projekt2

Projekt_2/Projekt_2.Rproj

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+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
+
+RnwWeave: Sweave
+LaTeX: pdfLaTeX

Projekt_2/projekt.R

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+# 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) )
+}
+
+startPoint <- 3
+
+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")
+
+