---
title: "Evaluation of sparse version of SuSiE"
author: "Kaiqian Zhang"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{SuSiE with sparse matrix operations}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(collapse = TRUE,comment = "#",fig.width = 4.5,
                      fig.height = 3,fig.align = "center",
                      fig.cap = "&nbsp;",dpi = 120)
```

## Set up environment

```{r, warning=FALSE}
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.

```{r}
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)
}
```

```{r}
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

```{r}
susie.dense <- susie(X.dense,y)
```

## `X` in a sparse form

```{r}
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.
