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116 lines
2.5 KiB
Go
116 lines
2.5 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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// Dlasv2 computes the singular value decomposition of a 2×2 matrix.
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// [ csl snl] [f g] [csr -snr] = [ssmax 0]
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// [-snl csl] [0 h] [snr csr] = [ 0 ssmin]
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// ssmax is the larger absolute singular value, and ssmin is the smaller absolute
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// singular value. [cls, snl] and [csr, snr] are the left and right singular vectors.
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//
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// Dlasv2 is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dlasv2(f, g, h float64) (ssmin, ssmax, snr, csr, snl, csl float64) {
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ft := f
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fa := math.Abs(ft)
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ht := h
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ha := math.Abs(h)
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// pmax points to the largest element of the matrix in terms of absolute value.
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// 1 if F, 2 if G, 3 if H.
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pmax := 1
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swap := ha > fa
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if swap {
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pmax = 3
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ft, ht = ht, ft
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fa, ha = ha, fa
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}
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gt := g
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ga := math.Abs(gt)
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var clt, crt, slt, srt float64
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if ga == 0 {
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ssmin = ha
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ssmax = fa
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clt = 1
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crt = 1
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slt = 0
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srt = 0
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} else {
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gasmall := true
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if ga > fa {
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pmax = 2
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if (fa / ga) < dlamchE {
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gasmall = false
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ssmax = ga
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if ha > 1 {
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ssmin = fa / (ga / ha)
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} else {
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ssmin = (fa / ga) * ha
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}
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clt = 1
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slt = ht / gt
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srt = 1
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crt = ft / gt
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}
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}
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if gasmall {
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d := fa - ha
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l := d / fa
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if d == fa { // deal with inf
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l = 1
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}
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m := gt / ft
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t := 2 - l
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s := math.Hypot(t, m)
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var r float64
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if l == 0 {
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r = math.Abs(m)
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} else {
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r = math.Hypot(l, m)
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}
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a := 0.5 * (s + r)
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ssmin = ha / a
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ssmax = fa * a
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if m == 0 {
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if l == 0 {
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t = math.Copysign(2, ft) * math.Copysign(1, gt)
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} else {
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t = gt/math.Copysign(d, ft) + m/t
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}
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} else {
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t = (m/(s+t) + m/(r+l)) * (1 + a)
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}
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l = math.Hypot(t, 2)
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crt = 2 / l
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srt = t / l
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clt = (crt + srt*m) / a
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slt = (ht / ft) * srt / a
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}
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}
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if swap {
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csl = srt
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snl = crt
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csr = slt
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snr = clt
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} else {
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csl = clt
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snl = slt
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csr = crt
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snr = srt
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}
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var tsign float64
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switch pmax {
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case 1:
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tsign = math.Copysign(1, csr) * math.Copysign(1, csl) * math.Copysign(1, f)
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case 2:
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tsign = math.Copysign(1, snr) * math.Copysign(1, csl) * math.Copysign(1, g)
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case 3:
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tsign = math.Copysign(1, snr) * math.Copysign(1, snl) * math.Copysign(1, h)
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}
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ssmax = math.Copysign(ssmax, tsign)
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ssmin = math.Copysign(ssmin, tsign*math.Copysign(1, f)*math.Copysign(1, h))
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return ssmin, ssmax, snr, csr, snl, csl
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}
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