Multiplying by a Compressor

Let $A$ be a matrix that we wish to compress for some subsequent calculation (e.g., approximating the column space or solving a least squares problem).

A = randn(1000, 500)

We can generate any number of compressors (see Compressors API). We can then multiply $A$ from the left or right by the compressor. We provide three examples below:

• The SparseSign compressor [2, Section 9.2].
• The Gaussian compressor.
• A Uniform Sampling of the columns of $A$.

using RLinearAlgebra

I1 = SparseSign(
    cardinality=Left(), #Apply the compressor to the rows of A
    compression_dim=20, #Reduce the number of rows of A to 20
    nnz=8,
    type=Float64
)

I2 = Gaussian(
    cardinality=Right(), #Apply the compressor to the columns of A
    compression_dim=10,  #Reduce the number of columns of A to 10
    type=Float64
)

I3 = Sampling(
    cardinality=Right(), #Apply the compressor to the columns of A
    compression_dim=15,  #Reduce the number of columns of A to 15
    distribution=Uniform()
)

The previous code block specifies the ingredients for constructing the three compressors. The next code block constructs the compressors using complete_compressor.

C1 = complete_compressor(I1, A)
C2 = complete_compressor(I2, A)
C3 = complete_compressor(I3, A)

We can now apply the compressors to $A$. The first compressor reduces the number of rows of $A$ from $1000$ to $20$.

CA1 = C1 * A
size(CA1)

(20, 500)

The second compressor reduces the number of columns of $A$ from $500$ to $10$.

CA2 = A * C2
size(CA2)

(1000, 10)

The final compressor reduces the number of columns of $A$ from $500$ to $15$.

CA3 = A * C3
size(CA3)

(1000, 15)