# Evaluation of sparse version of SuSiE

#### Kaiqian Zhang

#### 2021-11-12

## Set up environment

    library(Matrix)
    library(susieR)
    set.seed(1)

## Overview

In this vignette, we provide line profiles for revised version SuSiE, which allows for a sparse matrix structure. We compare speed performance when the form of the matrix `X` is dense and sparse.

In this minimal example, we observe that given a large sparse matrix, if it is in the dense form, the speed is around `40%` slower than that in a sparse form.

## Simulate data

We randomly simulate a `n=1000` by `p=1000` dense matrix and a sparse matrix at sparsity \(99\%\), i.e. \(99\%\) entries are zeros.

    create_sparsity_mat = function(sparsity, n, p) {
      nonzero          <- round(n*p*(1-sparsity))
      nonzero.idx      <- sample(n*p, nonzero)
      mat              <- numeric(n*p)
      mat[nonzero.idx] <- 1
      mat              <- matrix(mat, nrow=n, ncol=p)
      return(mat)
    }

    n <- 1000
    p <- 1000
    beta <- rep(0,p)
    beta[c(1,300,400,1000)] <- 10
    X.dense  <- create_sparsity_mat(0.99,n,p)
    X.sparse <- as(X.dense,"dgCMatrix")
    y <- c(X.dense %*% beta + rnorm(n))

## `X` in a dense form

    susie.dense <- susie(X.dense,y)

## `X` in a sparse form

    susie.sparse <- susie(X.sparse,y)

## Further step

We encourage people who are insterested in improving SuSiE can get insights from those line profiles provided.