I can't make sense of standalone variables with no definition [duplicate] - function

This question already has answers here:
What does "i" in "for i in range ()" mean?
(1 answer)
Why are variables "i" and "j" used for counters?
(23 answers)
Closed 19 days ago.
I keep running into problems with how I'm being spontaneously told to use i (or x or n) but there's no definitions for them and I'm struggling to find a pattern for when to use them and when not to. Do they mean something?? stand for a certain type of variable?
for example:
for i in range (1,10,5)<---the numbers don't matter but wtf is i from? my code didn't define it but somehow it just works whereas I can't use i for a placeholder like I can for x. Is there an index of this stuff somewhere? I understand creating variables, functions and types I just can't make sense of where these letters are supposed to go, when they're used, or why when they're not previously defined by me, the built-in functions, or standard math formulas. I'm still learning but things like this are slowing me down pretty bad :(
Thanks!
Menu = (1,2,3)
print(x)
for i in range (1,10,5)
"find all the factorials for the variables using a function"
....blah blah....blah.... but this was when function(n) popped up and the n was completely random

Related

Amplitude Spectrum of a function

My question is related to plotting amplitude spectrum.
Problem 1: (I have solved it) I have to represent the following function as a discrete set of N=100 numbers separated by time increment of 1/N:
e(t) = 3sin2.1t + 2sin1.9t
I did it using stem function in matlab and plotted it.
Problem 2: (I have question about it) The next thing was to repeat the same above all, using dataset of 200 points with time increment of 1/N and 1/2N.
My question is a bit basic but I just want to clear if I am following the right path to solve my problem.
I want to ask that for problem 2, for both 1/N and 1/2N, should I use N=200 (as I believe it is separate problem)?
A few of my mates have suggested using N=100 for 1/N and N=200 for 1/2N.
which one is the right thing?
Any help will be highly appreciated. Thanks

How would '1+1' look when just using 1 and 0? [duplicate]

This question already has answers here:
Is it possible to program in binary?
(6 answers)
Closed 2 years ago.
Is that possible? Can this be done using just 1 and 0 (true/false, on/off ...)?
If so, how would this code look?
If this example is too complex i am open to all other kinds of examples, but would like to have an operation included, because i have no idea how such operations get encoded (i guess they also are just an entry in a conversion chart)
The reason why i ask this, is that i want to give people a concrete example why datatypes and functions/operations are a practical abstraction (easier to read). Im writing a tutorial.
In a 1-bit wide integer = boolean value, carry-out has nowhere to go, so addition simplifies to just XOR.
Fun fact: XOR is add-without-carry. It's part of implementing a single-bit adder out of logic gates, e.g. a "half adder" that has 2 inputs (no carry-in) and produces a sum and carry-out. (sum = a xor b, carry = a AND b). A simple 32-bit adder could be build out of a half adder and 31 "full adders". Or more adders in parallel with tricks to optimize it for lower latency than a simple ripple-carry binary adders.
Carryless multiplication is a thing in some crypo, where summing partial products is done with XOR instead of normal binary addition.
See also What is the best way to add two numbers without using the + operator? for a software use of the same idea.

understanding the link between octave code and assignment equations

I have been struggling with some questions from my study guide and really am stuck - I have asked the lecturer for help but his answer was literally "but it's been done for you" (referring to gauss_seidel code that was written) - to which I think he missed the point. I'm struggling to understand the actual question and how to approach it.
The first question reads as follows:
Define the 100x100 square matrix A and the column vector b by:
A(ij)=I(ij)+1/((i-j)2+1) b_(i)=1+2/i 1<=i j<=100
where I_(ij) is the 100x100 identity matrix (i.e 1 on the main diagonal and 0 everywhere else). Solve for x using both the Gauss-Seidel method and the A\b construct.
We have written the code for the gauss_seidel method, and i think i understand what it does mostly, however, i do not understand how the above question fits into the method. I was thinking that i'm supposed to do something like the following in the octave window then calling the gauss_seidel method:
>> A=eye(100,100);
>> b= (this is where i get slightly confused)... I've tried doing
>> for b=1:n;
>> b=1+(2/n);
That is question 1.
Question 2 I have given an answer and asked him about but he has not responded.
It reads: The Hilbert matrix is a square n x n matrix defined by:
H_(ij)n = 1/i+j+1
Define bn to be a column vector of dimension n, and with each element 1. Construct bn and then solve for x, Hn xn=bn in the cases n=4.
What i did here was simply:
>> b=ones (4,1);
>> x=hilb(4)\b;
and then it gave me the output of x values. Im not sure if what i did here was correct... since it doesnt mention using any method at all it just says solve for x.
Im not sure how to relate the lecturers reply to understanding the problem.
If you could help me by maybe letting me know what im missing or how i should be thinking about this, it would really help.
the gauss_seidel code looks like this:
function xnew=gauss_seidel(A,b,xold)
n=size(A)(1);
At=A;
xnew=xold;
for k=1:n
At(k,k)=0;
end
for k=1:n
xnew(k)=(b(k)-At(k,:)*xnew)/A(k,k);
end
endfunction
Ive been writing pseudo since last Monday and I am only a little bit clearer on what the code does.
A(ij)=I(ij)+1/((i-j)2+1), b(i)=1+2/i, 1<=i, j<=100
All this is really saying is that we have to create A and b in such a way that i>=1 and j<=100. After doing that, you simply solve using the Gauss Seidel method.
So we'd create b like this:
b=zeros(100,1);
for k=1:100
b(k) = 1+(2/k);
end
This will create a column vector with a size of 100x1 with all the values that satisfy b(i)=1+2/i where i (or in the code,'k') was greater or equal to 1.
Then to create A :
myMatrix=zeros(100,100);
for i=1:100
for j=1:100
myMatrix(i,j) = 1/(((i-j)^2) + 1);
end
end
A=eye(100) + myMatrix;
Now we have created A in such a way that it equals A(ij)=I(ij)+1/((i-j)2+1) where i was greater or equal to 1 & j was less than or equal to 100.
The rest of the question is basically asking to to solve for the values of x using the Gauss Seidel method.
So it be something like this :
y=iterative_linear_solve(A,b,x0,TOL,max_it,method);
Don't forget about creating x0 as the initial assumption, tolerance and max iterations etc.
In terms of question 2, you did exactly what I would have done. I think you're good with that.
I'm not too sure how to answer this :
If you could help me by maybe letting me know what im missing or how i
should be thinking about this, it would really help.
All I can really say is that you need to look at the problems in such a way that you see Ax=b. For example in the first question we started by making b, and then A. After that we simply applied the A\b construct or the Gauss Seidel method and got our answer.
And that's essentially what you did for the second question.
Lastly, are you a UNISA student by chance? I am, haha. I've been struggling with this on my own for a while. The study guides don't seem to give a lot of info.

What is the difference between a subroutine and a function? [duplicate]

This question already has answers here:
Closed 10 years ago.
Possible Duplicate:
What is the difference between a ‘function’ and a ‘procedure’?
I searched online for an answer to this question, and the answer I got was that a function can return a value, modify a value, etc., but a subroutine cannot. But I am not satisfied with this explanation and it seems to me that the difference ought to be more than just a matter of terminology.
So I am looking for a more conceptual answer to the question.
A function mirrors the mathematical definition of a function, which is a mapping from 1 or more inputs to a value.1
A subroutine is a general-purpose term for any chunk of code that has a definite entry point and exit point.
However, the precise meaning of these terms will vary from context to context.
1. Obviously, this is not the formal mathematical definition of a function.
A generic definition of function in programming languages is a piece of code that accepts zero or more input values and returns zero or one output value.
The most common definition of subroutine is a function that does not return anything and normally does not accept anything. It is only a piece of code with a name.
Actually in most languages functions do not differ in the way you declare them. So a subroutine may be called a function, but a function not necessarily may be called a subroutine.
Also there is people that consider functions and subroutines the same thing with a different name.
Subroutine - Wikipedia
It's worth noting as an addendum to #Oli's answer that in the mathematical sense a function must be "well-defined", which is to say its output is uniquely determined by its inputs, while this often isn't the case in programming languages.
Those that do make this guarantee (and also that their functions not cause side-effects) are called pure functional languages, an example of which being Haskell. They have the advantage (among others) of their functions being provably correct in their behaviour, which is generally not possible if functions rely on external state and/or have side-effects.
A function must return some value and must not change a global variable or a variable declared outside of the function's body. Under this situation, a function can only mimic it's mathematical counter part (the thing which maps a mathematical object to another mathematical object)
A subroutine doesn't return anything and usually is impure as it has to change some global state or variable otherwise there is no point in calling it. There is no mathematical parallel for a subroutine.

Some questions about closures, not language specific! >:|

I'm doing some homework, and having a hard time understanding closures. This is in relation to boolean algebra mostly, not any specific programming language.
Here's an example:
Are the following sets closed under the following operations?
The language {a,b} under concatenation.
Now, from this: http://en.wikipedia.org/wiki/Closure_%28mathematics%29, it would seem that because the concatenation of the language {a,b} can produce results that are not members of the original set {a,b}, like ab, aa, bb, etc, the set is NOT closed under the concatenation operation.
Am I looking at this correctly? I feel its easy to misinterpret that definition. I feel like it might mean that if the operation produces results that CAN be created by the given language, then the set is closed under that operation.
Anyone want to take a stab at this and help me out? :)
Thanks!
In computational theory, you usually distinguish betweeen the set of symbols (characters, letters, etc.) and the set of words. It never really makes sense to discuss whether the set of characters is closed under an operation, instead you ask if some set of words is closed under an operation.
In the example you give, {a,b} is the symbol set; the set S of all words over that symbol set is closed under concatenation, since concatenating two words from S results in a word still in S.