mirror of
https://github.com/gonum/gonum.git
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91 lines
2.4 KiB
Go
91 lines
2.4 KiB
Go
// Copyright ©2018 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 mds
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import (
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"math"
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"gonum.org/v1/gonum/blas/blas64"
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"gonum.org/v1/gonum/mat"
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)
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// TorgersonScaling converts a dissimilarity matrix to a matrix containing
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// Euclidean coordinates. TorgersonScaling places the coordinates in dst and
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// returns it and the number of positive Eigenvalues if successful.
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// If the scaling is not successful, dst is returned, but will not be a valid scaling.
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// When the scaling is successful, mds will be resized to k columns wide.
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// Eigenvalues will be copied into eigdst and returned as eig if it is provided.
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//
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// If dst is nil, a new mat.Dense is allocated. If dst is not a zero matrix,
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// the dimensions of dst and dis must match otherwise TorgersonScaling will panic.
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// The dis matrix must be square or TorgersonScaling will panic.
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func TorgersonScaling(dst *mat.Dense, eigdst []float64, dis mat.Symmetric) (k int, mds *mat.Dense, eig []float64) {
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// https://doi.org/10.1007/0-387-28981-X_12
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n := dis.Symmetric()
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if dst == nil {
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dst = mat.NewDense(n, n, nil)
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} else if r, c := dst.Dims(); !dst.IsZero() && (r != n || c != n) {
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panic(mat.ErrShape)
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}
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b := mat.NewSymDense(n, nil)
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for i := 0; i < n; i++ {
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for j := i; j < n; j++ {
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v := dis.At(i, j)
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v *= v
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b.SetSym(i, j, v)
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}
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}
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c := mat.NewSymDense(n, nil)
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s := -1 / float64(n)
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for i := 0; i < n; i++ {
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c.SetSym(i, i, 1+s)
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for j := i + 1; j < n; j++ {
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c.SetSym(i, j, s)
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}
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}
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dst.Product(c, b, c)
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for i := 0; i < n; i++ {
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for j := i; j < n; j++ {
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b.SetSym(i, j, -0.5*dst.At(i, j))
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}
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}
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var ed mat.EigenSym
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ok := ed.Factorize(b, true)
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if !ok {
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return 0, dst, eigdst
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}
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ed.VectorsTo(dst)
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vals := ed.Values(nil)
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reverse(vals, dst.RawMatrix())
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copy(eigdst, vals)
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for i, v := range vals {
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if v < 0 {
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vals[i] = 0
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continue
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}
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k = i + 1
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vals[i] = math.Sqrt(v)
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}
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var tmp mat.Dense
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tmp.Mul(dst, mat.NewDiagonalRect(n, k, vals[:k]))
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dst = dst.Slice(0, n, 0, k).(*mat.Dense)
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dst.Copy(&tmp)
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return k, dst, eigdst
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}
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func reverse(values []float64, vectors blas64.General) {
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for i, j := 0, len(values)-1; i < j; i, j = i+1, j-1 {
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values[i], values[j] = values[j], values[i]
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blas64.Swap(blas64.Vector{N: vectors.Rows, Inc: vectors.Stride, Data: vectors.Data[i:]},
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blas64.Vector{N: vectors.Rows, Inc: vectors.Stride, Data: vectors.Data[j:]})
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}
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}
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