path_sim.Rmd

---
title: "Simulating path scoring"
author: "Mike Cuoco"
date: "2/15/2021"
output: html_document
editor_options:
  chunk_output_type: console
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(tidyverse)
library(glue)
library(latex2exp)
library(patchwork)
ggplot2::theme_set(theme_bw())
```

```{r}
# simulate paths
data = map_df(1:50, function(p){
  len = rep(p, p+1)
  consec = 0:p
  return(data.frame("length" = len, "consec" = consec))
})

alpha = list(0,0.1,0.5,1,5,10)
p.list = list()
p.list = map(alpha, function(a){
  data %>% 
    mutate(scores = length + a*((length-1)-consec), alpha = a) %>% 
    ggplot(aes(x = consec, y = length, z = scores, fill = scores)) + 
    geom_tile() +
    geom_contour(color = "white", alpha = 0.5) +
    coord_equal() +
    scale_fill_viridis_c() +
    guides(fill = FALSE) +
    labs(title = glue("alpha = {a}"), x = TeX('$unicolored(P)$'), y = TeX('$Edges(P)$'), fill = TeX('$Influence(P)$')) 
    # theme(legend.position = "left")
})

p = patchwork::wrap_plots(p.list, ncol = 3) + plot_annotation(title = TeX("$Influence(P)= Edges(P) + \\alpha \\cdot (Nodes(P) - unicolored(P))$"), subtitle = TeX("Colored by $Influence(P)$"))
ggsave(filename = "path_sim_alpha.png", width = 7, height = 5)

```