50 lines
1.1 KiB
Go
50 lines
1.1 KiB
Go
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// Copyright ©2016 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 gonum
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import "math"
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// Dlae2 computes the eigenvalues of a 2×2 symmetric matrix
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// [a b]
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// [b c]
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// and returns the eigenvalue with the larger absolute value as rt1 and the
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// smaller as rt2.
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//
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// Dlae2 is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dlae2(a, b, c float64) (rt1, rt2 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.Sqrt2
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}
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if sm < 0 {
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rt1 = 0.5 * (sm - rt)
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rt2 = (acmx/rt1)*acmn - (b/rt1)*b
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return rt1, rt2
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}
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if sm > 0 {
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rt1 = 0.5 * (sm + rt)
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rt2 = (acmx/rt1)*acmn - (b/rt1)*b
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return rt1, rt2
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}
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rt1 = 0.5 * rt
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rt2 = -0.5 * rt
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return rt1, rt2
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}
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