gen_sketch_mat.m

% def get_SJLT_matrix(m, n, s): 
%     # This function returns SJLT sketching matrix in the form of a sparse matrix.
%     # m: sketch size, n: number of data samples, s: sparsity
%     nonzeros = 2*binopdf(1, (s*n), 0.5) - 1 # Rademacher random variables

%     K = int(np.ceil(s*n / m)) # number of repetitions
%     shuffled_row_indices = np.zeros((K*m), dtype=np.int32)
%     all_row_indices = np.linspace(0, m-1, m, dtype=np.int32)
    
%     for k in range(K):
%         shuffled_row_indices[k*m:(k+1)*m] = np.random.permutation(all_row_indices)  

%     I = shuffled_row_indices[0:s*n]
%     J = np.repeat(np.linspace(0, n-1, n, dtype=np.int32), s)
%     V = nonzeros

%     S = scipy.sparse.coo_matrix((V,(I,J)), shape=(m,n), dtype=np.int8)
%     S = S.tocsr()
    
%     return S

% function [S] = get_RRS_matrix(m,n): 
%     # This function returns random row sampling sketching matrix in the form of a sparse matrix.
%     # n: number of data samples m: sketch size
    
%     nonzeros = np.ones([m])
    
%     all_row_indices = np.linspace(0, n-1, n, dtype=np.int32)
    
%     shuffled_row_indices = np.random.permutation(all_row_indices)  
    
%     I = np.linspace(0, m-1, m, dtype=np.int32)
%     J = shuffled_row_indices[0:m]
%     V = nonzeros

%     S = scipy.sparse.coo_matrix((V,(I,J)), shape=(m,n), dtype=np.int8)
%     S = S.tocsr() 
% end

function S = gen_sketch_mat(m, n, method)
    % Generate a sketch matrix.
    % A sketch matrix $S\in\mathbb{R}^{m\times n}$ has the property that
    % $\mathbb{E} S^T S = \mathbb{I}$.  
    % Args:
    %     m (int): number of rows of the sketch matrix (desired rank)
    %     n (int): number of columns of the sketch matrix (size of matrix
    %         to be sketched)
    %     method (str): method for generating the sketch matrix.  Currently,
    %         only random normal sketch matrices are supported.
    % Returns:
    %     np.ndarray: a sketch matrix
    

    if method == "Gaussian"
        S = randn(m, n) / sqrt(m);
    elseif method == "Rademacher"
        % Produces r.v. in {0, 1} with equal probability
        S = ((randn(m, n) > 0) * 2 - 1) /  sqrt(m);
    % elseif method == "SJLT":
    %     S = get_SJLT_matrix(m,n,sparsity) / sqrt(sparsity)
    % elseif method == "RRS":
    %     S = get_RRS_matrix(m,n) * sqrt(n/m)
    else
        fprintf("Unrecognized sketch type: " + method);
    end

end