sim_the_anneal.Rmd

---
title: "simulate_some_annealz"
author: "Andrew"
date: "20/08/2021"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```


`DEFINE function to optimize h(X)`

```{r}

fake_xs <- rnorm(42, 19, 4)

loglike_numbers <- function(numbers, mu) sum(dnorm(x = numbers, mean = mu, sd = 4, log = TRUE))


loglike_numbers(fake_xs, 7)
library(tidyverse)

tibble(possible_mus = -3:30) %>% 
  mutate(ll = map_dbl(possible_mus, loglike_numbers, numbers = fake_xs)) %>% 
  ggplot(aes(x = possible_mus, y = ll)) + geom_point() + 
  geom_vline(xintercept = 19)

```


`DEFINE the sampling function c(X)`

```{r}

see_of_x <- function(x, sigma = 1) { x + rnorm(1, sd = sigma) }

xx <- numeric(40)
xx[1] <- 30

## walk like a drunk: test my see of x function
for(i in 2:40){
  xx[i] <- see_of_x(xx[i-1], sigma = .001)
}

plot(xx, type = "l")
```



 `DEFINE temperature sequence`

```{r}


temp_line <- function(runs, tstart, tcool){
  exp(log(tstart) + log(tcool)*0:(runs-1))
}

temp_line_str <- function(runs, tstart) {
  seq(tstart, 0, length.out = runs)
}

tibble(time = 1:300,
       temp = temp_line(300, 8, 0.9)) %>% 
  ggplot(aes(x = time, y = temp)) + 
  geom_point()

tibble(time = 1:300,
       prob = exp(-13/temp_line(300, 70, 0.97))) %>% 
  ggplot(aes(x = time, y = prob)) + 
  geom_point()

```




```
    REPEAT
        DRAW sample X from c(x)
        COMPUTE difference diff = h(X) - h(X_0)
        IF diff > 0 ACCEPT X
        ELSE 
            COMPUTE acceptance probability p = exp(diff/T)
            DRAW value P from random uniform on (0,1)
            IF P < p
                ACCEPT X
            ELSE
                REJECT X
        UPDATE temperature
    UNTIL nsteps is reached
```


```{r}
# function to take temperature, diff, and give back TRUE or FALSE (will a negative be kept)

keep_neg_diff <- function(diff, Tmp){
  stopifnot(diff<0)
  runif(1, min = 0, max = 1) < exp(diff/Tmp)
}

keep_neg_diff(-30, Tmp = 40)


keep_neg_diff(10, Tmp = 0)

```


```{r}

## function to take x0 and x1 and a function and temp and return either x0 (reject) or x1 ( accept)
keep_or_reject <- function(x0, x1, fun, temp){
  diff <- fun(x1) - fun(x0)
  # browser()
  if (diff > 0) {
    return(x1)
  } else if (keep_neg_diff(diff, Tmp = temp)){
    return(x1)
  } else {
    return(x0)
  }
}

```


```{r}
# evaluate for these only

ll_fakenums_f_x <- function(x) loglike_numbers(fake_xs, mu = x)

# make temperatures
runs <- 299

temps <- temp_line(runs, 3, 0.98)

xx <- numeric(runs + 1)

startval <- 10


xx[1] <- startval


for (i in 2:runs){
  maybe <- see_of_x(xx[i-1])
  xx[i] <- keep_or_reject(x0 = xx[i-1], x1 = maybe, fun = ll_fakenums_f_x, temp = temps[i-1])
}

plot(xx, type = "l")
```