ripser_distribution.Rmd

---
title: "Ripser Distributions"
author: "Ken Wang"
date: "9/22/2020"
output:
  html_document:
    df_print: paged
  pdf_document: default
  html_notebook: default
---

```{r,message=FALSE,warning=FALSE}
library("ripserr")
library(tidyverse)
```

```{r}
deg0_mean = function(num, trial = 100, range = 10){
  rand = data.frame(replicate(2 * trial,runif(num, range * -1, range))) # random uniform
  result = data.frame(deg0=numeric(trial),deg1=numeric(trial))
  for(i in 1:trial){
    rips = vietoris_rips(rand[,c(i,i + trial)]) # rips
    result$deg0[i] = mean(rips$death[1:(num-1)]) # mean of all bars
    result$deg1[i] = nrow(rips) - (num - 1) # number of deg 1 bars
  }
  return(colMeans(result)) # mean of all trials
}
```

```{r}
deg0_len_dist = data.frame(num=c(10,20,30,40,50,60,70,80,90,100,150,200,500))
results = map(deg0_len_dist$num,deg0_mean)
results = as.data.frame(t(as.matrix(as.data.frame(results))))
results = data.frame(num=deg0_len_dist$num,results)
rownames(results)=NULL

results %>%
  ggplot(aes(x=num,y=deg0))+
  geom_point()+
  geom_line()
```

```{r}
results %>%
  ggplot(aes(x=num,y=deg1))+
  geom_point()+
  geom_line()
```