I have a function with 2 symbolic variables which is very complicated and long. I want to have it plotted in a surface. The function looks like this:
y^(1/2)*x - y^(1/2)*(x - 1)*((40*y^2 + 60*y^(1/2) - 60*y^(3/2) - 10)/(90*y^(1/2)) + ...
Whenever I try to plot, I get: "Undefined function 'plotfunc3d' for input arguments of type 'sym'" or "Conversion to double from sym is not possible".
How can I plot a surface? Thanks.
As the error indicates, you're trying to plot a symbolic equation using functions designed for Matlab's default floating-point datatypes. Your question is terse and you didn't even indicate how you're trying to plot the function in question, so I'll just give suggestions.
You have two options. You can use a plot function designed for symbolic math or you can substitute in floating point values for all of your parameters and values. Here is a list of ez- plotting methods that can be used for symbolic equations.
Secondly, you can use the subs function to substitute in values, or vectors/matrices of values into a symbolic equation. You can also try using double if you end up with an equation that is stil symbolic but not in terms of any variables, e.g., double(sym('pi')).
I can't really be more specific because your question wasn't, but you can also try Googling "Matlab plot symbolic function" for more results.
Related
I am trying to plot symbolic variable in MATLAB, for which I have used the same strategy that is available in an answer to a similar question.
This is my code, which outputs a blank graph:
syms t w
x=exp(-t^2)
h=exp(-t)*heaviside(t)+exp(t)*heaviside(-t)
X=fourier(x,w);
H=fourier(h,w);
right=ifourier( rewrite(X*H, 'exp'),t)
fplot(right,[0 8])
How can I make the graph appear?
The problem is that MATLAB ifourier function cannot compute the inverse Fourier transform of the product X*H.
Check that X*H returns:
X*H
Rewriting the expression does not change it at all:
rewrite(X*H, 'exp')
Either way, when computing the inverse Fourier transform:
right=ifourier( X*H,t)
Documentation on the ifourier function states that:
If ifourier cannot transform the input, then it returns an unevaluated
call to fourier.
Since it cannot evaluate explicitly the function, it cannot plot it.
I have a problem in which I have to interpolate 4D data d = f(a, b, c) often, because the interpolation happens within an optimisation routine. Now, at first I programmed this using Matlab's interpn function. However, the program obviously became very slow, because the cubic splines had to be constructed upon each iteration within the optimisation.
I have read about 2D spline interpolation and I am basically looking for its 4D equivalent: pp = spline(a,b,c,d). Also, I found the scatteredInterpolant function (I have a non-uniform grid), but this function only gives me options for 'linear', 'nearest', or 'natural' and not the 'spline' option I'm looking for.
I could imagine that Matlab would have the function that is underneath the interpn function available, but I can't seem to find it. Does anyone know such a function that returns the piecewise polynomial or some other form of a spline function for a 4D interpolant, preferably Matlab-original?
P.s. I have also looked into a workaround; typing edit interpn, I have tried copying the Matlab function interpn, naming it differently and editing it such that it returns F instead of Vq, the interpolating function. However, doing this it says it doesn't recognise the methodandextrapval function, the first nested Matlab built-in it encounters.
im using Matlab to trying to solve 2 equations with 2 variables.
I define the 2 functions, f2(n_1,n_2),f3(n_1,n_2) which both depend on f1(n_1,n_2), then I defined the vectorised function G(n_1,n_2) which contain both of them.
Later I defined a the desired stating point, and tried to solve. but when running the code it raise an error which I'm not fully understand.
the above mentioned is displayed in the code below:
the code:
clear, close all; clc
%Const
N0=25;
G1=1;G2=1;
a1=6;a2=3;
k1=1;k2=4;
%main
syms n_1 n_2
X_0=[-5;5];
f1=N0-a1.*n_1-a2.*n_2;
f2=f1.*G1.*n_1-k1.*n_1;
f3=f1.*G2.*n_2-k2.*n_2;
G=#(n_1,n_2) [f2;f3];
s = fsolve(G,X_0);
the error:
Error using fsolve (line 269)
FSOLVE requires all values returned by functions to be of data type double.
Error in Ex1_Q3_DavidS (line 37)
s = fsolve(G,X_0);
thanks
fsolve is a function that uses numerical methods to find the root of a numerical function.
A numerical function is, for example f=#(x)x^2=2;. In MATLAB, you can evaluate f() at any number and it will return a number, but there is no higher order mathematical abstraction to it. This is however the fastest way to do maths in a computer, as it is not a higher intelligence, just a glorified calculator.
Some people however, want to give higher intelligence to computers and coded very complex symbolic toolboxes that with sets of rules try to teach computers to think semi-like humans and solve symbolic equations, as you do in paper. To solve those equations a function called solve is introduced in MATLAB.
You are doing symbolic math, but using the numeric solver. It does not work, just use the symbolic solver for symbolic math.
Using the code,
syms x(t)
y=x^2
diff(y,t)
diff(y,x)
I get the following error:
2*D(x)(t)*x(t)
Error using sym/diff (line 26)
All arguments, except for the first one, must not be symbolic functions.
Is there a way to tackle this? Thanks for your time.
I dont know much about the Symbolic Math Toolbox, but taking a derivative wrt to a function does not seem to be supported (at least in a direct fashion) for diff.
You can substitute a variable, compute a derivative, and substitute the function back. Like so:
syms z
subs(diff(subs(y,x,z),z),z,x)
ans(t) = 2*x(t)
I'm trying to write a generic function for finding the cosine of a value inputted into the function. The formula for cosine that I'm using is:
n
cosx = sum((-1)^n*x^(2n)/(2n)!)
n=1
I've looked at the matlab documentation and this page implies that the "sum" function should be able to do it so I tried to test it by entering:
sum(x^n, n=1..3)
but it just gives me "Error: The expression to the left of the equals sign is not a valid target for an assignment".
Is summing an infinite series something that matlab is able to do by default or do I have to simulate it using a function and loops?
Well if you want to approximate it to a finite number of terms you can do it in Matlab without toolboxes or loops:
sumCos = #(x, n)(sum(((-1).^(0:n)).*(x.^(2*(0:n)))./(factorial(2*(0:n)))));
and then use it like this
sumCos(pi, 30)
The first parameter is the angle, the second is the number of terms you want to take the series to (i.e. effects the precision). This is a numerical solution which I think is really what you're after.
btw I took the liberty of correcting your initial sum, surely n must start from 0 if you are trying to approximate cos
If you want to understand my formula (which surely you do) then you need to read up on some essential Matlab basics namely the colon operator and then the concept of using . to perform element-wise operations.
In MATLAB itself, no, you cannot solve an infinite sum. You would have to estimate it as you suggested. The page you were looking at is part of the Symbolic Math toolbox, which is an add-on to MATLAB. In particular, you were looking at MuPAD, which is rather similar to Mathematica. It is a symbolic math workspace, whereas MATLAB is more of a numeric math workspace. If you own the Symbolic Math toolbox, you can either use MuPAD as you tried to above, or you can use the symsum function from within MATLAB itself to carry out sums of series.