# Required library

library(png)

library(scales)

library(magick)

# Function to create a 2D posterior grid for a text message

create_posterior <- function(message, grid_size = 100) {

  # Temporary file to save the image

  temp_file <- tempfile(fileext = ".png")

  # Create the text image with lower resolution

  png(temp_file, width = grid_size, height = grid_size, bg = "white")

  # Reset graphical parameters

  par(mar = c(0, 0, 0, 0), xaxs = "i", yaxs = "i", family = "sans")

  plot.new()

  plot.window(xlim = c(0, 1), ylim = c(0, 1))

  # Render text with multi-line support

  text(0.5, 0.5, 

       labels = message, 

       cex = 4,         # Font size

       font = 2,        # Bold

       adj = 0.5,       # Center alignment

       xpd = NA)        # Allow drawing outside plot region

  dev.off()

  # Read the image back into R

  img <- readPNG(temp_file)

  # Remove the temporary file

  unlink(temp_file)

  # Convert to grayscale and create probability grid

  grid_values <- apply(img[,,1:3], c(1,2), mean) < 0.5

  grid_values <-ifelse(grid_values==0,0.05,1)

  posterior <- matrix(as.numeric(grid_values), nrow = grid_size, ncol = grid_size)

  # Flip the posterior vertically

  posterior <- posterior[nrow(posterior):1, ]

  return(posterior)

}

# Metropolis-Hastings MCMC sampler

metropolis_hastings_posterior <- function(posterior, n_iterations = 1e+4, thinning = 100,

                                          start = c(1,1)) {

  grid_dims <- dim(posterior)

  grid_height <- grid_dims[1]

  grid_width <- grid_dims[2]

  # Initialize first point

  current_x <- start[1]

  current_y <- start[2]

  # Storage for samples

  samples <- matrix(0, nrow = n_iterations %/% thinning + 1, ncol = 2)

  samples[1, ] <- c(current_x, current_y)

  # Current probability

  current_prob <- posterior[current_y, current_x]

  for (i in 1:n_iterations) {

    if(i %% thinning ==0){

      # Propose new point (random walk)

      proposed_x <- current_x + sample(-5:5, 1)

      proposed_y <- current_y + sample(-5:5, 1)

      # Boundary check

      proposed_x <- max(1, min(proposed_x, grid_width))

      proposed_y <- max(1, min(proposed_y, grid_height))

      # Proposed probability

      proposed_prob <- posterior[proposed_y, proposed_x]

      # Acceptance probability

      if(current_prob==0)

        acceptance_prob=1

      else

        acceptance_prob <- min(1, proposed_prob / current_prob)

      # Accept or reject

      if (runif(1) < acceptance_prob) {

        current_x <- proposed_x

        current_y <- proposed_y

        current_prob <- proposed_prob

      }

      # Store new current point

      samples[i %/% thinning + 1, ] <- c(current_x, current_y)

    }

  }

  return(list(samples = samples))

}

# Main execution

# Read file

file_path <- "Xmas.txt"

message <- readLines(file_path)

# Convert to uppercase and combine lines

message <- toupper(paste(message, collapse = "\n"))

# Create the posterior with lower resolution

grid_size <- 250  # Reduced grid size

posterior <- create_posterior(message, grid_size)

set.seed(12345)

# Run Metropolis-Hastings MCMC

mcmc_result_red <- metropolis_hastings_posterior(posterior, n_iterations = 1e+5, 

                                                 thinning =1, start=c(1,1))

mcmc_result_green <- metropolis_hastings_posterior(posterior, n_iterations = 1e+5, 

                                                   thinning =1, start=c(250,250))

# Path plot

plot(mcmc_result_green$samples[, 1], mcmc_result_green$samples[, 2], 

      type = "l", col = alpha("darkgreen",0.15),

      xlab = "x", ylab = "y", 

      xlim = c(1, dim(posterior)[2]), 

      ylim = c(1, dim(posterior)[1]), 

      asp = 1)

lines(mcmc_result_red$samples[, 1], mcmc_result_red$samples[, 2], 

     type = "l", col = alpha("red",0.15),

     xlab = "x", ylab = "y", 

     xlim = c(1, dim(posterior)[2]), 

     ylim = c(1, dim(posterior)[1]), 

     asp = 1)

# Function to create animated GIF of MCMC path

create_mcmc_gif <- function(posterior, mcmc_result_red, mcmc_result_green, 

                            output_file = "mcmc_path.gif", skip = 500, max_frames = 300) {

  # Prepare temporary directory for frames

  temp_dir <- tempdir()

  # Create frames

  frames <- seq(1, nrow(mcmc_result_red$samples), by = skip)

  frames <- frames[1:min(length(frames), max_frames)]

  image_files <- c()

  for (i in frames) {

    # Temporary PNG file for this frame

    temp_png <- file.path(temp_dir, paste0("frame_", i, ".png"))

    # Create plot for this frame

    png(temp_png, width = 800, height = 800)

    par(mar = c(4, 4, 2, 1))

    # Plot the posterior grid

    image(1:nrow(posterior), 1:ncol(posterior), posterior,

          col = "white",

          xlab = "x", ylab = "y")

    # Plot the path up to this point

    points(mcmc_result_green$samples[1:i, 1], mcmc_result_green$samples[1:i, 2],

           type = "l", col = alpha("darkgreen",0.15),, lwd = 2)

    points(mcmc_result_green$samples[i, 1], mcmc_result_green$samples[i, 2],

           col = "blue", pch = 16, cex = 1.5)

    points(mcmc_result_red$samples[1:i, 1], mcmc_result_red$samples[1:i, 2],

           type = "l", col = alpha("red",0.15),, lwd = 2)

    points(mcmc_result_red$samples[i, 1], mcmc_result_red$samples[i, 2],

           col = "blue", pch = 16, cex = 1.5)

    dev.off()

    image_files <- c(image_files, temp_png)

  }

  # Create GIF

  image_list <- image_read(image_files)

  image_write(image_animate(image_list, fps = 10), 

              path = output_file)

  # Clean up temporary files

  unlink(image_files)

  return(output_file)

}

gif_path <- create_mcmc_gif(posterior, mcmc_result_red, mcmc_result_green, "mcmc_path.gif")

cat("GIF created at:", gif_path, "\n")