In MATLAB

Easy Problem 1

Vectorize the following loops:

Part A

for i = 1:5

vec1(i) = (5*i+2)^3;

end

vec1

Part B

i = 1;

while i<=5

vec2(i) = i^2+4;

i = i+1;

end

vec2

Part C

Can you vectorize the following? Why?

vec3(1) = 1;

i = 1;

while i<5

i = i+1;

vec3(i) = (vec3(i-1)+2)^2;

end

vec3

Part D

You can vectorize the following:

for i = 1:10

a = i^2+1;

if a>10

vec4(i) = a;

else

vec4(i) = 0;

end

end

vec4

Part E

What is the inner (scalar) and outer (matrix) products of the following two vectors?

vec5 = (1:5);

vec6 = (2:6);

Ramp up Problem

Part A

We are given the function $f(x,y) = x^2 + y^2 + xy$. Write an inline function that accepts vectors of x and y to generate the value of the function. Output the answer for |x = -2:2| and |y = -1:3|.

Part B

Use a scatter plot |scatter3(arg1,arg2,arg3)| to visualize your answer now using |x=-2:0.1:2| and |y=-2:0.1:2|.

Part C

Plot this function (2D surface) between x = (-2,2) and y = (-2,2) using the |scatter3()| function. You will need to generate all permutation of (x,y) points as follows:

x = [1 2]; y = [2 3];

xp = [1 2 1 2];

yp = [2 2 3 3];

You will need to write a code that generates these |xp| and |yp| for given x and y vectors of equal length.

Touchdown Problem 3

Q3.

Convert the following for loops into vectorized forms

clear x

variable x is used above, see what happens if you don't do so

Part A

cumsum = 0;

not specifying this throws an error

for i = 1:2:10

cumsum = cumsum + i;

end

Part B

j = 1;

for i = 1:2:6

x(j) = 2+4*(i-1)^2;

j = j+1;

Part C

tstart=0; tend=20; ni=8;

t(1) = tstart;

y(1)=12 + 6*cos(2*pi*t(1)/(tend-tstart));

for i=2:ni+1

t(i) = t(i-1)+(tend-tstart)/ni;

y(i)=12 + 6*cos(2*pi*t(i)/(tend-tstart));

end

Part D

What is the problem with the following piece of code? Will it work for |x = 2|? What can you do to rectify it?

x = 3;if x>2

y = 1

else if x<2

y = 0

end