dodanie potegi i wbudowanej funkcji pochodnej

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MikolajPaterka 2022-06-12 17:55:12 +02:00
parent f965ceec53
commit cc07821b22

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@ -1,15 +1,22 @@
library(numDeriv)
# Function to calculate gradient # Function to calculate gradient
# @x - vector of values (2) # @x - vector of values (2)
grad <- function(x){ grad <- function(x){
return( (x - 7)^2 * x * (7*x^3 - 34*x^2 - 39*x + 168) ) return( (x - 7)^2 * x * (7*x^3 - 34*x^2 - 39*x + 168) )
} }
#grad <- function(x){
# return()
#}
startPoint <- -2 startPoint <- -2
f <- function(x){ f <- function(x){
return( x^2 * (x + 3) * (x - 4) * (x - 7)^3 ) return( x^2 * (x + 3) * (x - 4) * (x - 7)^3 )
} }
# Function to minimize function # Function to minimize function
# @x0 - starting point # @x0 - starting point
# @epsilon - maximum error # @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") 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")