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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"
"gonum.org/v1/gonum/lapack"
)
// Dlanst computes the specified norm of a symmetric tridiagonal matrix A.
// The diagonal elements of A are stored in d and the off-diagonal elements
// are stored in e.
func (impl Implementation) Dlanst(norm lapack.MatrixNorm, n int, d, e []float64) float64 {
switch {
case norm != lapack.MaxRowSum && norm != lapack.MaxColumnSum && norm != lapack.Frobenius && norm != lapack.MaxAbs:
panic(badNorm)
case n < 0:
panic(nLT0)
}
if n == 0 {
return 0
}
switch {
case len(d) < n:
panic(shortD)
case len(e) < n-1:
panic(shortE)
}
switch norm {
default:
panic(badNorm)
case lapack.MaxAbs:
anorm := math.Abs(d[n-1])
for i := 0; i < n-1; i++ {
sum := math.Abs(d[i])
if anorm < sum || math.IsNaN(sum) {
anorm = sum
}
sum = math.Abs(e[i])
if anorm < sum || math.IsNaN(sum) {
anorm = sum
}
}
return anorm
case lapack.MaxColumnSum, lapack.MaxRowSum:
if n == 1 {
return math.Abs(d[0])
}
anorm := math.Abs(d[0]) + math.Abs(e[0])
sum := math.Abs(e[n-2]) + math.Abs(d[n-1])
if anorm < sum || math.IsNaN(sum) {
anorm = sum
}
for i := 1; i < n-1; i++ {
sum := math.Abs(d[i]) + math.Abs(e[i]) + math.Abs(e[i-1])
if anorm < sum || math.IsNaN(sum) {
anorm = sum
}
}
return anorm
case lapack.Frobenius:
var scale float64
sum := 1.0
if n > 1 {
scale, sum = impl.Dlassq(n-1, e, 1, scale, sum)
sum = 2 * sum
}
scale, sum = impl.Dlassq(n, d, 1, scale, sum)
return scale * math.Sqrt(sum)
}
}
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