###
###  Contour and Heat Map
###      1. from data
###      2. from function
###-----------------------------------


#---------------
# 1. From Data
#
# R Graph Gallery:
# https://www.r-graph-gallery.com/2d-density-plot-with-ggplot2.html#distr


library(ggplot2)


#--- Simulated Data
A <- data.frame( x=rnorm(20000, 10,  3), y=rnorm(20000, 10, 3) )
B <- data.frame( x=rnorm(20000, 20,  2), y=rnorm(20000, 20, 2) )
C <- data.frame( x=rnorm(10000, 12,  1), y=rnorm(10000, 12, 1) )
D1 <- rbind(A,B,C)

dim(D1)


#--- Basic scatterplot
ggplot(D1, aes(x=x, y=y) ) + geom_point()


#--- 2d histogram
  ggplot(D1, aes(x=x, y=y) ) + geom_bin2d() + theme_bw()

  ggplot(D1, aes(x=x, y=y) ) + geom_bin2d(bins = 70) +
    scale_fill_continuous(type = "viridis")


#--- Hexbin chart
  ggplot(D1, aes(x=x, y=y) ) + geom_hex()

  ggplot(D1, aes(x=x, y=y) ) + geom_hex(bins = 70) +
    scale_fill_continuous(type = "viridis") +
    theme_bw()



#--- 2d density plot
  ggplot(D1, aes(x=x, y=y) ) + geom_density_2d()


  # Area only
  ggplot(D1, aes(x=x, y=y) ) +
    stat_density_2d(aes(fill = ..level..), geom = "polygon") +
    scale_fill_continuous(type = "viridis")


  # Area + contour
  ggplot(D1, aes(x=x, y=y) ) +
    stat_density_2d(aes(fill = ..level..), geom = "polygon", colour="white") +
    scale_fill_continuous(type = "viridis")

  # Using raster
  ggplot(D1, aes(x=x, y=y) ) +
    stat_density_2d(aes(fill = ..density..), geom = "raster", contour = FALSE) +
    scale_x_continuous(expand = c(0, 0)) +
    scale_y_continuous(expand = c(0, 0)) +
    theme( legend.position='none' )






#---------------
# 2. From Function
#


#--- 2a. Multivariate normal
library(ggplot2)
library(mvtnorm)


sigma= matrix(c(3,2,2,5), 2,2)
f = function(x) mvtnorm::dmvnorm(x, mean=c(4,4), sigma=sigma)

X = seq(0,10,.1)
Y = seq(0,10,.1)
XY <- expand.grid(X=X, Y=Y)

Z = apply(XY, 1, f)
D1 <- data.frame(cbind(XY, Z=Z))
head(D1)


ggplot( D1, aes(x=X, y=Y, z=Z)) + geom_contour()

ggplot( D1, aes(x=X, y=Y, z=Z)) + geom_contour_filled()

ggplot( D1, aes(x=X, y=Y, z=Z)) + geom_contour(bins=20)

ggplot( D1, aes(x=X, y=Y, z=Z)) +
  geom_raster(aes(fill = Z)) +
  geom_contour(colour = "white")




#--- 2b. Custom function
library(ggplot2)

f = function(x,y) {
    if (length(x) == length(y)) {
        return(3*x^2 - y^2 + 2*x)
    } else {
        return(NA)
    }
  }

X = seq(0,10,.1)
Y = seq(-5,10,.1)
XY <- expand.grid(X=X, Y=Y)

Z = f(XY[,1], XY[,2])
D1 <- data.frame(cbind(XY, Z=Z))
head(D1)

ggplot( D1, aes(x=X, y=Y, z=Z)) + geom_contour_filled()


f(1,2)
f(1,-2)
f(0,0)

# add h=0 line.
# draw f=1 line.




#--------------
# More examples

https://rpubs.com/dkahle/ggmap-geom-contour-filled

# Scroll to middle of the article
https://www.tidyverse.org/blog/2020/03/ggplot2-3-3-0/