add new constructor for TensorCI2 to initialize with local pivots list

src/tensorci2.jl

@@ -53,6 +53,25 @@ function TensorCI2{ValueType}(
     return tci
 end
 
+"""
+    Initialize a TCI2 object with local pivot lists.
+"""
+function TensorCI2{ValueType}(
+    func::F,
+    localdims::Union{Vector{Int},NTuple{N,Int}},
+    Iset::Vector{Vector{MultiIndex}},
+    Jset::Vector{Vector{MultiIndex}}
+) where {F,ValueType,N}
+    tci = TensorCI2{ValueType}(localdims)
+    tci.Iset = Iset
+    tci.Jset = Jset
+    pivots = reconstractglobalpivotsfromijset(localdims, tci.Iset, tci.Jset)
+    tci.maxsamplevalue = maximum(abs, (func(bit) for bit in pivots))
+    abs(tci.maxsamplevalue) > 0.0 || error("maxsamplevalue is zero!")
+    invalidatesitetensors!(tci)
+    return tci
+end
+
 @doc raw"""
     function printnestinginfo(tci::TensorCI2{T}) where {T}
 
@@ -150,6 +169,24 @@ function updateerrors!(
     nothing
 end
 
+function reconstractglobalpivotsfromijset(
+    localdims::Union{Vector{Int},NTuple{N,Int}},
+    Isets::Vector{Vector{MultiIndex}}, 
+    Jsets::Vector{Vector{MultiIndex}}
+) where {N}
+    pivots = []
+    l = length(Isets)
+    for i in 1:l
+        for Iset in Isets[i]
+            for Jset in Jsets[i]
+                for j in 1:localdims[i]
+                    pushunique!(pivots, vcat(Iset, [j], Jset))
+                end
+            end
+        end
+    end
+    return pivots
+end
 
 """
 Add global pivots to index sets

test/test_tensorci2.jl

@@ -393,6 +393,22 @@ import QuanticsGrids as QD
     end
 
 
+    @testset "initialize_with_local_pivots_list" begin
+        Random.seed!(1234)
+
+        N = 10
+        M = rand(Float64, N, N)
+        f(v) = M[v[1], v[2]] # 2D function
+        localdims = fill(N, 2)
+        mbd = 5
+
+        tci, ranks, errors = TCI.crossinterpolate2(Float64, f, localdims; maxbonddim=mbd)
+        tci2 = TCI.TensorCI2{Float64}(f, localdims, tci.Iset, tci.Jset)
+        @test tci2.maxsamplevalue == tci.maxsamplevalue
+        @test tci2.Iset == tci.Iset
+        @test tci2.Jset == tci.Jset
+    end
+
     @testset "crossinterpolate2_ttcache" begin
         ValueType = Float64