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83 lines
1.7 KiB
Go
83 lines
1.7 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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// Dlaev2 computes the Eigen decomposition of a symmetric 2×2 matrix.
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// The matrix is given by
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// [a b]
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// [b c]
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// Dlaev2 returns rt1 and rt2, the eigenvalues of the matrix where |RT1| > |RT2|,
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// and [cs1, sn1] which is the unit right eigenvalue for RT1.
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// [ cs1 sn1] [a b] [cs1 -sn1] = [rt1 0]
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// [-sn1 cs1] [b c] [sn1 cs1] [ 0 rt2]
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//
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// Dlaev2 is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dlaev2(a, b, c float64) (rt1, rt2, cs1, sn1 float64) {
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sm := a + c
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df := a - c
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adf := math.Abs(df)
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tb := b + b
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ab := math.Abs(tb)
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acmx := c
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acmn := a
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if math.Abs(a) > math.Abs(c) {
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acmx = a
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acmn = c
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}
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var rt float64
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if adf > ab {
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rt = adf * math.Sqrt(1+(ab/adf)*(ab/adf))
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} else if adf < ab {
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rt = ab * math.Sqrt(1+(adf/ab)*(adf/ab))
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} else {
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rt = ab * math.Sqrt(2)
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}
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var sgn1 float64
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if sm < 0 {
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rt1 = 0.5 * (sm - rt)
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sgn1 = -1
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rt2 = (acmx/rt1)*acmn - (b/rt1)*b
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} else if sm > 0 {
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rt1 = 0.5 * (sm + rt)
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sgn1 = 1
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rt2 = (acmx/rt1)*acmn - (b/rt1)*b
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} else {
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rt1 = 0.5 * rt
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rt2 = -0.5 * rt
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sgn1 = 1
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}
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var cs, sgn2 float64
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if df >= 0 {
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cs = df + rt
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sgn2 = 1
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} else {
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cs = df - rt
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sgn2 = -1
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}
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acs := math.Abs(cs)
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if acs > ab {
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ct := -tb / cs
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sn1 = 1 / math.Sqrt(1+ct*ct)
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cs1 = ct * sn1
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} else {
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if ab == 0 {
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cs1 = 1
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sn1 = 0
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} else {
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tn := -cs / tb
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cs1 = 1 / math.Sqrt(1+tn*tn)
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sn1 = tn * cs1
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}
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}
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if sgn1 == sgn2 {
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tn := cs1
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cs1 = -sn1
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sn1 = tn
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}
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return rt1, rt2, cs1, sn1
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}
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