optimasi numerik

Nama dan NIM : Nadia Din Salima Al Kamila (230605110140)

Dosen Pengampu : Prof. Dr. Suhartono, M.Kom

Universitas : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Fakultas : Sains dan Teknologi

Program Studi : Teknik Informatika

library(mosaicCalc)

## Loading required package: mosaic

## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2

## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.

## 
## Attaching package: 'mosaic'

## The following objects are masked from 'package:dplyr':
## 
##     count, do, tally

## The following object is masked from 'package:Matrix':
## 
##     mean

## The following object is masked from 'package:ggplot2':
## 
##     stat

## The following objects are masked from 'package:stats':
## 
##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var

## The following objects are masked from 'package:base':
## 
##     max, mean, min, prod, range, sample, sum

## Loading required package: mosaicCore

## 
## Attaching package: 'mosaicCore'

## The following objects are masked from 'package:dplyr':
## 
##     count, tally

## The legacy packages maptools, rgdal, and rgeos, underpinning the sp package,
## which was just loaded, will retire in October 2023.
## Please refer to R-spatial evolution reports for details, especially
## https://r-spatial.org/r/2023/05/15/evolution4.html.
## It may be desirable to make the sf package available;
## package maintainers should consider adding sf to Suggests:.
## The sp package is now running under evolution status 2
##      (status 2 uses the sf package in place of rgdal)

## 
## Attaching package: 'mosaicCalc'

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

# Contoh Optimisasi sederhana

x <- seq(-6, 5, by = 0.1)

y <- sin(x) + sin(2*x)

plot(x, y, type = "l", col = "red", lwd = 2, xlab = "Nilai x", ylab = "Nilai f(x)", main = "Grafik Fungsi f(x)")

Optimisasi numerik Fungsi R/mosaic adalah fungsi yang dapat digunakan untuk mencari nilai argmax dan argmin di atas domain tertentu. Cara kerjanya mirip dengan fungsi argmax dan argmin, namun alih-alih menghasilkan grafik, fungsi ini mengembalikan bingkai data yang berisi nilai argmax di satu baris dan argmin di baris lainnya

```r
h <- rfun(~ x, seed=7293)
argM(h(x) ~ x, bounds(x=-5:5))

## # A tibble: 2 × 3
##        x .output. concavity
##    <dbl>    <dbl>     <dbl>
## 1 -1.68      1.93         1
## 2  0.173     8.25        -1

h <- rfun(~ x + y, seed=7293)
argM(h(x, y) ~ x + y, bounds(x=-5:5, y=-5:5))

## # A tibble: 1 × 3
##       x      y .output.
##   <dbl>  <dbl>    <dbl>
## 1  3.73 -0.359   -0.186

h <- rfun(~ sin(x) + cos(y), seed=7293)
argM(h(x, y) ~ x + y, bounds(x=-5:5, y=-5:5))

## # A tibble: 1 × 3
##       x      y .output.
##   <dbl>  <dbl>    <dbl>
## 1  3.73 -0.359   -0.186

kolom memberikan nilai output fungsi untuk input . Kolom ini memberi tahu apakah cekung fungsi positif atau negatif. Mendekati puncak, cekung akan negatif; Di dekat lembah, cekungan positif. Akibatnya, Anda dapat melihat bahwa baris pertama dari bingkai data sesuai dengan minimum lokal dan baris kedua adalah maksimum ```