Execution primitives, Data primitives and operations

[ct-clmsn]

Execution primitives

• Provide a Phylanx 'context' in users create variables. This should make execution easier to manage for end users.
• Determine if contexts should be managed without user interaction (default behavior)
  • Create a "stack-machine" for creating contexts and manipulating contexts
  • Users push/pop contexts in a fashion similar to OpenGL or determine if contexts can be exposed to users without stack-machine interfaces
    • Users create contexts and tell phylanx to execute them.

Data Primitives

• Scalar
  • bool
  • int
  • double
  • float
  • complex
• N-dimensional arrays (bool, int, double, float, complex)
• N-dimensional array initialized by 0, 1, or a random value (Gaussian random should be fine)
• N-dimensional array layout by row and column
• N-dimensional array layout by space filling curves (Peano, z-order, Moore, Hilbert).
  • Array tiles/blocks stored on a node are arranged in-memory using a space filling curve.
  • Space-filling curves create a "cache oblivious" effect.
  • Example: https://link.springer.com/chapter/10.1007/11752578_126
• N-dimensional array storage using 'resilient' (NoSQL/cloud) data structures
• Sparse N-dimensional array

Operation Primitives

• The 5 basic operations:
  • map (Adding map_operation() primitive #307), parallel_map (Adding parallel_map(), map() now preserves execution ordering #371)
  • filter (Filter operation #308)
  • fold (Fold operation #309)
  • scan
  • join_update
• N-dimensional array operation "get shape"
• N-dimensional indexing
• DAG node to represent numpy-style 'broadcast' for operations
• Element-wise addition
• Element-wise subtraction
• Matrix multiplication (@Hapoo, see adding multiply primitive #38)
• Element-wise division (@hkaiser, see More primitives #49)
• Element-wise power/square root (@parsa, see Square root and Power primitives added #100 )
• Exponential function (@justwagle, see Exponential primitive #45)
• Consider creating special nodes for HPX's linear algebra/BLAS wrapper
• SpMV (Sparse Matrix-Vector Multiply)
• SDDMM (Sampled Dense-Dense Matrix Product)
• MTTKRP (Matricized Tensor Times Kharti-Rao Product)
• Matrix transposition
• Matrix inversion
• Matrix determinant
• Axis operations (set, swap, ...)
• Slicing - returns a view
• Joining (joins matrices) (see hstack and vstack primitives #170)
• Diagonal slicing - Return an array or matrix (dense/sparse) slice
• Triangular indexing - Get the upper or lower triangle of an array
• Project product operation (dot product)
• Vector product operation (cross product) (@parsa, see Cross product primitive implemented #99)
• Checkpoint operation for a node
• Scalar, nd-array, and matrix types should either have a method to create a 'randomize' node or there should be a function provided by phylanx that randomizes input primitives
• Support expressing linear algebra operations
• Retrieve the index set of an nd-array, vector, or matrix
• Use the index set of an nd-array, vector, or matrix for masks/logical assignment
  • i.e. A[ A.indices() % 2 == 0 ] = 1.0

I/O Primitives

• Store operation to variable nodes (@Hapoo)
• Read and write results from/to disk (@hkaiser, see Adding file_read and file_write primitives #27)
• Write results to Uri/url
• Write results to standard output (@hkaiser, see Adding new primitive: console_output (cout()) #103)

Control Structure Primitives

• Conditional operators (==, !=, <, >, <=, >=) (@hkaiser, see More primitives #49)
• Boolean operations (&&, ||) (@hkaiser, see More primitives #49)
• Unary operations (!, -) (@hkaiser, see Adding unary_minus and unary_not primitives #52)
• if(cond, true_case, false_case) (@aserio, see Adding if2 #74)
• while(cond, body) repeat evaluating body until cond becomes false (@hkaiser, see More primitives #49)
• block(...): sequentially evaluate all given arguments (@hkaiser, see Adding block and parallel_block primitives #54)
• parallel_block(...): concurrently evaluate all given arguments (@hkaiser, see Adding block and parallel_block primitives #54)

[ct-clmsn]

Question about the dot product operation . Should operations like dot product be represented as a combination of DAG operations? Should operations like dot product be "special nodes" with custom or C++ optimized logic?

[hkaiser]

In the first step supporting 0, 1, and 2 dimensional data will be a good starting point to get the whole infrastructure in place.

[ct-clmsn]

@hkaiser @stevenrbrandt I've started implementing some algorithms in Python (matrix factorizations) in the unit testing directory. This should help demonstrate some end-user challenges that we'll have to sort out and help guide the front/back end implementations. Hopefully the examples clarify the use case(s) a bit.

[ct-clmsn]

exploratory data analysis enabling primitives:

• log (Generic primitives map static #365)
• floor (Generic primitives map static #365)
• ceil (Generic primitives map static #365)
• abs (Generic primitives map static #365)
• min/max (Argmin & Argmax Primitives #253, Creating statistics plugin #706))
• eye (Eye primitive #681)
• tile (Adding Tile primitive #694)
• repeat
• reshape (Adding Reshape primitive #691)
• mean (axis) (Mean primitive #297, Creating statistics plugin #706)
• covariance matrix
• eig (eigenvalues + right eigenvalues of square matrices)
• lstsq

[hkaiser]

We have started to add 3D data structure support to some of the primitives (see #665).