Example Code (some of which we cover today)

Exercises

Operators & functions

  1. Assign variables a,b,c to different integer values
  2. Create an anonymous function of the quadratic equation:

$$ \frac{-b \pm \sqrt{b^2-4ac}}{2a} $$

  1. Consider a,b,c as coefficients in a quadratic equation ax2+bx+c
  2. Find when x=0 using your quadratic equation

Challenge: Integrate the exponent of cosine of x between 0 and half pi

Matrices 1

  1. Create a column vector A with elements 1000 2000 3000
  2. Create a row vector B with elements 4000 5000 6000
  3. Combine the two vectors to create a 2x3 matrix C
  4. Multiply all elements by 2

Challenge: See if you can identify the differences between functions repelem() and repmat().

Strings

  1. Assign variables to the following strings: 'Strings', ' ', 'are ', 'nice' '.'
  2. Concatenate the strings in order with a new line between 'Strings' and ' '
  3. Create a second string with your name.

Challenge:

  1. Use strrep() to replace your name with my name
  2. Use strsplit() and join() to rearrange the sentence order

HINT: Cells group arrays of different sizes. Indexing rules for cells are the same, but use {} instead of () in particular cases.

Plotting Basics

  1. Create values of y, where y = tangent(x), with 1000 x values between 80 and 100 HINT: use the function tan()
  2. Display this plot with the following properties:

Challenge "For" loops in matlab are written as for i = r; <command(s)>; end where r is any valid range eg (1:1000) See if you can create animate a plot by using a for loop and drawnow()

Subplots

Use 1000 x values between 1 and 10 for the following

  1. plot the functions log(x) and sin(x) on the same subplot with ylim 0-2.5
  2. plot the function the square root of ( e to the x ) in a subplot below 1.

After plotting, add a title to the top subplot

Challenge Make the second subplot twice as wide as the top

Plotting 3D

  1. Using surf and imagesc in seperate figures: plot the surface 1/x2 + 1/y2 between -3 & 3 for both x and y
  2. Display the colorbar in each
  3. Display the plots between -2 & 2 for both x and y
  4. change the colormap

Challenge "For" loops in matlab are written as for i = r; <command(s)>; end where r is any valid range eg (1:1000) See if you can create animate a 3d plot by using a for loop and drawnow()

Index & Subscripts

  1. Create a random matrix between -10 and 90, with 10 rows and 9 columns. HINT: create a matrix with integers values between 0 & 100 first
  2. Select values between the 3rd and 4th column and the 2nd and 6th and set these values equal to 3
  3. Remove the 4th column.
  4. Check the number of columns in the matrix.
  5. Remove the 10th element from the matrix.
  6. Check the size of the matrix again.

Thought for food: A third type of indexing exists in matlab - logical indexing. We used this secretly when using basic logic and the find function. Try this: A=randi(10,10) i=A==10 sum(sum(i)) ind=find(i) numel(ind) %Compare with the sum step above A(i) A(i)=3 i=A==10 sum(sum(i)) %Compare with other sum above

Matrices 2

  1. Create a 2x5 matrix where with elements are equal to a phone number (800 555 1234)
  2. Use the function size to verify the size

Challenge Use reshape() to reshape this matrix into a square matrix, then use diag() on the output

Matrices 3

  1. Create a random matrix of size 3x2,
  2. Matrix Multiply it by an identity matrix
  3. Element wise multiply by 10
  4. Sum all the Elements (both vertical and horizontal)
  5. Visualize your matrix

Challenge:

  1. Use normrnd() to draw values from a normal distribution of mean 5 and standard deviation 3
  2. Use histogram() to visualize your results

EXTRA

1. Matrix manipulation

6. Logical indexing

Answers

Operators & functions

a=1; b=3; c=5; p = -b + sqrt(b2-4*a*c)/(2*a); % use up arrow n = -b - sqrt(b2-4*a*c)/(2*a);

Matrices 1

A = [1000; 2000; 3000]; B = [4000, 5000, 6000]; C = [A' B].*2;

Strings

A='Strings' B=' ' C='are ' D='nice' E='.' string1=[A newline B C D E]; string2='David White' cellA={string1, string2} %OR cellA{1}=string1; cellA{2}=string2;

Plotting Basics

x=linspace(80,100,1000) y=tan(x) plot(x,y,'m<','MarkerFaceColor','b')

Subplots

x=linspace(1,10,1000) figure(1) subplot(2,1,1) plot(x,log(x));hold on plot(x,sin(x));hold off subplot(2,1,2) plot(x,sqrt(exp(x))) subplot(2,1,1) title('title')

Plotting 3D

l=linspace(-3,3,100); [x,y]=meshgrid(l); z = 1./x2 + 1./y2; a=subplot(2,1,1) surf(x,y,z) b=subplot(2,1,2); imagesc(z) colormap(b,winter);

Index & Subscripts

A=randi(100,10,9)-10 A(2:6,3:4)=3 A(:,4)=[] size(A,2) %should be 8 A(1)=[]; size(A); should be 1x79

Matrices 3

sum(sum(rand(3,2).*eye(3,2)*10)) %single digits are treated as scalars, which are always element wise

EXTRA

Matrix Manipulation

A=[5:1.5:3202]'; A=resize(A,4,533); A=repelem(A,2,3): A(:,4)=[];

Logical indexing

A=randi(10,10,12)+5; A(A==4)=4; i=(A>10); A(i)=A(i)+1; [n,m]=find(A==8)