ENEL101 Problem set 5 M File Programming

Description

Q1. Write a function that accepts a general row vector X as an input and generates a row vector
P such that P contains all of the positive elements of X.
Q2. Write a function that determines y for a given input x. Assume that 𝑥 is a scalar (as opposed
to being a vector or a matrix).
𝑦 𝑥 = −0.2𝑥( + 7𝑥+ 𝑒-..(/
Q3. Modify the function above such that the input 𝑥 can be a 2×2 matrix.
Q4. Write a function that uses the switch – case statement (refer to pg.189-192 in the textbook).
The function takes a vector of strings in a structure (see assign5.m to see how this is done) and a
number 𝑥 as input. Each string is the case condition which specifies the type of operation to be
performed on ‘x’. The two cases for mathematical operations are ‘invert’ and ‘root2’. The
function produces a numeric output for a given numeric value of 𝑥 and the condition 𝑠. If 𝑠 is
anything other than ‘invert’ or ‘root2’, the function sets the output equal to 0. Place the results
in a row vector corresponding to operations as listed in the structure 𝑠 i.e. for the list of
operations ‘invert’,’root2’,’none’ and x=0.5 the answer will be [2.0000 0.7071 0].
ENEL101 Assignment 5 Page 2 of 3
Q5. Write a function that takes the coefficients 𝑎, 𝑏, 𝑐 of a quadratic equation of the form 𝑎𝑥+ +
𝑏𝑥 + 𝑐 = 0 as inputs and calculates the discriminant 𝐷 = 𝑏+ − 4𝑎𝑐. Then,
If 𝐷 > 0 the program sets 𝑛𝑢𝑚𝑟𝑜𝑜𝑡 = 2.
If 𝐷 < 0 the program sets 𝑛𝑢𝑚𝑟𝑜𝑜𝑡 = 0.
If 𝐷 = 0 the program sets 𝑛𝑢𝑚𝑟𝑜𝑜𝑡 = 1.
Q6. Fibonacci numbers are the numbers in a sequence in which the first two elements are 0 and
1, and the value of each subsequent element is the sum of the previous two elements as
0,1,1,2,3,5,8,13, …. Write a function that takes an integer 𝑛 > 2 as input and stores the first 𝑛
Fibonacci numbers in a column vector. You do not need to check for the condition of 𝑛 > 2.
Q7. Write a function that finds the fifth root of input P using Newton’s method, applying the
recursive formula
𝑥EFG = 𝑥E − 𝑥E
H − 𝑃
5 𝑥E
J
For the first value use 𝑥G = 𝑃. Continue with the recursive formula until the estimated relative
error 𝐸 < 0.00001 where
𝐸 = 𝑥EFG − 𝑥E
𝑥E
The function must output a 1×2 vector, with the first element being the answer (the fifth root)
and the second element being the number of iterations that were needed.
Q8. Given a point 𝑥. = 0.25 and function 𝑓 𝑥 = 𝑥+𝑒/ approximate the function’s derivative
at 𝑥. using the four-point difference formula
𝑑 𝑓 𝑥
𝑑 𝑥 = 𝑓 𝑥. − 2ℎ − 𝑓 𝑥. − ℎ + 𝑓 𝑥. + ℎ − 𝑓(𝑥. + 2ℎ)
12 ℎ
using ℎ = /Q
G. (ℎ must be a small number relative to 𝑥.). The function must output a 1×3 vector,
the first element being the numerator, the second the denominator, and the third the resulting
approximation.