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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"
// Dlasq5 computes one dqds transform in ping-pong form.
// i0 and n0 are zero-indexed.
//
// Dlasq5 is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dlasq5(i0, n0 int, z []float64, pp int, tau, sigma float64) (i0Out, n0Out, ppOut int, tauOut, sigmaOut, dmin, dmin1, dmin2, dn, dnm1, dnm2 float64) {
// The lapack function has inputs for ieee and eps, but Go requires ieee so
// these are unnecessary.
switch {
case i0 < 0:
panic(i0LT0)
case n0 < 0:
panic(n0LT0)
case len(z) < 4*n0:
panic(shortZ)
case pp != 0 && pp != 1:
panic(badPp)
}
if n0-i0-1 <= 0 {
return i0, n0, pp, tau, sigma, dmin, dmin1, dmin2, dn, dnm1, dnm2
}
eps := dlamchP
dthresh := eps * (sigma + tau)
if tau < dthresh*0.5 {
tau = 0
}
var j4 int
var emin float64
if tau != 0 {
j4 = 4*i0 + pp
emin = z[j4+4]
d := z[j4] - tau
dmin = d
// In the reference there are code paths that actually return this value.
// dmin1 = -z[j4]
if pp == 0 {
for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
j4 := j4loop - 1
z[j4-2] = d + z[j4-1]
tmp := z[j4+1] / z[j4-2]
d = d*tmp - tau
dmin = math.Min(dmin, d)
z[j4] = z[j4-1] * tmp
emin = math.Min(z[j4], emin)
}
} else {
for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
j4 := j4loop - 1
z[j4-3] = d + z[j4]
tmp := z[j4+2] / z[j4-3]
d = d*tmp - tau
dmin = math.Min(dmin, d)
z[j4-1] = z[j4] * tmp
emin = math.Min(z[j4-1], emin)
}
}
// Unroll the last two steps.
dnm2 = d
dmin2 = dmin
j4 = 4*((n0+1)-2) - pp - 1
j4p2 := j4 + 2*pp - 1
z[j4-2] = dnm2 + z[j4p2]
z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
dnm1 = z[j4p2+2]*(dnm2/z[j4-2]) - tau
dmin = math.Min(dmin, dnm1)
dmin1 = dmin
j4 += 4
j4p2 = j4 + 2*pp - 1
z[j4-2] = dnm1 + z[j4p2]
z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
dn = z[j4p2+2]*(dnm1/z[j4-2]) - tau
dmin = math.Min(dmin, dn)
} else {
// This is the version that sets d's to zero if they are small enough.
j4 = 4*(i0+1) + pp - 4
emin = z[j4+4]
d := z[j4] - tau
dmin = d
// In the reference there are code paths that actually return this value.
// dmin1 = -z[j4]
if pp == 0 {
for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
j4 := j4loop - 1
z[j4-2] = d + z[j4-1]
tmp := z[j4+1] / z[j4-2]
d = d*tmp - tau
if d < dthresh {
d = 0
}
dmin = math.Min(dmin, d)
z[j4] = z[j4-1] * tmp
emin = math.Min(z[j4], emin)
}
} else {
for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 {
j4 := j4loop - 1
z[j4-3] = d + z[j4]
tmp := z[j4+2] / z[j4-3]
d = d*tmp - tau
if d < dthresh {
d = 0
}
dmin = math.Min(dmin, d)
z[j4-1] = z[j4] * tmp
emin = math.Min(z[j4-1], emin)
}
}
// Unroll the last two steps.
dnm2 = d
dmin2 = dmin
j4 = 4*((n0+1)-2) - pp - 1
j4p2 := j4 + 2*pp - 1
z[j4-2] = dnm2 + z[j4p2]
z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
dnm1 = z[j4p2+2]*(dnm2/z[j4-2]) - tau
dmin = math.Min(dmin, dnm1)
dmin1 = dmin
j4 += 4
j4p2 = j4 + 2*pp - 1
z[j4-2] = dnm1 + z[j4p2]
z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2])
dn = z[j4p2+2]*(dnm1/z[j4-2]) - tau
dmin = math.Min(dmin, dn)
}
z[j4+2] = dn
z[4*(n0+1)-pp-1] = emin
return i0, n0, pp, tau, sigma, dmin, dmin1, dmin2, dn, dnm1, dnm2
}