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// Copyright ©2016 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"
// Dlae2 computes the eigenvalues of a 2×2 symmetric matrix
// [a b]
// [b c]
// and returns the eigenvalue with the larger absolute value as rt1 and the
// smaller as rt2.
//
// Dlae2 is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dlae2(a, b, c float64) (rt1, rt2 float64) {
sm := a + c
df := a - c
adf := math.Abs(df)
tb := b + b
ab := math.Abs(tb)
acmx := c
acmn := a
if math.Abs(a) > math.Abs(c) {
acmx = a
acmn = c
}
var rt float64
if adf > ab {
rt = adf * math.Sqrt(1+(ab/adf)*(ab/adf))
} else if adf < ab {
rt = ab * math.Sqrt(1+(adf/ab)*(adf/ab))
} else {
rt = ab * math.Sqrt2
}
if sm < 0 {
rt1 = 0.5 * (sm - rt)
rt2 = (acmx/rt1)*acmn - (b/rt1)*b
return rt1, rt2
}
if sm > 0 {
rt1 = 0.5 * (sm + rt)
rt2 = (acmx/rt1)*acmn - (b/rt1)*b
return rt1, rt2
}
rt1 = 0.5 * rt
rt2 = -0.5 * rt
return rt1, rt2
}