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

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## HW5 Q2

```{r matrix completion}
library(R.matlab) 
library(matlab)
n1 <- 50
n2 <- 50
A <- matrix(sample(-50:50,n1*n2, replace=TRUE),n1,n2) 
r <- 2
decomp <- svd(A)
U <- decomp$u
s <- decomp$d
V <- decomp$v

s[(r+1): length(s)] <- 0
S <-diag(s)

X <- U %*% S %*% t(V)
X0 <- X
# Removing 20% of the observations
A <- matrix(runif(n1*n2, min = 0, max = 1),n1,n2)>0.5
X[A] <- 0
m <- sum(sum(A==0))
m
# Initialization
Y <- matrix(0,n1,n2)
delta <- (n1*n2)/m
tau <- 250
# Iterations
vec <- rep(0,500)
err <- rep(0,500)
for (i in 1:500){
  decomp <- svd(Y)
  U <- decomp$u
  S <- decomp$d
  V <- decomp$v
  S_t <- S-tau
  S_t[S_t<0] <- 0
  Z <- U%*%diag(S_t)%*%t(V)
  P <- X-Z
  P[A] <- 0
  Y0 <- Y
  Y <- Y0 + delta*P
  vec[i] <- sum(sum((Y-Y0)^2))
  err[i] <- sum(sum((X0-Z)^2))/sum(sum((X0)^2))
}
#plot(vec,type="l")
#plot(err,type="l")
Ar <- as.vector(A)
Xr <- as.vector(X0)
Xr <- Xr[Ar]
Zr <- as.vector(Z)
Zr <- Zr[Ar]
#dev.off()
par(mfrow=c(1,2))
plot(Xr,type="l")
lines(Zr, col="red",lty=2)
plot(Xr-Zr,type="l")
#dev.off()
par(mfrow=c(1,2))
imagesc(Z, main ="M")
imagesc(X0, main ="M0")

```