ndarray: cat, hcat, vcat (#380)

e.g. `hcat`
```julia
julia> x
4 mx.NDArray{Float64,1} @ CPU0:
 1.0
 2.0
 3.0
 4.0

julia> y
4 mx.NDArray{Float64,1} @ CPU0:
 2.0
 4.0
 6.0
 8.0

julia> [x y]
4×2 mx.NDArray{Float64,2} @ CPU0:
 1.0  2.0
 2.0  4.0
 3.0  6.0
 4.0  8.0
```

NEWS.md

@@ -117,7 +117,33 @@
   x .% 2
   2 .% x
   ```
-
+
+* `cat`, `vcat`, `hcat` is implemented. (#TBD)
+
+  E.g. `hcat`
+  ```julia
+  julia> x
+  4 mx.NDArray{Float64,1} @ CPU0:
+   1.0
+   2.0
+   3.0
+   4.0
+
+  julia> y
+  4 mx.NDArray{Float64,1} @ CPU0:
+   2.0
+   4.0
+   6.0
+   8.0
+
+  julia> [x y]
+  4×2 mx.NDArray{Float64,2} @ CPU0:
+   1.0  2.0
+   2.0  4.0
+   3.0  6.0
+   4.0  8.0
+  ```
+
 * Transposing a column `NDArray` to a row `NDArray` is supported now. (#TBD)
 
   ```julia

src/ndarray.jl

@@ -522,6 +522,32 @@ function deepcopy(arr::NDArray)
   NDArray(MX_NDArrayHandle(out_ref[]))
 end
 
+"""
+    hcat(x::NDArray...)
+"""
+Base.hcat(xs::NDArray{T}...) where T = cat(2, xs...)
+
+"""
+    vcat(x::NDArray...)
+"""
+Base.vcat(xs::NDArray{T}...) where T = cat(1, xs...)
+
+"""
+    cat(dim, xs::NDArray...)
+
+Concate the `NDArray`s which have the same element type along the `dim`.
+Building a diagonal matrix is not supported yet.
+"""
+function Base.cat(dim::Int, xs::NDArray{T}...) where T
+  ns = ndims.(xs)
+  d = Base.max(dim, maximum(ns))
+  xs′ = map(zip(ns, xs)) do i
+    n, x = i
+    (d > n) ? reshape(x, -2, Base.ones(Int, d - n)...) : x
+  end
+  concat(xs′..., dim = d - dim)
+end
+
 """
     @inplace
 

test/unittest/ndarray.jl

@@ -179,6 +179,67 @@ function test_endof()
   end
 end  # function test_endof
 
+function test_cat()
+  function check_cat(f, A, B = 2A)
+    C = [A B]
+    D = [A; B]
+    x = NDArray(A)
+    y = NDArray(B)
+    z = NDArray(C)
+    d = NDArray(D)
+
+    if f == :hcat
+      @test copy([x y]) == [A B]
+      @test copy([x y 3y x]) == [A B 3B A]
+      @test copy([z y x]) == [C B A]
+    elseif f == :vcat
+      @test copy([x; y]) == [A; B]
+      @test copy([x; y; 3y; x]) == [A; B; 3B; A]
+      @test copy([x; d]) == [A; D]
+      @test copy([d; x]) == [D; A]
+    else
+      @assert false
+    end
+  end
+
+  let A = [1, 2, 3, 4]
+    info("NDArray::hcat::1D")
+    check_cat(:hcat, A)
+
+    info("NDArray::vcat::1D")
+    check_cat(:vcat, A)
+  end
+
+  let A = [1 2; 3 4]
+    info("NDArray::hcat::2D")
+    check_cat(:hcat, A)
+
+    info("NDArray::vcat::2D")
+    check_cat(:vcat, A)
+  end
+
+  let A = rand(4, 3, 2)
+    info("NDArray::hcat::3D")
+    check_cat(:hcat, A)
+
+    info("NDArray::vcat::3D")
+    check_cat(:vcat, A)
+  end
+
+  let A = rand(4, 3, 2, 2)
+    info("NDArray::hcat::4D")
+    check_cat(:hcat, A)
+
+    info("NDArray::vcat::4D")
+    check_cat(:vcat, A)
+  end
+
+  let A = [1, 2, 3, 4]
+    info("NDArray::cat::3D/1D")
+    check_cat(:vcat, reshape(A, 4, 1, 1), 2A)
+  end
+end  # function test_cat
+
 function test_plus()
   dims   = rand_dims()
   t1, a1 = rand_tensors(dims)
@@ -927,6 +988,7 @@ end  # function test_hyperbolic
   test_linear_idx()
   test_first()
   test_endof()
+  test_cat()
   test_plus()
   test_minus()
   test_mul()