Binary search in block for nD TrivialTensorizer (#355)

* binary search in block for nd TrivialTensorizer

* Tuple in nD TrivialTensorizer iteration

Author: jishnub

src/Multivariate/TensorSpace.jl

@@ -35,7 +35,7 @@ Base.keys(a::Tensorizer) = oneto(length(a))
 
 function start(a::TrivialTensorizer{d}) where {d}
     # ((block_dim_1, block_dim_2,...), (itaration_number, iterator, iterator_state)), (itemssofar, length)
-    block = SVector{d}(Ones{Int}(d))
+    block = ntuple(one, d)
     return (block, (0, nothing, nothing)), (0,length(a))
 end
 
@@ -64,7 +64,7 @@ function next(a::TrivialTensorizer{d}, iterator_tuple) where {d}
 
     # increase block, or initialize new block
     _res, iter_state = iterate(iterator, iter_state)
-    res = SVector{d}(_res)
+    res = Tuple(SVector{d}(_res))
     block = res.+1
     j = j+1
 
@@ -79,8 +79,8 @@ end
 
 
 # (blockrow,blockcol), (subrow,subcol), (rowshift,colshift), (numblockrows,numblockcols), (itemssofar, length)
-start(a::Tensorizer2D) = _start(a::Tensorizer2D)
-start(a::TrivialTensorizer{2}) = _start(a::Tensorizer2D)
+start(a::Tensorizer2D) = _start(a)
+start(a::TrivialTensorizer{2}) = _start(a)
 
 _start(a) = (1,1), (1,1), (0,0), (a.blocks[1][1],a.blocks[2][1]), (0,length(a))
 
@@ -171,10 +171,22 @@ block(::TrivialTensorizer{2},n::Int) =
     Block(floor(Integer,sqrt(2n) + 1/2))
 
 function block(::TrivialTensorizer{d},n::Int) where {d}
-    order::Int = 0
+    binomial(d, d) >= n && return Block(1)
+    order = 1
     while binomial(order+d, d) < n
-        order = order + 1
+        order *= 2
     end
+    searchords = order÷2:order
+    # perform a binary search
+    while length(searchords) > 1
+        midpt = searchords[length(searchords)÷2]
+        if binomial(midpt+d, d) < n
+            searchords = (midpt + 1):last(searchords)
+        else
+            searchords = first(searchords):midpt
+        end
+    end
+    order = searchords[]
     return Block(order+1)
 end