Check whether E(N0-1) is negligible, 1 eigenvalue. */
if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) -
4] > tol2 * z__[nn - 7]) {
goto L30;
}
L20:
z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma;
--(*n0);
goto L10;
/* Check whether E(N0-2) is negligible, 2 eigenvalues. */
L30:
if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[
nn - 11]) {
goto L50;
}
L40:
if (z__[nn - 3] > z__[nn - 7]) {
s = z__[nn - 3];
z__[nn - 3] = z__[nn - 7];
z__[nn - 7] = s;
}
if (z__[nn - 5] > z__[nn - 3] * tol2) {
t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5;
s = z__[nn - 3] * (z__[nn - 5] / t);
if (s <= t) {
s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.) + 1.)));
} else {
s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s)));
}
t = z__[nn - 7] + (s + z__[nn - 5]);
z__[nn - 3] *= z__[nn - 7] / t;
z__[nn - 7] = t;
}
z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma;
z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma;
*n0 += -2;
goto L10;
L50:
if (*pp == 2) {
*pp = 0;
}
/* Reverse the qd-array, if warranted. */
if (*dmin__ <= 0. || *n0 < n0in) {
if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) {
ipn4 = *i0 + *n0 << 2;
i__1 = *i0 + *n0 - 1 << 1;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
temp = z__[j4 - 3];
z__[j4 - 3] = z__[ipn4 - j4 - 3];
z__[ipn4 - j4 - 3] = temp;
temp = z__[j4 - 2];
z__[j4 - 2] = z__[ipn4 - j4 - 2];
z__[ipn4 - j4 - 2] = temp;
temp = z__[j4 - 1];
z__[j4 - 1] = z__[ipn4 - j4 - 5];
z__[ipn4 - j4 - 5] = temp;
temp = z__[j4];
z__[j4] = z__[ipn4 - j4 - 4];
z__[ipn4 - j4 - 4] = temp;
/* L60: */
}
if (*n0 - *i0 <= 4) {
z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1];
z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp];
}
/* Computing MIN */
d__1 = *dmin2, d__2 = z__[(*n0 << 2) + *pp - 1];
*dmin2 = min(d__1,d__2);
/* Computing MIN */
d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1]
, d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3];
z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2);
/* Computing MIN */
d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 =
min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4];
z__[(*n0 << 2) - *pp] = min(d__1,d__2);
/* Computing MAX */
d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1,
d__2), d__2 = z__[(*i0 << 2) + *pp + 1];
*qmax = max(d__1,d__2);
*dmin__ = -0.;
}
}
/* Choose a shift. */
dlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, dn2,
tau, ttype, g);
/* Call dqds until DMIN > 0. */
L70:
dlasq5_(i0, n0, &z__[1], pp, tau, dmin__, dmin1, dmin2, dn, dn1, dn2,
ieee);
*ndiv += *n0 - *i0 + 2;
++(*iter);
/* Check status. */
if (*dmin__ >= 0. && *dmin1 > 0.) {
/* Success. */
goto L90;
} else if (*dmin__ < 0. && *dmin1 > 0. && z__[(*n0 - 1 << 2) - *pp] < tol
* (*sigma + *dn1) && abs(*dn) < tol * *sigma) {
/* Convergence hidden by negative DN. */
z__[(*n0 - 1 << 2) - *pp + 2] = 0.;
*dmin__ = 0.;
goto L90;
} else if (*dmin__ < 0.) {
/* TAU too big. Select new TAU and try again. */
++(*nfail);
if (*ttype < -22) {
/* Failed twice. Play it safe. */
*tau = 0.;
} else if (*dmin1 > 0.) {
/* Late failure. Gives excellent shift. */
*tau = (*tau + *dmin__) * (1. - eps * 2.);
*ttype += -11;
} else {
/* Early failure. Divide by 4. */
*tau *= .25;
*ttype += -12;
}
goto L70;
} else if (disnan_(dmin__)) {
/* NaN. */
if (*tau == 0.) {
goto L80;
} else {
*tau = 0.;
goto L70;
}
} else {
/* Possible underflow. Play it safe. */
goto L80;
}
/* Risk of underflow. */
L80:
dlasq6_(i0, n0, &z__[1], pp, dmin__, dmin1, dmin2, dn, dn1, dn2);
*ndiv += *n0 - *i0 + 2;
++(*iter);
*tau = 0.;
L90:
if (*tau < *sigma) {
*desig += *tau;
t = *sigma + *desig;
*desig -= t - *sigma;
} else {
t = *sigma + *tau;
*desig = *sigma - (t - *tau) + *desig;
}
*sigma = t;
return 0;
/* End of DLASQ3 */
} /* dlasq3_ */
/* Subroutine */ HYPRE_Int dlasq3_(integer *i0, integer *n0, doublereal *z__,
integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig,
doublereal *qmax, integer *nfail, integer *iter, integer *ndiv,
logical *ieee)
{
/* -- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
May 17, 2000
Purpose
=======
DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds.
In case of failure it changes shifts, and tries again until output
is positive.
Arguments
=========
I0 (input) INTEGER
First index.
N0 (input) INTEGER
Last index.
Z (input) DOUBLE PRECISION array, dimension ( 4*N )
Z holds the qd array.
PP (input) INTEGER
PP=0 for ping, PP=1 for pong.
DMIN (output) DOUBLE PRECISION
Minimum value of d.
SIGMA (output) DOUBLE PRECISION
Sum of shifts used in current segment.
DESIG (input/output) DOUBLE PRECISION
Lower order part of SIGMA
QMAX (input) DOUBLE PRECISION
Maximum value of q.
NFAIL (output) INTEGER
Number of times shift was too big.
ITER (output) INTEGER
Number of iterations.
NDIV (output) INTEGER
Number of divisions.
TTYPE (output) INTEGER
Shift type.
IEEE (input) LOGICAL
Flag for IEEE or non IEEE arithmetic (passed to DLASQ5).
=====================================================================
Parameter adjustments */
/* Initialized data */
static integer ttype = 0;
static doublereal dmin1 = 0.;
static doublereal dmin2 = 0.;
static doublereal dn = 0.;
static doublereal dn1 = 0.;
static doublereal dn2 = 0.;
static doublereal tau = 0.;
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static doublereal temp, s, t;
static integer j4;
extern /* Subroutine */ HYPRE_Int dlasq4_(integer *, integer *, doublereal *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *)
, dlasq5_(integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, logical *), dlasq6_(
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *);
extern doublereal dlamch_(char *);
static integer nn;
static doublereal safmin, eps, tol;
static integer n0in, ipn4;
static doublereal tol2;
--z__;
/* Function Body */
n0in = *n0;
eps = dlamch_("Precision");
safmin = dlamch_("Safe minimum");
tol = eps * 100.;
/* Computing 2nd power */
d__1 = tol;
tol2 = d__1 * d__1;
/* Check for deflation. */
L10:
if (*n0 < *i0) {
return 0;
}
if (*n0 == *i0) {
goto L20;
}
nn = (*n0 << 2) + *pp;
if (*n0 == *i0 + 1) {
goto L40;
}
/* Check whether E(N0-1) is negligible, 1 eigenvalue. */
if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) -
4] > tol2 * z__[nn - 7]) {
goto L30;
}
L20:
z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma;
--(*n0);
goto L10;
/* Check whether E(N0-2) is negligible, 2 eigenvalues. */
L30:
if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[
nn - 11]) {
goto L50;
}
L40:
if (z__[nn - 3] > z__[nn - 7]) {
s = z__[nn - 3];
z__[nn - 3] = z__[nn - 7];
z__[nn - 7] = s;
}
if (z__[nn - 5] > z__[nn - 3] * tol2) {
t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5;
s = z__[nn - 3] * (z__[nn - 5] / t);
if (s <= t) {
s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.) + 1.)));
} else {
s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s)));
}
t = z__[nn - 7] + (s + z__[nn - 5]);
z__[nn - 3] *= z__[nn - 7] / t;
z__[nn - 7] = t;
}
z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma;
z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma;
*n0 += -2;
goto L10;
L50:
/* Reverse the qd-array, if warranted. */
if (*dmin__ <= 0. || *n0 < n0in) {
if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) {
ipn4 = (*i0 + *n0) << 2;
i__1 = (*i0 + *n0 - 1) << 1;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
temp = z__[j4 - 3];
z__[j4 - 3] = z__[ipn4 - j4 - 3];
z__[ipn4 - j4 - 3] = temp;
temp = z__[j4 - 2];
z__[j4 - 2] = z__[ipn4 - j4 - 2];
z__[ipn4 - j4 - 2] = temp;
temp = z__[j4 - 1];
z__[j4 - 1] = z__[ipn4 - j4 - 5];
z__[ipn4 - j4 - 5] = temp;
temp = z__[j4];
z__[j4] = z__[ipn4 - j4 - 4];
z__[ipn4 - j4 - 4] = temp;
/* L60: */
}
if (*n0 - *i0 <= 4) {
z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1];
z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp];
}
/* Computing MIN */
d__1 = dmin2, d__2 = z__[(*n0 << 2) + *pp - 1];
dmin2 = min(d__1,d__2);
/* Computing MIN */
d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1]
, d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3];
z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2);
/* Computing MIN */
d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 =
min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4];
z__[(*n0 << 2) - *pp] = min(d__1,d__2);
/* Computing MAX */
d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1,
d__2), d__2 = z__[(*i0 << 2) + *pp + 1];
*qmax = max(d__1,d__2);
*dmin__ = 0.;
}
}
/* L70:
Computing MIN */
d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*n0 << 2) + *pp - 9], d__1 =
min(d__1,d__2), d__2 = dmin2 + z__[(*n0 << 2) - *pp];
if (*dmin__ < 0. || safmin * *qmax < min(d__1,d__2)) {
/* Choose a shift. */
dlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, &dmin1, &dmin2, &dn, &dn1,
&dn2, &tau, &ttype);
/* Call dqds until DMIN > 0. */
L80:
dlasq5_(i0, n0, &z__[1], pp, &tau, dmin__, &dmin1, &dmin2, &dn, &dn1,
&dn2, ieee);
*ndiv += *n0 - *i0 + 2;
++(*iter);
/* Check status. */
if (*dmin__ >= 0. && dmin1 > 0.) {
/* Success. */
goto L100;
} else if (*dmin__ < 0. && dmin1 > 0. && z__[((*n0 - 1) << 2) - *pp] <
tol * (*sigma + dn1) && abs(dn) < tol * *sigma) {
/* Convergence hidden by negative DN. */
z__[((*n0 - 1) << 2) - *pp + 2] = 0.;
*dmin__ = 0.;
goto L100;
} else if (*dmin__ < 0.) {
/* TAU too big. Select new TAU and try again. */
++(*nfail);
if (ttype < -22) {
/* Failed twice. Play it safe. */
tau = 0.;
} else if (dmin1 > 0.) {
/* Late failure. Gives excellent shift. */
tau = (tau + *dmin__) * (1. - eps * 2.);
ttype += -11;
} else {
/* Early failure. Divide by 4. */
tau *= .25;
ttype += -12;
}
goto L80;
} else if (*dmin__ != *dmin__) {
/* NaN. */
tau = 0.;
goto L80;
} else {
/* Possible underflow. Play it safe. */
goto L90;
}
}
/* Risk of underflow. */
L90:
dlasq6_(i0, n0, &z__[1], pp, dmin__, &dmin1, &dmin2, &dn, &dn1, &dn2);
*ndiv += *n0 - *i0 + 2;
++(*iter);
tau = 0.;
L100:
if (tau < *sigma) {
*desig += tau;
t = *sigma + *desig;
*desig -= t - *sigma;
} else {
t = *sigma + tau;
*desig = *sigma - (t - tau) + *desig;
}
*sigma = t;
return 0;
/* End of DLASQ3 */
} /* dlasq3_ */