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// Copyright ©2016 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"
// Dlaqr1 sets v to a scalar multiple of the first column of the product
// (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)
// where H is a 2×2 or 3×3 matrix, I is the identity matrix of the same size,
// and i is the imaginary unit. Scaling is done to avoid overflows and most
// underflows.
//
// n is the order of H and must be either 2 or 3. It must hold that either sr1 =
// sr2 and si1 = -si2, or si1 = si2 = 0. The length of v must be equal to n. If
// any of these conditions is not met, Dlaqr1 will panic.
//
// Dlaqr1 is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dlaqr1(n int, h []float64, ldh int, sr1, si1, sr2, si2 float64, v []float64) {
switch {
case n != 2 && n != 3:
panic("lapack: n must be 2 or 3")
case ldh < n:
panic(badLdH)
case len(h) < (n-1)*ldh+n:
panic(shortH)
case !((sr1 == sr2 && si1 == -si2) || (si1 == 0 && si2 == 0)):
panic(badShifts)
case len(v) != n:
panic(shortV)
}
if n == 2 {
s := math.Abs(h[0]-sr2) + math.Abs(si2) + math.Abs(h[ldh])
if s == 0 {
v[0] = 0
v[1] = 0
} else {
h21s := h[ldh] / s
v[0] = h21s*h[1] + (h[0]-sr1)*((h[0]-sr2)/s) - si1*(si2/s)
v[1] = h21s * (h[0] + h[ldh+1] - sr1 - sr2)
}
return
}
s := math.Abs(h[0]-sr2) + math.Abs(si2) + math.Abs(h[ldh]) + math.Abs(h[2*ldh])
if s == 0 {
v[0] = 0
v[1] = 0
v[2] = 0
} else {
h21s := h[ldh] / s
h31s := h[2*ldh] / s
v[0] = (h[0]-sr1)*((h[0]-sr2)/s) - si1*(si2/s) + h[1]*h21s + h[2]*h31s
v[1] = h21s*(h[0]+h[ldh+1]-sr1-sr2) + h[ldh+2]*h31s
v[2] = h31s*(h[0]+h[2*ldh+2]-sr1-sr2) + h21s*h[2*ldh+1]
}
}