github.com/jingcheng-WU/gonum@v0.9.1-0.20210323123734-f1a2a11a8f7b/lapack/gonum/dlae2.go (about)

     1  // Copyright ©2016 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package gonum
     6  
     7  import "math"
     8  
     9  // Dlae2 computes the eigenvalues of a 2×2 symmetric matrix
    10  //  [a b]
    11  //  [b c]
    12  // and returns the eigenvalue with the larger absolute value as rt1 and the
    13  // smaller as rt2.
    14  //
    15  // Dlae2 is an internal routine. It is exported for testing purposes.
    16  func (impl Implementation) Dlae2(a, b, c float64) (rt1, rt2 float64) {
    17  	sm := a + c
    18  	df := a - c
    19  	adf := math.Abs(df)
    20  	tb := b + b
    21  	ab := math.Abs(tb)
    22  	acmx := c
    23  	acmn := a
    24  	if math.Abs(a) > math.Abs(c) {
    25  		acmx = a
    26  		acmn = c
    27  	}
    28  	var rt float64
    29  	if adf > ab {
    30  		rt = adf * math.Sqrt(1+(ab/adf)*(ab/adf))
    31  	} else if adf < ab {
    32  		rt = ab * math.Sqrt(1+(adf/ab)*(adf/ab))
    33  	} else {
    34  		rt = ab * math.Sqrt2
    35  	}
    36  	if sm < 0 {
    37  		rt1 = 0.5 * (sm - rt)
    38  		rt2 = (acmx/rt1)*acmn - (b/rt1)*b
    39  		return rt1, rt2
    40  	}
    41  	if sm > 0 {
    42  		rt1 = 0.5 * (sm + rt)
    43  		rt2 = (acmx/rt1)*acmn - (b/rt1)*b
    44  		return rt1, rt2
    45  	}
    46  	rt1 = 0.5 * rt
    47  	rt2 = -0.5 * rt
    48  	return rt1, rt2
    49  }