library(numDeriv)

# Function to calculate gradient
# @x - vector of values (2)
grad <- function(x){
  return( (x - 7)^2 * x * (7*x^3 - 34*x^2 - 39*x + 168) )
}

#grad <- function(x){
#  return()
#}

startPoint <- -2

f <- function(x){
  return( x^2 * (x + 3) * (x - 4) * (x - 7)^3 )
}


# Function to minimize function
# @x0 - starting point
# @epsilon - maximum error
# @alpha - learning rate
# @i.max - maximum number of iterations
grad.descent <- function(x0 = startPoint, 
                         epsilon = 0.01, 
                         alpha = 0.00001, 
                         i.max = 1e6){
  gradient <- grad(x0) # Initialize gradient
  x.path <- x0 
  loss <- c()
  for (i in 1:i.max){
    x.new <- x0 - alpha * gradient # Update
    gradient <- grad(x.new) # Gradinet in new point
    points(x = x.new, y = f(x.new), pch = 20, col = 'green', cex = 0.5)
    currentLoss <- (f(x0) - f(x.new))^2
    print(currentLoss)
    loss <- append(loss, currentLoss )
    if (currentLoss < epsilon){ # STOP
      break 
    }
    x0 <- x.new
    x.path <- rbind(x.path, x.new)
  }
  return(list(x.new, x.path, i, loss))
}

x <- seq(-3, 8.5, by=0.1)
y <- f(x)
g <- grad(x)
zero <-

plot(x, y, type="l", ylim = c(-15000, 30000))
lines(x, g, col="yellow")
abline(h = 0, col="gray")

result <- grad.descent()
round(f(result[[1]][1]), 3) # Wartość funkcji w znalezionym punkcie
round(result[[1]], 2) # Znaleziony punkt

points(x = startPoint, y = f(startPoint), pch = 20, col = 'red', cex = 2) # Staring point
points(x = result[[1]], y = f(result[[1]]), pch = 20, col = 'blue', cex = 2)

plot(result[[4]], type="l")


# dodatek -----------------------------------------------------------------

#-----all 

# Function to calculate gradient
# @x - vector of values (2)
# nie wiem czemu wczytywanie nie zamiania na int
#k <- as.integer(readline(prompt = ""))
k <- 3

#oblicznie warosći x
f <- function(k,x){
  return( x^(k-1) * (x + 3) * (x - 4) * (x - 7)^k )
}

# fukcja - wzów
function_formula = expression(x^(k-1) * (x + 3) * (x - 4) * (x - 7)^k)
# pochodna - wzór
derivative_formula <- D(function_formula, 'x') 

x <- seq(-3, 8.5, by=0.1)
y <- f(k,x)
g <- eval(derivative_formula)
zero <-
startPoint <- -2



# Function to minimize function
# @x0 - starting point
# @epsilon - maximum error
# @alpha - learning rate
# @i.max - maximum number of iterations
grad.descent <- function(x0 = startPoint, 
                         epsilon = 0.0001, 
                         alpha = 0.00001, 
                         i.max = 1e6,
                         k = 3){
  #gradient <- grad(x0) # Initialize gradient
  x <- x0
  gradient <- eval(function_formula)
  x.path <- x0 
  loss <- c()
  for (i in 1:i.max){
    # tu zmieniłem z "-" na "+"
    x.new <- x0 + alpha * gradient # Update
    x <- x.new
    gradient <- eval(function_formula) # Gradinet in new point
    points(x = x.new, y = f(k,x.new), pch = 20, col = 'green', cex = 0.5)
    currentLoss <- (f(k, x0) - f(k,x.new))^2
    print(currentLoss)
    loss <- append(loss, currentLoss )
    if (currentLoss < epsilon){ # STOP
      break 
    }
    x0 <- x.new
    x.path <- rbind(x.path, x.new)
  }
  return(list(x.new, x.path, i, loss))
}


plot(x, y, type="l", ylim = c(-15000, 30000))
lines(x, g, col="yellow")
abline(h = 0, col="gray")

result <- grad.descent()

round(f(k,result[[1]][1]), 3) # Wartość funkcji w znalezionym punkcie
round(result[[1]], 2) # Znaleziony punkt

points(x = startPoint, y = f(k,startPoint), pch = 20, col = 'red', cex = 2) # Staring point
points(x = result[[1]], y = f(k,result[[1]]), pch = 20, col = 'blue', cex = 2)

plot(result[[4]], type="l")