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<- sample(0:1, size = 1, prob = c(p, 1-p)) + if(next.game == 0) B <- B+1 + if(next.game == 1) A <- A+1 + + # best-of-series finishes when any team reaches 3 + if(A == 3 || B == 3) + { + x <- k + break + } + } + return(x) +} + + +my.matches <- numeric(length = 1e3) +for(i in 1:1e3) +{ + my.matches[i] <- my.tennis(.7) +} + +ans <- mean(my.matches) +ans + +################################### diff --git a/MTH208/Assignments/assign2_sol (2).R b/MTH208/Assignments/assign2_sol (2).R new file mode 100644 index 0000000..5736ea4 --- /dev/null +++ b/MTH208/Assignments/assign2_sol (2).R @@ -0,0 +1,21 @@ + +################ my code ############ +my.prop.color <- function(img, col) +{ + col.mat <- as.array(img[,,1,]) + dims <- dim(col.mat) + + dist <- matrix(0, nrow = dims[1], ncol = dims[2]) + for(i in 1:dims[1]) + { + for(j in 1:dims[2]) + { + dist[i,j] <- norm(col.mat[i,j, ] - col, "2") + } + } + + props <- sum(dist < .5)/(dims[1]*dims[2]) + return(props) +} + +################################### diff --git a/MTH208/Assignments/assign3_sol.R b/MTH208/Assignments/assign3_sol.R new file mode 100644 index 0000000..10b2c08 --- /dev/null +++ b/MTH208/Assignments/assign3_sol.R @@ -0,0 +1,18 @@ + +library(rvest) +html <- read_html("https://www.icc-cricket.com/rankings/womens/player-rankings/odi/batting") + +# Get the whole data as a table +# First element in the list +tab <- html_table(html)[[1]] + +# Replace first column with 1:100 +tab$Pos <- 1:100 + +# Remove last column +tab <- tab[, -5] + +# convert to data.frame +# this step is not very necessary +MY_icc_rank <- as.data.frame(tab) + diff --git a/MTH208/Assignments/assign4_sol.R b/MTH208/Assignments/assign4_sol.R new file mode 100644 index 0000000..26965c4 --- /dev/null +++ b/MTH208/Assignments/assign4_sol.R @@ -0,0 +1,13 @@ +library(rvest) + +html <- read_html("https://prsindia.org/covid-19/cases") + +foo <- html %>% html_table() +foo <- foo[[1]] + +MY_india_rates <- foo[-1, ] +MY_india_rates <- MY_india_rates[ ,-1] +MY_india_rates <- as.data.frame(MY_india_rates) + +save(MY_india_rates, file = "covid.Rdata") + diff --git a/MTH208/Assignments/assign5_sol.R b/MTH208/Assignments/assign5_sol.R new file mode 100644 index 0000000..23930c5 --- /dev/null +++ b/MTH208/Assignments/assign5_sol.R @@ -0,0 +1,6 @@ + +my.func2 <- function(vec) +{ + temp <- log(vec) + return(temp/sum(temp)) +} diff --git a/MTH208/Assignments/assign6_sol.cp b/MTH208/Assignments/assign6_sol.cp new file mode 100644 index 0000000..d87dd3c --- /dev/null +++ b/MTH208/Assignments/assign6_sol.cp @@ -0,0 +1,22 @@ +// cope and paste your code here. + +#include +using namespace Rcpp; + + +// [[Rcpp::export]] +NumericMatrix my_divideC(NumericMatrix x, NumericMatrix y) { + int n = x.nrow(); + int m = x.ncol(); + + NumericMatrix out(n,m); + + for(int i = 0; i < n; i++) + { + for(int j = 0; j < m; j++) + { + out(i,j) = x(i,j) / y(i,j); + } + } + return out; +} diff --git a/MTH208/Assignments/assign7_sol.R b/MTH208/Assignments/assign7_sol.R new file mode 100644 index 0000000..8ec82eb --- /dev/null +++ b/MTH208/Assignments/assign7_sol.R @@ -0,0 +1,20 @@ +### Solution to assignment 7 + +dat <- read.csv("data.csv") +dat$X1 <- as.factor(dat$X1) +dat$X2 <- as.factor(dat$X2) +dat$X3 <- as.factor(dat$X3) + +## X2 is the variable that separates Var1 and Var2 +## into 3 visible groups + +plot(dat$Var1, dat$Var2, col = dat$X2, + xlab = "Variable 1", ylab = "Variable 2", + main = "Simpson's Paradox with X2", pch = 16) +for(i in 1:length(levels(dat$X2))) +{ + foo <- subset(dat, dat$X2 == levels(dat$X2)[i]) + abline(lm(foo$Var2 ~ foo$Var1), col = i) +} +legend("topleft", legend = levels(dat$X2), + title = "X2", fill = 1:3) \ No newline at end of file diff --git a/MTH208/Assignments/assignment1.pdf b/MTH208/Assignments/assignment1.pdf new file mode 100644 index 0000000..933f9cd Binary files /dev/null and b/MTH208/Assignments/assignment1.pdf differ diff --git a/MTH208/Assignments/assignment2.pdf b/MTH208/Assignments/assignment2.pdf new file mode 100644 index 0000000..7dff1a9 Binary files /dev/null and b/MTH208/Assignments/assignment2.pdf differ diff --git a/MTH208/Assignments/assignment3.pdf b/MTH208/Assignments/assignment3.pdf new file mode 100644 index 0000000..27f990e Binary files /dev/null and b/MTH208/Assignments/assignment3.pdf differ diff --git a/MTH208/Assignments/assignment4.pdf b/MTH208/Assignments/assignment4.pdf new file mode 100644 index 0000000..2cce24c Binary files /dev/null and b/MTH208/Assignments/assignment4.pdf differ diff --git a/MTH208/Assignments/assignment5.pdf b/MTH208/Assignments/assignment5.pdf new file mode 100644 index 0000000..94bed7b Binary files /dev/null and b/MTH208/Assignments/assignment5.pdf differ diff --git a/MTH208/Assignments/assignment6.pdf b/MTH208/Assignments/assignment6.pdf new file mode 100644 index 0000000..dff0cea Binary files /dev/null and b/MTH208/Assignments/assignment6.pdf differ diff --git a/MTH208/Assignments/assignment7.pdf b/MTH208/Assignments/assignment7.pdf new file mode 100644 index 0000000..35840e3 Binary files /dev/null and b/MTH208/Assignments/assignment7.pdf differ diff --git a/MTH208/EndSem/Cans2.cpp b/MTH208/EndSem/Cans2.cpp new file mode 100644 index 0000000..6d3aa1a --- /dev/null +++ b/MTH208/EndSem/Cans2.cpp @@ -0,0 +1,27 @@ +#include +using namespace Rcpp; + + +// [[Rcpp::export]] +NumericVector sumsC(NumericMatrix x, int s) +{ + // Declaring the output vector + NumericVector colSum(s); + + // Filling the output vector with zeros + for (int i = 0; i < s; i++) + { + colSum[i] = 0; + } + + // Calculating the column sums + for (int i = 0; i < x.nrow(); i++) + { + for (int j = 0; j < s; j++) + { + colSum[j] = colSum[j] + x(i, j); + } + } + + return colSum; +} diff --git a/MTH208/EndSem/README.md b/MTH208/EndSem/README.md new file mode 100644 index 0000000..d1ca1c3 --- /dev/null +++ b/MTH208/EndSem/README.md @@ -0,0 +1 @@ +Answers are of a student, not the professor's. diff --git a/MTH208/EndSem/ans1.R b/MTH208/EndSem/ans1.R new file mode 100644 index 0000000..3e8b3c0 --- /dev/null +++ b/MTH208/EndSem/ans1.R @@ -0,0 +1,20 @@ +autoreg_fast <- function(n, rho) +{ + # Allocating space to the out vector beforehand + out <- numeric(length = n) + + # A slight improvement was observed when calculating + # the random values at once + errors <- rnorm(n - 1) + + # Doing the required calculations + out[1] <- 0 + for(t in 2:n) + { + error <- errors[t-1] + error <- rho*out[t-1] + error + out[t] <- error + } + + return(out) +} diff --git a/MTH208/EndSem/ans2.R b/MTH208/EndSem/ans2.R new file mode 100644 index 0000000..9e86bae --- /dev/null +++ b/MTH208/EndSem/ans2.R @@ -0,0 +1,14 @@ +library(Rcpp) + +sourceCpp(file = "Cans2.cpp") + +sel_sums <- function(mat){ + # Obtaining the size of the square matrix + p = dim(mat)[1] + + # Randomly choosing a number s between 1 and p (inclusive) + s = sample(1:p, size = 1) + + # Calling the sourced C++ function + return(sumsC(mat, s)) +} diff --git a/MTH208/EndSem/ans3.R b/MTH208/EndSem/ans3.R new file mode 100644 index 0000000..775959a --- /dev/null +++ b/MTH208/EndSem/ans3.R @@ -0,0 +1,21 @@ +load("ques3.Rdata") + +# Size of the square matrix +p <- dim(mat)[1] + +# Eigenvalues of the matrix +eigen.values <- eigen(mat, only.values = TRUE)$values + +# Declaring the log of the answer +log.ans <- 0 + +# Adding sum terms obtained on logarithm +log.ans <- log.ans + (p * log(2.7)) - (p * log(p)) + sum(log(1:p)) + +# Adding the logarithm of the determinant term +log.ans <- log.ans + ((1/p) * sum(log(eigen.values))) + +# Adding (effectively subtracting) the logarithm of the trace term +log.ans <- log.ans - log(sum(eigen.values)) + +ans <- exp(log.ans) diff --git a/MTH208/EndSem/ans4.R b/MTH208/EndSem/ans4.R new file mode 100644 index 0000000..185ef22 --- /dev/null +++ b/MTH208/EndSem/ans4.R @@ -0,0 +1,26 @@ +library(MASS) +library(tidyverse) + +# Calculating incidents per year of every ship +dat <- ships %>% + select(type, service, incidents) %>% + filter(service != 0) %>% + mutate(`Incidents per Year` = (incidents / (service / 12))) + +# Creating boxplot of Incidents per year v/s Type of Ship +plt <- ggplot(dat) + + geom_boxplot( + aes(x = type, y = `Incidents per Year`) + ) + + labs( + title = "Incidents per Year of different types of Ships" + ) + + xlab("Type of Ship") + +## This plot disproves the hypothesis. +## The ships of type B were also used for most +## number of months which had led to most number +## of accidents. Ship type E had the most number +## incidents per year. + +plt diff --git a/MTH208/EndSem/endsem.pdf b/MTH208/EndSem/endsem.pdf new file mode 100644 index 0000000..27a8ce3 Binary files /dev/null and b/MTH208/EndSem/endsem.pdf differ diff --git a/MTH208/EndSem/ques3.Rdata b/MTH208/EndSem/ques3.Rdata new file mode 100644 index 0000000..55b067a Binary files /dev/null and b/MTH208/EndSem/ques3.Rdata differ diff --git a/MTH208/MidSem/README.md b/MTH208/MidSem/README.md new file mode 100644 index 0000000..d1ca1c3 --- /dev/null +++ b/MTH208/MidSem/README.md @@ -0,0 +1 @@ +Answers are of a student, not the professor's. diff --git a/MTH208/MidSem/ans1.R b/MTH208/MidSem/ans1.R new file mode 100644 index 0000000..02626f5 --- /dev/null +++ b/MTH208/MidSem/ans1.R @@ -0,0 +1,22 @@ +# 'n' is the number of people in the room +# The function returns TRUE when 2 people share the same birthday +birthday <- function (n){ + # Getting the random birthdays of people in the room + bdates <- sample(1:365, size = n, replace = TRUE) + + # Taking a vector containing unique birthdays + uniq_dates <- unique(bdates) + + # Checking whether all birthdays are unique or not + if (length(bdates) != length(uniq_dates)){ + return(TRUE) + } else { + return(FALSE) + } +} + +outcomes25 <- replicate(1000, birthday(25)) +ans25 <- length(outcomes25[outcomes25]) / 1000 + +outcomes50 <- replicate(1000, birthday(50)) +ans50 <- length(outcomes50[outcomes50]) / 1000 diff --git a/MTH208/MidSem/ans2.R b/MTH208/MidSem/ans2.R new file mode 100644 index 0000000..a82ebee --- /dev/null +++ b/MTH208/MidSem/ans2.R @@ -0,0 +1,24 @@ +library(imager) + +# An imager image is taken as input +flip <- function (img){ + # Convert the image pixel and color values into an array + orig.img.arr <- as.array(img[, , 1, ]) + + # Create an empty array to contain values of new image + new.img.arr <- array(0, dim = dim(orig.img.arr)) + + # The following loop fills the new image array + img.dims <- dim(orig.img.arr) + for (i in 1:img.dims[1]){ + for (j in 1:img.dims[2]){ + for (k in 1:img.dims[3]){ + new.img.arr[i, j, k] <- orig.img.arr[img.dims[1] + 1 - i, j, k] + } + } + } + + # Create an imager image from the array and return it + new.img <- as.cimg(new.img.arr) + return(new.img) +} diff --git a/MTH208/MidSem/ans3.R b/MTH208/MidSem/ans3.R new file mode 100644 index 0000000..6b70032 --- /dev/null +++ b/MTH208/MidSem/ans3.R @@ -0,0 +1,19 @@ +library(tibble) +library(tidyverse) + +# Read the titanic data from the csv file +titanic.data <- as_tibble(read_csv("titanic.csv")) + +# Convert the Survived column into a factor having the values "Died" and "Survived" +titanic.data$Survived <- factor(titanic.data$Survived) +levels(titanic.data$Survived) <- c("Died", "Survived") + +# The final graph +finalP <- ggplot(titanic.data, aes(x = Survived, y = Fare)) + + geom_boxplot(aes(color = Sex)) + + labs(title = "Fare vs Survival", + subtitle = "Irrespective of Sex, richer people survived", + x = "", + y = "Fare" + ) + + coord_flip() diff --git a/MTH208/MidSem/boat.jpeg b/MTH208/MidSem/boat.jpeg new file mode 100644 index 0000000..0b72a73 Binary files /dev/null and b/MTH208/MidSem/boat.jpeg differ diff --git a/MTH208/MidSem/midsem.pdf b/MTH208/MidSem/midsem.pdf new file mode 100644 index 0000000..f66d3d9 Binary files /dev/null and b/MTH208/MidSem/midsem.pdf differ diff --git a/MTH208/MidSem/titanic.csv b/MTH208/MidSem/titanic.csv new file mode 100644 index 0000000..87428ba --- /dev/null +++ b/MTH208/MidSem/titanic.csv @@ -0,0 +1,713 @@ +PassengerId,Survived,Pclass,Sex,Age,SibSp,Parch,Fare,Embarked +1,0,3,male,22,1,0,7.25,S +2,1,1,female,38,1,0,71.2833,C +3,1,3,female,26,0,0,7.925,S +4,1,1,female,35,1,0,53.1,S +5,0,3,male,35,0,0,8.05,S +7,0,1,male,54,0,0,51.8625,S +8,0,3,male,2,3,1,21.075,S +9,1,3,female,27,0,2,11.1333,S +10,1,2,female,14,1,0,30.0708,C +11,1,3,female,4,1,1,16.7,S +12,1,1,female,58,0,0,26.55,S +13,0,3,male,20,0,0,8.05,S +14,0,3,male,39,1,5,31.275,S +15,0,3,female,14,0,0,7.8542,S 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+radius <- as.integer(readline("Enter the value of radius of circle : ")) +area <- function(radius) +{ + return( pi * radius * radius ) +} + +cat("Area of the circle of radius" , radius , "is" , area(radius)) + + +#Question 2 + +first_num <- as.integer(readline("Enter the first number : ")) +sec_num <- as.integer(readline("Enter the second number : ")) + +if( first_num == sec_num){ + cat(first_num , "and" , sec_num , "both are equal") +} else if ( first_num < sec_num ){ + cat(sec_num , "is greater than" , first_num ) +} else if ( first_num > sec_num ){ + cat(first_num , "is greater than" , sec_num) +} + +#Question 3 + +dice_num <- numeric(1000) +even_count <- 0 + +for(i in 1:1000) +{ + dice_num[i] <- sample(x = 1:6 , size = 1 ) + if(dice_num[i] %% 2 == 0) + { + even_count = even_count + 1 + } +} +cat("Numner of even count is" , even_count) + +#Question 4 + +ran_num <- numeric(1000) +ran_num = runif( n <- 1000 , min <- 0 , max <- 1 ) +cat("Number between 0.1 and 0.2 is" , length(subset(ran_num , ran_num > 0.1 & ran_num < 0.2))) + + +#Question 5 + + +num_count <- function() +{ + i <- 1 + prob_toy <- numeric(100) + while(length(unique(prob_toy)) != 8 & i <= 50 ) + { + prob_toy[i] <- sample(x = c('Harry', 'Dumbledore', 'Hermione', 'Ron', 'Neville', 'Mcgonagall', 'Dobby'), size <- 1 ,replace = FALSE, prob <- c(.25, .20, .20, .15, .10, .05, .05) ) + i = i + 1 + } + #print(prob_toy) + + return(i) +} + +num_count_vector <- numeric(1000) +for(i in 1:1000) +{ + num_count_vector[i] <- num_count() +} + +#num_count_vector +cat("To collect all toys average number of packet bought is" , mean(num_count_vector)) + + + + + + + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/MTH208/Pratice Problem/Sheet2.R b/MTH208/Pratice Problem/Sheet2.R new file mode 100644 index 0000000..0ecd97b --- /dev/null +++ b/MTH208/Pratice Problem/Sheet2.R @@ -0,0 +1,157 @@ +#Problem1 + +odd <- seq(1, by = 2 , length.out = 1000) + +#Problem2 + +fib <- numeric(500) +fib[1] <- fib[2] <- 1 + +for(i in 3:500) +{ + fib[i] <- fib[i-1] + fib[i-2] +} + +#Problem3 + +even <- function() +{ + if(sample(x = 1:6 , size = 1) %% 2 ==0) + return(1) + else + return(0) +} + +#Problem4 + +result <- function(n) +{ + if(n %% 2 ==0) + for_win = (n/2) + 1 + else + for_win = (n+1) / 2 + + count_head = 0 + count_tail = 0 + + for(i in 1:n) + { + count_head = count_head + rbinom(1 , 1 , 0.5) + } + + if(count_head >= 8) + print("Win") + else + print("Loss") +} + +result(15) + +#Problem5 + +array(1, dim = c(5,5)) +matrix(1,nrow =5 , ncol =5) + +#Problem6 + +diag( 1:5 ) + +#Problem7 + +dice_num = numeric(100) +for( i in 1:100 ) + dice_num[i] = sample( 1:6 , size = 1) + +array( dice_num , dim = c(10,10) ) + +#Problem8 + +n = 2 +rho = 5 + +mat = matrix( 1 , ncol = n , nrow = n ) +diag(mat) = rho + +mat + +#Problem9 + +n = 2 +rho = 3 + +mat = matrix( 0 , ncol = n , nrow = n ) + +mat + +#Problem10 + +odd.mat <- function(mat1) +{ + return(mat1(col(mat1) %% 2 == 1)) +} +test.mat = array( data = 1:16 , dim = c(4,4)) +odd.mat(test.mat) + +#Problem 6 + +days = 0 +tablet.full = 100 +tablet.half = 0 +count = 1 +while(count) +{ + count = rbinom(n = 1 ,size = 1 , prob = tablet.full/(tablet.full + tablet.half)) + if(count) + { + tablet.full = tablet.full - 1 + tablet.half = tablet.half + 1 + days = days + 1 + } + + else + { + count = 0 + } + +} + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/MTH208/Pratice Problem/problem_set.pdf b/MTH208/Pratice Problem/problem_set.pdf new file mode 100644 index 0000000..defba31 Binary files /dev/null and b/MTH208/Pratice Problem/problem_set.pdf differ diff --git a/MTH208/ProjectGuidelines.pdf b/MTH208/ProjectGuidelines.pdf new file mode 100644 index 0000000..ca67b1c Binary files /dev/null and b/MTH208/ProjectGuidelines.pdf differ diff --git a/MTH208/Worksheets/.DS_Store b/MTH208/Worksheets/.DS_Store new file mode 100644 index 0000000..d7823bb Binary files /dev/null and b/MTH208/Worksheets/.DS_Store differ diff --git a/MTH208/Worksheets/readme.md b/MTH208/Worksheets/readme.md new file mode 100644 index 0000000..11198da --- /dev/null +++ b/MTH208/Worksheets/readme.md @@ -0,0 +1,6 @@ +please note the following: +1) The files for everyworksheet is available +2) Each zip file contains the files for the worksheet and the worksheet. +3) The solutions inside the zip file are a student's attempt to the worksheet. +4) The solutions in this folder were provided by the Instructor. +5) There were no solutions for the worksheets : 8,9 and 10. diff --git a/MTH208/Worksheets/sample 13.qmd b/MTH208/Worksheets/sample 13.qmd new file mode 100644 index 0000000..b31e65d --- /dev/null +++ b/MTH208/Worksheets/sample 13.qmd @@ -0,0 +1,143 @@ +# Welcome to this Sample Document + +### Solving quadratic equations + +Consider equations of the form $ax^2 + bx + c = 0$. This is a quadratic equation; changing the values of $a$, $b$, and $c$, changes the shape of the quadratic. There are two solutions to a quadratic equation: + +$$ +x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}. +$$ + +Let's draw a quadratic curve for different values of $a, b$, and $c$. + +```{r} +a <- 10 +b <- 3 +c <- -5 +x <- seq(-2, 2, length = 1e3) +fx <- a*x^2 + b*x + c +plot(x, fx, type = 'l', xlab = "x", ylab = "Quadratic function") +# adding line for solution +abline(h = 0, lty = 2, col = "red") +``` + +In the above, we can also change the way the plot appears. I will rerun the above code, without displaying the code, and only producing the plot of figure height "4" units and figure width "4" units + +```{r} +#| echo: false +#| fig-cap: "A quadratic function" +#| fig-width: 4 +#| fig-height: 4 +a <- 10 +b <- 3 +c <- -5 +x <- seq(-2, 2, length = 1e3) +fx <- a*x^2 + b*x + c +plot(x, fx, type = 'l', xlab = "x", ylab = "Quadratic function") +# adding line for solution +abline(h = 0, lty = 2, col = "red") +``` + +### Studying the Cricket dataset + +We will study the cricket dataset more closely now. The `battingbowling.csv` file in your repository contains information regarding various potential all-rounders in men's ODI cricket. The players' batting average, bowling average, and team is present in the dataset. + +We will make a few visualizations. But first, we will need a few libraries. + +```{r} +library(ggplot2) +library(tibble) +``` + +Let's load the data the data and convert it to a tibble. + +```{r} +cric <- read.csv("battingbowling.csv") +cric <- as_tibble(cric) +cric +``` + +Let's create a side-by-side boxplot of the Batting averages: + +```{r} +#| fig-width: 5 +#| fig-height: 3 +p <- ggplot(cric, aes(x = Team,y = Batting)) +p + geom_boxplot(fill = "tomato")+ + labs(title = "Batting Average", + subtitle = "Side-by-side boxplot for Teams", + y = "Batting Average") +``` + +We can do the same thing for the Bowling average as well (notice that I am not showing the code for this) + +```{r} +#| echo: false +#| fig-width: 5 +#| fig-height: 3 +#| fig-align: "center" +p <- ggplot(cric, aes(x = Team,y = Bowling)) +p + geom_boxplot(fill = "lightblue")+ + labs(title = "Bowling Average", + subtitle = "Side-by-side boxplot for Teams", + y = "Bowling Average") +``` + +Next, we make a scatterplot of the Batting and Bowling average, colored by the Team the player is associated with: + +```{r} +#| fig-width: 7 +#| fig-height: 4 +#| fig-align: "center" +p <- ggplot(cric, aes(x = Batting, y = Bowling)) +p + geom_point(aes(color = Team, shape = Team)) +``` + +Additionally, we want to write down, in text, the names of the players with batting average more than 35 and bowling average less than 40. Below is a plot for that. + +```{r} +#| echo: false +#| fig-width: 7 +#| fig-height: 4 +#| fig-align: "center" + +foo <- subset(cric, Batting > 35 & Bowling < 40) + +p <- ggplot(cric, aes(x = Batting, y = Bowling)) +p + geom_point(aes(color = Team, shape = Team)) + + geom_hline(yintercept = 40, color = "tomato", linetype = "dashed") + + geom_vline(xintercept = 35, color = "tomato", linetype = "dashed") + + geom_text(data = foo, hjust = -.3, + aes(x = Batting, y = Bowling, label = X), size = 3) +``` + +### Some more mathematical equations + +Let's practice some mathematical typing. + +1. Consider a rotation matrix: + +$$ +A = \left(\begin{array}{cc} \cos(\theta) & \sin(\theta) \\ -\sin(\theta) & \cos(\theta) \end{array} \right) +$$ + +Our goal is to find the determinant of the above + +```{=tex} +\begin{align*} +\text{det}(A) & = \cos(\theta) \cos(\theta) - \sin(\theta) (-\sin(\theta)\\ + & =\sin^2(\theta) + \cos^2(\theta) \\ + & = 1 . +\end{align*} +``` +2. Consider the series $A = \sum_{i=1}^{n} i$: + + ```{=tex} + \begin{align*} + 2A & = \sum_{i=1}^{n} i + \sum_{i=1}^{n} i\\ + & = (1 + 2 + \dots + n) + (1 + 2 + \dots + n)\\ + & = (1 + n) + (2 + n-1) + \dots (n + 1)\\ + & = n \cdot (n+1)\\ + \Rightarrow A & = \frac{n(n+1)}{2}\,. + \end{align*} + ``` diff --git a/MTH208/Worksheets/solutions1.R b/MTH208/Worksheets/solutions1.R new file mode 100644 index 0000000..76d0f80 --- /dev/null +++ b/MTH208/Worksheets/solutions1.R @@ -0,0 +1,41 @@ +### Worksheet 1 + +## Problem 1 +# We can also add conditions +# for only positive integers +fact <- function(n) +{ + track <- 1 + for(i in 1:n) + { + track <- track * i + } + return(track) +} + + +## Problem 2 +euler <- function(n) +{ + nlim <- (1 + 1/n)^(n) + return(nlim) +} +euler(3) +# checking comparisons with e +euler(10000) - exp(1) + + +## Problem 3 +seat <- read.csv("https://dvats.github.io/assets/course/mth208/seating.csv") + +# suppose by roll no. is 221332 +seat[seat$Roll == 221332, ] + +## Problem 4 +# make sure seating.csv is downloaded +# to your working directory +# use getwd() to find your working directory +seat <- read.csv("seating.csv") + + + diff --git a/MTH208/Worksheets/solutions11.R b/MTH208/Worksheets/solutions11.R new file mode 100644 index 0000000..745d023 --- /dev/null +++ b/MTH208/Worksheets/solutions11.R @@ -0,0 +1,78 @@ +#################################### +## Solutions for Worksheet 11 +#################################### + +## Problem 1 +# set your working repository correctly +load("IMDB_movies.Rdata") +head(dat) # data is called dat + +## Problem 2 +hist(dat$rating, main = "Histrogram of movie ratings", + xlab = "Ratings") +hist(dat$rating, main = "Histrogram of movie ratings", + xlab = "Ratings", col = "white") + +## Problem 3 +boxplot(dat$rating, main = "Boxplot of Ratings") +boxplot(dat$rating, main = "Boxplot of Ratings", col = "pink") + +## Problem 4 +boxplot(dat$men_rating, dat$women_rating, + names = c("Men", "Women"), + main = "Boxplot of ratings by gender") + +## Problem 5 +hist(dat$men_rating, main = "Hitogram of Ratings", + xlab = "Ratings", xlim = range(c(dat$men_rating, dat$women_rating)), + col = adjustcolor("blue", alpha.f = .5)) +hist(dat$women_rating, col = adjustcolor("red", alpha.f = .5), xlab = "Ratings", + add = TRUE) +legend("topright", c("Men", "Women"), + fill = c(adjustcolor("blue", alpha.f = .5), + adjustcolor("red", alpha.f = .5))) + +## Problem 6 +plot(dat$over.votes, dat$rating, + xlab = "# Votes", ylab = "Ratings") +# another one with different dots +plot(dat$over.votes, dat$rating, + xlab = "# Votes", ylab = "Ratings", pch = 16) + +## Problem 7 +ind <- dat$rating > 8.9 +# adding text to the lst plot +text(dat$over.votes[ind], dat$rating[ind], + labels = dat$name[ind]) + +## Problem 8 +year.categ <- (dat$year < 1996) + 1 # 2 or 1 based on before 96 or not +plot(dat$over.votes, dat$rating, + xlab = "# Votes", ylab = "Ratings", + pch = 16, col = year.categ) # col = number based on year category +legend("topright", pch = 16, col = c(2,1), + legend = c("before 1996", "after 1996")) + +## Problem 9 +plot(dat$year, dat$over.votes, ylab = "# votes", xlab = "Year") +# we see that for movies with highest number of votes, the ratings are +# high. Also, from the above plot we see that older movies +# naturally don't have a lot of votes +# there is some response bias naturally then, in that when someone +# likes a movie a lot, they are more compelled to vote + + +## Problem 10 +# type = "n" makes an empty plot with the right axes +plot(dat$over.votes, dat$rating, + xlab = "# Votes", ylab = "Ratings", + pch = 16, col = year.categ, type = "n") +for(i in 1:length(dat$rating)) +{ + # gives a .1 second pause before running the next line + Sys.sleep(.1) + + # plot the ith point + points(dat$over.votes[i], dat$rating[i], + pch = 16, col = year.categ[i]) +} diff --git a/MTH208/Worksheets/solutions12.R b/MTH208/Worksheets/solutions12.R new file mode 100644 index 0000000..8cbaaf1 --- /dev/null +++ b/MTH208/Worksheets/solutions12.R @@ -0,0 +1,43 @@ +#################################### +## Solutions for Worksheet 11 +#################################### +library(ggplot2) +library(tibble) + +## Load the dataset +load("covid.Rdata") + +names(india_covid) <- c("state", "confirmed", "active", "cured", "death") +covid <- as_tibble(india_covid) + + +## Create ordered barplot where the color is +## the rate of death in the state + +covid <- covid[order(covid$confirmed), ] +covid$state <- factor(covid$state, levels = covid$state) +covid$rate <- round(covid$death/covid$confirmed, 3) + +g <- ggplot(covid, aes(x = state, y = log10(confirmed))) +g + geom_bar(stat = 'identity', aes(fill = rate)) + +labs(y = "Log of Confirmed Cases", x = "State/UT", + title = "Covid India Data", subtitle = "Confirmed Cases shaded by rate of death") + +coord_flip() + +# Ideally, we would think that as confirmed cases increase, it affects +# the rate of death will also increase, as the hospitals become more burdened. +# However, Nagaland and Punjab have high rates of death, but reltively low +# confirmed cases. We may hypothesise that treatment may have not been done +# sufficiently in these countries + + +# Same plot as above, except with text as the rate +covid <- covid[order(covid$confirmed), ] + +g <- ggplot(covid, aes(x = state, y = log10(confirmed), label = rate)) +g + geom_point(stat='identity', fill="black", size=8) + +geom_segment(aes(y = 0, x = state, yend = log10(confirmed), xend = state), color = "black") + +geom_text(color="white", size=2) + +labs(y = "Log of Confirmed Cases", x = "State/UT", + title = "Covid India Data", subtitle = "Confirmed Cases with rate as text") + +coord_flip() \ No newline at end of file diff --git a/MTH208/Worksheets/solutions14 .zip b/MTH208/Worksheets/solutions14 .zip new file mode 100644 index 0000000..260ecbe Binary files /dev/null and b/MTH208/Worksheets/solutions14 .zip differ diff --git a/MTH208/Worksheets/solutions15.zip b/MTH208/Worksheets/solutions15.zip new file mode 100644 index 0000000..4973343 Binary files /dev/null and b/MTH208/Worksheets/solutions15.zip differ diff --git a/MTH208/Worksheets/solutions16.R b/MTH208/Worksheets/solutions16.R new file mode 100644 index 0000000..786031c --- /dev/null +++ b/MTH208/Worksheets/solutions16.R @@ -0,0 +1,138 @@ +####################################### +### Solutions to Worksheet 16 +####################################### +library(profvis) +library(rbenchmark) +library(imager) + + +## Problem 1 +profvis({ + attempts <- function(age) + { + count <- 0 + remain <- age # age no. of candles remain in the beginning + while(remain > 0) + { + count <- count + 1 + # randomly choose any number between 1 and remain + blow_out <- sample(1:remain, size = 1) + remain <- remain - blow_out + } + return(count) + } + att_vec <- replicate(1e4, attempts(25)) +}) +# Replicate calls function sapply in the background. + + +## Problem 2 +attempts <- function(age) +{ + count <- 0 + remain <- age # age no. of candles remain in the beginning + while(remain > 0) + { + count <- count + 1 + # randomly choose any number between 1 and remain + blow_out <- sample(1:remain, size = 1) + remain <- remain - blow_out + } + return(count) +} + +reps <- 1e3 +benchmark(replicate(reps, attempts(25)), + { + att_vec <- numeric(length = reps) + for(i in 1:reps) + { + att_vec[i] <- attempts(25) + }}, + replications = 100) +# Almost the same looks like + +## Problem 3 +reps <- 1e4 +benchmark(replicate(reps, attempts(25)), + { + att_vec <- numeric(length = reps) + for(i in 1:reps) + { + att_vec[i] <- attempts(25) + }}, + replications = 20) +# Almost the same looks like + +## Problem 4 +reps <- 1e4 +benchmark({ + att_vec <- NULL + for(i in 1:reps) + { + att_vec <- c(att_vec, attempts(25)) + }}, + { att_vec <- numeric(length = reps) + for(i in 1:reps) + { + att_vec[i] <- attempts(25) + }}, + replicate(reps, attempts(25)), + replications = 25) + + +## Problem 5 +profvis({ + dog <- load.image("dog.jpeg") # make sure this is in your working directory + col.mat <- as.array(dog[, ,1, ]) + + dims <- dim(col.mat) + rot <- array(0, dim = dims) + + for(i in 1:dims[1]) + { + for(j in 1:dims[2]) + { + rot[i, j, ] <- col.mat[dims[1] - i + 1, dims[2] - j + 1, ] + } + } +}) + + +# Alternative code +profvis({ + dog <- load.image("dog.jpeg") + dims <- dim(dog) + rot <- dog[dims[1]:1, dims[2]:1, ] +}) + +# Benchmarking +benchmark({ + dog <- load.image("dog.jpeg") # make sure this is in your working directory + col.mat <- as.array(dog[, ,1, ]) + + dims <- dim(col.mat) + rot <- array(0, dim = dims) + + for(i in 1:dims[1]) + { + for(j in 1:dims[2]) + { + rot[i, j, ] <- col.mat[dims[1] - i + 1, dims[2] - j + 1, ] + } + } +}, +{ + dog <- load.image("dog.jpeg") + dims <- dim(dog) + rot <- dog[dims[1]:1, dims[2]:1, ] +}, replications = 20) +# second code is much faster! + +## Problem 6 +n <- 1e4 +m <- 1e4 +A <- matrix(runif(n*m), ncol = m, nrow = n) +benchmark(colMeans(A), apply(A, 2, mean), replications = 10) +# takes some time, colMeans is ~ 15 times faster!! + diff --git a/MTH208/Worksheets/solutions17.R b/MTH208/Worksheets/solutions17.R new file mode 100644 index 0000000..afbbdfa --- /dev/null +++ b/MTH208/Worksheets/solutions17.R @@ -0,0 +1,103 @@ +####################################### +### Solutions to Worksheet 17 +####################################### + +library(rbenchmark) + + +# Problem 1 + +num1 <- numeric(length = 1e3) # 8000 +object.size(num1) +num2 <- numeric(length = 1e6) # 8000000 +object.size(num2) + +mat1 <- matrix(runif(100*1000), nrow = 100, ncol = 1000) #8x10^5 +object.size(mat1) +mat2 <- matrix(0, nrow = 100, ncol = 1000) #8x10^5 +object.size(mat2) + +arr <- array(0, dim = c(100,100,100)) #8x10^6 +object.size(arr) + + +## Problem 2 + +benchmark({ + norms <- numeric(length = 1e4) + for(i in 1:1e4) + { + norms[i] <- rnorm(1) + } +}, rnorm(1e4), replications = 20) +# without loop is MUCH faster + +## Problem 3 +benchmark(rnorm(1e4), runif(1e4), replications = 100) +# runif is much faster because rnorm needs runif in the background + + +## Problem 4 +rho_mat_1 <- function(n, rho = .50) +{ + mat <- matrix(0, nrow = n, ncol = n) + for(i in 1:n) + { + for(j in 1:n) + { + mat[i,j] <- rho^(abs(i-j)) + } + } +} + +rho_mat_2 <- function(n, rho = .50) +{ + mat <- matrix(rho, nrow = n, ncol = n) + mat <- mat^(abs(col(mat) - row(mat))) + return(mat) +} + +benchmark(rho_mat_1(n = 10), rho_mat_2(n = 10)) +benchmark(rho_mat_1(n = 100), rho_mat_2(n = 100)) +benchmark(rho_mat_1(n = 1000), rho_mat_2(n = 1000), replications = 20) + +## Problem 5 +# log transformation is useful + +stirling <- function(n) +{ + #lfactorial is log of factorial + rtn <- lfactorial(n) - n*log(n) + n - log(2*pi*n)/2 + return(exp(rtn)) +} + +x <- seq(10, 1e6, length = 1e3) +y <- sapply(x, stirling) +plot(x, y, type = "l", xlab = "n", ylab = "Stirling Function") + + +## Problem 6 +x <- 1:1000 +benchmark(sqrt(sum(x^2)), norm(x, "2")) +# norm is slower because it is made for matrices, not vectors + + +## Problem 7 +func <- function(n = 1e3) +{ + nums <- 1:(n^2) + mat <- matrix(nums, nrow = n, ncol = n) + means <- apply(mat, 2, mean) + norm.means <- sqrt(sum(means^2)) + return(norm.means) +} + +fast_func <- function(n = 1e3) +{ + mat <- matrix(1:(n^2), nrow = n, ncol = n) + means <- colMeans(mat) + norm.means <- sqrt(sum(means^2)) + return(norm.means) +} + +benchmark(func(), fast_func()) diff --git a/MTH208/Worksheets/solutions18.zip b/MTH208/Worksheets/solutions18.zip new file mode 100644 index 0000000..c392ef7 Binary files /dev/null and b/MTH208/Worksheets/solutions18.zip differ diff --git a/MTH208/Worksheets/solutions19.zip b/MTH208/Worksheets/solutions19.zip new file mode 100644 index 0000000..f97502e Binary files /dev/null and b/MTH208/Worksheets/solutions19.zip differ diff --git a/MTH208/Worksheets/solutions2.R b/MTH208/Worksheets/solutions2.R new file mode 100644 index 0000000..879a5e5 --- /dev/null +++ b/MTH208/Worksheets/solutions2.R @@ -0,0 +1,47 @@ +### Solutions to Worksheet 2 ### + +## Problem 1 +seat <- read.csv("https://dvats.github.io/assets/course/mth208/seating.csv") + +# MSc students have id 22xxxx, so all MSc students +# have roll number > 220000 +msc <- seat[seat$Roll > 220000, ] # data of only msc students +length(msc$Roll) + + +## Problem 2 +cricket <- read.csv("https://dvats.github.io/assets/course/mth208/battingbowling.csv") + + +## Problem 2(a) +allround_index <- (cricket$Batting > 25 & cricket$Bowling < 40) +allround <- cricket[allround_index, ] + +# presents the frequencies of all teams +table(allround$Team) + +# NZ is largers, SA is smallest + + +## Problem 3 +plot(x = 1:10, y = 1:10, type = "l", xlab = "x", ylab = "y", main = "Y = X Plot") + + +## Problem 4 +# Making a function for (1 + 1/n)^n +fx <- function(n) +{ + rtn <- (1 + 1/n)^n + return(rtn) +} + +# defining a vector of n = 1, ..., 1000 +n <- 1:1e3 + +# calculating fn for each n +# function is easily vectorizable +fn <- fx(n) + +# making a plot +plot(n, fn, type = "l") +abline(h = exp(1), col = "red") diff --git a/MTH208/Worksheets/solutions20.R b/MTH208/Worksheets/solutions20.R new file mode 100644 index 0000000..77ec190 --- /dev/null +++ b/MTH208/Worksheets/solutions20.R @@ -0,0 +1,72 @@ + +####################################### +### Solutions to Worksheet 20 +####################################### + +## Problem 1 +dat <- read.csv("auto-mpg.csv") +head(dat) + +cor(dat$mpg, dat$acceleration) + + +## Problems 2 and 3 + +# as acceleration increases, mpg increases +# does this agree with your understanding of cars? +plot(dat$acceleration, dat$mpg, pch = 16, + xlab = "Acceleration", ylab = "Miles Per Gallon") +abline(lm(dat$mpg ~ dat$acceleration)) + +plot(dat$acceleration, dat$mpg, pch = 16, + col = dat$cylinders, + xlab = "Acceleration", ylab = "Miles Per Gallon") + +for(i in unique(dat$cylinders)) +{ + foo <- subset(dat, dat$cylinders == i) + abline(lm(foo$mpg ~ foo$acceleration), col = i) +} +legend("topleft", col = unique(dat$cylinders), + legend = unique(dat$cylinders), pch = 16, + title = "Cylinders") + + +## Problem 5 +head(iris) +plot(iris$Sepal.Length, iris$Sepal.Width, + xlab = "Sepal Length", ylab = "Sepal Width", + pch = 16) +abline(lm(iris$Sepal.Width ~ iris$Sepal.Length)) + + +# Simpson's paradox here +plot(iris$Sepal.Length, iris$Sepal.Width, + xlab = "Sepal Length", ylab = "Sepal Width", + pch = 16, col = iris$Species) + +for(i in 1:length(levels(iris$Species))) +{ + level <- levels(iris$Species)[i] + foo <- subset(iris, iris$Species == level) + abline(lm(foo$Sepal.Width ~ foo$Sepal.Length), col = i) +} + + +### Problem 6 +dat <- read.csv("fire-dat.csv") +cor(dat$firefight, dat$injured) # highly positively correlated +plot(dat$firefight, dat$injured) + + + +### Problem 7 +dat <- read.csv("fire-intense.csv") +cor(dat) # highly positively correlated everywhere +plot(dat) + + + + + + diff --git a/MTH208/Worksheets/solutions21.R b/MTH208/Worksheets/solutions21.R new file mode 100644 index 0000000..fbc7628 --- /dev/null +++ b/MTH208/Worksheets/solutions21.R @@ -0,0 +1,50 @@ +# Loading numerical part of data +dat <- read.csv("LowRepeated.csv", skip = 5, header = FALSE) + +# loading other parts of data +demo <- read.csv("LowRepeated.csv", nrows = 5, header = FALSE) + +# generic plot +plot(dat[,1], dat[,2], type = 'l', + xlab = "Wavelength", lwd = 2, + ylab = "Reflectance") + +# extracting dates, times, and variety +dates <- as.factor(demo[1, -1]) +variety <- as.factor(demo[5, -1]) +times <- as.factor(demo[2, -1]) + +# making all 4 plots +par(mfrow = c(2,2)) +plot(dat[,1], dat[,2], type = "n", + ylab = "Reflectance", xlab = "Wavelength") +for(k in 2:ncol(dat)) +{ + lines(dat[,1], dat[,k], col = 1) +} + + +plot(dat[,1], dat[,2], type = "n", + ylab = "Reflectance", xlab = "Wavelength") +for(k in 2:ncol(dat)) +{ + lines(dat[,1], dat[,k], col = dates[k-1]) +} +legend("topleft", col = c(1,2), legend = levels(dates), lty = 1) + + +plot(dat[,1], dat[,2], type = "n", + ylab = "Reflectance", xlab = "Wavelength") +for(k in 2:ncol(dat)) +{ + lines(dat[,1], dat[,k], col = times[k-1]) +} +legend("topleft", col = 1:length(levels(times)), legend = levels(times), lty = 1) + + +plot(dat[,1], dat[,2], type = "n", + ylab = "Reflectance", xlab = "Wavelength") +for(k in 2:ncol(dat)) +{ + lines(dat[,1], dat[,k], col = variety[k-1]) +} diff --git a/MTH208/Worksheets/solutions22.R b/MTH208/Worksheets/solutions22.R new file mode 100644 index 0000000..db1b926 --- /dev/null +++ b/MTH208/Worksheets/solutions22.R @@ -0,0 +1,29 @@ +####################################### +## Solutions to Worksheet 22 +####################################### + +## Problem 7 +library(MASS) +data(accdeaths) + +# plot is made in a proper axis +plot(accdeaths, ylab = "Accidental Deaths") + + +## Problem 8 + +# old plot +data(anorexia) +hist(anorexia$Postwt, xlab = "Weight", ylim = c(0, 30), + main = "Histogram of Weights") +hist(anorexia$Prewt, add = TRUE, + col = adjustcolor("blue", alpha.f = .3)) +legend("topright", legend = c("After", "Before"), + fill = c("grey", adjustcolor("blue", alpha.f = .3))) + +# new plot. I choose to make a boxplot +# of the differences, as a function of +# the treatments. +boxplot(anorexia$diff ~ anorexia$Treat, + xlab = "Treatment", ylab = "Difference in Weights") + diff --git a/MTH208/Worksheets/solutions3.R b/MTH208/Worksheets/solutions3.R new file mode 100644 index 0000000..ba33aba --- /dev/null +++ b/MTH208/Worksheets/solutions3.R @@ -0,0 +1,109 @@ +### Solutions to Worksheet 3 ### + +######################################### +## Problem 1 +# 1(a) +# 1000 tosses of a coin +tosses <- rbinom(n = 1e3, size = 1, prob = 0.50) +sum(tosses)/1000 # proportion of heads +# can also do this +mean(tosses) + +# 1(b) +# 1000 tosses of a coin +tosses <- rbinom(n = 1e3, size = 1, prob = 0.30) +mean(tosses) # proportion of heads + + +######################################### +## Problem 2 +# 2(a) +# suppose 1 = red, 2 = green, 3 = blue +sample(1:3, size = 1, prob = c(3,2,2)/7) + +# 2(b) +A <- matrix(c(3, 1, -2, 4, 5, 3, -1, 2, -2), nrow = 3, ncol = 3) + +# p_vec will store p_i eventually +p_vec <- numeric(length = 3) + +# running a loop for each column +# to find the norm (the numerator) +for(k in 1:ncol(A)) +{ + p_vec[k] <- norm(A[ ,k], type = "2") +} +# divide by the sum +p_vec <- p_vec/sum(p_vec) + +sample(1:3, size = 1, prob = p_vec) + + +######################################### +## Problem 3 +# 3(a) +attempts <- function() +{ + sums <- 0 + count <- 0 + while(sums <= 1) + { + sums <- sums + runif(n = 1, min = 0, max = 1) + count <- count + 1 + } + return(count) +} +attempts() + +# 3(b) +att_vec <- numeric(length = 1e3) +for(i in 1:1e3) +{ + att_vec[i] <- attempts() +} + +# 3(c) +mean(att_vec) + + + +######################################### +## Problem 4 + +# function that calculates number of blows +# 4(a) +attempts <- function(age) +{ + count <- 0 + remain <- age # age no. of candles remain in the beginning + while(remain > 0) + { + count <- count + 1 + + # randomly choose any number between 1 and remain + blow_out <- sample(1:remain, size = 1) + remain <- remain - blow_out + } + + return(count) +} +attempts(age = 25) + +# 4(b) +att_vec <- numeric(length = 1e3) +for(i in 1:1e3) +{ + att_vec[i] <- attempts(25) +} + +# 4(c) +mean(att_vec) + + +# 4(d) +att_vec <- numeric(length = 1e3) +for(i in 1:1e3) +{ + att_vec[i] <- attempts(30) +} +mean(att_vec) \ No newline at end of file diff --git a/MTH208/Worksheets/solutions4.R b/MTH208/Worksheets/solutions4.R new file mode 100644 index 0000000..8ad940e --- /dev/null +++ b/MTH208/Worksheets/solutions4.R @@ -0,0 +1,118 @@ +##### Worksheet 4 solutions ##### + +library(imager) + +############################## +# Problem 1 +dog <- load.image("dog.jpeg") +col.mat<-as.array(dog[, ,1, ]) + +dims <- dim(col.mat) + +# Calculate distance to purest color +# for each pixel +dist <- matrix(0, nrow = dims[1], ncol = dims[2]) +for(i in 1:dims[1]) +{ + for(j in 1:dims[2]) + { + # replace c(0,1,0) with c(1,0,0) or c(0,0,1) for other problems + dist[i,j] <- norm(col.mat[i,j, ] - c(0,1,0), "2") + } +} + +# find pixels with smallest distance +ind1 <- which(dist == min(dist), arr.ind = TRUE) + +# another way +# read ?apply help page to understand the command below +dist <- apply(col.mat, c(1,2), function(s) norm(s - c(0,1,0), "2")) +ind2 <- which(dist == min(dist), arr.ind = TRUE) + +# checking to see that ind1 = ind2. Hence both methods are same +ind1 == ind2 + +plot(dog) +points(ind1, col = "red") + + + + +################################### +# Problem 3 + +col1 <- load.image("col1.png") +# col1 has 4 color channels for some reason. +# Removing the last one. +col1 <- as.cimg(col1[ , , , 1:3]) + +col2 <- load.image("col2.png") +col3 <- load.image("col3.png") + + +# I will make a function that calculates the +# difference matrix from a color for each image + +diff.col <- function(img, col) +{ + col.mat <- as.array(img[, , 1, ]) + dims <- dim(col.mat) + + # Calculate distance to given color + dist <- matrix(0, nrow = dims[1], ncol = dims[2]) + for(i in 1:dims[1]) + { + for(j in 1:dims[2]) + { + # distance from the col give by user + dist[i,j] <- norm(col.mat[i,j, ] - col, "2") + } + } + # return the distance matrix of each pixel + return(dist) +} + +## Making another function for each color +## for a given image. Then for whichever primary +## color the mean of the distance matrix is smallest +## That will be the guess. +which.color <- function(img) +{ + dist.cols <- numeric(length = 3) + + # make a matrix of ones. + # this is a shortcut to define all three + # primary colors in one go. + colors.matrix <- diag(3) + for(k in 1:3) + { + # picking kth column of colors.matrix as we are picking + # the kth primary color to compare to + dist.cols[k] <- mean(diff.col(img, col = colors.matrix[ ,k])) + } + + # which color has the smallest distance + ind <- which.min(dist.cols) + guess <- c("red", "green", "blue")[ind] + + return(guess) +} + +which.color(col1) # guessing for col1 +which.color(col2) # guessing for col2 +which.color(col3) # guessing for col3 + + +################################### +# Problem 4 + +pic1 <- load.image("land1.jpeg") +pic2 <- load.image("land2.jpeg") + +# We can reuse function diff.col! +# measuring average distance to c(1,1,1) for both pics +distance.to.white1 <- mean(diff.col(pic1, c(1,1,1))) +distance.to.white2 <- mean(diff.col(pic2, c(1,1,1))) + +ifelse(distance.to.white1 < distance.to.white2, "Land1", "Land2") + diff --git a/MTH208/Worksheets/solutions5.R b/MTH208/Worksheets/solutions5.R new file mode 100644 index 0000000..6d809c7 --- /dev/null +++ b/MTH208/Worksheets/solutions5.R @@ -0,0 +1,180 @@ +####################################### +## Worksheet 5 Solutions ############## +####################################### + +library(imager) + +############################## +# Problem 1 +# 180 deg means that n x m remains n x m +# and directions are flipped +dog <- load.image("dog.jpeg") +col.mat <- as.array(dog[, ,1, ]) + +dims <- dim(col.mat) +rot <- array(0, dim = dims) + +for(i in 1:dims[1]) +{ + for(j in 1:dims[2]) + { + rot[i, j, ] <- col.mat[dims[1] - i + 1, dims[2] - j + 1, ] + } +} + +# Let's plot size by side +par(mfrow = c(1,2)) +plot(dog) +plot(as.cimg(rot)) + + + +############################## +# Problem 2 +# 90 deg means that n x m becomes m x n +# and then appropriate rotation +dog <- load.image("dog.jpeg") +col.mat <- as.array(dog[, ,1, ]) + +dims <- dim(col.mat) +rot <- array(0, dim = c(dims[2], dims[1], dims[3])) + +for(i in 1:dims[1]) +{ + for(j in 1:dims[2]) + { + # i component becomes j + rot[j, i, ] <- col.mat[i, dims[2] - j + 1, ] + } +} + +# Let's plot size by side +par(mfrow = c(1,2)) +plot(dog) +plot(as.cimg(rot)) + + + + +############################## +# Problem 3 +# 90 deg means that n x m becomes m x n +# and then appropriate rotation +dog <- load.image("dog.jpeg") +col.mat <- as.array(dog[, ,1, ]) + +dims <- dim(col.mat) +rot <- array(0, dim = c(dims[2], dims[1], dims[3])) + +for(i in 1:dims[1]) +{ + for(j in 1:dims[2]) + { + # i component becomes j + rot[j, i, ] <- col.mat[dims[1] - i + 1, j, ] + } +} + +# Let's plot size by side +par(mfrow = c(1,2)) +plot(dog) +plot(as.cimg(rot)) + + + + +############################## +# Problem 4 +# 90 deg means that n x m becomes m x n +# and then appropriate rotation +dog <- load.image("dog.jpeg") +col.mat <- as.array(dog[, ,1, ]) + +dims <- dim(col.mat) +rot <- array(0, dim = c(dims[2], dims[1], dims[3])) + +for(i in 1:dims[1]) +{ + for(j in 1:dims[2]) + { + # i component becomes j + rot[j, i, ] <- col.mat[dims[1] - i + 1, j, ] + } +} + +# Let's plot size by side +par(mfrow = c(1,2)) +plot(dog) +plot(as.cimg(rot)) + + + + +############################## +# Problem 5 + +# cropping image first +dog <- load.image("dog.jpeg") +col.mat <- as.array(dog[, ,1, ]) +col.mat <- col.mat[1:600, 1:600, ] + +reduce <- array(0, dim = c(300, 300, 3)) +red.dims <- dim(reduce) + +# I will take an average of the 2 by 2 pixels +# and then assign the average value to the reduce +averaging <- rep(0,3) +for(i in 1:red.dims[1]) +{ + for(j in 1:red.dims[2]) + { + ind1 <- (2*(i-1) + 1): (2*i) + ind2 <- (2*(j-1) + 1): (2*j) + + # taking the average rbg in the 2 by 2 area + averaging[1] <- mean(col.mat[ind1, ind2, 1]) + averaging[2] <- mean(col.mat[ind1, ind2, 2]) + averaging[3] <- mean(col.mat[ind1, ind2, 3]) + + reduce[i, j, ] <- averaging + } +} +par(mfrow = c(1,2)) +plot(dog) +plot(as.cimg(reduce)) +save.image(as.cimg(reduce), file = "dog_300.jpeg") + + +############################## +# Problem 5 + +# cropping image first +dog <- load.image("dog.jpeg") +col.mat <- as.array(dog[, ,1, ]) +col.mat <- col.mat[1:600, 1:600, ] + +reduce <- array(0, dim = c(60, 60, 3)) +red.dims <- dim(reduce) + +# I will take an average of the 10 by 10 pixels +# and then assign the average value to the reduce +averaging <- rep(0,3) +for(i in 1:red.dims[1]) +{ + for(j in 1:red.dims[2]) + { + ind1 <- (10*(i-1) + 1): (10*i) + ind2 <- (10*(j-1) + 1): (10*j) + + # taking the average rbg in the 10 by 10 area + averaging[1] <- mean(col.mat[ind1, ind2, 1]) + averaging[2] <- mean(col.mat[ind1, ind2, 2]) + averaging[3] <- mean(col.mat[ind1, ind2, 3]) + + reduce[i, j, ] <- averaging + } +} +par(mfrow = c(1,2)) +plot(dog) +plot(as.cimg(reduce)) +save.image(as.cimg(reduce), file = "dog_60.jpeg") \ No newline at end of file diff --git a/MTH208/Worksheets/solutions6.R b/MTH208/Worksheets/solutions6.R new file mode 100644 index 0000000..b2cfd9f --- /dev/null +++ b/MTH208/Worksheets/solutions6.R @@ -0,0 +1,45 @@ +################################ +## Solutions to Worksheet 7 +################################ +library(rvest) + +###### Question 1 +# loading html +html <- read_html("https://www.iitk.ac.in/math/visitors-post-doctoral-fellow") +# names are in head2 class +name <- html %>% html_elements(".head2") %>% html_text() + + +###### Question 2 +html <- read_html("https://www.imdb.com/chart/top/") + +# getting a tag in titlecolumn class and the text in there +name <- html %>% + html_elements(".titleColumn a") %>% + html_text() + +###### Question 2 +# name is done, getting year +year <- html %>% + html_elements(".secondaryInfo") %>% + html_text() %>% + substring(2,5) %>% # removing brackets + as.numeric() # changing to number + +# getting rating +rating <- html %>% + html_elements(".ratingColumn.imdbRating") %>% + html_elements("strong") %>% + html_text() %>% + as.numeric() # convering to numeric + +votes <- html %>% + html_elements(".ratingColumn strong") %>% + html_attr("title") %>% + substring(14) # removing the first 13 characters + + +# making dataset +dat <- data.frame(name, year, rating, votes) + + diff --git a/MTH208/Worksheets/solutions7.R b/MTH208/Worksheets/solutions7.R new file mode 100644 index 0000000..c3186b7 --- /dev/null +++ b/MTH208/Worksheets/solutions7.R @@ -0,0 +1,153 @@ +##################################### +## Solutions to Worksheet 7 +##################################### +library(rvest) + +# describe how many movies to scrape +# first make it work for a few, and then +# set nmov = 250 +nmov <- 100 + +## Finding the codes of all the movies +html <- read_html("https://www.imdb.com/chart/top/") +codes <- html %>% + html_elements(".seen-widget") %>% + html_attr("data-titleid") +codes <- codes[1:nmov] + +# name, year, rating, and votes is available +# in the top 250 page +name <- html %>% + html_elements(".titleColumn a") %>% + html_text() +name <- name[1:nmov] + +year <- html %>% + html_elements(".secondaryInfo") %>% + html_text() %>% + substring(2,5) %>% # removing brackets + as.numeric() # changing to number +year <- name[1:nmov] + +# getting rating +rating <- html %>% + html_elements(".ratingColumn.imdbRating") %>% + html_elements("strong") %>% + html_text() %>% + as.numeric() # convering to numeric +rating <- rating[1:nmov] + +over.votes <- html %>% + html_elements(".ratingColumn strong") %>% + html_attr("title") %>% + substring(14) # removing the first 13 characters + +over.votes <- substring(over.votes, 1, nchar(over.votes) - 13) +over.votes <- gsub(',', "", over.votes)%>% + as.numeric() +over.votes <- over.votes[1:nmov] + +## Creating all URLS for 250 movies +urls <- paste("https://www.imdb.com/title/", codes, "/ratings", sep = "") + +ranks <- 1:nmov +all_ratings <- list(length = nmov) # list of lists +for(i in 1:nmov) +{ + print(paste("Starting movie", i)) + movie_html <- read_html(urls[i]) + all_ratings[[i]] <- movie_html %>% html_table() +} + +# all_ratings is a list where each element of +# the list, is a list of all tables in the movie + +# extracting number of votes for 1-10 +votes <- matrix(0, ncol = 10, nrow = nmov) +colnames(votes) <- all_ratings[[1]][[1]]$Rating + +rating_gen <- matrix(0, nrow = nmov, ncol = 2) +colnames(rating_gen) <- c("men_rating", c("women_rating")) + + +votes_gen <- matrix(0, nrow = nmov, ncol = 2) +colnames(votes_gen) <- c("men_votes", c("women_votes")) + + +for(i in 1:nmov) +{ + votes1to10 <- all_ratings[[i]][[1]]$Votes + votes1to10 <- gsub(',', '',votes1to10) %>% as.numeric() + votes[i, ] <- votes1to10 + + sub <- all_ratings[[i]][[2]][, 1:2] + sub_rating <- sub$`All Ages` + sub_rating <- gsub('\n', '', sub_rating) + sub_rating <- gsub(' ', '', sub_rating) + + gen1 <- substring(sub_rating, 1, 3) %>% + as.numeric() + rating_gen[i,] <- gen1[-1] + + gen2 <- substring(sub_rating, 4) + gen2 <- gsub(',', '', gen2) %>% + as.numeric() + votes_gen[i, ] <- gen2[-1] +} + +dat <- data.frame(ranks, name, year, + rating, over.votes, + votes, rating_gen, + votes_gen) + + + +##### Problem 2 #### + +# URL of the images +urls_img <- paste("https://www.imdb.com/title/", codes, sep = "") +images <- character(length = nmov) # will store the vector of image locations +for(i in 1:nmov) +{ + print(paste("Starting movie", i)) + movie_html <- read_html(urls_img[i]) + images[i] <- movie_html %>% html_element(".ipc-image") %>% html_attr("src") +} + + +##### Problem 3 #### + +# creating a function that calculates the distance from +# a given color. Code was in Worksheet 4 solutions +diff.col <- function(img, col) +{ + col.mat <- as.array(img[, , 1, ]) + dims <- dim(col.mat) + + # Calculate distance to given color + dist <- matrix(0, nrow = dims[1], ncol = dims[2]) + for(i in 1:dims[1]) + { + for(j in 1:dims[2]) + { + # distance from the col give by user + dist[i,j] <- norm(col.mat[i,j, ] - col, "2") + } + } + # return the mean distance from color + return(mean(dist)) +} + + +## Now calculating distance average distance black +library(imager) +black <- numeric(length = nmov) +for(i in 1:nmov) +{ + img <- load.image(images[i]) + black[i] <- diff.col(img, col = c(0,0,0)) +} + +# Which movies are within .2 distance to black on average +index <- which(black < .2) +dat[index, ] diff --git a/MTH208/Worksheets/worksheet-11-pjham-main.zip b/MTH208/Worksheets/worksheet-11-pjham-main.zip new file mode 100644 index 0000000..c7f50c2 Binary files /dev/null and b/MTH208/Worksheets/worksheet-11-pjham-main.zip differ diff --git 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