Taichi: [Lang] tensor as local temporary variable / do we have tensor slice support?

[archibate]

Concisely describe the proposed feature
Currently, we operate tensor elements in taichi-scope, not the tensor itself.
But I think it would be convenient to operate tensor as a whole-thing in taichi-scope.
Consider the following code:

@ti.kernel
def blur(y: ti.ext_arr(), x: ti.ext_arr(), ker: ti.ext_arr()):
  for i, j in x:
   y[i, j] = sum(x[i-1:i+1, j-1:j+1] * ker) / sum(ker)  # slicing sub-tensor

blur(img_out, img_in, [[0, 1, 0], [1, 2, 1], [0, 1, 0]])

With such syntax sugar, we made a very simple-to-write and easy-to-read gaussian blur kernel or whatever depends on ker. Also useful simplifying convolution kernels with such sugar.

Describe the solution you'd like (if any)
We may have Matrix for the type of temp variable holding x[i-1:i+1, j-1:j+1].

1. read from a range of tensor, result combined in a matrix (which is shown in the example code).
2. write back a matrix to a specific range of tensor (must equal in size).

My concerns about using Matrix:

1. Can only apply to 1D and 2D.
2. what if x is already a tensor of matrices? we obtain a matrix of matrices by x[1:3,2:4]? we may want another return type instead of Matrix, say: x[1:3, 2:4] is a type of ti.TempTensor?

Additional Comments
may also want steping like y[i-3:i+3:2] where 2 is the step-length.
Ultimately I think this only require python ASTTransformer change.

[archibate]

Talk about ti.TempTensor...
I'm also thinking about ti.wince (张量缩并):

C = ti.wince(A, ti.ij, B, ti.jk)  # `j` follows Einstein's sum rule

represents: C_{ik} = \sum_j A_{ij} B_{jk}

Or simply sugar it into: C = A.ij * B.jk?

[archibate]

The ti.wince will finally translated into range-for's. So also consider ti.static_wince for static-optimized-small-range-for's.

[yuanming-hu]

First of all, your writing in this issue is really clear and concise. Great job.

My input: to implement sum(x[i-1:i+1, j-1:j+1] * ker) we might need to introduce a set of IR that allows allocation of local arrays, something like ArrayAllocStmt, which extends the current AllocStmt.

The this can be translated into something like

%1 = ArrayAllocStmt
for i, j in ...
  ... multiple ker[i, j] with x[...] and write the result into %1
...compute the sum of %1 using a for loop...

[archibate]

ArrayAllocStmt(size=4) can be translated to int a[4] in C-like backends.