# ------------------------------------------------------------------ # File name: beginnings.R # # A line starting with # character is a comment line and is not interpreted by R # Use comment lines liberally in your R scripts # As you study these scripts, make sure to type each line in your copy of R # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ # R as a calculator 2+3.1 # Semicolon is a statement separator 2*3; 2/3 # R displays 7 digits by default. You can display more digits with options(). # More than 15 digits could be unreliable # This is a global option; remains in effect until further notice options(digits = 15) # ^ for power 2/3; 2.1^3.1 # R has built-in mathematical constants and functions 2*pi sin(2*pi) # This is e exp(1) sqrt(2) # Variables and their values are saved in the memory # The assignment operators = or <- are equivalent. The right-hand-side # is evaluated first and the result is assigned to the variable on the left. # Variable names must start with a letter and can have letters, digits, underscore, and period. # R distinguishes between upper and lower case # Try to use suggestive, not cryptic, variable names # x is a varible with value 2.1 x = 2.1 # To print the value of the variable x x # Same assignment as = in the previous statement x <- 2.1 x # plus_2 is another variable holding 2 plus_2 = 2.0 # Add the value of x and value of plus_2 and assign it as the new value of x # old value of x is lost x = x + plus_2 # Printing in R can be accomplished in three basic ways: # simply type the variable name x # print(x) function: simply prints the value of x; its use sometimes necessary # in loops and user-defined functions print(x) # cat() function concatenates strings, inside double quotes, and interpolated values of variables cat("x =", x, "\n") cat("root2 =", sqrt(2), "\n", "root3 =", sqrt(3), "\n") # A variable can also hold a string in quotes my_name = "Huseyin Kocak" cat("My name is", my_name) # You can quit R by quit()
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# ------------------------------------------------------------------ # File name: R_help.R # # R has readily accessible help facilities from the command line # Below is an annotated summary of common help commands # For more extensive information, see R Help # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ # To see a sequence of simple graphics pictures demo(graphics) # To see a sequence of 3D graphics demo(persp) # To list available demonstrations in base package of R demo() # To list all arithmetic operators in R help(Arithmetic) # To get help on the log function help(log) # To display R help on the plot() function help(plot) # Same as help(plot) ?plot # To see example of the usage of plot function example(plot) # To list all R commands containing the string plot; could be too much info help.search("plot") # Same as help.search("plot") ??plot # To get more help on the help() function help()
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# ------------------------------------------------------------------ # File name: vectors.R # # R is efficient in computing with vector variables # By default, a variable holding a single number is a vector of length 1 # Below is an annotated summary of common operations with vector variables # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ # R function c() combines (concatanes) values into a vector x = c(1.5, -3.2, 0.45, 4.1, 10) print(x) # Entry of a vector can be addressed by its index, its position in the vector # Unlike other programming languages, index of a vector in R starts from 1 # To print the first entry of x print(x[1]) # To print the 4th entry of x print(x[4]) # To change the value of the 4th entry of x to 7.6 x[4] = 7.6 print(x) # Can add an entry to a vector x[6] = 91 print(x) # An entry of a vector can be deleted using -index x = x[-6] print (x) # R function length() returns the number of entries of a vector # There are numerous function for vectors; try, for example # sort(), rev(), min(), mean(), sum(), prod() length_of_x = length(x) print(length_of_x) # Arithmetic of vectors is done entry-wise # + addition, - subtraction, * product, / division, %*% crossproduct vector_1 = c(1.1, 2.3, 4.5) vector_2 = c(-1, 1.2, 0.5) vector_sum = vector_1 + vector_2 print(vector_sum) # Vector entries can be strings or booleans nucleotides = c("A", "C", "G", "T") print(nucleotides) # Vectors with patterns are useful. We will see a better way to generate them x = c(0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0) print (x) squareRoot_x = sqrt(x) print(squareRoot_x)
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# ------------------------------------------------------------------ # File name: script.R # # A simple R script to plot square root function # The graph will be output to the screen in a separate graphics window # # To execute R commands in a file, type source("filename.R") at the propmt # R looks for files in a "working directory"; type getwd() to find out this directory # Use setwd() to set working directory. For example, if the file script_plot.R is in the # /Users/hk/Documents/R_scripts directory, type # setwd("/Users/hk/Documents/R_scripts/") then source("script.R") # In Unix, you can start R from the directory containing your R scripts # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ x = seq(from = 0, to = 10, by = 0.5) square_root_x = sqrt(x) plot(x, square_root_x)
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# ------------------------------------------------------------------ # File name: plot_options.R # # plot() is a high-level R function that opens a new plotting window # Here, we will show some basic options to plot() with a sequence of plots # of square root function with increasing complexity # Type ?plot to see details of basic options; you can see # 657 available colores by typing colors() # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ x = seq(from = 0, to = 10, by = 0.5) square_root_x = sqrt(x) # Plot x-values vs. square_root_x values with default options plot(x, square_root_x) # To pause between plots par(ask = TRUE) # To add title plot(x, square_root_x, main = "My First Plot") # To add label to y-axis plot(x, square_root_x, main = "My First Plot", ylab = "sqrt(x)") # To set limits of y-axis plot(x, square_root_x, main = "My First Plot", ylab = "sqrt(x)", ylim = c(0, 10)) # To add color plot(x, square_root_x, main = "My First Plot", ylab = "sqrt(x)", ylim = c(0, 10), col = "blue") # To over strike with both plotting characters, pch, and connecting lines plot(x, square_root_x, main = "My First Plot", ylab = "sqrt(x)", ylim = c(0, 10), col = "blue", type = "o") # To set the line type plot(x, square_root_x, main = "My First Plot", ylab = "sqrt(x)", ylim = c(0, 10), col = "blue", type = "o", lty = "dotted") # To set plotting character plot(x, square_root_x, main = "My First Plot", ylab = "sqrt(x)", ylim = c(0, 10), col = "blue", type = "o", lty = "dotted", pch = 22)
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# ------------------------------------------------------------------ # File name: saving_to_file.R # # Saving the plot of square root function to a png file # You can also save a picture as a pdf file by using the # pdf() function with .pdf file extension # # The file is saved in the current working directory of R # Existing file with same name is overwritten # The graph will not be output to the screen, so you should save # after you get the desired picture # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ png("square_root_function.png", bg = "gray", width = 600, height = 600) x = seq(from = 0, to = 10, by = 0.5) square_root_x = sqrt(x) plot(x, square_root_x, main ="Graph of Square root function", xlim = c(0, 10), ylim = c(0, 10), col = "red", type = "o") dev.off()
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# ------------------------------------------------------------------ # File name: add_to_plot.R # # plot() is a high-level plotting function that opens a new plotting window # using low-level functions, one can add to the open plot # some of the commonly used adding functions are: # points(), lines(), abline(), legend(), text() # Below, we will plot a function and add to plot # its inverse function, a line, text, and a legend # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ t = seq(from = 0, to = 10, by = 0.5) # To pause between plots par(ask = TRUE) plot (t, sqrt(2 * t), main = "Adding to Plot", sub = "A function and its inverse", xlab = "", ylab = "", xlim = c(0, 10), ylim = c(0, 10), pch = 16, type = "o") # To add the inverse function points(t, 0.5 * t * t, col = "red" , pch = 16, type = "o") # To add the line with intercept = 0, slope = 1 abline(0, 1, col = "gray", lwd = 3, lty = "dashed") # To add text text(7, 7.3, "45-degree line", srt = 45) legend("bottomright", legend = c("funtion", "inverse"), pch = 16, col = c("black", "red")) # One can add graphs of mathematical functions using, for example: # lines(curve(sin(x) + cos(x) + 5, add = TRUE))
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# ------------------------------------------------------------------ # File name: curve_plotting.R # # curve() is a high-level mathematical plotting function that opens a new plotting window # Variable in the mathematical formula must be x # Can add more graphs by setting add = TRUE # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ curve(sin(x), xlim = c(-4*pi, 4*pi), ylim = c(-2, 2), col = "red", ylab = "") # To plot horizontal line using h abline(h=0, lty= "dotted") # To mark the origin points(0, 0, pch = 3) curve(cos(x), col = "blue", add = TRUE) curve(sin(x) + cos(x), col = "purple", lwd = 3, add = TRUE) title("sin(x) + cos(x)") legend("bottomright", legend = c("sin(x)", "cos(x)", "sin(x) + cos(x)"), lty = 1, col = c("red", "blue", "purple"))
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# clock by Hlynka # Look up in the R manual the function arrows() # Add title, beautify it as you please plot(-1:1, -1:1, type = "n", xlab = "", ylab = "" ) K = 12 text(exp(1i * 2 * pi * c(2:1,12:3) / K), col = "red") arrows( 0, 0, 0, 0.9) arrows( 0, 0, 0.7*cos(pi/6), 0.7*sin(pi/6))
# ------------------------------------------------------------------ # File name: if_else.R # # This code asks the user to enter a number. # If the number is non-negative, it prints the sqrt of the number; # otherwise, it exits with a message. # Decision is accomplished with an if() else statement # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ cat("Please enter a number to compute its square root \n") # To get input from keyboard (single item) x = scan(nmax = 1, quiet = TRUE) cat("The number you have entered is", x, "\n") # Else must be on the same line as the closing brace of if if(x >= 0) { cat("square root of", x, "is", sqrt(x), "\n") } else { cat("Sorry, please enter a nonnegative number \n") } cat("Bye!. \n")
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# ------------------------------------------------------------------ # File name: for_loops.R # # for loop in R iterates a block of statements with a counter running through # values in a sequence. Syntax of for loop is: # for (counter in sequence) { # statements # } # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ sequence = seq (1, 10) for(counter in sequence) { squared = counter * counter cat("counter = ", counter, "\t", "squared = ", squared, "\n" ) } # In the following more complicated example of for loop, we will compute 10 generations of # a population growing according to the discrete logistic model and save the # population densities as a vector cat("Densities of generations with discrete logistic growth model \n") # Initialize vector holding population densities; x[1] = 0.2 x = 0.2 cat("generation =", 1, "\t", "population density =", x[1], "\n" ) # Growth rate r = 2.45 number_of_generations = 10 for(i in 1:(number_of_generations - 1)) { x[i+1] = r*x[i] * (1.0 - x[i]) cat("generation =", i+1, "\t", "population density =", x[i+1], "\n" ) } # To see x as a vector print (x)
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# ------------------------------------------------------------------ # File name: while_loops.R # # while loop iterates a block of statements as long as a condition (boolean) remains true. # Syntax of while loop is: # while (boolean){ # statements # } # break exits the loop # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ # To generate a table of numbers and their squares counter = 1 while (counter <= 10){ square = counter * counter cat("counter = ", counter, "\t", "square = ", square, "\n" ) counter = counter + 1 } # Newton-Raphson iteration for finding sqrt(2) with a specified tolerance # x = starting value # delta = absolute value of the difference between two consecutive iterates # while performs Newton-Raphson iterates as long as delta remains greater than # a desired tolerance cat("Newton-Raphson iteration for computing sqrt(2) with a specified tolerance \n") options(digits = 15) x = 3.1 tolerance = 1e-8 cat("x =", x, "\t", "tolerance =", tolerance, "\n") x_next = 0.5 * (x + 2/x) delta = abs(x_next - x) cat("x =", x_next, "\t", "delta =", delta, "\n") x = x_next while (delta > tolerance){ x_next = 0.5 * (x + 2/x) delta = abs(x_next - x) cat("x =", x_next, "\t", "delta =", delta, "\n") x = x_next }
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# ------------------------------------------------------------------ # File name: writing_functions.R # # User-defined functions have the form # name = function(parameters ){ # statements # return() # } # After sourcing this file, the functions herein will be loaded into memory. # The first function just prints out my address. Usage: my_address() # The second function computes and returns the Taylor series approximation of sin(x) to # a specified number of terms. Usage: sine_series(0.5, 5) to compute the # sin of 0.5 for 5 terms. # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ my_address = function(){ cat("Huseyin Kocak\n") cat("Department of Computer Science\n") cat("University of Miami\n") cat("Coral Gables, FL 33146\n") } options(digits = 15) sine_series = function(x, number_of_terms){ sum = 0 for(n in 0:(number_of_terms-1)){ sum = sum + ( ((-1)^n) / factorial(2 * n + 1) ) * (x^(2 * n + 1) ) } return(sum) }
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newtonFor_A = function(A, x, number_of_iterations)to compute the square root of any positive number A.
#newton iteration for finding sqrt(2)
#parameters
# x = starting value
# number_of_iterations = number of iterations
#usage: newtonFor(3.1, 8)
#to get more digits use options(digits=15)
newtonFor = function(x, number_of_iterations){ #begin function
print(x)
for ( i in 1:number_of_iterations){ #index i will run from 1 to number_of_iterations
x = 0.5*(x + 2/x) #replace old x with new value
print (x)
} #end for
} #end function
# This script is from R for Beginners, by E. Paradis.
# ricker function iterates the Ricker model, a difference equation for
# modeling the growth of a single population, and plots fifty generations
# for three values of parameter r.
ricker <- function(nzero, r, K=1, time=50, from=0, to=time)
{
N=0
N[1] <- nzero
for (i in 1:time) N[i+1] <- N[i]*exp(r*(1 - N[i]/K))
Time <- 0:time
plot(Time, N, type="o", xlim=c(from, to))
}
layout(matrix(1:3, 3, 1))
ricker(0.1, 1); title("Ricker model with r = 1")
ricker(0.1, 2); title("r = 2")
ricker(0.1, 3); title("r = 3")
# ------------------------------------------------------------------ # File name: curve_fitting.R # # Linear Model function lm(y~x) computes the least square fit line to data points; # y as a function of x. Type ?formula for help with legal formulas. # lm() can also be used to fit nonlinear models where the parameters enter into model linearly. # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ # Fit a line to two data points; a good test of lm() x2 = c(1, 2) y2 = c(1.5, 2.5) plot(x2, y2, main="Unique line through 2 points", xlim=c(0, 4), ylim = c(0, 4)) # Compute the least square line, save output in ls_fit_line ls_fit_line = lm(y2 ~ x2) print(ls_fit_line) # Plot the least square line stored in ls_fit_line abline(ls_fit_line, col="red") # Print the vector containing intercept and slope the line print(coef(ls_fit_line)) # Lots more info print(summary(ls_fit_line)) par(ask=TRUE) # Compute least-square line fit for 3 data points x3 = c(1, 2, 3) y3 = c(1.5, 2.5, 2.8) plot(x3, y3, main="Best-fit line through 3 points", xlim=c(0, 4), ylim = c(0, 4)) fit3 = lm(y3 ~ x3) abline(fit3, col = "red") print(fit3) # Lots more info about the fitness print(summary(fit3)) # Compute the parabola through 3 data points plot(x3, y3, main="Unique parabola through 3 points", xlim=c(0, 6), ylim = c(0, 6)) fit_parabola3 = lm(y3 ~ x3 + I(x3^2)) print(fit_parabola3 ) curve(coef(fit_parabola3)[1] + coef(fit_parabola3)[2]* x + coef(fit_parabola3)[3]*x^2, 0, 6, col = "red", add=TRUE) # Compute a best-fit parabola for 4 data points x4 = c(1, 2, 3, 4) y4 = c(1.5, 2.5, 2.8, 1.7) plot(x4, y4, main="Best-fit parabola through 4 points", xlim=c(0, 6), ylim = c(0, 6)) fit_parabola4 = lm(y4 ~ x4 + I(x4^2)) print(fit_parabola4) curve(coef(fit_parabola4)[1] + coef(fit_parabola4)[2]* x + coef(fit_parabola4)[3]*x^2, 0, 6, col = "red", add=TRUE) # Add the predicted points points(x4, predict(fit_parabola4), col = "green")
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# ------------------------------------------------------------------ # File name: beetle_parameters.R # # Problem: # Flour beetles with initial 112 individiuals are grown # in a laboratory are counted daily for 15 days. # Assuming that the beetle population grows according to the logistic differential # equation (dy/dt) = ay + by^2, where y[t] is the population size at time t, # estimate the values of the parameters a and b. # # Solution: # Rewrite the differential equation as (dy/dt)/y = a + by so that r.h.s is linear in y # Approximate the derivative with (y[t+h] - y[t])/h, here h=1, # Compute 15 points, ((y[t+h] - y[t])/y[t], y[t]) and determine the best fit line. # Intercept = a and slope = b. # # Version: 2.1 # Authors: H. Kocak, University of Miami and B. Koc, Stetson University # References: # https://www.r-project.org # ------------------------------------------------------------------ # First, record the data and plot it daily count of beetles for 16 days # Beetle count for 15 days y = c(112, 152, 212, 258, 306, 309, 315, 310, 298, 290, 303, 295, 311, 308, 299, 309) # Time in days t = seq(0, length(y)-1) plot(t, y, main = "Daily beetle counts", type = "o", xlab = "days", ylab = "beetles") # Remove the last data point (why?) y_1 = y[-length(y)] # To pause between plots par(ask=TRUE) # Create a rate vector and load it with computed rates scaled_rate = 0 for(i in 1:(length(y)-1)) { scaled_rate[i] = (y[i+1] - y[i]) / y[i] } #print(rate) # Plot 15 points and compute best line for them plot(y_1, scaled_rate, col = "red", main = "Least square fit to scaled rates") best_fit_line = lm(scaled_rate~y_1) #compute line using lm() and save abline(best_fit_line) #add the graph of the line print(best_fit_line) #print intercept and slope of line # If you know statistics, you can try the following commands for more information # print(summary(best_fit_line)) # plot(best_fit_line)
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