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// Copyright ©2015 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package gonum
import "math"
// 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.
//
// Dlasq3 is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dlasq3(i0, n0 int, z []float64, pp int, dmin, sigma, desig, qmax float64, nFail, iter, nDiv int, ttype int, dmin1, dmin2, dn, dn1, dn2, g, tau float64) (
i0Out, n0Out, ppOut int, dminOut, sigmaOut, desigOut, qmaxOut float64, nFailOut, iterOut, nDivOut, ttypeOut int, dmin1Out, dmin2Out, dnOut, dn1Out, dn2Out, gOut, tauOut float64) {
switch {
case i0 < 0:
panic(i0LT0)
case n0 < 0:
panic(n0LT0)
case len(z) < 4*n0:
panic(shortZ)
case pp != 0 && pp != 1 && pp != 2:
panic(badPp)
}
const cbias = 1.5
n0in := n0
eps := dlamchP
tol := eps * 100
tol2 := tol * tol
var nn int
var t float64
for {
if n0 < i0 {
return i0, n0, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau
}
if n0 == i0 {
z[4*(n0+1)-4] = z[4*(n0+1)+pp-4] + sigma
n0--
continue
}
nn = 4*(n0+1) + pp - 1
if n0 != i0+1 {
// Check whether e[n0-1] is negligible, 1 eigenvalue.
if z[nn-5] > tol2*(sigma+z[nn-3]) && z[nn-2*pp-4] > tol2*z[nn-7] {
// Check whether e[n0-2] is negligible, 2 eigenvalues.
if z[nn-9] > tol2*sigma && z[nn-2*pp-8] > tol2*z[nn-11] {
break
}
} else {
z[4*(n0+1)-4] = z[4*(n0+1)+pp-4] + sigma
n0--
continue
}
}
if z[nn-3] > z[nn-7] {
z[nn-3], z[nn-7] = z[nn-7], z[nn-3]
}
t = 0.5 * (z[nn-7] - z[nn-3] + z[nn-5])
if z[nn-5] > z[nn-3]*tol2 && t != 0 {
s := z[nn-3] * (z[nn-5] / t)
if s <= t {
s = z[nn-3] * (z[nn-5] / (t * (1 + math.Sqrt(1+s/t))))
} else {
s = z[nn-3] * (z[nn-5] / (t + math.Sqrt(t)*math.Sqrt(t+s)))
}
t = z[nn-7] + (s + z[nn-5])
z[nn-3] *= z[nn-7] / t
z[nn-7] = t
}
z[4*(n0+1)-8] = z[nn-7] + sigma
z[4*(n0+1)-4] = z[nn-3] + sigma
n0 -= 2
}
if pp == 2 {
pp = 0
}
// Reverse the qd-array, if warranted.
if dmin <= 0 || n0 < n0in {
if cbias*z[4*(i0+1)+pp-4] < z[4*(n0+1)+pp-4] {
ipn4Out := 4 * (i0 + n0 + 2)
for j4loop := 4 * (i0 + 1); j4loop <= 2*((i0+1)+(n0+1)-1); j4loop += 4 {
ipn4 := ipn4Out - 1
j4 := j4loop - 1
z[j4-3], z[ipn4-j4-4] = z[ipn4-j4-4], z[j4-3]
z[j4-2], z[ipn4-j4-3] = z[ipn4-j4-3], z[j4-2]
z[j4-1], z[ipn4-j4-6] = z[ipn4-j4-6], z[j4-1]
z[j4], z[ipn4-j4-5] = z[ipn4-j4-5], z[j4]
}
if n0-i0 <= 4 {
z[4*(n0+1)+pp-2] = z[4*(i0+1)+pp-2]
z[4*(n0+1)-pp-1] = z[4*(i0+1)-pp-1]
}
dmin2 = math.Min(dmin2, z[4*(i0+1)-pp-2])
z[4*(n0+1)+pp-2] = math.Min(math.Min(z[4*(n0+1)+pp-2], z[4*(i0+1)+pp-2]), z[4*(i0+1)+pp+2])
z[4*(n0+1)-pp-1] = math.Min(math.Min(z[4*(n0+1)-pp-1], z[4*(i0+1)-pp-1]), z[4*(i0+1)-pp+3])
qmax = math.Max(math.Max(qmax, z[4*(i0+1)+pp-4]), z[4*(i0+1)+pp])
dmin = math.Copysign(0, -1) // Fortran code has -zero, but -0 in go is 0
}
}
// Choose a shift.
tau, ttype, g = impl.Dlasq4(i0, n0, z, pp, n0in, dmin, dmin1, dmin2, dn, dn1, dn2, tau, ttype, g)
// Call dqds until dmin > 0.
loop:
for {
i0, n0, pp, tau, sigma, dmin, dmin1, dmin2, dn, dn1, dn2 = impl.Dlasq5(i0, n0, z, pp, tau, sigma)
nDiv += n0 - i0 + 2
iter++
switch {
case dmin >= 0 && dmin1 >= 0:
// Success.
goto done
case dmin < 0 && dmin1 > 0 && z[4*n0-pp-1] < tol*(sigma+dn1) && math.Abs(dn) < tol*sigma:
// Convergence hidden by negative dn.
z[4*n0-pp+1] = 0
dmin = 0
goto done
case 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 - 2*eps)
ttype -= 11
} else {
// Early failure. Divide by 4.
tau = tau / 4
ttype -= 12
}
case math.IsNaN(dmin):
if tau == 0 {
break loop
}
tau = 0
default:
// Possible underflow. Play it safe.
break loop
}
}
// Risk of underflow.
dmin, dmin1, dmin2, dn, dn1, dn2 = impl.Dlasq6(i0, n0, z, pp)
nDiv += n0 - i0 + 2
iter++
tau = 0
done:
if tau < sigma {
desig += tau
t = sigma + desig
desig -= t - sigma
} else {
t = sigma + tau
desig += sigma - (t - tau)
}
sigma = t
return i0, n0, pp, dmin, sigma, desig, qmax, nFail, iter, nDiv, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau
}
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