This commit is contained in:
Jakub Adamski 2022-06-06 12:28:33 +02:00
parent 92a76194f8
commit 89cbcf7b9a
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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

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Projekt_2/README.md Normal file
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Projekt_2/projekt.R Normal file
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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")