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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] } }