I have the following code for my matlab function that is supposed to take the lcm of multiple numbers. I have the following:
function y = lcm1(x)
n = length(x);
if n < 2
y = x;
elseif n == 2
y = lcm(x(1), x(2));
else
y = lcm(x(1), x(2));
for i = 3:n
y = lcm(x(i) ,y);
end
end
However it won't seem to run but I can't find the error if anyone can see this? I am aware that this is painfully simple.
Thanks for any help
It's nothing wrong with the function you have, although Luis' version is a slight improvement.
Follow the below instructions if you can't make it run:
Make sure the file has the same name as the function name, in this case lcm1. Note that the full path (if it's not too long) is shown in the top bar. It must end with ...\lcm1.m.
Make sure the folder you save it in is in the MATLAB path. In my case this folder is "C:\Users\Robert\Documents\MATLAB". You can find the current folder here:
Note that I have a few folders that are grey in the MATLAB folder, (graphViz4Matlab). MATLAB can't find any files / functions inside these folders. By double clicking you will make it the current folder, and by right clicking on it you get several options including adding it to the MATLAB path. You probably want to add it to the path, which should make it appear black.
When the above is done, writing lcm1(1:5) in the command window in MATLAB should result in (as you can see in the second screenshot above:
lcm1(1:5)
ans =
60
Your code seems to work fine.
A slightly neater approach is to use recursion:
function y = lcm1(x)
n = length(x);
if n < 2 %// 0 or 1 elements: nothing to do
y = x;
elseif n == 2 %// 2 elements: call lcm to do the actual work
y = lcm(x(1), x(2));
else %// combine first two numbers with lcm, then call lcm1 again
y = lcm1([lcm(x(1), x(2)) x(3:end)]);
end
Related
CODE DELETED
Hi, the code above is my (slightly modified) rooo.m file.
I'm just trying to plot the function by typing into (octave) terminal
x = 1:1:40;
plot(x, rooo(x), '+');
But this will only print the graph of y=1.
I believe it's because of the y = 1; in the first line (btw the function itself returns the right value, say when I type rooo(3)).
When I change it to some other number (say b), the graph will show y =b.
Does anyone have an idea why this is happening??
I think it's not working because if you type rooo(x) at the command line, it will return a scalar result of 1, instead of a vector. The 1 < n logical condition doesn't work as you intended to when n is a vector.
Here is a suggestion to make it work (maybe not the most elegant but it seems to work):
CODE DELETED
Which, when called as in your question, gives the following plot
The results seem to be different from the ones reported in MATLAB though.
An alternative, if you don't want to modify your function, is to change the way you call it:
>> x = 1:1:40;
>> y = ones(size(x));
>> for k=1:length(x)
y(k) = rooo(x(k));
end
>> plot(x,y,'+')
This gives the same result as the above suggestion.
It's not working because you never enter the while loop with x starting at 1. Since
1 < n == 1 < x is false at the very beginning, the function returns.
However when you call rooo(3) or actually rooo(Anything > 1) it does work. With x = 1.1:1:40 the plot looks like this ( I made it with Matlab) :
I'm working on chapter 8 of A Course in Mathematical Biology. The textbook uses Maple, but includes this link, Computer course of Chapter 8 in Matlab. I'm told to put the following in an m-file:
% defining a recursive function in an m-file
function y = plot_traj(a)
RM = inline('a*x.*exp(-x)', 'a', 'x')
% Note that we are using an inline function. Sometimes it’s easier to do this.
% collecting list of x-coordinates
for i = 1:31,
X(i) = i - 1
end
% collecting list of y-coordinates
for i = 1:30,
Y(i+1)=RM(a,iter(i));
iter(i+1) = Y(i+1);
end
y = plot(X, Y, '*');
Now, save your m-file (as plot traj.m) and close it. Type the following into the command window:
>> plot traj(0.8)
>> plot traj(1.0)
>> plot traj(5.0)
>> plot traj(8.0)
>> plot traj(13.0)
>> plot traj(14.5)
>> plot traj(20.0)
However, when I type plot traj(0.8) into the command window I get this:
>> plot_traj(0.8)
Undefined function or variable "iter".
Error in plot_traj (line 13)
Y(i)=RM(a,iter(i));
I don't see anything wrong with line 13, and I've made sure that my code is exactly what is in the chapter. I've been doing fine with the codes up until this point. I'd appreciate it if anyone could provide some assistance. Thank you.
The problem at line 13 is that the iter local variable array has not been defined. So on the first iteration, the code tries to access iter(1) and fails. I looked at the link you provided and they missed it too. Based on previous examples in the Matlab_Course.pdf (and figure 8.6), the iter array should be initialized as
iter(1) = 1.0;
Just add this line prior to the for loop and you should be good to continue. I suspect also that this line should be added too (again based on the document)
Y(1)=iter(1);
to make sure that both iter and Y have the same length.
Note that it is a good habit to pre-allocate memory to arrays to avoid the internal resizing of matrices/arrays on each iteration of the loop (which can have a negative impact on performance). For this loop
for i = 1:30,
Y(i+1)=RM(a,iter(i));
iter(i+1) = Y(i+1);
end
you can observe that i iterates over 1 through 30, and we always populate Y(i+1) and iter(i+1). So both Y and iter are 31x1 vectors. We can allocate memory to each prior to entering the for loop as
iter = zeros(31,1);
Y = zeros(31,1);
iter(1) = 1;
Y(1) = iter(1);
The same should be done for X as well.
I wrote some code that works just fine to evaluate theta on its own with some test input. However, I would like to take this code and turn it into a function that I can call within another matlab file. I keep getting the error message, "Function definitions are not permitted in this context."
I want to be able to define four vectors in another matlab file and call SP1 to evaluate theta for those inputs. I'm not sure where I'm going wrong, though. Please help!
Thanks so much.
clc
clear all
function theta = SP1(p,q1,w1,r)
% INPUT:
%function theta = SP1(p,q1,w1,r)
% p = [5; -7; 12];
% q1 = [17.3037; -3.1128; 2.48175];
% w1 = [1/sqrt(8); sqrt(3/8); 1/sqrt(2)];
% r = [1; 2; -3];
% Define vectors u and v as well as u' and v'.
u = p - r;
v = q1 - r;
w1_t = transpose(w1);
u_prime = u - w1 * w1_t * u;
v_prime = v - w1 * w1_t * v;
% Calculate theta if conditions are met for a solution to exist.
if (abs(norm(u_prime)-norm(v_prime))<0.01) & (abs((w1_t * u)-(w1_t * v))<0.01)
X = w1_t*cross(u_prime,v_prime);
Y = dot(u_prime,v_prime);
theta = atan2(X,Y)
else if (norm(u_prime) == 0 | norm(v_prime) == 0)
disp('Infinite Number of Solutions')
else
disp('Conditions not satisfied to find a solution')
end
end
I think you can just remove the top two lines,
clc
clear all
and save the rest of the code starting with function as SP1.m file.
Then you should be able to call this function as SP1 from other m files.
I think you're confused about how functions work. The first line of a function definition defines how many inputs and outputs MATLAB expects:
function theta = SP1(p,q1,w1,r)
This means that calling a function SP1 will require you to give four inputs, and will return one output. It doesn't mean that:
Your inputs need to be named p, q1 and so on
Your output will be called theta automatically
The function will automatically take in the input variables p, q1, etc if they exist in the workspace.
It also doesn't do any checking on the inputs; so if you require that inputs be of a certain type, size, etc. you need to write your own error checking at the start of the file. You might intend that those inputs be 3x1 vectors, but there's nothing in the function to tell MATLAB that. So, SP1(1,2,3,4) will work, to some extent - it will take those inputs and try to run them through the function, and if they don't cause an error it will give you an output. The output might be wrong, but the computer doesn't know that.
Once you have a function you can call it multiple ways from the command line or from within other functions or scripts. As previously mentioned you don't have to stick to the naming of variables within the function, as long as input variables exist when the function is called MATLAB will accept them:
theta = SP1(p8,q27,w35,not_r);
myoutput = SP1(any,variable,I,like);
I don't necessarily have to give an output (but then the first output will be routed to ans)
SP1(this,will,also,work);
If I have some variables stored in a *.mat file (the case you seem to be asking about), I can do it like this:
load('mydata.mat'); %this file contains stored variables p, q1, w1 and r
theta = SP1(p,q1,w1,r);
I am new to Matlab and I have to use fixed point iteration to find the x value for the intersection between y = x and y = sqrt(10/x+4), which after graphing it, looks to be around 1.4. I'm using an initial guess of x1 = 0. This is my current Matlab code:
f = #(x)sqrt(10./(x+4));
x1 = 0;
xArray(10) = [];
for i = 1:10
x2 = f(x1);
xArray(i) = x2;
x1 = x1 + 1;
end
plot(xArray);
fprintf('%15.8e\n',xArray);
Now when I run this it seems like my x is approaching 0.8. Can anyone tell me what I am doing wrong?
Well done. You've made a decent start at this.
Lets look at the graphical solution. BTW, this is how I'd have done the graphical part:
ezplot(#(x) x,[-1 3])
hold on
ezplot(#(x) sqrt(10./(x+4)),[-1 3])
grid on
Or, I might subtract the two functions, then looking for a zero of the difference, so where it crosses the x axis.
This is what the fixed point iteration does anyway, trying to solve for x, such that
x = sqrt(10/(x+4))
So how would I change your code to fix it? First of all, I'd want to use more descriptive names for the variables. You don't get charged by the character, and making your code easier to read & follow will pay off greatly in the future for you.
There were a couple of code issues. To initialize a vector, use a form like one of these:
xArray = zeros(1,10);
xArray(1,10) = 0;
Note that if xArray was ALREADY defined because you have been working on this problem, the latter form will only zero out that single element. So the first form is best by a large margin. It affirmatively creates an array, or overwrites an existing array if it is already present in your workspace.
Finally, I like to initialize an array like this with something special, rather than zero, so we can see when an element was overwritten. NaNs are good for this.
Next, there was no need to add one to x1 in your code. Again, I'd strongly suggest using better variable names. It is also a good idea to use comments. Be liberal.
I'd suggest the idea of a convergence tolerance. You can also have an iteration counter.
f = #(x)sqrt(10./(x+4));
% starting value
xcurrent = 0;
% count the iterations, setting a maximum in maxiter, here 25
iter = 0;
maxiter = 25;
% initialize the array to store our iterations
xArray = NaN(1,maxiter);
% convergence tolerance
xtol = 1e-8;
% before we start, the error is set to be BIG. this
% just lets our while loop get through that first iteration
xerr = inf;
% the while will stop if either criterion fails
while (iter < maxiter) && (xerr > xtol)
iter = iter + 1;
xnew = f(xcurrent);
% save each iteration
xArray(iter) = xnew;
% compute the difference between successive iterations
xerr = abs(xnew - xcurrent);
xcurrent = xnew;
end
% retain only the elements of xArray that we actually generated
xArray = xArray(1:iter);
plot(xArray);
fprintf('%15.8e\n',xArray);
What was the result?
1.58113883e+00
1.33856229e+00
1.36863563e+00
1.36479692e+00
1.36528512e+00
1.36522300e+00
1.36523091e+00
1.36522990e+00
1.36523003e+00
1.36523001e+00
1.36523001e+00
For a little more accuracy to see how well we did...
format long g
xcurrent
xcurrent =
1.36523001364783
f(xcurrent)
ans =
1.36523001338436
By the way, it is a good idea to know why the loop terminated. Did it stop for insufficient iterations?
The point of my response here was NOT to do your homework, since you were close to getting it right anyway. The point is to show some considerations on how you might improve your code for future work.
There is no need to add 1 to x1. your output from each iteration is input for next iteration. So, x2 from output of f(x1) should be the new x1. The corrected code would be
for i = 1:10
x2 = f(x1);
xArray(i) = x2;
x1 = x2;
end
f(x)x^3+4*x^2-10 in [1,2] find an approximate root
I’m currently a Physics student and for several weeks have been compiling data related to ‘Quantum Entanglement’. I’ve now got to a point where I have to plot my data (which should resemble a cos² graph - and does) to a sort of “best fit” cos² graph. The lab script says the following:
A more precise determination of the visibility V (this is basically how 'clean' the data is) follows from the best fit to the measured data using the function:
f(b) = A/2[1-Vsin(b-b(center)/P)]
Granted this probably doesn’t mean much out of context, but essentially A is the amplitude, b is an angle and P is the periodicity. Hence this is also a “wave” like the experimental data I have found.
From this I understand, as previously mentioned, I am making a “best fit” curve. However, I have been told that this isn’t possible with Excel and that the best approach is Matlab.
I know intermediate JavaScript but do not know Matlab and was hoping for some direction.
Is there a tutorial I can read for this? Is it possible for someone to go through it with me? I really have no idea what it entails, so any feed back would be greatly appreciated.
Thanks a lot!
Initial steps
I guess we should begin by getting a representation in Matlab of the function that you're trying to model. A direct translation of your formula looks like this:
function y = targetfunction(A,V,P,bc,b)
y = (A/2) * (1 - V * sin((b-bc) / P));
end
Getting hold of the data
My next step is going to be to generate some data to work with (you'll use your own data, naturally). So here's a function that generates some noisy data. Notice that I've supplied some values for the parameters.
function [y b] = generateData(npoints,noise)
A = 2;
V = 1;
P = 0.7;
bc = 0;
b = 2 * pi * rand(npoints,1);
y = targetfunction(A,V,P,bc,b) + noise * randn(npoints,1);
end
The function rand generates random points on the interval [0,1], and I multiplied those by 2*pi to get points randomly on the interval [0, 2*pi]. I then applied the target function at those points, and added a bit of noise (the function randn generates normally distributed random variables).
Fitting parameters
The most complicated function is the one that fits a model to your data. For this I use the function fminunc, which does unconstrained minimization. The routine looks like this:
function [A V P bc] = bestfit(y,b)
x0(1) = 1; %# A
x0(2) = 1; %# V
x0(3) = 0.5; %# P
x0(4) = 0; %# bc
f = #(x) norm(y - targetfunction(x(1),x(2),x(3),x(4),b));
x = fminunc(f,x0);
A = x(1);
V = x(2);
P = x(3);
bc = x(4);
end
Let's go through line by line. First, I define the function f that I want to minimize. This isn't too hard. To minimize a function in Matlab, it needs to take a single vector as a parameter. Therefore we have to pack our four parameters into a vector, which I do in the first four lines. I used values that are close, but not the same, as the ones that I used to generate the data.
Then I define the function I want to minimize. It takes a single argument x, which it unpacks and feeds to the targetfunction, along with the points b in our dataset. Hopefully these are close to y. We measure how far they are from y by subtracting from y and applying the function norm, which squares every component, adds them up and takes the square root (i.e. it computes the root mean square error).
Then I call fminunc with our function to be minimized, and the initial guess for the parameters. This uses an internal routine to find the closest match for each of the parameters, and returns them in the vector x.
Finally, I unpack the parameters from the vector x.
Putting it all together
We now have all the components we need, so we just want one final function to tie them together. Here it is:
function master
%# Generate some data (you should read in your own data here)
[f b] = generateData(1000,1);
%# Find the best fitting parameters
[A V P bc] = bestfit(f,b);
%# Print them to the screen
fprintf('A = %f\n',A)
fprintf('V = %f\n',V)
fprintf('P = %f\n',P)
fprintf('bc = %f\n',bc)
%# Make plots of the data and the function we have fitted
plot(b,f,'.');
hold on
plot(sort(b),targetfunction(A,V,P,bc,sort(b)),'r','LineWidth',2)
end
If I run this function, I see this being printed to the screen:
>> master
Local minimum found.
Optimization completed because the size of the gradient is less than
the default value of the function tolerance.
A = 1.991727
V = 0.979819
P = 0.695265
bc = 0.067431
And the following plot appears:
That fit looks good enough to me. Let me know if you have any questions about anything I've done here.
I am a bit surprised as you mention f(a) and your function does not contain an a, but in general, suppose you want to plot f(x) = cos(x)^2
First determine for which values of x you want to make a plot, for example
xmin = 0;
stepsize = 1/100;
xmax = 6.5;
x = xmin:stepsize:xmax;
y = cos(x).^2;
plot(x,y)
However, note that this approach works just as well in excel, you just have to do some work to get your x values and function in the right cells.