gonum.org/v1/gonum@v0.14.0/lapack/gonum/dlanst.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 (
     8  	"math"
     9  
    10  	"gonum.org/v1/gonum/lapack"
    11  )
    12  
    13  // Dlanst computes the specified norm of a symmetric tridiagonal matrix A.
    14  // The diagonal elements of A are stored in d and the off-diagonal elements
    15  // are stored in e.
    16  func (impl Implementation) Dlanst(norm lapack.MatrixNorm, n int, d, e []float64) float64 {
    17  	switch {
    18  	case norm != lapack.MaxRowSum && norm != lapack.MaxColumnSum && norm != lapack.Frobenius && norm != lapack.MaxAbs:
    19  		panic(badNorm)
    20  	case n < 0:
    21  		panic(nLT0)
    22  	}
    23  	if n == 0 {
    24  		return 0
    25  	}
    26  	switch {
    27  	case len(d) < n:
    28  		panic(shortD)
    29  	case len(e) < n-1:
    30  		panic(shortE)
    31  	}
    32  
    33  	switch norm {
    34  	default:
    35  		panic(badNorm)
    36  	case lapack.MaxAbs:
    37  		anorm := math.Abs(d[n-1])
    38  		for i := 0; i < n-1; i++ {
    39  			sum := math.Abs(d[i])
    40  			if anorm < sum || math.IsNaN(sum) {
    41  				anorm = sum
    42  			}
    43  			sum = math.Abs(e[i])
    44  			if anorm < sum || math.IsNaN(sum) {
    45  				anorm = sum
    46  			}
    47  		}
    48  		return anorm
    49  	case lapack.MaxColumnSum, lapack.MaxRowSum:
    50  		if n == 1 {
    51  			return math.Abs(d[0])
    52  		}
    53  		anorm := math.Abs(d[0]) + math.Abs(e[0])
    54  		sum := math.Abs(e[n-2]) + math.Abs(d[n-1])
    55  		if anorm < sum || math.IsNaN(sum) {
    56  			anorm = sum
    57  		}
    58  		for i := 1; i < n-1; i++ {
    59  			sum := math.Abs(d[i]) + math.Abs(e[i]) + math.Abs(e[i-1])
    60  			if anorm < sum || math.IsNaN(sum) {
    61  				anorm = sum
    62  			}
    63  		}
    64  		return anorm
    65  	case lapack.Frobenius:
    66  		var scale float64
    67  		sum := 1.0
    68  		if n > 1 {
    69  			scale, sum = impl.Dlassq(n-1, e, 1, scale, sum)
    70  			sum = 2 * sum
    71  		}
    72  		scale, sum = impl.Dlassq(n, d, 1, scale, sum)
    73  		return scale * math.Sqrt(sum)
    74  	}
    75  }