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