---
title: "LOL Simulations"
author: "Eric Bridgeford"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{sims}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r}
require(lolR)
require(ggplot2)
require(MASS)
n <- 1000
d <- 15
```

```{r}
plot_sim <- function(X, Y, name, d1=1, d2=2) {
  data <- data.frame(x1=X[,d1], x2=X[,d2], y=Y)
  data$y <- factor(data$y)
  ggplot(data, aes(x=x1, y=x2, color=y)) +
    geom_point() +
    xlab("x1") +
    ylab("x2") +
    ggtitle(name)
}
```
Below, we visualize the different simulation settings with `n=400` in `d=50` dimensions:

# Trunk, 2 Class

```{r, fig.width=5}
testdat <- lol.sims.rtrunk(n, d, b=20)
X <- testdat$X
Y <- testdat$Y
print(plot_sim(X, Y, "Trunk, 2 Class"))
```

# Rotated Trunk, 2 Class, non-equal priors

In this simulation, we show the trunk, estimate a rotation matrix to apply to the mean and covariances, and use a non-equal prior with more class 1 than class 2.

```{r, fig.width=5}
testdat <- lol.sims.rtrunk(n, d, rotate=TRUE, priors=c(0.8, 0.2), b=20)
X <- testdat$X
Y <- testdat$Y
print(plot_sim(X, Y, "Rotated Trunk, 2 Class, non-equal priors"))
```

# Trunk, 3 Class

```{r, fig.width=5}
testdat <- lol.sims.rtrunk(n, d, b=20, K=3)
X <- testdat$X
Y <- testdat$Y
print(plot_sim(X, Y, "Trunk, 3 Class"))
```

# Mean Difference

```{r, fig.width=5}
testdat <- lol.sims.mean_diff(n, d)
X <- testdat$X
Y <- testdat$Y
print(plot_sim(X, Y, "Mean Difference 2 Class"))
```

# Toeplitz

```{r, fig.width=5}
testdat <- lol.sims.toep(n, d)
X <- testdat$X
Y <- testdat$Y
print(plot_sim(X, Y, "Toeplitz"))
```

# QD- Toeplitz

```{r, fig.width=5}
testdat <- lol.sims.qdtoep(n, d)
X <- testdat$X
Y <- testdat$Y
print(plot_sim(X, Y, "QD-Toeplitz"))
```

# XOR

```{r, fig.width=5}
testdat <- lol.sims.xor2(n, d)
X <- testdat$X
Y <- testdat$Y
print(plot_sim(X, Y, "XOR"))
```

# Cigar

```{r, fig.width=5}
testdat <- lol.sims.cigar(n, d)
X <- testdat$X
Y <- testdat$Y
print(plot_sim(X, Y, "Cigar"))
```

# Fat Tails

```{r, fig.width=5}
testdat <- lol.sims.fat_tails(n, d)
X <- testdat$X
Y <- testdat$Y
print(plot_sim(X, Y, "Fat Tails"))
```

# Cross

```{r, fig.width=5}
testdat <- lol.sims.cross(n, d, a=4, b=.25)
X <- testdat$X
Y <- testdat$Y
print(plot_sim(X, Y, "Cross", d1=7, d2=8))
```