baggepinnen/spectraldistances.jl

Measure the distance between two spectra/signals using optimal transport and related metrics

This repository implements all optimal-transport based distances between spectra detailed in the following pre print

"New Metrics Between Rational Spectra and their Connection to Optimal Transport", Bagge Carlson and Chitre 2020

Supplementary material to the paper is provided in a separate repository.

The package also contains a number of generic solvers for optimal transport problems:

• Fixed support in 1d (histograms)
• Varying discrete support (atoms/dirac masses) with non-uniform masses in any dimension
• Barycenters supported on fixed number of atoms, but possibly with non-uniform masses
• Barycentric coordinates
• Continuous support in 1d

See the documentation for instructions.

Installation

using Pkg
pkg"add SpectralDistances"

Interpolation between two rational spectra under four different metrics.

Barycenter of three spectra and mixed spectrum which can be decomposed into a combination of the three input spectra

Example: Barycentric interpolation of spectrograms

The image below illustrates interpolation between 4 Mel spectrograms, each one representing a short whistle. See the folder examples for the code.

See the docs for more examples.

spectraldistances.jl's Issues

Failed to precompile SpectralDistances

julia> using SpectralDistances
[ Info: Precompiling SpectralDistances [2b0dec9d-f767-4f95-9e73-7df56487de68]
ERROR: LoadError: 
Stacktrace:
  [1] error()
    @ Base ./error.jl:44
  [2] convert(#unused#::Type{SciMLBase.ReturnCode.T}, retcode::Symbol)
    @ SciMLBase ~/.julia/packages/SciMLBase/3WNvC/src/retcodes.jl:361
  [3] SciMLBase.ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, SciMLBase.NullParameters, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, OrdinaryDiffEq.var"#lorenz#583", LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, OrdinaryDiffEq.BS3{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.InterpolationData{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, OrdinaryDiffEq.var"#lorenz#583", LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.BS3Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.BS3ConstantCache{Float64, Float64}, typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}}, DiffEqBase.DEStats, Nothing}(u::Vector{Vector{Float64}}, u_analytic::Nothing, errors::Nothing, t::Vector{Float64}, k::Vector{Vector{Vector{Float64}}}, prob::SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, SciMLBase.NullParameters, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, OrdinaryDiffEq.var"#lorenz#583", LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, alg::OrdinaryDiffEq.BS3{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, interp::OrdinaryDiffEq.InterpolationData{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, OrdinaryDiffEq.var"#lorenz#583", LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.BS3Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.BS3ConstantCache{Float64, Float64}, typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}}, dense::Bool, tslocation::Int64, destats::DiffEqBase.DEStats, alg_choice::Nothing, retcode::Symbol)
    @ SciMLBase ~/.julia/packages/SciMLBase/3WNvC/src/solutions/ode_solutions.jl:32
  [4] (SciMLBase.ODESolution{Float64, 2})(u::Vector{Vector{Float64}}, u_analytic::Nothing, errors::Nothing, t::Vector{Float64}, k::Vector{Vector{Vector{Float64}}}, prob::SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, SciMLBase.NullParameters, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, OrdinaryDiffEq.var"#lorenz#583", LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, alg::OrdinaryDiffEq.BS3{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, interp::OrdinaryDiffEq.InterpolationData{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, OrdinaryDiffEq.var"#lorenz#583", LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.BS3Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.BS3ConstantCache{Float64, Float64}, typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}}, dense::Bool, tslocation::Int64, destats::DiffEqBase.DEStats, alg_choice::Nothing, retcode::Symbol)
    @ SciMLBase ~/.julia/packages/SciMLBase/3WNvC/src/solutions/ode_solutions.jl:48
  [5] solution_new_retcode(sol::SciMLBase.ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, SciMLBase.NullParameters, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, OrdinaryDiffEq.var"#lorenz#583", LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, OrdinaryDiffEq.BS3{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.InterpolationData{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, OrdinaryDiffEq.var"#lorenz#583", LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.BS3Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.BS3ConstantCache{Float64, Float64}, typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}}, DiffEqBase.DEStats, Nothing}, retcode::Symbol)
    @ SciMLBase ~/.julia/packages/SciMLBase/3WNvC/src/solutions/ode_solutions.jl:248
  [6] solve!(integrator::OrdinaryDiffEq.ODEIntegrator{OrdinaryDiffEq.BS3{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, true, Vector{Float64}, Nothing, Float64, SciMLBase.NullParameters, Float64, Float64, Float64, Float64, Vector{Vector{Float64}}, SciMLBase.ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, SciMLBase.NullParameters, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, OrdinaryDiffEq.var"#lorenz#583", LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, OrdinaryDiffEq.BS3{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.InterpolationData{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, OrdinaryDiffEq.var"#lorenz#583", LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.BS3Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.BS3ConstantCache{Float64, Float64}, typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}}, DiffEqBase.DEStats, Nothing}, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, OrdinaryDiffEq.var"#lorenz#583", LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, OrdinaryDiffEq.BS3Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.BS3ConstantCache{Float64, Float64}, typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, OrdinaryDiffEq.PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Nothing, SciMLBase.CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Int64, Tuple{}, Tuple{}, Tuple{}}, Vector{Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit})
    @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/QXAKd/src/solve.jl:496
  [7] #__solve#559
    @ ~/.julia/packages/OrdinaryDiffEq/QXAKd/src/solve.jl:5 [inlined]
  [8] __solve
    @ ~/.julia/packages/OrdinaryDiffEq/QXAKd/src/solve.jl:1 [inlined]
  [9] #solve_call#39
    @ ~/.julia/packages/DiffEqBase/S7V8q/src/solve.jl:221 [inlined]
 [10] solve_call
    @ ~/.julia/packages/DiffEqBase/S7V8q/src/solve.jl:207 [inlined]
 [11] #solve_up#41
    @ ~/.julia/packages/DiffEqBase/S7V8q/src/solve.jl:248 [inlined]
 [12] solve_up
    @ ~/.julia/packages/DiffEqBase/S7V8q/src/solve.jl:237 [inlined]
 [13] #solve#40
    @ ~/.julia/packages/DiffEqBase/S7V8q/src/solve.jl:234 [inlined]
 [14] solve(prob::SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, SciMLBase.NullParameters, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, OrdinaryDiffEq.var"#lorenz#583", LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, args::OrdinaryDiffEq.BS3{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/S7V8q/src/solve.jl:226
 [15] top-level scope
    @ ~/.julia/packages/OrdinaryDiffEq/QXAKd/src/OrdinaryDiffEq.jl:189
 [16] include
    @ ./Base.jl:419 [inlined]
 [17] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt64}}, source::String)
    @ Base ./loading.jl:1554
 [18] top-level scope
    @ stdin:1
in expression starting at /home/ymtoo/.julia/packages/OrdinaryDiffEq/QXAKd/src/OrdinaryDiffEq.jl:1
in expression starting at stdin:1
ERROR: LoadError: Failed to precompile OrdinaryDiffEq [1dea7af3-3e70-54e6-95c3-0bf5283fa5ed] to /home/ymtoo/.julia/compiled/v1.8/OrdinaryDiffEq/jl_tIioGw.
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] compilecache(pkg::Base.PkgId, path::String, internal_stderr::IO, internal_stdout::IO, keep_loaded_modules::Bool)
    @ Base ./loading.jl:1707
  [3] compilecache
    @ ./loading.jl:1651 [inlined]
  [4] _require(pkg::Base.PkgId)
    @ Base ./loading.jl:1337
  [5] _require_prelocked(uuidkey::Base.PkgId)
    @ Base ./loading.jl:1200
  [6] macro expansion
    @ ./loading.jl:1180 [inlined]
  [7] macro expansion
    @ ./lock.jl:223 [inlined]
  [8] require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1144
  [9] include
    @ ./Base.jl:419 [inlined]
 [10] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt64}}, source::String)
    @ Base ./loading.jl:1554
 [11] top-level scope
    @ stdin:1
in expression starting at /home/ymtoo/.julia/packages/ControlSystems/nIXAR/src/ControlSystems.jl:1
in expression starting at stdin:1
ERROR: LoadError: Failed to precompile ControlSystems [a6e380b2-a6ca-5380-bf3e-84a91bcd477e] to /home/ymtoo/.julia/compiled/v1.8/ControlSystems/jl_Y5YZvn.
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] compilecache(pkg::Base.PkgId, path::String, internal_stderr::IO, internal_stdout::IO, keep_loaded_modules::Bool)
    @ Base ./loading.jl:1707
  [3] compilecache
    @ ./loading.jl:1651 [inlined]
  [4] _require(pkg::Base.PkgId)
    @ Base ./loading.jl:1337
  [5] _require_prelocked(uuidkey::Base.PkgId)
    @ Base ./loading.jl:1200
  [6] macro expansion
    @ ./loading.jl:1180 [inlined]
  [7] macro expansion
    @ ./lock.jl:223 [inlined]
  [8] require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1144
  [9] include
    @ ./Base.jl:419 [inlined]
 [10] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt64}}, source::Nothing)
    @ Base ./loading.jl:1554
 [11] top-level scope
    @ stdin:1
in expression starting at /home/ymtoo/.julia/packages/SpectralDistances/4bAKU/src/SpectralDistances.jl:1
in expression starting at stdin:1
ERROR: Failed to precompile SpectralDistances [2b0dec9d-f767-4f95-9e73-7df56487de68] to /home/ymtoo/.julia/compiled/v1.8/SpectralDistances/jl_RVo1FY.
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:35
 [2] compilecache(pkg::Base.PkgId, path::String, internal_stderr::IO, internal_stdout::IO, keep_loaded_modules::Bool)
   @ Base ./loading.jl:1707
 [3] compilecache
   @ ./loading.jl:1651 [inlined]
 [4] _require(pkg::Base.PkgId)
   @ Base ./loading.jl:1337
 [5] _require_prelocked(uuidkey::Base.PkgId)
   @ Base ./loading.jl:1200
 [6] macro expansion
   @ ./loading.jl:1180 [inlined]
 [7] macro expansion
   @ ./lock.jl:223 [inlined]
 [8] require(into::Module, mod::Symbol)
   @ Base ./loading.jl:1144

Julia and package versions:

julia> versioninfo()
Julia Version 1.8.3
Commit 0434deb161e (2022-11-14 20:14 UTC)
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 8 × Intel(R) Core(TM) i7-10510U CPU @ 1.80GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-13.0.1 (ORCJIT, skylake)
  Threads: 1 on 8 virtual cores
Environment:
  LD_LIBRARY_PATH = /opt/ros/noetic/lib::/usr/local/cuda/lib64

(jl_9WHt5Y) pkg> st
Status `/tmp/jl_9WHt5Y/Project.toml`
  [2b0dec9d] SpectralDistances v0.1.13

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Not compatible with Zygote v0.6.0

The error is due to package BackwardsLinalg.

(jl_AtlhSq) pkg> st
Status `/tmp/jl_AtlhSq/Project.toml`
  [2b0dec9d] SpectralDistances v0.1.11

(jl_AtlhSq) pkg> add Zygote#v0.6.0
  Resolving package versions...
ERROR: Unsatisfiable requirements detected for package BackwardsLinalg [442b4e1a]:
 BackwardsLinalg [442b4e1a] log:
 ├─possible versions are: 0.1.0-0.1.1 or uninstalled
 ├─restricted by compatibility requirements with Zygote [e88e6eb3] to versions: uninstalled
 │ └─Zygote [e88e6eb3] log:
 │   ├─possible versions are: 0.6.0 or uninstalled
 │   └─Zygote [e88e6eb3] is fixed to version 0.6.0
 └─restricted by compatibility requirements with SpectralDistances [2b0dec9d] to versions: 0.1.1 — no versions left
   └─SpectralDistances [2b0dec9d] log:
     ├─possible versions are: 0.1.0-0.1.11 or uninstalled
     └─restricted to versions * by an explicit requirement, leaving only versions 0.1.0-0.1.11

possible test failure in upcoming Julia version 1.5

A PkgEval run for a PR which changes the generated numbers for randn! indicates that the tests of this package might fail in Julia 1.5 (and on Julia current master). Apologies if this is a false positive.
cf. https://github.com/JuliaCI/NanosoldierReports/blob/7de24e455342298cbef56826b5827f0d7640d2c1/pkgeval/by_hash/b89e35c_vs_098ef24/logs/SpectralDistances/1.5.0-DEV-71a4a114c2.log