[SPARK-4409] Additional (but limited) Linear Algebra Utils (original) (raw)

This ticket is to discuss the addition of a very limited number of local matrix manipulation and generation methods that would be helpful in the further development for algorithms on top of BlockMatrix (SPARK-3974), such as Randomized SVD, and Multi Model Training (SPARK-1486).
The proposed methods for addition are:
For `Matrix`

• map: maps the values in the matrix with a given function. Produces a new matrix.
• update: the values in the matrix are updated with a given function. Occurs in place.

Factory methods for `DenseMatrix`:

• *zeros: Generate a matrix consisting of zeros
• *ones: Generate a matrix consisting of ones
• *eye: Generate an identity matrix
• *rand: Generate a matrix consisting of i.i.d. uniform random numbers
• *randn: Generate a matrix consisting of i.i.d. gaussian random numbers
• *diag: Generate a diagonal matrix from a supplied vector
  *These methods already exist in the factory methods for `Matrices`, however for cases where we require a `DenseMatrix`, you constantly have to add `.asInstanceOf[DenseMatrix]` everywhere, which makes the code "dirtier". I propose moving these functions to factory methods for `DenseMatrix` where the putput will be a `DenseMatrix` and the factory methods for `Matrices` will call these functions directly and output a generic `Matrix`.

Factory methods for `SparseMatrix`:

• speye: Identity matrix in sparse format. Saves a ton of memory when dimensions are large, especially in Multi Model Training, where each row requires being multiplied by a scalar.
• sprand: Generate a sparse matrix with a given density consisting of i.i.d. uniform random numbers.
• sprandn: Generate a sparse matrix with a given density consisting of i.i.d. gaussian random numbers.
• diag: Generate a diagonal matrix from a supplied vector, but is memory efficient, because it just stores the diagonal. Again, very helpful in Multi Model Training.

Factory methods for `Matrices`:

• Include all the factory methods given above, but return a generic `Matrix` rather than `SparseMatrix` or `DenseMatrix`.
• horzCat: Horizontally concatenate matrices to form one larger matrix. Very useful in both Multi Model Training, and for the repartitioning of BlockMatrix.
• vertCat: Vertically concatenate matrices to form one larger matrix. Very useful for the repartitioning of BlockMatrix.