From 0a57421622270568bc4a842e3d3a5702641d7690 Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Mon, 21 Nov 2022 16:46:19 +0400
Subject: [PATCH] Support empty LowRankFun

---
 src/Multivariate/LowRankFun.jl | 23 +++++++++++++----------
 src/Multivariate/ProductFun.jl |  3 ++-
 src/Multivariate/VectorFun.jl  |  2 +-
 3 files changed, 16 insertions(+), 12 deletions(-)

diff --git a/src/Multivariate/LowRankFun.jl b/src/Multivariate/LowRankFun.jl
index b82dc8a9..bb0a179e 100644
--- a/src/Multivariate/LowRankFun.jl
+++ b/src/Multivariate/LowRankFun.jl
@@ -34,7 +34,6 @@ struct LowRankFun{S<:Space,M<:Space,SS<:AbstractProductSpace,T<:Number} <: Bivar
                                   B::Vector{VFun{M,T}},
                                   space::SS) where {S,M,SS,T}
         @assert length(A) == length(B)
-        @assert length(A) > 0
         new{S,M,SS,T}(A,B,space)
     end
 end
@@ -57,29 +56,33 @@ size(f::LowRankFun) = size(f,1),size(f,2)
 
 function LowRankFun(X::Array{T},dx::S,dy::M) where {S<:Space,M<:Space,T<:Number}
     U,Σ,V=svd(X)
-    m=max(1,count(s->s>10eps(T),Σ))
+    m=count(s->s>10eps(T),Σ)
 
-    A=VFun{S,T}[Fun(dx,U[:,k].*sqrt(Σ[k])) for k=1:m]
-    B=VFun{M,T}[Fun(dy,conj(V[:,k]).*sqrt(Σ[k])) for k=1:m]
+    A=VFun{S,T}[Fun(dx, (@view U[:,k]).*sqrt(Σ[k])) for k=1:m]
+    B=VFun{M,T}[Fun(dy, conj.(@view V[:,k]).*sqrt(Σ[k])) for k=1:m]
 
-    LowRankFun(A,B)
+    LowRankFun(A, B, dx ⊗ dy)
 end
 
 ## Construction in a TensorSpace via a Vector of Funs
 
 function LowRankFun(X::Vector{VFun{S,T}},d::TensorSpace{SV,DD}) where {S,T,DD<:EuclideanDomain{2},SV}
-    @assert d[1] == space(X[1])
-    LowRankFun(X,d[2])
+    if !isempty(X)
+        @assert factor(d, 1) == space(X[1])
+    else
+        @assert factor(d, 1) isa S
+    end
+    LowRankFun(X, factor(d, 2), factor(d, 1))
 end
 
-function LowRankFun(X::Vector{VFun{S,T}},dy::Space) where {S,T}
-    m=mapreduce(ncoefficients,max,X)
+function LowRankFun(X::Vector{VFun{S,T}},dy::Space,dx::Space = nothing) where {S,T}
+    m=mapreduce(ncoefficients,max,X, init=0)
     M=zeros(T,m,length(X))
     for k=1:length(X)
         M[1:ncoefficients(X[k]),k]=X[k].coefficients
     end
 
-    LowRankFun(M,space(X[1]),dy)
+    LowRankFun(M, dx === nothing ? space(X[1]) : dx, dy)
 end
 
 
diff --git a/src/Multivariate/ProductFun.jl b/src/Multivariate/ProductFun.jl
index 896927db..62bfa777 100644
--- a/src/Multivariate/ProductFun.jl
+++ b/src/Multivariate/ProductFun.jl
@@ -340,7 +340,8 @@ end
 *(f::ProductFun,B::Fun) = transpose(B*transpose(f))
 
 
-LowRankFun(f::ProductFun{S,V,SS}) where {S,V,SS<:TensorSpace} = LowRankFun(f.coefficients,factor(space(f),2))
+LowRankFun(f::ProductFun{S,V,SS}) where {S,V,SS<:TensorSpace} =
+    LowRankFun(f.coefficients, space(f))
 LowRankFun(f::Fun) = LowRankFun(ProductFun(f))
 
 function differentiate(f::ProductFun{S,V,SS},j::Integer) where {S,V,SS<:TensorSpace}
diff --git a/src/Multivariate/VectorFun.jl b/src/Multivariate/VectorFun.jl
index 30288318..b8c63222 100644
--- a/src/Multivariate/VectorFun.jl
+++ b/src/Multivariate/VectorFun.jl
@@ -198,4 +198,4 @@ end
 
 #TODO: fix for complex
 evaluate(A::AbstractArray{T},x::Number) where {T<:Fun} =
-    typeof(first(A)(x))[Akj(x) for Akj in A]
+    [Akj(x) for Akj in A]