| // 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" |
| |
| // Dlas2 computes the singular values of the 2×2 matrix defined by |
| // [F G] |
| // [0 H] |
| // The smaller and larger singular values are returned in that order. |
| // |
| // Dlas2 is an internal routine. It is exported for testing purposes. |
| func (impl Implementation) Dlas2(f, g, h float64) (ssmin, ssmax float64) { |
| fa := math.Abs(f) |
| ga := math.Abs(g) |
| ha := math.Abs(h) |
| fhmin := math.Min(fa, ha) |
| fhmax := math.Max(fa, ha) |
| if fhmin == 0 { |
| if fhmax == 0 { |
| return 0, ga |
| } |
| v := math.Min(fhmax, ga) / math.Max(fhmax, ga) |
| return 0, math.Max(fhmax, ga) * math.Sqrt(1+v*v) |
| } |
| if ga < fhmax { |
| as := 1 + fhmin/fhmax |
| at := (fhmax - fhmin) / fhmax |
| au := (ga / fhmax) * (ga / fhmax) |
| c := 2 / (math.Sqrt(as*as+au) + math.Sqrt(at*at+au)) |
| return fhmin * c, fhmax / c |
| } |
| au := fhmax / ga |
| if au == 0 { |
| return fhmin * fhmax / ga, ga |
| } |
| as := 1 + fhmin/fhmax |
| at := (fhmax - fhmin) / fhmax |
| c := 1 / (math.Sqrt(1+(as*au)*(as*au)) + math.Sqrt(1+(at*au)*(at*au))) |
| return 2 * (fhmin * c) * au, ga / (c + c) |
| } |
