More flexible radial basis embedding

examples/potential/forces.jl

@@ -1,38 +1,34 @@
-using EquivariantModels, Lux, StaticArrays, Random, LinearAlgebra, Zygote 
+using EquivariantModels, Lux, StaticArrays, Random, LinearAlgebra, Zygote, Polynomials4ML
 using Polynomials4ML: LinearLayer, RYlmBasis, lux 
-using EquivariantModels: degord2spec, specnlm2spec1p, xx2AA
+using EquivariantModels: degord2spec, specnlm2spec1p, xx2AA, simple_radial_basis
 rng = Random.MersenneTwister()
 
 ##
 
 rcut = 5.5 
 maxL = 0
-Aspec, AAspec = degord2spec(; totaldegree = 6, 
-                              order = 3, 
+totdeg = 6
+ord = 3
+
+fcut(rcut::Float64,pin::Int=2,pout::Int=2) = r -> (r < rcut ? abs( (r/rcut)^pin - 1)^pout : 0)
+ftrans(r0::Float64=.0,p::Int=2) = r -> ( (1+r0)/(1+r) )^p
+radial = simple_radial_basis(legendre_basis(totdeg),fcut(rcut),ftrans())
+
+Aspec, AAspec = degord2spec(radial; totaldegree = totdeg, 
+                              order = ord, 
                               Lmax = maxL, )
 
-l_basis, ps_basis, st_basis = equivariant_model(AAspec, maxL)
+l_basis, ps_basis, st_basis = equivariant_model(AAspec, radial, maxL; islong = false)
 X = [ @SVector(randn(3)) for i in 1:10 ]
-B = l_basis(X, ps_basis, st_basis)[1][1]
+B = l_basis(X, ps_basis, st_basis)[1]
 
-# now build another model with a better transform 
-L = maximum(b.l for b in Aspec) 
+# now extend the above BB basis to a model
 len_BB = length(B) 
-get1 = WrappedFunction(t -> t[1])
-embed = Parallel(nothing; 
-       Rn = Chain(trans = WrappedFunction(xx -> [1/(1+norm(x)) for x in xx]), 
-                   poly = l_basis.layers.embed.layers.Rn, ), 
-      Ylm = Chain(Ylm = lux(RYlmBasis(L)),  ) )
-
-model = Chain( 
-         embed = embed, 
-         A = l_basis.layers.A, 
-         AA = l_basis.layers.AA, 
-         # AA_sort = l_basis.layers.AA_sort, 
-         BB = l_basis.layers.BB, 
-         get1 = WrappedFunction(t -> t[1]), 
-         dot = LinearLayer(len_BB, 1), 
-         get2 = WrappedFunction(t -> t[1]), )
+
+model = append_layer(l_basis, WrappedFunction(t -> real(t)); l_name=:real)
+model = append_layer(model, LinearLayer(len_BB, 1); l_name=:dot)
+model = append_layer(model, WrappedFunction(t -> t[1]); l_name=:get1)
+
 ps, st = Lux.setup(rng, model)
 out, st = model(X, ps, st)
 
@@ -158,7 +154,7 @@ end
 
 using JuLIP
 JuLIP.usethreads!(false) 
-ps.dot.W[:] .= 0.01 * randn(length(ps.dot.W)) 
+ps.dot.W[:] .= 1e-2 * randn(length(ps.dot.W)) 
 
 at = rattle!(bulk(:W, cubic=true, pbc=true) * 2, 0.1)
 calc = Pot.LuxCalc(model, ps, st, rcut)
@@ -217,4 +213,4 @@ end
 loss(at, calc, p_vec)
 
 
-ReverseDiff.gradient(p -> loss(at, calc, p), p_vec)
+# ReverseDiff.gradient(p -> loss(at, calc, p), p_vec)

examples/potential/test_potential.jl

@@ -17,7 +17,7 @@ function grad_test2(f, df, X::AbstractVector; verbose = true)
    verbose && @printf("---------|----------- \n")
    verbose && @printf("    h    | error \n")
    verbose && @printf("---------|----------- \n")
-   for h in 0.1.^(-3:9)
+   for h in 0.1.^(0:12)
       gh = [ (f(X + h * EE[:, i]) - F) / h for i = 1:nX ]
       verbose && @printf(" %.1e | %.2e \n", h, norm(gh - ∇F, Inf))
    end
@@ -27,10 +27,16 @@ rng = Random.MersenneTwister()
 
 rcut = 5.5 
 maxL = 0
-L = 0
-Aspec, AAspec = degord2spec(; totaldegree = 6, 
-                                  order = 3, 
-                                  Lmax = 0, )
+totdeg = 6
+ord = 3
+
+fcut(rcut::Float64,pin::Int=2,pout::Int=2) = r -> (r < rcut ? abs( (r/rcut)^pin - 1)^pout : 0)
+ftrans(r0::Float64=.0,p::Int=2) = r -> ( (1+r0)/(1+r) )^p
+radial = simple_radial_basis(legendre_basis(totdeg),fcut(rcut),ftrans())
+
+Aspec, AAspec = degord2spec(radial; totaldegree = totdeg, 
+                              order = ord, 
+                              Lmax = maxL, )
 cats = AtomicNumber.([:W, :Cu, :Ni, :Fe, :Al])
 ipairs = collect(Combinatorics.permutations(1:length(cats), 2))
 allcats = collect(SVector{2}.(Combinatorics.permutations(cats, 2)))
@@ -52,7 +58,7 @@ for bb in ori_AAspec
    push!(new_AAspec, newbb)
 end
 
-luxchain, ps, st = equivariant_model(new_AAspec, L; categories=allcats, islong = false)
+luxchain, ps, st = equivariant_model(new_AAspec, radial, L; categories=allcats, islong = false)
 
 at = rattle!(bulk(:W, cubic=true, pbc=true) * 2, 0.1)
 iCu = [5, 12]; iNi = [3, 8]; iAl = [10]; iFe = [6];
@@ -67,7 +73,7 @@ get_Z0S(zz0, ZZS) = [SVector{2}(zz0, zzs) for zzs in ZZS]
 Z0S = get_Z0S(z0, Zs)
 
 # input of luxmodel
-X = (Rs, Z0S)
+X = [Rs, Z0S]
 
 out, st = luxchain(X, ps, st)
 
@@ -85,12 +91,13 @@ model(X, ps, st)
 g = Zygote.gradient(X -> model(X, ps, st)[1], X)[1]
 
 
-F(Rs) = model((Rs, Z0S), ps, st)[1]
-dF(Rs) = Zygote.gradient(rs -> model((rs, Z0S), ps, st)[1], Rs)[1]
+F(Rs) = model([Rs, Z0S], ps, st)[1]
+dF(Rs) = Zygote.gradient(rs -> model([rs, Z0S], ps, st)[1], Rs)[1]
 
 ##
 @info("test derivative w.r.t X")
 print_tf(@test fdtest(F, dF, Rs; verbose=true))
+println()
 
 
 @info("test derivative w.r.t parameter")

src/EquivariantModels.jl

@@ -1,5 +1,6 @@
 module EquivariantModels
 
+include("radial.jl")
 include("utils.jl")
 include("lux_utils.jl")
 include("categorical.jl")

src/builder.jl

@@ -1,6 +1,6 @@
 using LinearAlgebra
 using SparseArrays: SparseMatrixCSC, sparse
-using RepLieGroups.O3: Rot3DCoeffs, Rot3DCoeffs_real, Rot3DCoeffs_long, re_basis, SYYVector
+using RepLieGroups.O3: Rot3DCoeffs, Rot3DCoeffs_real, Rot3DCoeffs_long, re_basis, SYYVector, mm_filter
 using Polynomials4ML: legendre_basis, RYlmBasis, natural_indices, degree
 using Polynomials4ML.Utils: gensparse
 using Lux: WrappedFunction
@@ -16,6 +16,8 @@ P4ML = Polynomials4ML
 RPE_filter(L) = bb -> (length(bb) == 0) || ((abs(sum(b.m for b in bb)) <= L) && iseven(sum(b.l for b in bb)+L))
 RPE_filter_long(L) = bb -> (length(bb) == 0) || (abs(sum(b.m for b in bb)) <= L)
 
+RPE_filter_real(L) = bb -> (length(bb) == 0) || mm_filter([b.m for b in bb],L) && iseven(sum(b.l for b in bb)+L)
+
 """
 _rpi_A2B_matrix(cgen::Union{Rot3DCoeffs{L,T},Rot3DCoeffs_real{L,T},Rot3DCoeffs_long{L,T}},
                 spec::Vector{Vector{NamedTuple}})
@@ -36,16 +38,12 @@ function _rpi_A2B_matrix(cgen::Union{Rot3DCoeffs{L,T}, Rot3DCoeffs_real{L,T}, Ro
    for i = 1:length(spec)
       # get the specification of the ith basis function, which is a tuple/vec of NamedTuples
       pib = spec[i]
-      # skip it unless all m are zero, because we want to consider each
-      # (nn, ll) block only once.
-      # if !all(b.m == 0 for b in pib)
-      #    continue
-      # end
-      # But we can not do this anymore for L≥1, so I add an nnllset
 
       # get the rotation-coefficients for this basis group
       # the bs are the basis functions corresponding to the columns
 
+      # The nnlllist is created because we want to consider each
+      # (nn, ll) block only once.
       nn = SVector([onep.n for onep in pib]...)
       ll = SVector([onep.l for onep in pib]...) # get a SVector of ll index
       if haskey(pib[1],:s)
@@ -102,7 +100,12 @@ function _rpi_A2B_matrix(cgen::Union{Rot3DCoeffs{L,T}, Rot3DCoeffs_real{L,T}, Ro
                if !isnothing(idxAA)
                   push!(Irow, idxB)
                   push!(Jcol, idxAA)
-                  push!(vals, U[irow, icol])
+                  if norm(U[irow, icol] - real.(U[irow, icol]))<1e-12
+                     push!(vals, real.(U[irow, icol]))
+                  else
+                     push!(vals, U[irow, icol])
+                  end
+                  # push!(vals, U[irow, icol])
                end
             end
          end
@@ -119,42 +122,38 @@ end
 
 # TODO: symmetry group O(d)?
 """
-xx2AA(spec_nlm, d=3, categories=[]; radial_basis=legendre_basis)
-Construct a lux chain that maps a configuration to the corresponding the AA basis
+xx2AA(spec_nlm, radial; d=3, categories=[])
+Construct a lux chain that maps a configuration to the corresponding AA basis
 spec_nlm: Specification of the AA bases
+radial : specified radial basis, with both basis and its specification
+===
+OptionalField: 
 d: Input dimension
 categories : A list of categories
-radial_basis : specified radial basis, default using P4ML.legendre_basis
 """
-function xx2AA(spec_nlm; categories=[], d=3, radial_basis = legendre_basis) # Configuration to AA bases - this is what all chains have in common
+
+function xx2AA(spec_nlm, radial::Radial_basis; categories=[], d=3, rSH = false) # Configuration to AA bases - this is what all chains have in common
    # from spec_nlm to all possible spec1p
    spec1p, lmax, nmax = specnlm2spec1p(spec_nlm)
    dict_spec1p = Dict([spec1p[i] => i for i = 1:length(spec1p)])
-   Ylm = CYlmBasis(lmax)
-   Rn = radial_basis(nmax)
-   # TODO: make it Rnl = radial_basis(nmax,lmax)
+   Ylm = rSH ? RYlmBasis(lmax) : CYlmBasis(lmax)
+   # Rn = radial_basis(nmax)
 
    if !isempty(categories)
-      # Read categories from x - TODO: discuss which format we like it to be...
-      # For now we just give get_cat(x) a random value
-      #get_cat(x) = length(categories) > 1 ? (iseven(floor(norm(x))) ? categories[1] : categories[2]) : categories[1]
-      #_get_cat(x) = get_cat.(x)
-
       # Define categorical bases
       δs = CategoricalBasis(categories)
       l_δs = P4ML.lux(δs)
    end
 
-   spec1pidx = isempty(categories) ? getspec1idx(spec1p, Rn, Ylm) : getspec1idx(spec1p, Rn, Ylm, δs)
-   # TODO: write getspec1idx for Rnl basis
+   spec1pidx = isempty(categories) ? getspec1idx(spec1p, radial.Radialspec, Ylm) : getspec1idx(spec1p, radial.Radialspec, Ylm, δs)
    bA = P4ML.PooledSparseProduct(spec1pidx)
 
    Spec = sort.([ [dict_spec1p[spec_nlm[k][j]] for j = 1:length(spec_nlm[k])] for k = 1:length(spec_nlm) ])
    Spec = sort(Spec, by=length)
    bAA = P4ML.SparseSymmProd(Spec)
 
    # wrapping into lux layers
-   l_Rn = P4ML.lux(Rn)
+   l_Rnl = radial.Rnl
    l_Ylm = P4ML.lux(Ylm)
    l_bA = P4ML.lux(bA)
    l_bAA = P4ML.lux(bAA)
@@ -169,13 +168,15 @@ function xx2AA(spec_nlm; categories=[], d=3, radial_basis = legendre_basis) # Co
    _norm(x) = norm.(x)
 
    if isempty(categories)
-      l_xnx = Lux.Parallel(nothing; normx = WrappedFunction(_norm), x = WrappedFunction(identity))
-      l_embed = Lux.Parallel(nothing; Rn = l_Rn, Ylm = l_Ylm)
-      luxchain = Chain(l_xnx = l_xnx, embed = l_embed, A = l_bA , AA = l_bAA)
-   else
-      l_xnxz = Lux.BranchLayer(normx = WrappedFunction(x -> _norm(x[1])), x = WrappedFunction(x -> x[1]), catlist = WrappedFunction(x -> x[2]))
-      l_embed = Lux.Parallel(nothing; Rn = l_Rn, Ylm = l_Ylm, δs = l_δs)
-      luxchain = Chain(l_xnxz = l_xnxz, embed = l_embed, A = l_bA , AA = l_bAA)
+      l_embed = Lux.Parallel(nothing; Rn = l_Rnl, Ylm = l_Ylm)
+      luxchain = Chain(embed = l_embed, A = l_bA , AA = l_bAA)
+   else      
+      l_Rnl = append_layer(Chain(get_pos = get_i(1), ), l_Rnl; l_name = :radial_poly)
+      l_Ylm = append_layer(Chain(get_pos = get_i(1), ), l_Ylm; l_name = :angle_poly)
+      l_δs = append_layer(Chain(get_cat = get_i(2), ), l_δs; l_name = :categorical)
+
+      l_embed = Lux.Parallel(nothing; Rn = l_Rnl, Ylm = l_Ylm, δs = l_δs)
+      luxchain = Chain(embed = l_embed, A = l_bA , AA = l_bAA) # Chain(l_xnxz = l_xnxz, embed = l_embed, A = l_bA , AA = l_bAA)
    end
 
    # luxchain = Chain(l_xnxz = l_xnxz, embed = l_embed, A = l_bA , AA = l_bAA)
@@ -192,15 +193,19 @@ L : Largest equivariance level
 categories : A list of categories
 radial_basis : specified radial basis, default using P4ML.legendre_basis
 """
-function equivariant_model(spec_nlm, L::Int64; categories=[], d=3, radial_basis=legendre_basis, group="O3", islong=true)
+function equivariant_model(spec_nlm, radial::Radial_basis, L::Int64; categories=[], d=3, group="O3", islong=true, rSH = false)
+   if rSH && L > 0
+      error("rSH is only implemented (for now) for L = 0")
+   end
+
    # first filt out those unfeasible spec_nlm
-   filter_init = islong ? RPE_filter_long(L) : RPE_filter(L)
+   filter_init = rSH ? RPE_filter_real(L) : (islong ? RPE_filter_long(L) : RPE_filter(L))
    spec_nlm = spec_nlm[findall(x -> filter_init(x) == 1, spec_nlm)]
 
    # sort!(spec_nlm, by = x -> length(x))
    spec_nlm = closure(spec_nlm,filter_init; categories = categories)
 
-   luxchain_tmp, ps_tmp, st_tmp = EquivariantModels.xx2AA(spec_nlm; categories = categories, d = d, radial_basis = radial_basis)
+   luxchain_tmp, ps_tmp, st_tmp = EquivariantModels.xx2AA(spec_nlm, radial; categories = categories, d = d, rSH = rSH)
    F(X) = luxchain_tmp(X, ps_tmp, st_tmp)[1]
 
    if islong
@@ -209,15 +214,15 @@ function equivariant_model(spec_nlm, L::Int64; categories=[], d=3, radial_basis=
       pos = Vector{Any}(undef, L+1)
 
       for l = 0:L
-         filter = RPE_filter(l)
-         cgen = Rot3DCoeffs(l) # TODO: this should be made group related
+         filter = rSH ? RPE_filter_real(L) : RPE_filter(l)
+         cgen = rSH ? Rot3DCoeffs_real(l) : Rot3DCoeffs(l) # TODO: this should be made group related
 
          tmp = spec_nlm[findall(x -> filter(x) == 1, spec_nlm)]
          C[l+1] = _rpi_A2B_matrix(cgen, tmp)
          pos[l+1] = findall(x -> filter(x) == 1, spec_nlm) # [ dict[tmp[j]] for j = 1:length(tmp)]
       end
    else
-      cgen = Rot3DCoeffs(L) # TODO: this should be made group related
+      cgen = rSH ? Rot3DCoeffs_real(L) : Rot3DCoeffs(L) # TODO: this should be made group related
       C = _rpi_A2B_matrix(cgen, spec_nlm)
    end
 
@@ -233,13 +238,13 @@ function equivariant_model(spec_nlm, L::Int64; categories=[], d=3, radial_basis=
 end
 
 # more constructors equivariant_model
-equivariant_model(totdeg::Int64, ν::Int64, L::Int64; categories=[], d=3, radial_basis=legendre_basis, group="O3", islong=true) = 
-     equivariant_model(degord2spec(;totaldegree = totdeg, order = ν, Lmax=L, radial_basis = radial_basis, islong = islong)[2], L; categories, d, radial_basis, group, islong)
+equivariant_model(totdeg::Int64, ν::Int64, radial::Radial_basis, L::Int64; categories=[], d=3, group="O3", islong=true, rSH = false) = 
+     equivariant_model(degord2spec(radial; totaldegree = totdeg, order = ν, Lmax=L, islong = islong)[2], radial, L; categories, d, group, islong, rSH)
 
 # With the _close function, the input could simply be an nnlllist (nlist,llist)
-equivariant_model(nn::Vector{Int64}, ll::Vector{Int64}, L::Int64; categories=[], d=3, radial_basis = legendre_basis, group = "O3", islong = true) = begin
+equivariant_model(nn::Vector{Int64}, ll::Vector{Int64}, radial::Radial_basis, L::Int64; categories=[], d=3, group = "O3", islong = true, rSH = false) = begin
    filter = islong ? RPE_filter_long(L) : RPE_filter(L)
-   equivariant_model(_close(nn, ll; filter = filter), L; categories, d, radial_basis, group, islong)
+   equivariant_model(_close(nn, ll; filter = filter), radial, L; categories, d, group, islong, rSH)
 end
 
 # ===== Codes that we might remove later =====
@@ -251,14 +256,14 @@ end
 # What can be adjusted in its input are: (1) total polynomial degree; (2) correlation order; (3) largest L
 # (4) weight of the order of spherical harmonics; (5) specified radial basis
 
-function equivariant_SYY_model(spec_nlm, L::Int64; categories=[], d=3, radial_basis=legendre_basis, group="O3")
+function equivariant_SYY_model(spec_nlm, radial::Radial_basis, L::Int64; categories=[], d=3, group="O3")
    filter_init = RPE_filter_long(L)
    spec_nlm = spec_nlm[findall(x -> filter_init(x) == 1, spec_nlm)]
 
    # sort!(spec_nlm, by = x -> length(x))
    spec_nlm = closure(spec_nlm, filter_init; categories = categories)
 
-   luxchain_tmp, ps_tmp, st_tmp = EquivariantModels.xx2AA(spec_nlm; categories = categories, d = d, radial_basis = radial_basis)
+   luxchain_tmp, ps_tmp, st_tmp = EquivariantModels.xx2AA(spec_nlm, radial; categories = categories, d = d)
    F(X) = luxchain_tmp(X, ps_tmp, st_tmp)[1]
 
    cgen = Rot3DCoeffs_long(L) # TODO: this should be made group related
@@ -274,11 +279,11 @@ function equivariant_SYY_model(spec_nlm, L::Int64; categories=[], d=3, radial_ba
    return luxchain, ps, st
 end
 
-equivariant_SYY_model(totdeg::Int64, ν::Int64, L::Int64; categories=[], d=3, radial_basis = legendre_basis,group = "O3") = 
-   equivariant_SYY_model(degord2spec(;totaldegree = totdeg, order = ν, Lmax = L, radial_basis = radial_basis, islong=true)[2], L; categories, d, radial_basis, group)
+equivariant_SYY_model(totdeg::Int64, ν::Int64, radial::Radial_basis, L::Int64; categories=[], d=3,group = "O3") = 
+   equivariant_SYY_model(degord2spec(radial; totaldegree = totdeg, order = ν, Lmax = L, islong=true)[2], radial, L; categories, d, group)
 
-equivariant_SYY_model(nn::Vector{Int64}, ll::Vector{Int64}, L::Int64; categories=[], d=3, radial_basis=legendre_basis, group="O3") = 
-   equivariant_SYY_model(_close(nn, ll; filter = RPE_filter_long(L)), L; categories, d, radial_basis, group)
+equivariant_SYY_model(nn::Vector{Int64}, ll::Vector{Int64}, radial::Radial_basis, L::Int64; categories=[], d=3, group="O3") = 
+   equivariant_SYY_model(_close(nn, ll; filter = RPE_filter_long(L)), radial, L; categories, d, group)
 
 ## TODO: The following should eventually go into ACEhamiltonians.jl rather than this package
 
@@ -312,9 +317,9 @@ function equivariant_luxchain_constructor(totdeg, ν, L; wL = 1, Rn = legendre_b
 
    Ylm = CYlmBasis(totdeg)
 
-   spec1p = make_nlms_spec(Rn, Ylm; totaldegree = totdeg, admissible = (br, by) -> br + wL * by.l <= totdeg)
+   spec1p = make_nlms_spec(simple_radial_basis(Rn), Ylm; totaldegree = totdeg, admissible = (br, by) -> br.n + wL * by.l <= totdeg)
    spec1p = sort(spec1p, by = (x -> x.n + x.l * wL))
-   spec1pidx = getspec1idx(spec1p, Rn, Ylm)
+   spec1pidx = getspec1idx(spec1p, simple_radial_basis(Rn).Radialspec, Ylm)
 
    # define sparse for n-correlations
    tup2b = vv -> [ spec1p[v] for v in vv[vv .> 0]  ]
@@ -370,9 +375,9 @@ end
 function equivariant_luxchain_constructor_new(totdeg, ν, L; wL = 1, Rn = legendre_basis(totdeg))
    Ylm = CYlmBasis(totdeg)
 
-   spec1p = make_nlms_spec(Rn, Ylm; totaldegree = totdeg, admissible = (br, by) -> br + wL * by.l <= totdeg)
+   spec1p = make_nlms_spec(simple_radial_basis(Rn), Ylm; totaldegree = totdeg, admissible = (br, by) -> br.n + wL * by.l <= totdeg)
    spec1p = sort(spec1p, by = (x -> x.n + x.l * wL))
-   spec1pidx = getspec1idx(spec1p, Rn, Ylm)
+   spec1pidx = getspec1idx(spec1p, simple_radial_basis(Rn).Radialspec, Ylm)
 
    # define sparse for n-correlations
    tup2b = vv -> [ spec1p[v] for v in vv[vv .> 0]  ]