ripser.Rmd

---
title: "Ripser"
author: "Ken Wang"
date: "9/15/2020"
output:
  html_document:
    df_print: paged
  pdf_document: default
  html_notebook: default
editor_options:
  chunk_output_type: inline
---

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

```{r}
trial = 1000
num = 100
rand = data.frame(replicate(2*trial,runif(num, -10, 10)))
deg0 = data.frame(matrix(0, nrow = num - 1, ncol = trial))
deg1 = data.frame(num=numeric(trial),birth_mean=numeric(trial),birth_min=numeric(trial),
                  birth_max=numeric(trial),death_mean=numeric(trial),death_min=numeric(trial),
                  death_max=numeric(trial),range_mean=numeric(trial),range_min=numeric(trial),
                  range_max=numeric(trial))

for(i in 1:trial){
  rips = vietoris_rips(rand[,c(i,i+trial)])
  deg0[,i] = rips$death[1:(num - 1)]
  rips1 = rips[num:nrow(rips),]
  rips1$range = rips1$death - rips1$birth
  deg1$num[i] = nrow(rips1)
  deg1$birth_min[i] = rips1$birth[nrow(rips1)]
  deg1$birth_max[i] = rips1$birth[1]
  deg1$birth_mean[i] = mean(rips1$birth)
  deg1$death_min[i] = min(rips1$death)
  deg1$death_max[i] = max(rips1$death)
  deg1$death_mean[i] = mean(rips1$death)
  deg1$range_min[i] = min(rips1$range)
  deg1$range_max[i] = max(rips1$range)
  deg1$range_mean[i] = mean(rips1$range)
}
```

```{r}
# degree 0
(range(deg0)) # range
deg0row_means = rowMeans(deg0) # rowmeans
plot1 = data.frame(num=1:(num-1),length=deg0row_means)
plot1 %>%
  ggplot(aes(x=num,y=length))+
  geom_bar(stat="identity", fill="steelblue")+
  theme_minimal()
```

```{r,warning=FALSE}
# degree 1
#summarise_all(deg1,list(min=min,max=max,mean=mean))
summary(deg1$num)
summary(deg1$birth_mean)
summary(deg1$birth_min)
summary(deg1$birth_max)
summary(deg1$death_mean)
summary(deg1$death_min)
summary(deg1$death_max)
summary(deg1$range_mean)
summary(deg1$range_min)
summary(deg1$range_max)
```

```{r}
deg0_1 = pivot_longer(deg0,cols=1:trial)
deg0_1 %>%
  ggplot()+
  geom_histogram(aes(x=value),stat="bin")
summary(deg0_1$value)

fit.gamma <- fitdist(deg0_1$value, distr = "gamma", method = "mle")
summary(fit.gamma)
plot(fit.gamma)

num1_dist = rgamma(n = length(deg0_1$value), fit.gamma$estimate[1], fit.gamma$estimate[2])
ks.test(deg0_1$value,num1_dist)

fit.weibull <- fitdist(deg0_1$value, distr = "weibull", method = "mle")
summary(fit.weibull)
plot(fit.weibull)

num1_dist1 = rweibull(n = nrow(deg0_1), fit.weibull$estimate[1],
                      fit.weibull$estimate[2])
ks.test(deg0_1$value,num1_dist1)
```

```{r}
is_norm_dist = function(values){
  fit.norm = fitdist(values, distr = "norm", method = "mle")
  r_dist = rnorm(n = length(values), fit.norm$estimate[1], fit.norm$estimate[2])
  ks.test(values,r_dist)
}
```


```{r}
deg1 %>%
  ggplot(aes(x=as.factor(num)))+
  geom_bar(fill="steelblue")+
  theme_minimal()

is_norm_dist(deg1$num)

fitBinom=fitdist(data=deg1$num-11, dist="binom", fix.arg=list(size=19),start=list(prob=0.1))
r_binom = rbinom(length(deg1$num), size = 19, prob = fitBinom$estimate)+11

ks.test(deg1$num,r_binom)
qqplot(deg1$num,r_binom)


probs = 1 - var(deg1$num)/mean(deg1$num)
trials = mean(deg1$num) / probs
r_binom2 = rbinom(length(deg1$num), size = as.integer(trials), prob = probs)

ks.test(deg1$num,r_binom2)
qqplot(deg1$num,r_binom2)

mean(deg1$num)
var(deg1$num)
```

```{r}
deg1 %>%
  ggplot()+
  geom_histogram(aes(x=birth_mean),stat="bin")

is_norm_dist(deg1$birth_mean)
```

```{r}
deg1 %>%
  ggplot()+
  geom_histogram(aes(x=birth_min),stat="bin")

is_norm_dist(deg1$birth_min)
```

```{r}
deg1 %>%
  ggplot()+
  geom_histogram(aes(x=birth_max),stat="bin")

is_norm_dist(deg1$birth_max)
```

```{r}
deg1 %>%
  ggplot()+
  geom_histogram(aes(x=death_mean),stat="bin")

is_norm_dist(deg1$death_mean)
```

```{r,warning=FALSE}
deg1 %>%
  ggplot()+
  geom_histogram(aes(x=death_min),stat="bin")

is_norm_dist(deg1$death_min)
```

```{r}
deg1 %>%
  ggplot()+
  geom_histogram(aes(x=death_max),stat="bin")

is_norm_dist(deg1$death_max)
```

```{r}
deg1 %>%
  ggplot()+
  geom_histogram(aes(x=range_mean),stat="bin")

is_norm_dist(deg1$range_mean)
```

```{r}
deg1 %>%
  ggplot()+
  geom_histogram(aes(x=range_min),stat="bin")

is_norm_dist(deg1$range_min)
```


```{r}
deg1 %>%
  ggplot()+
  geom_histogram(aes(x=range_max),stat="bin")

is_norm_dist(deg1$range_max)
```