dodanie potegi i wbudowanej funkcji pochodnej

Projekt_2/projekt.R

@@ -1,15 +1,22 @@
+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
@@ -57,3 +64,80 @@ 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")
+
+