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Enhance DArray Distribution with Processor Assignment #630

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Enhance DArray Distribution with Processor Assignment
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248 changes: 248 additions & 0 deletions docs/src/darray.md
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Expand Up @@ -211,6 +211,254 @@ across the workers in the Julia cluster in a relatively even distribution;
future operations on a `DArray` may produce a different distribution from the
one chosen by previous calls.

### Explicit Processor Mapping of DArray Blocks

This feature allows you to control how `DArray` blocks (chunks) are assigned to specific processors within the cluster. Controlling data locality is crucial for optimizing the performance of distributed algorithms.

You can specify the mapping using the optional `assignment` argument in the `DArray` constructor functions (`DArray`, `DVector`, and `DMatrix`), the `distribute` function, and also directly within constructor-like functions such as `rand`, `randn`, `sprand`, `ones`, and `zeros` using the `assignment` optional keyword argument.

The `assignment` argument accepts the following values:

* `:arbitrary` **(Default)**:

* If `assignment` is not provided or is set to symbol `:arbitrary`, Dagger's scheduler assigns blocks to processors automatically. This is the default behavior.

* `:blockrow`:

* Divides the matrix blocks row-wise (vertically in the terminal). Each processor gets a contiguous chunk of row blocks.

* `:blockcol`:

* Divides the matrix blocks column-wise (horizontally in the terminal). Each processor gets a contiguous chunk of column blocks.

* `:cyclicrow`:

* Assigns row-blocks to processors in a round-robin fashion. Blocks are distributed one row-block at a time. Useful for parallel row-wise tasks.

* `:cycliccol`:

* Assigns column-blocks to processors in a round-robin fashion. Blocks are distributed one column-block at a time. Useful for parallel column-wise tasks.

* Any other symbol used for `assignment` results in an error.

* `AbstractArray{<:Int, N}`:

* Provide an integer **N**-dimensional array of worker IDs. The dimension **N** must match the number of dimensions of the `DArray`.
* Dagger maps blocks to worker IDs in a block-cyclic manner according to this processor-array. The block at index `(i,j,...)` is assigned to the first CPU thread of the worker with ID `assignment[mod1(i, size(assignment,1)), mod1(j, size(assignment,2)), ...]`. This pattern repeats block-cyclically across all dimensions.

* `AbstractArray{<:Processor, N}`:

* Provide an **N**-dimensional array of `Processor` objects. The dimension **N** must match the number of dimensions of the `DArray` blocks.
* Blocks are mapped in a block-cyclic manner according to the `Processor` objects in the assignment array. The block at index `(i,j,...)` is assigned to the processor at `assignment[mod1(i, size(assignment,1)), mod1(j, size(assignment,2)), ...]`. This pattern repeats block-cyclically across all dimensions.

#### Examples and Usage

The `assignment` argument works similarly for `DArray`, `DVector`, and `DMatrix`, as well as the `distribute` function. The key difference lies in the dimensionality of the resulting distributed array. For functions like `rand`, `randn`, `sprand`, `ones`, and `zeros`, `assignment` is an keyword argument.

* `DArray`: For N-dimensional distributed arrays.

* `DVector`: Specifically for 1-dimensional distributed arrays.

* `DMatrix`: Specifically for 2-dimensional distributed arrays.

* `distribute`: General function to distribute arrays of any dimensionality.

* `rand`, `randn`, `sprand`, `ones`, `zeros`: Functions to create DArrays with initial values, also supporting `assignment`.

Here are some examples using a setup with one master process and three worker processes.

First, let's create some sample arrays for `distribute` (and constructor functions):

```julia
A = rand(7, 11) # 2D array
v = ones(15) # 1D array
M = zeros(5, 5, 5) # 3D array
```

1. **Arbitrary Assignment:**

```julia
Ad = distribute(A, Blocks(2, 2), :arbitrary)
# DMatrix(A, Blocks(2, 2), :arbitrary)

vd = distribute(v, Blocks(3), :arbitrary)
# DVector(v, Blocks(3), :arbitrary)

Md = distribute(M, Blocks(2, 2, 2), :arbitrary)
# DArray(M, Blocks(2,2,2), :arbitrary)

Rd = rand(Blocks(2, 2), 7, 11; assignment=:arbitrary)
# distribute(rand(7, 11), Blocks(2, 2), :arbitrary)
```

This creates distributed arrays with the specified block sizes, and assigns the blocks to processors arbitrarily. For example, the assignment for `Ad` might look like this:

```julia
4×6 Matrix{Dagger.ThreadProc}:
ThreadProc(4, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(2, 1) ThreadProc(4, 1) ThreadProc(3, 1)
ThreadProc(3, 1) ThreadProc(4, 1) ThreadProc(3, 1) ThreadProc(4, 1) ThreadProc(2, 1) ThreadProc(2, 1)
ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(3, 1) ThreadProc(4, 1) ThreadProc(4, 1)
ThreadProc(2, 1) ThreadProc(4, 1) ThreadProc(4, 1) ThreadProc(3, 1) ThreadProc(2, 1) ThreadProc(3, 1)
```

2. **Structured Assignments:**

* **`:blockrow` Assignment:**

```julia
Ad = distribute(A, Blocks(1, 2), :blockrow)
# DMatrix(A, Blocks(1, 2), :blockrow)
vd = distribute(v, Blocks(3), :blockrow)
# DVector(v, Blocks(3), :blockrow)
Md = distribute(M, Blocks(2, 2, 2), :blockrow)
# DArray(M, Blocks(2,2,2), :blockrow)
Od = ones(Blocks(1, 2), 7, 11; assignment=:blockrow)
# distribute(ones(7, 11), Blocks(1, 2), :blockrow)
```

This creates distributed arrays with the specified block sizes, and assigns contiguous row-blocks to processors evenly. For example, the assignment for `Ad` (and `Od`) will look like this:

```julia
7×6 Matrix{Dagger.ThreadProc}:
ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1)
ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1)
ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1)
ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1)
ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1)
ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1)
ThreadProc(4, 1) ThreadProc(4, 1) ThreadProc(4, 1) ThreadProc(4, 1) ThreadProc(4, 1) ThreadProc(4, 1) ThreadProc(4, 1)
```

* **`:blockcol` Assignment:**

```julia
Ad = distribute(A, Blocks(2, 2), :blockcol)
# DMatrix(A, Blocks(2, 2), :blockcol)
vd = distribute(v, Blocks(3), :blockcol)
# DVector(v, Blocks(3), :blockcol)
Md = distribute(M, Blocks(2, 2, 2), :blockcol)
# DArray(M, Blocks(2,2,2), :blockcol)
Rd = randn(Blocks(2, 2), 7, 11; assignment=:blockcol)
# distribute(randn(7, 11), Blocks(2, 2), :blockcol)
```

This creates distributed arrays with the specified block sizes, and assigns contiguous column-blocks to processors evenly. For example, the assignment for `Ad` (and `Rd`) will look like this:

```julia
4×6 Matrix{Dagger.ThreadProc}:
ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(3, 1) ThreadProc(4, 1)
ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(3, 1) ThreadProc(4, 1)
ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(3, 1) ThreadProc(4, 1)
ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(3, 1) ThreadProc(4, 1)
```

* **`:cyclicrow` Assignment:**

```julia
Ad = distribute(A, Blocks(1, 2), :cyclicrow)
# DMatrix(A, Blocks(1, 2), :cyclicrow)
vd = distribute(v, Blocks(3), :cyclicrow)
# DVector(v, Blocks(3), :cyclicrow)
Md = distribute(M, Blocks(2, 2, 2), :cyclicrow)
# DArray(M, Blocks(2,2,2), :cyclicrow)
Zd = zeros(Blocks(1, 2), 7, 11; assignment=:cyclicrow)
# distribute(zeros(7, 11), Blocks(1, 2), :cyclicrow)
```

This creates distributed arrays with the specified block sizes, and assigns row-blocks to processors in round-robin fashion. For example, the assignment for `Ad` (and `Zd`) will look like this:

```julia
7×6 Matrix{Dagger.ThreadProc}:
ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1)
ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1)
ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1)
ThreadProc(4, 1) ThreadProc(4, 1) ThreadProc(4, 1) ThreadProc(4, 1) ThreadProc(4, 1) ThreadProc(4, 1) ThreadProc(4, 1)
ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1) ThreadProc(1, 1)
ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1) ThreadProc(2, 1)
ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1) ThreadProc(3, 1)
```

* **`:cycliccol` Assignment:**

```julia
Ad = distribute(A, Blocks(2, 2), :cycliccol)
# DMatrix(A, Blocks(2, 2), :cycliccol)
vd = distribute(v, Blocks(3), :cycliccol)
# DVector(v, Blocks(3), :cycliccol)
Md = distribute(M, Blocks(2, 2, 2), :cycliccol)
# DArray(M, Blocks(2,2,2), :cycliccol)
Od = ones(Blocks(2, 2), 7, 11; assignment=:cycliccol)
# distribute(ones(7, 11), Blocks(2, 2), :cycliccol)
```

This creates distributed arrays with the specified block sizes, and assigns column-blocks to processors in round-robin fashion. For example, the assignment for `Ad` (and `Od`) will look like this:

```julia
4×6 Matrix{Dagger.ThreadProc}:
ThreadProc(1, 1) ThreadProc(2, 1) ThreadProc(3, 1) ThreadProc(4, 1) ThreadProc(1, 1) ThreadProc(2, 1)
ThreadProc(1, 1) ThreadProc(2, 1) ThreadProc(3, 1) ThreadProc(4, 1) ThreadProc(1, 1) ThreadProc(2, 1)
ThreadProc(1, 1) ThreadProc(2, 1) ThreadProc(3, 1) ThreadProc(4, 1) ThreadProc(1, 1) ThreadProc(2, 1)
ThreadProc(1, 1) ThreadProc(2, 1) ThreadProc(3, 1) ThreadProc(4, 1) ThreadProc(1, 1) ThreadProc(2, 1)
```

3. **Block-Cyclic Assignment with Integer Array:**

```julia
assignment_2d = [2 1; 4 3]
Ad = distribute(A, Blocks(2, 2), assignment_2d)
# DMatrix(A, Blocks(2, 2), [2 1; 4 3])

assignment_1d = [2,3,1,4]
vd = distribute(v, Blocks(3), assignment_1d)
# DVector(v, Blocks(3), [2,3,1,4])

assignment_3d = cat([1 2; 3 4], [4 3; 2 1], dims=3)
Md = distribute(M, Blocks(2, 2, 2), assignment_3d)
# DArray(M, Blocks(2, 2, 2), cat([1 2; 3 4], [4 3; 2 1], dims=3))
Rd = sprand(Blocks(2, 2), 7, 11, 0.2; assignment=assignment_2d)
# distribute(sprand(7,11, 0.2), Blocks(2, 2), assignment_2d)
```

The assignment is an integer matrix of worker IDs, the blocks are assigned in block-cyclic manner to the first CPU thread of each worker. The assignment for `Ad` (and `Rd`) would be:

```julia
4×6 Matrix{Dagger.ThreadProc}:
ThreadProc(2, 1) ThreadProc(1, 1) ThreadProc(2, 1) ThreadProc(1, 1) ThreadProc(2, 1) ThreadProc(1, 1)
ThreadProc(4, 1) ThreadProc(3, 1) ThreadProc(4, 1) ThreadProc(3, 1) ThreadProc(4, 1) ThreadProc(3, 1)
ThreadProc(2, 1) ThreadProc(1, 1) ThreadProc(2, 1) ThreadProc(1, 1) ThreadProc(2, 1) ThreadProc(1, 1)
ThreadProc(4, 1) ThreadProc(3, 1) ThreadProc(4, 1) ThreadProc(3, 1) ThreadProc(4, 1) ThreadProc(3, 1)
```

4. **Block-Cyclic Assignment with Processor Array:**

```julia
assignment_2d = [Dagger.ThreadProc(3, 2) Dagger.ThreadProc(1, 1);
Dagger.ThreadProc(4, 3) Dagger.ThreadProc(2, 2)]
Ad = distribute(A, Blocks(2, 2), assignment_2d)
# DMatrix(A, Blocks(2, 2), assignment_2d)

assignment_1d = [Dagger.ThreadProc(2,1), Dagger.ThreadProc(3,1), Dagger.ThreadProc(1,1), Dagger.ThreadProc(4,1)]
vd = distribute(v, Blocks(3), assignment_1d)
# DVector(v, Blocks(3), assignment_1d)

assignment_3d = cat([Dagger.ThreadProc(1,1) Dagger.ThreadProc(2,1); Dagger.ThreadProc(3,1) Dagger.ThreadProc(4,1)],
[Dagger.ThreadProc(4,1) Dagger.ThreadProc(3,1); Dagger.ThreadProc(2,1) Dagger.ThreadProc(1,1)], dims=3)
Md = distribute(M, Blocks(2, 2, 2), assignment_3d)
# DArray(M, Blocks(2, 2, 2), assignment_3d)
Rd = rand(Blocks(2, 2), 7, 11; assignment=assignment_2d))
# distribute(rand(7,11), Blocks(2, 2), assignment_2d)
```

The assignment is a matrix of `Processor` objects, the blocks are assigned in block-cyclic manner to each processor. The assignment for `Ad` (and `Rd`) would be:

```julia
4×6 Matrix{Dagger.ThreadProc}:
ThreadProc(3, 2) ThreadProc(1, 1) ThreadProc(3, 2) ThreadProc(1, 1) ThreadProc(3, 2) ThreadProc(1, 1)
ThreadProc(4, 3) ThreadProc(2, 2) ThreadProc(4, 3) ThreadProc(2, 2) ThreadProc(4, 3) ThreadProc(2, 2)
ThreadProc(3, 2) ThreadProc(1, 1) ThreadProc(3, 2) ThreadProc(1, 1) ThreadProc(3, 2) ThreadProc(1, 1)
ThreadProc(4, 3) ThreadProc(2, 2) ThreadProc(4, 3) ThreadProc(2, 2) ThreadProc(4, 3) ThreadProc(2, 2)
```

## Broadcasting

As the `DArray` is a subtype of `AbstractArray` and generally satisfies Julia's
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