LearningMATLAB.m

%Matrices
A = [3 2;4 5;27 17]
B = [4 7 6; 1 2 3]
C = A*B
D = A+B %does not run; dimensions of matrices are not equal
B' %Transpose of B

%{
Vectors
Vectors are just matrices with one of the dimensions equal to one
A row vector has only one row
A column vector has only one column
For example:
%}
R = [3 4 19 27 2] %row vector
C = R' %column vector
C = R; %The above command echoed C, but this does not b/c of the semicolon

%{
Creating a vector with internal MATLAB commands
Vector = start:increment:end (ending value is always less than or equal to end)
Vector = zeros(row, col); all entries are zero
Vector = ones(row, col);  all entries are one
Vector = rand(row, col);  pseudo-random entries from [0,1] (randn from normal)
%}
t = 1:1:365; %creates a row vector with start 1, increment 1, and end 365
s = 1:2:365; %creates a row vector with start 1, increment 2, and end 365
r = 1:2:364; %creates a row vector with start 1, increment 2, and end 363

q = zeros(3, 4)
p = ones(5, 1)
n = rand(1, 10)
n*10 %rand from [0,10]

%MATLAB built in functions
temp = 15*sin(2*pi*t/365)+12; %seasonal temp variable
%graphics to visualize result
plot(t, temp, '+');
xlabel('Time (days)');
ylabel('Smoothed temperature (degrees C)')

help
help plot
%help item

%plotting vectors
M = [4 83 5 13 12];
plot(M)
R = sort(R);
M = sin(R);
plot(R, M)
title('M vs R')

%Working with data frames - the below doesn't work. Why not? B/c i had blanks
load /Users/drewwadsworth/Documents/Education/"Menlo School"/"Menlo 11"/"AP Stats"/Pset4_Sem2_APStats/Pset4RStuffs.csv
load /Users/drewwadsworth/Documents/Pset4RStuffs.csv
%df(:,2) means "all rows from column 2 of df"
ace = Pset4RStuffs(:,1);
noAce = Pset4RStuffs(:,2);

plot(Pset4RStuffs) %individually plots columns
plot(ace, noAce, 'or') %plots noAce as function of ace

hist(ace, binwidth=5) %histogram of ace w binwidth 5

%solving Systems of equations A = coefficient matrix B = sums vector xy = A\B

%operations conducted element by element require a '.' after the vector name e.g. c.*c

M = M(2:4) %A(r1:r2, c1:c2) subset

rc = diff(M) %diff has size one less than its parameter

%ezplot plots functions
ezplot(@(X) sin(X))
ezplot(@(X,Y) sin(X) - Y)

%Practice Problems
%% 1
load /Users/drewwadsworth/downloads/ppt.dat %df for these problems

%% 2
help sum  %sums along the first non singleton dimension of a matrix
pptSum = sum(ppt'); %summed the transpose for years
years = 1960:1:1989;

plot(years, pptSum, 'o')
title('Annual Precipitation from 1960 to 1989')
xlabel('Year')
ylabel('Total Annual Precipitation')

%% 3
pptMean = mean(ppt) %monthly mean precipitation
bar(pptMean)
month = {'Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec'};
%The below sets the label for each x tick according to the given vector
set(gca, 'XTickLabel', month)
title('Mean Monthly Precipitation from 1960 to 1989')
xlabel('Month')
ylabel('Mean Monthly Precipitation')

%% normal plot with error bars showing standard deviation
help errorbar %creates a normal plot with specified error bars
help std %standard deviation of a vector - can also be applied to matrices
std(ppt)
errorbar(pptMean, std(ppt), 'xr')
set(gca, 'XTick', 1:12) %sets tick spacing to every one from the entries 1-12
set(gca, 'XTickLabel', month)
title('Mean Monthly Precipitation from 1960 to 1989 with One Standard Deviation Error Bars')
xlabel('Month')
ylabel('Mean Monthly Precipitation')

%% Comparing monthly precipitation mean and median
help median %like mean or std but for median
plot(pptMean-median(ppt), 'x') %plotting difference between mean and median of monthly precipitation
set(gca, 'XTick', 1:12)
set(gca, 'XTickLabel', month)
title('Difference in Mean and Median for Monthly Precipitation')
xlabel('Month')
ylabel('Mean Minus Median')

%% 4
help reshape %reshapes a matrix into a matrix of different dimensions
linearPPT = reshape(ppt, 1, 360)
bar(linearPPT)
set(gca, 'XTick', 1:360)  %Necessary for a 1 variable plot to change x ticks this way

%% Graph for 30 years w mean as a bar graph
figure(1); clf;
%Bar graph of monthly means
bar(pptMean)
month = {'Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec'};
%The below sets the label for each x tick according to the given vector
%set(gca, 'XTickLabel', month)

hold on %keep the above bar graph

focusYear = 1972;   %Year highlighted on the graph
startingYear = years(1);  %First Year graphed
%line graphs of each year
for i=1:30
  if i != focusYear - startingYear + 1
    %c = [(i/60) + 0.4, (i/60) + 0.4, (i/60) + 0.4];
    p1 = plot((1:12), ppt(i,:), 'Color', [0.5, 0.5 ,0.5]);
  else
    c = [1, 0, 0];
    pf = plot((1:12), ppt(i,:), 'Color', c, 'LineWidth', 2);
  end
end

set(gca, 'XTickLabel', month)

%Creating a legend
legend([p1 pf], [num2str(years(1)), ' - ', num2str(years(length(years)))], [num2str(focusYear)])

title('Monthly Precipitation from 1960 to 1989')
xlabel('Month')
ylabel('Monthly Precipitation')

%% 5
figure(1); clf;
fflush(stdout)
numYear = input("What year would you like?");
1962
startingYear = years(1);
indexOfYear = numYear - startingYear + 1;
year = ppt(indexOfYear, :);

%help min

['Minimum precipitation: ', num2str(min(year))]
['Maximum precipitation: ', num2str(max(year))]
['Mean precipitation: ', num2str(mean(year))]

%help stem

stem(year)
title(['Monthly Precipitation for ', num2str(numYear)])
xlabel('Month')
ylabel('Precipitation')
set(gca, 'XTick', 1:12)
set(gca, 'XTickLabel', month)

%% 6

%% Linear Regression
lm = polyfit(years, pptSum, 1)
%model: y = 915.04590 + 0.12603x
variabilityPercent = (corr(pptSum, lm(2) + lm(1)*years))^2
%Using corr instead of corrcoef because apparrently corrcoef isn't supported