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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) } }