---
title: "hw5"
author: "Mark Pearl"
date: "7/25/2021"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(stats)
library(mrbsizeR)
library(base)
library(QZ)
library(CVXR) 
```

## HW5 Q1 notebook

```{r q1}

s_vector <- seq(1,128,1)
source('l1eq_pd.R')

num_experiments <- 20
error_matrix <- matrix(0, num_experiments, 128)

M <- 512
N <- 256
x_matrix <- matrix(0, 128, 128)
error_vector <- rep(0,128)
x_num <- seq(1,num_experiments,1)

#Iterate through each experiement created
for (num_x in x_num) {
  print(paste0("Running experiment number ",num_x))
  x_full <- rsparsematrix(512, 1, nnz = 512, rand.x=rnorm)
  #Create A matrix consisting of guassian distribution of i.i.d variables 256 (rows) X 512 (columns)
  A <- matrix(rnorm(N*M), nrow = N, ncol = M)  
  #Iterate through each value in the s-vector representing number of sparse element in vector x
  for (s in s_vector) {
    x <- numeric(512)
    ind <- sample(1:512, s) # select s random locations which will have non zero values
    for (i in ind){
      x[i] <- x_full[i]
    }
    #x <- rsparsematrix(512, 1, nnz = s, rand.x=rnorm)
    y <- A%*%x
    x0 <- t(A)%*%y
    xp <- l1eq_pd(x0,A,y)
    print(paste0(s,"/128 ","LHS: ",norm(xp-x,type='2'),"<=","RHS: ",10^-4*norm(x,type='2')," ",norm(xp-x,type='2') <= 10^-4*norm(x,type='2')))
    
    #10^-4*
    if (norm(xp-x,type='2') <= 10^-4*norm(x,type='2')) {
      error_vector[s]=1
    }
    else{
      error_vector[s]=0
    } 
  }
  error_matrix[num_x,]=error_vector
}
```


``` {r output success/rate}
plot(colMeans(error_matrix),type='l',xlab='Sparsity',ylab='Success Rate')
```