Fix multiplication of MultivariateFun (#218)

* product of LowRankFun and ProductFun

* exponentiation for MultivariateFun

* version bump to v0.7.13

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunBase"
 uuid = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"
-version = "0.7.12"
+version = "0.7.13"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/Multivariate/LowRankFun.jl

@@ -424,3 +424,6 @@ sum(g::LowRankFun,n::Integer)=(n==1) ? dotu(g.B,map(sum,g.A)) : dotu(g.A,map(sum
 cumsum(g::LowRankFun,n::Integer)=(n==1) ? LowRankFun(map(cumsum,g.A),copy(g.B)) : LowRankFun(copy(g.A),map(cumsum,g.B))
 differentiate(g::LowRankFun,n::Integer)=(n==1) ? LowRankFun(map(differentiate,g.A),copy(g.B)) : LowRankFun(copy(g.A),map(differentiate,g.B))
 integrate(g::LowRankFun,n::Integer)=(n==1) ? LowRankFun(map(integrate,g.A),copy(g.B)) : LowRankFun(copy(g.A),map(integrate,g.B))
+
+zero(L::LowRankFun) = LowRankFun((x...)->zero(cfstype(L)), space(L))
+one(L::LowRankFun) = LowRankFun((x...)->one(cfstype(L)), space(L))

src/Multivariate/Multivariate.jl

@@ -51,18 +51,23 @@ coefficients(f::BivariateFun,sp::TensorSpace)=coefficients(f,sp[1],sp[2])
 points(f::BivariateFun,k...)=points(space(f),size(f,1),size(f,2),k...)
 
 
-function *(vx::LowRankFun,u0::ProductFun)
-    ret=zero(space(u0))
-    for k=1:length(vx.A)
-        a,b=vx.A[k],vx.B[k]
-        ret+=transpose(b*(transpose(a*u0)))
+function *(vx::LowRankFun, u0::ProductFun)
+    sum(zip(vx.A, vx.B)) do (a,b)
+        transpose(b*(transpose(a*u0)))
     end
-    ret
 end
 
 *(a::ProductFun,b::LowRankFun)=b*a
 *(a::MultivariateFun,b::MultivariateFun)=LowRankFun(a)*ProductFun(b)
 
+@inline function ^(a::MultivariateFun, n::Integer)
+    n < 0 && return ^(inv(a), -n)
+    n == 0 && return one(a)
+    n == 1 && return a
+    n == 2 && return a * a
+    return foldr(*, fill(a, n-2), init=a*a)
+end
+
 for OP in (:+,:-,:*,:/)
     @eval begin
         $OP(f::Fun,g::MultivariateFun)=$OP(ProductFun(f),g)

src/Multivariate/ProductFun.jl

@@ -344,3 +344,6 @@ end
 for op in (:tocanonical,:fromcanonical)
     @eval $op(f::ProductFun,x...) = $op(space(f),x...)
 end
+
+zero(P::ProductFun) = ProductFun((x...)->zero(cfstype(P)), space(P))
+one(P::ProductFun) = ProductFun((x...)->one(cfstype(P)), space(P))