77 lines
1.2 KiB
Plaintext
77 lines
1.2 KiB
Plaintext
---
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title: "hw5"
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author: "Mark Pearl"
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date: "7/25/2021"
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output: html_document
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---
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```{r setup, include=FALSE}
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knitr::opts_chunk$set(echo = TRUE)
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```
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## HW5 Q2
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```{r matrix completion}
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library(R.matlab)
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library(matlab)
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n1 <- 50
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n2 <- 50
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A <- matrix(sample(-50:50,n1*n2, replace=TRUE),n1,n2)
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r <- 2
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decomp <- svd(A)
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U <- decomp$u
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s <- decomp$d
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V <- decomp$v
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s[(r+1): length(s)] <- 0
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S <-diag(s)
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X <- U %*% S %*% t(V)
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X0 <- X
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# Removing 20% of the observations
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A <- matrix(runif(n1*n2, min = 0, max = 1),n1,n2)>0.5
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X[A] <- 0
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m <- sum(sum(A==0))
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m
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# Initialization
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Y <- matrix(0,n1,n2)
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delta <- (n1*n2)/m
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tau <- 250
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# Iterations
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vec <- rep(0,500)
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err <- rep(0,500)
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for (i in 1:500){
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decomp <- svd(Y)
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U <- decomp$u
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S <- decomp$d
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V <- decomp$v
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S_t <- S-tau
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S_t[S_t<0] <- 0
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Z <- U%*%diag(S_t)%*%t(V)
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P <- X-Z
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P[A] <- 0
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Y0 <- Y
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Y <- Y0 + delta*P
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vec[i] <- sum(sum((Y-Y0)^2))
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err[i] <- sum(sum((X0-Z)^2))/sum(sum((X0)^2))
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}
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#plot(vec,type="l")
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#plot(err,type="l")
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Ar <- as.vector(A)
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Xr <- as.vector(X0)
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Xr <- Xr[Ar]
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Zr <- as.vector(Z)
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Zr <- Zr[Ar]
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#dev.off()
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par(mfrow=c(1,2))
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plot(Xr,type="l")
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lines(Zr, col="red",lty=2)
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plot(Xr-Zr,type="l")
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#dev.off()
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par(mfrow=c(1,2))
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imagesc(Z, main ="M")
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imagesc(X0, main ="M0")
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```
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