Return Value

#Return value
angka_acak1=function(n,pw)
{x=runif(n)
y=runif(n)
z=(x+y)^pw
return(z)
}
angka_acak1(10,2)

##  [1] 2.7939779 2.0734877 2.0799235 2.8892293 3.5696991 3.6656072 3.3587086
##  [8] 0.4937837 1.5037374 1.9017707

angka_acak2=function(n,pw)
{x=runif(n)
y=runif(n)
z=(x+y)^pw
return(list(x=x,y=y,z=z))
}
angka_acak2(10,2)

## $x
##  [1] 0.9701025 0.9442438 0.1119429 0.6318445 0.1793794 0.3220215 0.1818114
##  [8] 0.3139015 0.1220624 0.4335189
## 
## $y
##  [1] 0.62574542 0.70607255 0.98695912 0.05765219 0.64466596 0.10881743
##  [7] 0.46698187 0.97395341 0.20247193 0.25436185
## 
## $z
##  [1] 2.5467307 2.7235442 1.2075856 0.4754057 0.6790507 0.1856222 0.4209327
##  [8] 1.6585702 0.1053225 0.4731799

angka_acak3=function(n=10,pw=2)
{x=runif(n)
y=runif(n)
z=(x+y)^pw
return(z)
}
angka_acak3()

##  [1] 0.1695761 0.6518543 0.9930833 0.5730776 2.0325465 0.4830299 2.0692052
##  [8] 1.8743093 0.1361227 0.6545134

angka_acak4=function()
{x=runif(n)
y=runif(n)
z=(x+y)^pw
return(z)
}
n <-5; pw <-3
angka_acak4()

## [1] 2.37107762 1.50661008 2.24940654 0.04042949 4.20381190

Latihan 1

#Buatlah fungsi untuk mencari median dari suatu vektor
med<-function(vect) {
n <-length(vect)
vects<-sort(vect)
if(n%%2 == 1) {m <-vects[(n+1)/2]}
else{m <-(vects[n/2]+vects[(n/2)+1])/2}
return(m)
}
x1<-c(1,5,3,7,3,4,2,7)
med(x1)

## [1] 3.5

Latihan 2

#Buatlah fungsi untuk mencari modus dari suatu vektor
 modus <- function(vect) 
{v <-unique(vect)
  f <-NULL
    for(i in v)
    {byk<-sum(vect==i)
    f <-c(f,byk)
    }
    fmax<-max(f)
    vf<-cbind(v,f)
    mode <-vf[f==fmax,]
    return(mode)
    }
modus(x1)

##      v f
## [1,] 3 2
## [2,] 7 2

Latihan 3

#Buatlah fungsi untuk menduga parameter pada regresi berganda!
p.est<-function(A){
if(!is.matrix(A))
stop("inputmustbeon matrix")
x1<-A[,-1]
y <-A[,1]
one<-rep(1,nrow(A))
x <-cbind(one,x1)
colnames(x)<-paste("x",1:ncol(x),sep="")
b.est<-as.vector(solve(t(x) %*% x) %*% (t(x) %*% y))
names(b.est)<-paste("b",0:(length(b.est)-1),sep="")
fitted.value<-as.vector(x%*%b.est)
error<-as.vector(y-fitted.value)
names(fitted.value)<-names(error)<-1:nrow(A)
list(beta.est=b.est,fit.val=fitted.value,error=error)
}
Pendapatan<-c(3.5,3.2,3.0,2.9,4.0,2.5,2.3)
Biaya.Iklan<-c(3.1,3.4,3.0,3.2,3.9,2.8,2.2)
Jumlah.Warung<-c(30,25,20,30,40,25,30)
X<-cbind(Pendapatan,Biaya.Iklan,Jumlah.Warung)
p.est(X)

## $beta.est
##          b0          b1          b2 
## -0.21381852  0.89843390  0.01745279 
## 
## $fit.val
##        1        2        3        4        5        6        7 
## 3.094910 3.277176 2.830539 3.184754 3.988185 2.738116 2.286320 
## 
## $error
##           1           2           3           4           5           6 
##  0.40508982 -0.07717642  0.16946108 -0.28475357  0.01181483 -0.23811608 
##           7 
##  0.01368033

model<-lm(Pendapatan~Biaya.Iklan+Jumlah.Warung)
model$coefficients

##   (Intercept)   Biaya.Iklan Jumlah.Warung 
##   -0.21381852    0.89843390    0.01745279

model$fitted.values

##        1        2        3        4        5        6        7 
## 3.094910 3.277176 2.830539 3.184754 3.988185 2.738116 2.286320

model$residuals

##           1           2           3           4           5           6 
##  0.40508982 -0.07717642  0.16946108 -0.28475357  0.01181483 -0.23811608 
##           7 
##  0.01368033

Latihan 4

set.seed(123)
X<-rbinom(100,10,0.5)
X

##   [1] 4 6 5 7 7 2 5 7 5 5 8 5 6 5 3 7 4 2 4 8 7 6 6 9 6 6 5 5 4 3 8 7 6 6 2 5 6
##  [38] 4 4 4 3 5 5 4 3 3 4 5 4 7 2 5 6 3 5 4 3 6 7 4 6 3 5 4 6 5 6 6 6 5 6 6 6 0
##  [75] 5 4 5 5 4 3 4 6 5 6 3 5 8 7 7 4 3 6 4 6 4 4 6 3 5 5

Latihan 1

(Integral)

library(Rcpp)

## Warning: package 'Rcpp' was built under R version 4.0.5

library(Ryacas)

## Warning: package 'Ryacas' was built under R version 4.0.5

## 
## Attaching package: 'Ryacas'

## The following object is masked from 'package:stats':
## 
##     integrate

## The following objects are masked from 'package:base':
## 
##     %*%, diag, diag<-, lower.tri, upper.tri

yac_str("Integrate(x) x^2 + 4*x")

## [1] "x^3/3+2*x^2"

f1 <-function(x) x^2 + 4*x
integrate(f1,lower = -10,upper = 10)

## 666.6667 with absolute error < 7.6e-12

Latihan 2

(Integral)

yac_str("Integrate(t) t^4 * Exp(-t)")

## [1] "4*(3*((-2)*(t+1)*Exp(-t)-t^2*Exp(-t))-t^3*Exp(-t))-t^4*Exp(-t)"

f2 <-function(t) t^(4) * exp(-t)
integrate(f2,lower = 0,upper = Inf)

## 24 with absolute error < 2.2e-05

gamma(5)

## [1] 24

Latihan 3

(Optimasi Satu Dimensi)

f3 <-function(x) sin(x) + sin(2*x) + cos(3*x)
curve(f3, from = 0, to = 2*pi)

optimize(f3, interval = c(0, 2*pi)) #minimum lokal

## $minimum
## [1] 3.033129
## 
## $objective
## [1] -1.054505

optimize(f3, interval = c(4, 2*pi)) #minimum global

## $minimum
## [1] 5.273383
## 
## $objective
## [1] -2.741405

optimize(f3, interval = c(0, 2*pi), maximum = T) #maksimum lokal

## $maximum
## [1] 4.0598
## 
## $objective
## [1] 1.096473

optimize(f3, interval = c(0, 1.5), maximum = T) #maksimum global

## $maximum
## [1] 0.3323289
## 
## $objective
## [1] 1.485871

Latihan 4

(Optimasi Fungsi Polinomial)

f4 <-function(x) 4*x^4-2*x^3-3*x
curve(f4, from = -1, to = 1.5)

optim(par = c(-0.5), fn= f4)

## Warning in optim(par = c(-0.5), fn = f4): one-dimensional optimization by Nelder-Mead is unreliable:
## use "Brent" or optimize() directly

## $par
## [1] 0.728418
## 
## $value
## [1] -1.832126
## 
## $counts
## function gradient 
##       36       NA 
## 
## $convergence
## [1] 0
## 
## $message
## NULL

Latihan 5

(Regresi Linear)

data5=data.frame(x=c(1,2,3,4,5,6),
y=c(1,3,5,6,8,12))
JKG <-function(data, b) {
with(data, sum((b[1]+b[2]*x-y)^2))
}
hasil1 <-optim(par = c(1,1), fn = JKG, data = data5)
hasil2 <-lm(y~x, data = data5)
plot(data5)
abline(hasil1$par,col=4)

hasil1$par

## [1] -1.266302  2.028449

hasil2$coefficients

## (Intercept)           x 
##   -1.266667    2.028571

hasil1$value

## [1] 2.819048

sum(hasil2$residuals^2)

## [1] 2.819048