--- /dev/null
+// 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) {
+ 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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