sparse-block-figure.Rmd

---
title: "Block Sparse Figure"
output:
  html_document:
    df_print: paged
---


```{r}
set.seed(442560557)
forms <- c(10, 7, 12, 9)
n <- length(forms)
cols <- rows <- sum(forms)
membership <- replicate(rows, rbinom(n, 1, 1/n))
bs <- sapply(seq(rows), function(i) {
  (rep(membership[,i], times=forms) == 1) & (rbinom(cols, 1, 0.75) == 1)
})
plot(0:1, 0:1, typ="n", xlim=c(0, cols+1), ylim=c(0, rows+1), ylab='', xlab='', axes=FALSE,
     main="Raw Data Example")
for(x in 1:cols)
  for(y in 1:rows)
    if(bs[x,y]) polygon(c(x, x+1, x+1, x), c(y, y, y+1, y+1), col='darkblue')
```

```{r}
plot(0:1, 0:1, typ="n", xlim=c(0, cols+1), ylim=c(0, rows+1), ylab='', xlab='', axes=FALSE,
     main="Block Sparse Sorted Example")

ord <- order(((2^(0:(n-1))) %*% membership)[1,])

bso <- bs[,ord]

for(x in 1:cols)
  for(y in 1:rows)
    if(bso[x,y]) polygon(c(x, x+1, x+1, x), c(y, y, y+1, y+1), col='darkblue')
box <- function(x1,x2, y1, y2) lines(c(x1, x2, x2, x1, x1), c(y1, y1, y2, y2, y1), col='red', lwd=2)
box( 1, 11,  8, 14)
box(11, 18, 14, 23)
box( 1, 11, 22, 23)
box(11, 18, 28, 31)
box(18, 30, 23, 31)
box(30, 39, 31, 39)
box(18, 30, 35, 39)
box(11, 18, 38, 39)
box( 1, 11, 36, 39)
box( 1, 11, 34, 35)

text( 5, 5, "Form 1", pos=1)
text(15, 5, "Form 2", pos=1)
text(24, 5, "Form 3", pos=1)
text(35, 5, "Form 4", pos=1)
```