Sympy/Matlab Plot y=mx, without any numerical value of m - matlab

I need to plot y = m*x where x ranges from, say 0 to 10. But m is a symbolic constant here, I dont want to supply a specific value.
Here's what my desired graph looks like (similar to how a class teacher would draw this):
[Consider m=a]
Sympy:
Tried doing this:
sympy.plot(m*x,(x,0,10))
but this shows the following error:
ValueError: The same variable should be used in all univariate expressions being plotted.
I cant really understand the error message, bit I am guessing it cant plot m as a (symbolic) constant in this case. Is it so? And in general, how can I do this?
Matlab:
Soon, I wanted to know if this is a limitation of sympy only, and thought maybe popular ones like matlab can do it? But with a bit of search on docs and SO, I couldnt find any. Both plot and fplot doesnt seem to cover this, they expect numerical values.
Others:
I am not acquainted with other plotting or CAS softwares, but it will be interesting to know if they support this out of the box
So, to repeat the main question, how to draw similar graphs, preferably without managing the plotting code yourself ?
The solution must be generic enough like plot to be applied to other equations.
[ The question was heavily edited from a sympy-specific question ]

Only for some functions with specific conditions you can plot thus in Maple. In Python (using matplotlib, sympy or any other packages) or Matlab you need to create code to manage that (assuming values and then replace ticks with literal ticks).

Related

Paraview - simple no-frills vector field plot from analytical formula

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U(x,y) = x^2 + 2y & V(x,y) = sin(x) + 1/y respectively,
then how would I plot it in Paraview on, for instance, the unit square? I'm trying to make a LIC plot similar to this: https://www.paraview.org/Wiki/File:Lic-b-427-hr-crop_small.png
I have researched Paraview extensively but can only find tutorials for graphing numerical data generated in some other complicated piece of software using a file format that I can neither understand nor find any examples of which to follow.
Also, an important clarification: I understand that in any case I must "translate" the math into a numerical data set in order to implement it into any software.
The thing is, I cannot find a simple, general procedure to graph a vector field from an equation in Paraview. There seems to only be specialized knowledge about everyone's particular situations (which are far, far more complex than mine), but few, if any, high-level instructions about how to import two scalar fields with no frills.

Extracting different values of a function vs time using MATLAB curve fitting

I feel like this should be something simple to solve - but I'm struggling to find the answer anywhere.
I have a set of 'R' values and a set of time values, I want to use curve fitting (I haven't used this part of the software before) to calculate the 'R' values at a different set of time values, literally just be able to access what is displayed in a figure created using curve fitting using a different set of time values (ie I can point the curser to the values I want on a figure and write them down but this is not efficient at all for the number of time values I have). Context is an orbital motion radius vs time.
Thanks in advance :)
You can use Matlab's fit function to do this very easily. Assuming you have your data in arrays r and t, you can do something like this:
f = fit(t, r, 'smoothingspline')
disp(f(5))
If you consult the documentation, you can see the various fit types available. (See https://www.mathworks.com/help/curvefit/fit.html)

Matlab: Fit a custom function to xy-data with given x-y errors

I have been looking for a Matlab function that can do a nonlinear total least square fit, basically fit a custom function to data which has errors in all dimensions. The easiest case being x and y data-points with different given standard deviations in x and y, for every single point. This is a very common scenario in all natural sciences and just because most people only know how to do a least square fit with errors in y does not mean it wouldn't be extremely useful. I know the problem is far more complicated than a simple y-error, this is probably why most (not even physicists like myself) learned how to properly do this with multidimensional errors.
I would expect that a software like matlab could do it but unless I'm bad at reading the otherwise mostly useful help pages I think even a 'full' Matlab license doesn't provide such fitting functionality. Other tools like Origin, Igor, Scipy use the freely available fortran package "ODRPACK95", for instance. There are few contributions about total least square or deming fits on the file exchange, but they're for linear fits only, which is of little use to me.
I'd be happy for any hint that can help me out
kind regards
First I should point out that I haven't practiced MATLAB much since I graduated last year (also as a Physicist). That being said, I remember using
lsqcurvefit()
in MATLAB to perform non-linear curve fits. Now, this may, or may not work depending on what you mean by custom function? I'm assuming you want to fit some known expression similar to one of these,
y = A*sin(x)+B
y = A*e^(B*x) + C
It is extremely difficult to perform a fit without knowning the form, e.g. as above. Ultimately, all mathematical functions can be approximated by polynomials for small enough intervals. This is something you might want to consider, as MATLAB does have lots of tools for doing polynomial regression.
In the end, I would acutally reccomend you to write your own fit-function. There are tons of examples for this online. The idea is to know the true solution's form as above, and guess on the parameters, A,B,C.... Create an error- (or cost-) function, which produces an quantitative error (deviation) between your data and the guessed solution. The problem is then reduced to minimizing the error, for which MATLAB has lots of built-in functionality.

Is there any way of annotating multiple plots using arrows with code in MATLAB?

When doing multiple plots on the same figure in MATLAB, is there any way of annotating them such that the legend entries have arrows pointing to the plots that they're named for?
Here's an example of what I have in mind. I'd like to do this using code.
Note that the MATLAB website mentions a way to do this using the annotation function. The problem with that function is that it takes x and y values (normalized for the plot) and puts the text there. Given that I am not certain where the datapoints will lie, this is unhelpful for what I want to do.
I don't mind if the text shows up at a random place, actually. What's important is to have an arrow or some way of pointing to the plot that it is referencing.
Take a look at the following Math works file exchange post:
http://www.mathworks.co.uk/matlabcentral/fileexchange/10656-data-space-to-figure-units-conversion
The code given here allows you to convert between data-space units and normalised figure units. The example given in the post seems to be doing almost exactly what you are asking.

Functional form of 2D interpolation in Matlab

I need to construct an interpolating function from a 2D array of data. The reason I need something that returns an actual function is, that I need to be able to evaluate the function as part of an expression that I need to numerically integrate.
For that reason, "interp2" doesn't cut it: it does not return a function.
I could use "TriScatteredInterp", but that's heavy-weight: my grid is equally spaced (and big); so I don't need the delaunay triangularisation.
Are there any alternatives?
(Apologies for the 'late' answer, but I have some suggestions that might help others if the existing answer doesn't help them)
It's not clear from your question how accurate the resulting function needs to be (or how big, 'big' is), but one approach that you could adopt is to regress the data points that you have using a least-squares or Kalman filter-based method. You'd need to do this with a number of candidate function forms and then choose the one that is 'best', for example by using an measure such as MAE or MSE.
Of course this requires some idea of what the form underlying function could be, but your question isn't clear as to whether you have this kind of information.
Another approach that could work (and requires no knowledge of what the underlying function might be) is the use of the fuzzy transform (F-transform) to generate line segments that provide local approximations to the surface.
The method for this would be:
Define a 2D universe that includes the x and y domains of your input data
Create a 2D fuzzy partition of this universe - chosing partition sizes that give the accuracy you require
Apply the discrete F-transform using your input data to generate fuzzy data points in a 3D fuzzy space
Pass the inverse F-transform as a function handle (along with the fuzzy data points) to your integration function
If you're not familiar with the F-transform then I posted a blog a while ago about how the F-transform can be used as a universal approximator in a 1D case: http://iainism-blogism.blogspot.co.uk/2012/01/fuzzy-wuzzy-was.html
To see the mathematics behind the method and extend it to a multidimensional case then the University of Ostravia has published a PhD thesis that explains its application to various engineering problems and also provides an example of how it is constructed for the case of a 2D universe: http://irafm.osu.cz/f/PhD_theses/Stepnicka.pdf
If you want a function handle, why not define f=#(xi,yi)interp2(X,Y,Z,xi,yi) ?
It might be a little slow, but I think it should work.
If I understand you correctly, you want to perform a surface/line integral of 2-D data. There are ways to do it but maybe not the way you want it. I had the exact same problem and it's annoying! The only way I solved it was using the Surface Fitting Tool (sftool) to create a surface then integrating it.
After you create your fit using the tool (it has a GUI as well), it will generate an sftool object which you can then integrate in (2-D) using quad2d
I also tried your method of using interp2 and got the results (which were similar to the sfobject) but I had no idea how to do a numerical integration (line/surface) with the data. Creating thesfobject and then integrating it was much faster.
It was the first time I do something like this so I confirmed it using a numerically evaluated line integral. According to Stoke's theorem, the surface integral and the line integral should be the same and it did turn out to be the same.
I asked this question in the mathematics stackexchange, wanted to do a line integral of 2-d data, ended up doing a surface integral and then confirming the answer using a line integral!