I'm trying to plot the following:
syms f_ih n
bi = (1-f_ih)/2
where f_ih is constrained by: 0 ≤ f_ih ≤ (n-1)/n. I'd like to show bi as a surface plot with independent variables n and f_ih, but ezsurf doesn't allow for variable bounds. How can I do this?
The command I'd love to run would simply be ezsurf(bi,[0,(n-1)/n]), but it's not that simple.
Thanks!
There's a good reason for requiring the domain to be numeric as opposed to symbolic: the function has to be evaluated in order to obtain actual numbers that can be plotted. It makes no sense to plot something that is purely symbolic like your equations (in Matlab or on paper) unless you specify n. Some functions may be scale invariant (not quite the right term mathematically), meaning they look the same when evaluated/plotted on different domains, but Matlab has no way of knowing. Choose a value of n that results in a plot that looks how want. Then, if you like, you can remove the numbers from the axes afterwards and label them as if it were for arbitrary n even though it's not.
Related
I have a problem detecting outliers in a set of data. Let's say I have two arrays x and y, and y is a quadratic function of x. Some of the values of y do not follow this function. How can I detect them?
I tried the rmoutliers function, but it doesn't seem to solve this problem since it only deals with normally distributed data.
Basically, I am trying to study some material behavior. The behavior is represented by y. I use an optimization method to get the different values of y as a function of x. Because sometimes the optimization doesn't yield accurate results, I get outliers.The relationship I am expecting should follow some nearly quadratic function, but the coefficients of this function are variable based one the provided set of data, so I can't use a certain function of x and use it to detect the outliers in the array of y values.
I am trying trying to graph the polynomial fit of a 2D dataset in Matlab.
This is what I tried:
rawTable = readtable('Test_data.xlsx','Sheet','Sheet1');
x = rawTable.A;
y = rawTable.B;
figure(1)
scatter(x,y)
c = polyfit(x,y,2);
y_fitted = polyval(c,x);
hold on
plot(x,y_fitted,'r','LineWidth',2)
rawTable.A and rawTable.A are randomly generated numbers. (i.e. the x dataset cannot be represented in the following form : x=0:0.1:100)
The result:
second-order polynomial
But the result I expect looks like this (generated in Excel):
enter image description here
How can I graph the second-order polynomial fit in MATLAB?
I sense some confusion regarding what the output of each of those Matlab function mean. So I'll clarify. And I think we need some details as well. So expect some verbosity. A quick answer, however, is available at the end.
c = polyfit(x,y,2) gives the coefficient vectors of the polynomial fit. You can get the fit information such as error estimate following the documentation.
Name this polynomial as P. P in Matlab is actually the function P=#(x)c(1)*x.^2+c(2)*x+c(3).
Suppose you have a single point X, then polyval(c,X) outputs the value of P(X). And if x is a vector, polyval(c,x) is a vector corresponding to [P(x(1)), P(x(2)),...].
Now that does not represent what the fit is. Just as a quick hack to see something visually, you can try plot(sort(x),polyval(c,sort(x)),'r','LineWidth',2), ie. you can first sort your data and try plotting on those x-values.
However, it is only a hack because a) your data set may be so irregularly spaced that the spline doesn't represent function or b) evaluating on the whole of your data set is unnecessary and inefficient.
The robust and 'standard' way to plot a 2D function of known analytical form in Matlab is as follows:
Define some evenly-spaced x-values over the interval you want to plot the function. For example, x=1:0.1:10. For example, x=linspace(0,1,100).
Evaluate the function on these x-values
Put the above two components into plot(). plot() can either plot the function as sampled points, or connect the points with automatic spline, which is the default.
(For step 1, quadrature is ambiguous but specific enough of a term to describe this process if you wish to communicate with a single word.)
So, instead of using the x in your original data set, you should do something like:
t=linspace(min(x),max(x),100);
plot(t,polyval(c,t),'r','LineWidth',2)
I have a 2D 2401*266 matrix K which corresponds to x values (t: stored in a 1*266 array) and y values(z: stored in a 1*2401 array).
I want to extrapolate the matrix K to predict some future values (corresponding to t(1,267:279). So far I have extended t so that it is now a 1*279 matrix using a for loop:
for tq = 267:279
t(1,tq) = t(1,tq-1)+0.0333333333;
end
However I am stumped on how to extrapolate K without fitting a polynomial to each individual row?
I feel like there must be a more efficient way than this??
There are countless of extrapolation methods in the literature, "fitting a polynomial to each row" would be just one of them, not necessarily invalid, not sure why you mention that you do no wan't to do it. For 2D data perhaps fitting a surface would lead to better results though.
However, if you want an easy, simple way (that might or might not work with your problem), you can always use the function interp2, for interpolation. If you chose spline or makima as interpolation functions, it will also extrapolate for any query point outside the domain of K.
Here is the given system I want to plot and obtain the vector field and the angles they make with the x axis. I want to find the index of a closed curve.
I know how to do this theoretically by choosing convenient points and see how the vector looks like at that point. Also I can always use
to compute the angles. However I am having trouble trying to code it. Please don't mark me down if the question is unclear. I am asking it the way I understand it. I am new to matlab. Can someone point me in the right direction please?
This is a pretty hard challenge for someone new to matlab, I would recommend taking on some smaller challenges first to get you used to matlab's conventions.
That said, Matlab is all about numerical solutions so, unless you want to go down the symbolic maths route (and in that case I would probably opt for Mathematica instead), your first task is to decide on the limits and granularity of your simulated space, then define them so you can apply your system of equations to it.
There are lots of ways of doing this - some more efficient - but for ease of understanding I propose this:
Define the axes individually first
xpts = -10:0.1:10;
ypts = -10:0.1:10;
tpts = 0:0.01:10;
The a:b:c syntax gives you the lower limit (a), the upper limit (c) and the spacing (b), so you'll get 201 points for the x. You could use the linspace notation if that suits you better, look it up by typing doc linspace into the matlab console.
Now you can create a grid of your coordinate points. You actually end up with three 3d matrices, one holding the x-coords of your space and the others holding the y and t. They look redundant, but it's worth it because you can use matrix operations on them.
[XX, YY, TT] = meshgrid(xpts, ypts, tpts);
From here on you can perform whatever operations you like on those matrices. So to compute x^2.y you could do
x2y = XX.^2 .* YY;
remembering that you'll get a 3d matrix out of it and all the slices in the third dimension (corresponding to t) will be the same.
Some notes
Matlab has a good builtin help system. You can type 'help functionname' to get a quick reminder in the console or 'doc functionname' to open the help browser for details and examples. They really are very good, they'll help enormously.
I used XX and YY because that's just my preference, but I avoid single-letter variable names as a general rule. You don't have to.
Matrix multiplication is the default so if you try to do XX*YY you won't get the answer you expect! To do element-wise multiplication use the .* operator instead. This will do a11 = b11*c11, a12 = b12*c12, ...
To raise each element of the matrix to a given power use .^rather than ^ for similar reasons. Likewise division.
You have to make sure your matrices are the correct size for your operations. To do elementwise operations on matrices they have to be the same size. To do matrix operations they have to follow the matrix rules on sizing, as will the output. You will find the size() function handy for debugging.
Plotting vector fields can be done with quiver. To plot the components separately you have more options: surf, contour and others. Look up the help docs and they will link to similar types. The plot family are mainly about lines so they aren't much help for fields without creative use of the markers, colours and alpha.
To plot the curve, or any other contour, you don't have to test the values of a matrix - it won't work well anyway because of the granularity - you can use the contour plot with specific contour values.
Solving systems of dynamic equations is completely possible, but you will be doing a numeric simulation and your results will again be subject to the granularity of your grid. If you have closed form solutions, like your phi expression, they may be easier to work with conceptually but harder to get working in matlab.
This kind of problem is tractable in matlab but it involves some non-basic uses which are pretty hard to follow until you've got your head round Matlab's syntax. I would advise to start with a 2d grid instead
[XX, YY] = meshgrid(xpts, ypts);
and compute some functions of that like x^2.y or x^2 - y^2. Get used to plotting them using quiver or plotting the coordinates separately in intensity maps or surfaces.
If I have an RC circuit with transfer function 1/(1+sRC) how do I draw the transfer function using MATLAB?
Num2=[1];
Den2=[R*C 1];
RCcirc=tf(Num2,Den2);
How do I declare the R and the C so that there are no errors?
tf is the wrong tool for plotting the transfer function. Try these instead:
Use linspace to generate a range of values for s. Give R and C reasonable values of your choice.
Read up on arithmetic operations in MATLAB, especially ./
Look at how to use plot and familiarize yourself with the command using some simple examples from the docs.
With these you should be able to plot the transfer function in MATLAB :)
First of all you need to understand what transfer function you want. Without defined values of R and C you won't get any transfer function. Compare it to this, you want to plot a sine wave: x = sin(w*t), I hope you can agree with me that you cannot plot such a function (including axes) unless I specifically say e.g. t is the time, ranging from 0 seconds to 10 seconds and w is a pulsation of 1 rad/s. It's exactly the same with your RC network: without any values, it is impossible for numerical software such as MATLAB to come up with a plot.
If you fill in those values, you can use th tf function to display the transfer function in whatever way you like (e.g. a bode plot).
On the other hand, if you just want the expression 1/(1+s*R*C), take a look at the symbolic toolbox, you can do such things there. But to make a plot, you will still have to fill in the R and C value (and even a value for your Laplace variable in this case).