Tugas_5

library(magick)

## Linking to ImageMagick 6.9.12.3
## Enabled features: cairo, freetype, fftw, ghostscript, heic, lcms, pango, raw, rsvg, webp
## Disabled features: fontconfig, x11

library(ggplot2)
library(matlib)
library(mvtnorm)

inp_img <- image_read("C:/Users/User/Pictures/Camera Roll/walpaper.jpeg")
inp_img

print(inp_img)

## # A tibble: 1 × 7
##   format width height colorspace matte filesize density
##   <chr>  <int>  <int> <chr>      <lgl>    <int> <chr>  
## 1 JPEG     474    266 sRGB       FALSE    16267 72x72

inp_img1 <- image_read("https://i.pinimg.com/originals/60/36/b8/6036b814ffe8ace9122cb4cfb65a2e34.jpg")
inp_img1

image_info(inp_img)

## # A tibble: 1 × 7
##   format width height colorspace matte filesize density
##   <chr>  <int>  <int> <chr>      <lgl>    <int> <chr>  
## 1 JPEG     474    266 sRGB       FALSE    16267 72x72

plot(inp_img)

mod_img <- image_modulate(inp_img, brightness = 120, saturation = 20,
hue = 20)

v1 <- c(2, -1, 3)
v2 <- c(-1, 0, 4)

v1 + v2

## [1]  1 -1  7

A <- matrix(c(3, 0, -5, -1, -3, 4), nrow = 2, ncol = 3, byrow = TRUE)
B <- matrix(c(-5, 5, 2, 1, -2, 0), nrow = 2, ncol = 3, byrow = TRUE)

A + B

##      [,1] [,2] [,3]
## [1,]   -2    5   -3
## [2,]    0   -5    4

A <- matrix(c(3, 0, -5, -1, -3, 4), nrow = 2, ncol = 3, byrow = TRUE)

-3 * A

##      [,1] [,2] [,3]
## [1,]   -9    0   15
## [2,]    3    9  -12

v1 <- c(2, -1, 3)
v2 <- c(-1, 0, 4)

v1 %*% v2

##      [,1]
## [1,]   10

A <- matrix(c(3, 0, -5, -1, -3, 4), nrow = 2, ncol = 3, byrow = TRUE)
B <- matrix(c(-5, 5, 2, 1, -2, 0), nrow = 3, ncol = 2, byrow = TRUE)

A %*% B

##      [,1] [,2]
## [1,]   -5   15
## [2,]   -9   -8

A <- matrix(c(4, -1, -5, 0, 1, -2), 2, 3, byrow = TRUE)

t(A)

##      [,1] [,2]
## [1,]    4    0
## [2,]   -1    1
## [3,]   -5   -2

sigma <- matrix(c(4,2,2,3), ncol = 2, nrow = 2)

mu <- c(1, 2)

n <- 1000
x <- rmvnorm(n = n, mean = mu, sigma = sigma)
d <- data.frame(x)

p2 <- ggplot(d, aes(x = X1, y = X2)) +
geom_point(alpha = .5) +
geom_density_2d()
p2

y <- x - mu

E <- eigen(sigma)
E$vectors

##            [,1]       [,2]
## [1,] -0.7882054  0.6154122
## [2,] -0.6154122 -0.7882054

dd <- data.frame(y)

p3 <- ggplot(dd, aes(x = X1, y = X2)) +
geom_point(alpha = .5) +
geom_density_2d()
p3