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42 lines
1.1 KiB
Go
42 lines
1.1 KiB
Go
// Copyright ©2015 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package native
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import "math"
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// Dlas2 computes the singular values of the 2×2 matrix defined by
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// [F G]
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// [0 H]
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// The smaller and larger singular values are returned in that order.
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func (impl Implementation) Dlas2(f, g, h float64) (ssmin, ssmax float64) {
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fa := math.Abs(f)
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ga := math.Abs(g)
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ha := math.Abs(h)
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fhmin := math.Min(fa, ha)
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fhmax := math.Max(fa, ha)
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if fhmin == 0 {
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if fhmax == 0 {
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return 0, ga
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}
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v := math.Min(fhmax, ga) / math.Max(fhmax, ga)
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return 0, math.Max(fhmax, ga) * math.Sqrt(1+v*v)
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}
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if ga < fhmax {
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as := 1 + fhmin/fhmax
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at := (fhmax - fhmin) / fhmax
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au := (ga / fhmax) * (ga / fhmax)
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c := 2 / (math.Sqrt(as*as+au) + math.Sqrt(at*at+au))
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return fhmin * c, fhmax / c
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}
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au := fhmax / ga
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if au == 0 {
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return fhmin * fhmax / ga, ga
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}
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as := 1 + fhmin/fhmax
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at := (fhmax - fhmin) / fhmax
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c := 1 / (math.Sqrt(1+(as*au)*(as*au)) + math.Sqrt(1+(at*au)*(at*au)))
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return 2 * (fhmin * c) * au, ga / (c + c)
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}
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