[SOLVED] Ece-210-b homework #1 the basics

Read the rest of this document – hopefully it helps with the coding, and it details
style points that you’ll want to remember. As for code… do the following. You
may wish to read the matlab docs for a few of these!
Scale-‘ers Create the following scalar variables (with these names – they’ll be
referenced later). These should all be doable in one line.
1. a = |sin(π/3) + j/sec(−5π/3)| (| · | denotes absolute value)
2. l =
√3
8
3. u =
vuut
2
6!
X
80
n=1
n (hint: use sum and the colon operator)
4. m =

Im⌊ln √
66
7j

⌋
2
(⌊·⌋ denotes the floor function. Note that
floor and the natural log work on complex numbers!)

Mother…? Create the following vectors & matrices. Reference the above variables by name rather than writing the expressions again.
1. A = (a column vector with those four scalars in any order)
2. F =

a l
u m
(bonus points if you index A to do it)

3. T = F-transpose (should be short!)
4. B = TF-inverse (verify this by multiplying B by TF)
5. C =

T F
F T
(should be a 4 × 4 matrix)

Cruelty Use mean to compute the mean of all four entries in B, as well as the
row-wise means of C. Store the latter in a 4 × 1 column vector.
Odd Types Try evaluating T+F. Then T+1. Then, just for kicks, C+A. What
happens? Does this remotely make sense? Tell me your thoughts.
Not What It Seems… This matlab thing seems great for evaluating functions
and manipulating matrices. What about something a little less… limited?

Create a (row or column) vector with k = 3 elements, with values evenly
spaced between zero and one (think linspace). Square each individual element, take the sum, and divide by k. See what you get. Repeat
this for k = 5, 10, 300, 1e6. Could you have predicted the value you’re
approaching? How?

A Style
For historical purposes, I’ve included Jon Lam’s reminder on style (first given
in a matlab seminar before my time), as it succinctly covers most of the important points:
Remember, Good Code Style™ is important! Here are some recommendations, but feel free to do what suits you, so long as it is consistent and logical.
• Begin your scripts with clc, clear and close all. (Don’t remember
what these do? Use help!)

• Suppress outputs of intermediate values by ending the line with a semicolon. Long outputs printed in the command window are hard to follow.
I prefer suppressing all outputs and storing answers in descriptive variables.
• Follow a convention for variable names. It can be snake_case, camelCase,
PascalCase, alllowercase, etc. Names that are too short (e.g., x) are
not descriptive, and variableNamesThatAreTooLongLikeThis become
tedious. The exception to the first rule is when the name is clear from
context, e.g., x and t to denote time series data, but even then it is
usually nice to subscript them (e.g., x_1 and t_1 if you are working with
multiple time-series). Be sensible!

• Long lines tend to be hard to read, especially on smaller screens. Try to
limit lines to 80 characters. (MATLAB has a visual indicator for this.)
To break an expression over multiple lines, use ellipses (…), e.g.:
this_is_a_long_variable_name …
= some_long_expression …
* another_long_expression;

• Use comments to explain code. (Recall that comments start with %.)
The better and more consistently your variables are named, the less
commenting you need to keep your code maintainable.
• Using sections and consistent spacing makes for easier reading/debugging.
Section separators must have two percent signs at the beginning of the
line, followed by the space, followed by the section title.

Here’s a snippet of matlab code written in the above style:
useful comment
z }| {
% broadcasting should not be attempted here!
weighted_sum
| {z }
snake_case name
spaced well
z}|{
= sum( values_read
| {z }
consistent
spaced well
z }| {
.* weights
| {z }
concise
); ← no printing!
There’s more to say on style (of course), and we’ll get to that as the semester
progresses.

A.1 Arranging MATLAB Files
This should be more of a reminder – I’ll go over this in class, and the lecture
notes are formatted similarly to this. You can also deviate from this style if
you believe it right – I provide these guidelines as, well, guidelines, so you have
somewhere to start.
Begin the file with a preamble:
%%%% A Title Befitting the Extraordinary Works You Have Produced
% Your Name, The Date
% A description, perhaps across multiple lines if the project was
% sufficiently complex, of what you have created.
close all; clear; clc;

This tells whoever reads it what it is and clears out the matlab environment in
preparation for further works.
Each section of the file should start with a section designator (%%) to allow
running sections individually. This will make your life easier, as you’ll be able
to run (and thus debug) sections of the file individually using matlab’s Run
Section button (under Editor). It’s somewhat similar to notebook-style programming (e.g., Jupyter), if you’re familiar with that.

A section might look like this:
%% The First Task
% (1) in the beginning…
x = linspace(0, 1, 1000);
y = sin(x);
% (2) …there was Mathworks!
figure;
plot(x, y);
title(‘why did i bother putting a title here?’);

For reference, this is what my submission for this assignment might look
like:

% Just the basics…
close all; clear; clc;
%% Scale-‘ers
% …
% (1) …
a = …;
% (2) …
l = …;
% …
%% Mother…?
% …
% and so on…

B Reading the Docs
There are two ways to get documentation: via help and via Mathworks’ website.
The built-in help command yields text-format help for a given command.
For example:
>> help log
log Natural logarithm.
log(X) is the natural logarithm of the elements of X.
Complex results are produced if X is not positive.
See also log1p, log2, log10, exp, logm, reallog.

Documentation for log
Other uses of log
This documentation is pretty terse and is useful as a refresher if you’ve forgotten
how to do something.
If you want more depth (or are learning a function for the first time), Mathworks provides extensive documentation for matlab at mathworks.com/help/matlab/.
If you need help on anything from syntax to function arguments to design
strategies, this is the place to go! StackOverflow is, of course, a wonderful resource too, but being able to read Mathworks’ own documentation is a useful
skill.

For this assignment, you might check out the following pages:
1. the colon (:) operator: mathworks.com/help/matlab/ref/colon.html
2. the sum function: mathworks.com/help/matlab/ref/sum.html
3. the mean function: mathworks.com/help/matlab/ref/mean.html
4. the page for floor
5. the page for imag
6. …
…you get the idea. These pages are also available within the matlab interface
itself via the built-in command doc, which takes arguments like help does.
B.1 How To Learn Something New
What do you do when you need to do something but don’t know the first thing
about it?

I don’t have a magic answer for this. So much in software comes down to
knowing where the right documentation lies, and, frustratingly, there’s no one
answer about how to find it. Knowing a few places to look is helpful – hence
the references to Mathworks, help, and SO above – but that doesn’t solve everything, and traditional software documentation is not written in a way that
makes learning a library, a language, etc. from scratch very easy. I’m no expert
in researching stuff in general, neither am I one in software, but here’s what I
do when I need something I don’t have:

1. Realize I need new knowledge. This is more important than you might
think and I’m kinda bad at it. Signs you might need to learn something
are: your work seems harder than expected, you keep doing the same
thing over and over, you suspect the problem you’re working on is useful
outside the bounds of what you’re doing, you’re bored – in gereral, someone might have encountered exactly what you’re facing now and already
worked out a solution to it.

2. Feed it into a search engine (or several – using Bing and Google simultaneously often gives non-overlapping results). But not just once: I often
reword queries on the order of ten times before I find what I’m looking
for. Pay attention to language – how do other people describe the problem you’re facing? What words do they use that you could use in your
next search?

3. If you find examples with links to the relevant documentation pages, great
– use those. But type them yourself rather than copying them. This ensures you think about what you’re writing – which, after all, is the point.

4. If you’re left with software docs: good luck. More on that below.
Reading software documentation is a research art in itself. Most of the time,
docs are set up heirarchically, starting with general packages and working their
way down towards individual features. The “How To ReadThis Manual” section
of the docs for gnu make gives what is often a decent approach: read the first
few sections of whatever you find, looking for general information, and skip
the technical details on the first pass. Look up language or concepts you don’t
know, either in the manual itself or on the wider internet. Learning from docs
is, again, a skill, and an explorative process. It will take time.

Speaking of exploration: one unorthodox means of discovery is to simply
read other people’s code and look for things you don’t understand. Don’t be
afraid of talking to them, either!