69 lines
1.6 KiB
R
69 lines
1.6 KiB
R
library(numDeriv)
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k <- 3
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# obliczenie wartości x
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f <- function(k,x){
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return( x^(k-1) * (x + 3) * (x - 4) * (x - 7)^k )
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}
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# funkcja wzór
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function_formula = expression(x^(k-1) * (x + 3) * (x - 4) * (x - 7)^k)
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# pochodna wzó
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derivative_formula <- D(function_formula, 'x')
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x <- seq(-3, 8.5, by=0.1)
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y <- f(k,x)
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g <- eval(derivative_formula)
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startPoint <- -2
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grad.descent <- function(x0 = startPoint,
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epsilon = 0.0001,
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alpha = 0.00001,
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i.max = 1e6,
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k = 3){
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# gradient
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x <- x0
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gradient <- eval(function_formula)
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x.path <- x0
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loss <- c()
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for (i in 1:i.max){
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x.new <- x0 + alpha * gradient # Update
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x <- x.new
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gradient <- eval(function_formula) # Gradient in new point
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points(x = x.new, y = f(k,x.new), pch = 20, col = 'green', cex = 0.5)
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currentLoss <- (f(k, x0) - f(k,x.new))^2
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print(currentLoss)
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loss <- append(loss, currentLoss )
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if (currentLoss < epsilon){ # STOP
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break
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}
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x0 <- x.new
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x.path <- rbind(x.path, x.new)
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}
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return(list(x.new, x.path, i, loss))
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}
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plot(x, y, type="l", ylim = c(-15000, 30000))
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lines(x, g, col="yellow")
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abline(h = 0, col="gray")
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result <- grad.descent(k = k)
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# Wartość funkcji w znalezionym punkcie
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round(f(k,result[[1]][1]), 3)
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# Znaleziony punkt
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round(result[[1]], 2)
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# Staring point
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points(x = startPoint, y = f(k,startPoint), pch = 20, col = 'red', cex = 2)
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points(x = result[[1]], y = f(k,result[[1]]), pch = 20, col = 'blue', cex = 2)
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# loss
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plot(result[[4]], type="l")
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