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5f0141ca4c
Changes made in dsp/fourier/internal/fftpack break the formatting used there, so these are reverted. There will be complaints in CI. [git-generate] gofmt -w . go generate gonum.org/v1/gonum/blas go generate gonum.org/v1/gonum/blas/gonum go generate gonum.org/v1/gonum/unit go generate gonum.org/v1/gonum/unit/constant go generate gonum.org/v1/gonum/graph/formats/dot go generate gonum.org/v1/gonum/graph/formats/rdf go generate gonum.org/v1/gonum/stat/card git checkout -- dsp/fourier/internal/fftpack
99 lines
2.8 KiB
Go
99 lines
2.8 KiB
Go
// Copyright ©2017 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 network
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import (
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"gonum.org/v1/gonum/graph/spectral"
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"gonum.org/v1/gonum/mat"
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)
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// Diffuse performs a heat diffusion across nodes of the undirected
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// graph described by the given Laplacian using the initial heat distribution,
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// h, according to the Laplacian with a diffusion time of t.
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// The resulting heat distribution is returned, written into the map dst and
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// returned,
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//
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// d = exp(-Lt)×h
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//
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// where L is the graph Laplacian. Indexing into h and dst is defined by the
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// Laplacian Index field. If dst is nil, a new map is created.
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//
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// Nodes without corresponding entries in h are given an initial heat of zero,
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// and entries in h without a corresponding node in the original graph are
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// not altered when written to dst.
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func Diffuse(dst, h map[int64]float64, by spectral.Laplacian, t float64) map[int64]float64 {
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heat := make([]float64, len(by.Index))
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for id, i := range by.Index {
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heat[i] = h[id]
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}
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v := mat.NewVecDense(len(heat), heat)
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var m, tl mat.Dense
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tl.Scale(-t, by)
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m.Exp(&tl)
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v.MulVec(&m, v)
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if dst == nil {
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dst = make(map[int64]float64)
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}
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for i, n := range heat {
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dst[by.Nodes[i].ID()] = n
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}
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return dst
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}
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// DiffuseToEquilibrium performs a heat diffusion across nodes of the
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// graph described by the given Laplacian using the initial heat
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// distribution, h, according to the Laplacian until the update function
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//
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// h_{n+1} = h_n - L×h_n
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//
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// results in a 2-norm update difference within tol, or iters updates have
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// been made.
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// The resulting heat distribution is returned as eq, written into the map dst,
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// and a boolean indicating whether the equilibrium converged to within tol.
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// Indexing into h and dst is defined by the Laplacian Index field. If dst
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// is nil, a new map is created.
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//
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// Nodes without corresponding entries in h are given an initial heat of zero,
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// and entries in h without a corresponding node in the original graph are
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// not altered when written to dst.
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func DiffuseToEquilibrium(dst, h map[int64]float64, by spectral.Laplacian, tol float64, iters int) (eq map[int64]float64, ok bool) {
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heat := make([]float64, len(by.Index))
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for id, i := range by.Index {
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heat[i] = h[id]
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}
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v := mat.NewVecDense(len(heat), heat)
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last := make([]float64, len(by.Index))
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for id, i := range by.Index {
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last[i] = h[id]
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}
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lastV := mat.NewVecDense(len(last), last)
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var tmp mat.VecDense
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for {
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iters--
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if iters < 0 {
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break
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}
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lastV, v = v, lastV
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tmp.MulVec(by.Matrix, lastV)
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v.SubVec(lastV, &tmp)
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if normDiff(heat, last) < tol {
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ok = true
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break
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}
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}
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if dst == nil {
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dst = make(map[int64]float64)
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}
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for i, n := range v.RawVector().Data {
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dst[by.Nodes[i].ID()] = n
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}
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return dst, ok
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}
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