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Say there are two variables: x and y. Let x be a function of y, e.g. set x 2 * y.
If future lines of the code alter the value of y, the value of x does not seem to automatically update, without me specifying again: set x 2 * y.
Is it possible to create a variable as a function of other variables, which automatically updates without having to set it again?


Instead of using variables for this, you should define a reporter:
to-report x
report 2 * y
end
though, for the sake of those reading your code and for your future self looking back at your code, use more descriptive variable names than x and y :)

Related

How to make vectors be of same length in my Matlab script?

I am trying to plot some data. The script I wrote below has worked fine before, but now I have no idea why it's not working.
Here is the code:
x = [335,41,14,18,15,9,7,9,20607,5,5,143,3,5,72,134,2,28,172,3,72,173,280,186,20924,1,1,22,3,3,1,2,13,1,3,2,11,66,12983,176,123,192,64,258,182,123,299,58,198,7,113,342,72,8376,122,20,19,2,3,28,8,36,8,56,43,2,48,127,395,4664,186,46,236,219,258,69,203,189,169,72,100,78,109,46,112,3929,272,40,4,31,2,97,36,5,35,56,2,237,1672,256,224,28,163,341,151,263,157,397,94,380,173,75,87,272,1194,133,6,112,1,6,2,26,25,64,8,40,57,106,525,150,248,125,269,264,256,357,153,64,152,283,1,2,2,454,154,39,1,1,64,151,242,1,18,99,1,36,607,55,54,110,225,108,37,1,144,162,137,107,21,360,362,18,51,25,43,1,3,6,1,27,7,45,326,32,103,50,124,155,39,180,143,33,116,46,7,151,120,19,4,2,4,110,2,7,4,9,4,27,216,323,148,1,1,2,1,47,113,150,1,2,144,16,4827,1,1,1,14];
size = length(x);
disp(size);
z = 0;
for i = 1:size
z = z + 1;
y(i) = z;
end
scatter(x,y);
This code should ensure that y is of same length as x as we are only filling in y as long as x is (since we are using a for loop from 1 through to size, where size is basically the number of indices in x), but I keep getting this error. I checked with disp and it turns out that my x and y vectors have different lengths, x is 227 and y is 256. Can anyone help me out with this trivial issue?

This is most likely because y was created to be a different size before you ran that piece of code you showed us. Somewhere in your script before you call this piece of code, y was created to be a 256 element vector and now you are reusing this variable in this part of the code by populating elements in the y vector. The variable x has 227 elements and the loop you wrote will change y's first 227 elements as you have looped for as many times as there are elements in x. However, the remaining 29 elements are still there from before. The reusing of the variable y is probably why your script is failing as now the sizes between both variables are not the same. As such, explicitly recreate y before calling scatter.
Actually, that for loop is not needed at all. The purpose of the loop is to create an increasing array from 1 up to as many elements as you have in x.
Just do this instead:
y = 1:size;
I also do not like that you are creating a variable called size. It is overshadowing the function size, which finds the number of elements in each dimension that the input array contains.
With the recommendations I've stated above, replace your entire code with this:
x = [335,41,14,18,15,9,7,9,20607,5,5,143,3,5,72,134,2,28,172,3,72,173,280,186,20924,1,1,22,3,3,1,2,13,1,3,2,11,66,12983,176,123,192,64,258,182,123,299,58,198,7,113,342,72,8376,122,20,19,2,3,28,8,36,8,56,43,2,48,127,395,4664,186,46,236,219,258,69,203,189,169,72,100,78,109,46,112,3929,272,40,4,31,2,97,36,5,35,56,2,237,1672,256,224,28,163,341,151,263,157,397,94,380,173,75,87,272,1194,133,6,112,1,6,2,26,25,64,8,40,57,106,525,150,248,125,269,264,256,357,153,64,152,283,1,2,2,454,154,39,1,1,64,151,242,1,18,99,1,36,607,55,54,110,225,108,37,1,144,162,137,107,21,360,362,18,51,25,43,1,3,6,1,27,7,45,326,32,103,50,124,155,39,180,143,33,116,46,7,151,120,19,4,2,4,110,2,7,4,9,4,27,216,323,148,1,1,2,1,47,113,150,1,2,144,16,4827,1,1,1,14];
numX = numel(x);
y = 1 : numX;
scatter(x,y);
The vector y is now explicitly created instead of reusing the variable that was created with a previous size in the past. It also uses the colon operator to explicitly create this sequence instead of using a for loop. That for loop is just not needed. numel determines the total number of elements for an input matrix. I don't like using length as a personal preference because it finds the number of elements in the largest dimension. This may work fine for vectors, but it has really made some hard to spot bugs in code that I've written in the past.

(MATLAB) On drawing elements randomly from vectors and rows randomly from matrices without replacement in for loops

So, two related questions for code I'm writing for an experiment I'm building in MATLAB. Firstly, I have a 20 row column vector, called block1 (with a number in each of the 20 slots).
I want to draw a number randomly from the vector without replacement and repeat this until there are no numbers left in the vector (so 20 times total). I have the following line within a for loop (which is set to run for 20 iterations), which draws the random number from the vector and sets it equal to variable rand_num:
rand_num = randsample(block1,1,false)
It draws the random number just fine, but the problem is that the draw without replacement part doesn't work. Initially I thought this was because the vector was reset at the beginning of each iteration of the for loop. To make sure, I debugged and found that even when I stop the for loop before the first iteration finishes (and after the random number has been drawn), there are still 20 numbers in the vector (when there should be 19). Any ideas as to how I can fix this?
The second question is as follows. For the same experiment, I have a 20 by 6 matrix called pick_matrix. During each iteration of the same for loop as above, I want to pick one row at random from the matrix (including every element in that row; so 6 elements total for each row) without replacement and assign that row to variable random_row.
I figured out the code to pick a row at random and assign it to random_row, but I'm having the same problem as with the last question: the without replacement part isn't working.

randsample works fine, and exactly as expected. You just need to call it once before your loop rather than twenty times within the loop. Read the help carefully - randsample does not change anything about the input variable block1. Generally speaking (ignoring globals and such), input variables are not changed by Matlab functions, even if they are changed within a function, unless they are then explicitly output.
e.g. consider this:
function y = myfunc(x);
x = x*2;
y = x*3;
disp(x)
end
Within the function, x is doubled. Say I have a variable x in my workspace, value 10. If I call y = myfunc(2), I will see "4" displaced - and y will be output as 12, not 6. However, the x in my base workspace is never changed, which is exactly the expected behaviour.
If I want x to be changed, I have to set it explicitly as output to the function and deliberately call the function in such a way as to overwrite my variable x, e.g [x y] = myfunc(2);
As suggested in the comments, you could use randperm instead if you're taking every number, but a more generic example using randsample to take a random pick of 10 from 20:
% sampling without replacement is default
rand_nums = randsample(block1, 10);
rand_ind = randperm(20,10); % 10 numbers from 1:20
for n = 1:10
rand_num = rand_nums(n);
rand_row = pick_matrix(rand_ind(n),:);
% whatever you need to do with these things goes here
end

What is this code doing? Machine Learning

I'm just learning matlab and I have a snippet of code which I don't understand the syntax of. The x is an n x 1 vector.
Code is below
p = (min(x):(max(x)/300):max(x))';
The p vector is used a few lines later to plot the function
plot(p,pp*model,'r');

It generates an arithmetic progression.
An arithmetic progression is a sequence of numbers where the next number is equal to the previous number plus a constant. In an arithmetic progression, this constant must stay the same value.
In your code,
min(x) is the initial value of the sequence
max(x) / 300 is the increment amount
max(x) is the stopping criteria. When the result of incrementation exceeds this stopping criteria, no more items are generated for the sequence.
I cannot comment on this particular choice of initial value and increment amount, without seeing the surrounding code where it was used.
However, from a naive perspective, MATLAB has a linspace command which does something similar, but not exactly the same.

Certainly looks to me like an odd thing to be doing. Basically, it's creating a vector of values p that range from the smallest to the largest values of x, which is fine, but it's using steps between successive values of max(x)/300.
If min(x)=300 and max(x)=300.5 then this would only give 1 point for p.
On the other hand, if min(x)=-1000 and max(x)=0.3 then p would have thousands of elements.
In fact, it's even worse. If max(x) is negative, then you would get an error as p would start from min(x), some negative number below max(x), and then each element would be smaller than the last.
I think p must be used to create pp or model somehow as well so that the plot works, and without knowing how I can't suggest how to fix this, but I can't think of a good reason why it would be done like this. using linspace(min(x),max(x),300) or setting the step to (max(x)-min(x))/299 would make more sense to me.

This code examines an array named x, and finds its minimum value min(x) and its maximum value max(x). It takes the maximum value and divides it by the constant 300.
It doesn't explicitly name any variable, setting it equal to max(x)/300, but for the sake of explanation, I'm naming it "incr", short for increment.
And, it creates a vector named p. p looks something like this:
p = [min(x), min(x) + incr, min(x) + 2*incr, ..., min(x) + 299*incr, max(x)];

Can matlab (or mupad) evaluate symbolic expressions containing non-commuting operators?

Say I give something like AB+AB+BA to matlab (or mupad), and ask it to simplify it. the answer should be: 2AB+BA. Can this be done in matlab or mupad?
Edit:
Ok, this is feeling rediculous. I'm trying to do this in either matlab or mulab, and.. it's frustrating not knowing how to do what should be the simplest things, and not being able to find the answers right away via google.
I want to expand the following, multiplied together, as a taylor series:
eq1 := exp(g*l*B):
eq2 := exp(l*A):
eq3 := exp((1-g)*l*B):
g is gamma, l is lambda (don't know how to represent either of these in matlab or mulab). A and B don't commute. I want to multiply the three exponentials together, expand, select all terms of a given power in lambda, and simplify the result. Is there a simple way to do this? or should I give up and go to another system, like maple?

This is mupad, not matlab:
operator("x", _vector_product, Binary, 1999):
A x B + A x B + B x A
returns
2 A x B + B x A
The vetor product is used, simply because it matches the described requirements.

How to generate random matlab vector with these constraints

I'm having trouble creating a random vector V in Matlab subject to the following set of constraints: (given parameters N,D, L, and theta)
The vector V must be N units long
The elements must have an average of theta
No 2 successive elements may differ by more than +/-10
D == sum(L*cosd(V-theta))
I'm having the most problems with the last one. Any ideas?
Edit
Solutions in other languages or equation form are equally acceptable. Matlab is just a convenient prototyping tool for me, but the final algorithm will be in java.
Edit
From the comments and initial answers I want to add some clarifications and initial thoughts.
I am not seeking a 'truly random' solution from any standard distribution. I want a pseudo randomly generated sequence of values that satisfy the constraints given a parameter set.
The system I'm trying to approximate is a chain of N links of link length L where the end of the chain is D away from the other end in the direction of theta.
My initial insight here is that theta can be removed from consideration until the end, since (2) in essence adds theta to every element of a 0 mean vector V (shifting the mean to theta) and (4) simply removes that mean again. So, if you can find a solution for theta=0, the problem is solved for all theta.
As requested, here is a reasonable range of parameters (not hard constraints, but typical values):
5<N<200
3<D<150
L==1
0 < theta < 360

I would start by creating a "valid" vector. That should be possible - say calculate it for every entry to have the same value.
Once you got that vector I would apply some transformations to "shuffle" it. "Rejection sampling" is the keyword - if the shuffle would violate one of your rules you just don't do it.
As transformations I come up with:
switch two entries
modify the value of one entry and modify a second one to keep the 4th condition (Theoretically you could just shuffle two till the condition is fulfilled - but the chance that happens is quite low)
But maybe you can find some more.
Do this reasonable often and you get a "valid" random vector. Theoretically you should be able to get all valid vectors - practically you could try to construct several "start" vectors so it won't take that long.

Here's a way of doing it. It is clear that not all combinations of theta, N, L and D are valid. It is also clear that you're trying to simulate random objects that are quite complex. You will probably have a hard time showing anything useful with respect to these vectors.
The series you're trying to simulate seems similar to the Wiener process. So I started with that, you can start with anything that is random yet reasonable. I then use that as a starting point for an optimization that tries to satisfy 2,3 and 4. The closer your initial value to a valid vector (satisfying all your conditions) the better the convergence.
function series = generate_series(D, L, N,theta)
s(1) = theta;
for i=2:N,
s(i) = s(i-1) + randn(1,1);
end
f = #(x)objective(x,D,L,N,theta)
q = optimset('Display','iter','TolFun',1e-10,'MaxFunEvals',Inf,'MaxIter',Inf)
[sf,val] = fminunc(f,s,q);
val
series = sf;
function value= objective(s,D,L,N,theta)
a = abs(mean(s)-theta);
b = abs(D-sum(L*cos(s-theta)));
c = 0;
for i=2:N,
u =abs(s(i)-s(i-1)) ;
if u>10,
c = c + u;
end
end
value = a^2 + b^2+ c^2;
It seems like you're trying to simulate something very complex/strange (a path of a given curvature?), see questions by other commenters. Still you will have to use your domain knowledge to connect D and L with a reasonable mu and sigma for the Wiener to act as initialization.

So based on your new requirements, it seems like what you're actually looking for is an ordered list of random angles, with a maximum change in angle of 10 degrees (which I first convert to radians), such that the distance and direction from start to end and link length and number of links are specified?
Simulate an initial guess. It will not hold with the D and theta constraints (i.e. specified D and specified theta)
angles = zeros(N, 1)
for link = 2:N
angles (link) = theta(link - 1) + (rand() - 0.5)*(10*pi/180)
end
Use genetic algorithm (or another optimization) to adjust the angles based on the following cost function:
dx = sum(L*cos(angle));
dy = sum(L*sin(angle));
D = sqrt(dx^2 + dy^2);
theta = atan2(dy/dx);
the cost is now just the difference between the vector given by my D and theta above and the vector given by the specified D and theta (i.e. the inputs).
You will still have to enforce the max change of 10 degrees rule, perhaps that should just make the cost function enormous if it is violated? Perhaps there is a cleaner way to specify sequence constraints in optimization algorithms (I don't know how).
I feel like if you can find the right optimization with the right parameters this should be able to simulate your problem.

You don't give us a lot of detail to work with, so I'll assume the following:
random numbers are to be drawn from [-127+theta +127-theta]
all random numbers will be drawn from a uniform distribution
all random numbers will be of type int8
Then, for the first 3 requirements, you can use this:
N = 1e4;
theta = 40;
diffVal = 10;
g = #() randi([intmin('int8')+theta intmax('int8')-theta], 'int8') + theta;
V = [g(); zeros(N-1,1, 'int8')];
for ii = 2:N
V(ii) = g();
while abs(V(ii)-V(ii-1)) >= diffVal
V(ii) = g();
end
end
inline the anonymous function for more speed.
Now, the last requirement,
D == sum(L*cos(V-theta))
is a bit of a strange one...cos(V-theta) is a specific way to re-scale the data to the [-1 +1] interval, which the multiplication with L will then scale to [-L +L]. On first sight, you'd expect the sum to average out to 0.
However, the expected value of cos(x) when x is a random variable from a uniform distribution in [0 2*pi] is 2/pi (see here for example). Ignoring for the moment the fact that our limits are different from [0 2*pi], the expected value of sum(L*cos(V-theta)) would simply reduce to the constant value of 2*N*L/pi.
How you can force this to equal some other constant D is beyond me...can you perhaps elaborate on that a bit more?