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// Copyright ©2018 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 mds
import (
"math"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/mat"
)
// TorgersonScaling converts a dissimilarity matrix to a matrix containing
// Euclidean coordinates. TorgersonScaling places the coordinates in dst and
// returns it and the number of positive Eigenvalues if successful.
// Note that Eigen Decomposition is numerically unstable and so Eigenvalues
// near zero should be examined and the value returned for k is advisory only.
// If the scaling is not successful, dst will be empty upon return.
// When the scaling is successful, dst will be resized to k columns wide.
// Eigenvalues will be copied into eigdst and returned as eig if it is provided.
//
// TorgersonScaling will panic if dst is not empty.
func TorgersonScaling(dst *mat.Dense, eigdst []float64, dis mat.Symmetric) (k int, eig []float64) {
// https://doi.org/10.1007/0-387-28981-X_12
n := dis.SymmetricDim()
if dst.IsEmpty() {
dst.ReuseAs(n, n)
} else {
panic("mds: receiver matrix not empty")
}
b := mat.NewSymDense(n, nil)
for i := 0; i < n; i++ {
for j := i; j < n; j++ {
v := dis.At(i, j)
v *= v
b.SetSym(i, j, v)
}
}
c := mat.NewSymDense(n, nil)
s := -1 / float64(n)
for i := 0; i < n; i++ {
c.SetSym(i, i, 1+s)
for j := i + 1; j < n; j++ {
c.SetSym(i, j, s)
}
}
dst.Product(c, b, c)
for i := 0; i < n; i++ {
for j := i; j < n; j++ {
b.SetSym(i, j, -0.5*dst.At(i, j))
}
}
var ed mat.EigenSym
ok := ed.Factorize(b, true)
if !ok {
return 0, eigdst
}
ed.VectorsTo(dst)
vals := ed.Values(nil)
reverse(vals, dst.RawMatrix())
copy(eigdst, vals)
for i, v := range vals {
if v < 0 {
vals[i] = 0
continue
}
k = i + 1
vals[i] = math.Sqrt(v)
}
var tmp mat.Dense
tmp.Mul(dst, mat.NewDiagonalRect(n, k, vals[:k]))
*dst = *dst.Slice(0, n, 0, k).(*mat.Dense)
dst.Copy(&tmp)
return k, eigdst
}
func reverse(values []float64, vectors blas64.General) {
for i, j := 0, len(values)-1; i < j; i, j = i+1, j-1 {
values[i], values[j] = values[j], values[i]
blas64.Swap(blas64.Vector{N: vectors.Rows, Inc: vectors.Stride, Data: vectors.Data[i:]},
blas64.Vector{N: vectors.Rows, Inc: vectors.Stride, Data: vectors.Data[j:]})
}
}
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