I'm trying to create a power law (x3) contour plot in the code.
Please look at the following question and the accepted answer: (logarithmic vector :temp)
How to create nonlinear spaced vector in Matlab?
I want a power law vector for temp instead of logarithmic.
Many thanks
In general, you can choose your spacing based on any function. For instance, here y is a function of x. But x is not linearly spaced. Instead, it is a function of another variable, t, which is linearly spaced. x(t) defines the spacing:
t = 0:.02:2;
x = #(u) u.^3; % or any other function
y = #(u) sin(u); % or any other function
figure; plot(x(t), y(x(t)), '*b')
With this output:
Related
I would like to plot the roots of the cubic equation x^{3}+Ax^{2}+1=0 in matlab. I know that there are 3 real roots for A<-1.88 and 1 if A>-1.88. I would like to plot the 3 real roots as a function of A and when it switches to 1 real root and 2 complex to plot the real root and the real part of the complex conjugate solutions all in the same plot (perhaps as 2-3 graphs).
I am a matlab beginner though. I tried
syms x A
r = solve(x^3 + A*x^2+1 == 0, x);
ezplot(vpa(r(1)),[-10,10])
ezplot(vpa(r(2)),[-10,10])
ezplot(vpa(r(3)),[-10,10])
but vpa doesnt know how to numerically evaluate r.
There's no need to do symbolic math for this,
A = (-3:0.01:0)'; % create a vector of values for A
r = arrayfun(#(A)real(roots([1 A 0 1])),A,'uni',false); % calculate the polynomial roots for all values of A
r = [r{:}]; % convert result to a numeric array
plot(A,r'); % plot the result
grid on;
title('Real parts of Polynomial');
xlabel('A');
Suppose we have this Hamiltonian:
n = 10;
H = ones(n,n);
The density matrix is:
Ro = sym('r',[n,n]);%Density matrix
The equation of motion is:
H*Ro-Ro*H
The above equation of motion is the right hand side of the equation, the left hand side is the time derivative of density matrix.
How can I solve the equation of motion in Matlab without the symbolic math toolbox? I need to change the value of n. It can be up to 100.
In your dynamics function, reshape between vectors and matrices in order to use MATLAB's standard ode functions, which (to my knowledge) require vector inputs. Note, the symbolic toolbox isn't used anywhere in this solution. R can be any size n-by-n, within the constraints of your machine's memory.
function dR = dynfun(R,H)
%// R = n^2-by-1 vector
%// H = n-by-n matrix
n = sqrt(length(R));
R = reshape(R,[n,n]); %// reshape R to n-by-n matrix
dR = H*R-R*H;
dR = dR(:); %// reshape dR to n^2-by-1 vector
end
Call the ODE solver:
[tout,Rout] = ode45(#(t,R) dynfun(R,H), [0,T], R0(:));
where T is final time, R0 is n-by-n initial condition, tout are the output time steps, and Rout is the solution trajectory. Note due to the reshaping, Rout will be k-by-n^2, where k is the number of time steps. You'll need to reshape each row of Rout if you want to have the actual matrices over time.
I'm looking to create a function that takes an equation and marks the maxima and/or minima, and asymptotes on a graph.
From Calc 1, I remember using the Second Derivative Test.
I started by solving for the roots of the first derivative - but am not sure how I can plot where the point in this vector intersect my original equation.
syms x; %//
f = sin(x) %// Define equation as a function
df=diff(f) %// First derivatives
ddf=diff(df) %// Second Derivatives
I found the roots for the x-values of these points with dfRoots = solve(df)
and then created a vector of them called dfRoots_realDouble
dfRoots_double = double(dfRoots);
dfRoots_realDouble = real(dfRoots_double);
dfRoots_realDouble represent the x-values i need, but I dont know how to plot them as points and separate minima from maxima, etc
I'd like to be able to put in any function, like sin(6*(x^5) + 7*(x^3)+8*(x^2)) on [-1,1] and it highlight all the maxima with one marker, and all the minima with another.
If you sort the roots, you will have an alternating vector of maximums and minimums. Use the second derivative to determine if your vector of roots starts with a maximum or a minimum and then split the vector.
roots = sort([-3 4 2 -5]);
is_max = (subs(ddf, x, roots(1)) < 0)
if is_max
max_points = roots(1:2:end)
min_points = roots(2:2:end)
else
max_points = roots(2:2:end)
min_points = roots(1:2:end)
end
% plot with two different symbols
plot(max_points, subs(f, x, max_points), 'or',...
min_points, subs(f, x, min_points), '*k')
I want to write a bimodal Probability Density Function (PDF with multiple peaks, Galtung S) without using the pdf function from statistics toolbox. Here is my code:
x = 0:0.01:5;
d = [0.5;2.5];
a = [12;14]; % scale parameter
y = 2*a(1).*(x-d(1)).*exp(-a(1).*(x-d(1)).^2) + ...
2*a(2).*(x-d(2)).*exp(-a(2).*(x-d(2)).^2);
plot(x,y)
Here's the curve.
plot(x,y)
I would like to change the mathematical formula to to get rid of the dips in the curve that appear at approx. 0<x<.5 and 2<x<2.5.
Is there a way to implement x>d(1) and x>d(2) in line 4 of the code to avoid y < 0? I would not want to solve this with a loop because I need to convert the formula to CDF later on.
If you want to plot only for x>max(d1,d2), you can use logical indexing:
plot(x(x>max(d)),y(x>max(d)))
If you to plot for all x but plot max(y,0), you just can write so:
plot(x,max(y,0))
I'm trying to do a scatter plot with a line of best fit in matlab, I can get a scatter plot using either scatter(x1,x2) or scatterplot(x1,x2) but the basic fitting option is shadowed out and lsline returns the error 'No allowed line types found. Nothing done'
Any help would be great,
Thanks,
Jon.
lsline is only available in the Statistics Toolbox, do you have the statistics toolbox? A more general solution might be to use polyfit.
You need to use polyfit to fit a line to your data. Suppose you have some data in y and you have corresponding domain values in x, (ie you have data approximating y = f(x) for arbitrary f) then you can fit a linear curve as follows:
p = polyfit(x,y,1); % p returns 2 coefficients fitting r = a_1 * x + a_2
r = p(1) .* x + p(2); % compute a new vector r that has matching datapoints in x
% now plot both the points in y and the curve fit in r
plot(x, y, 'x');
hold on;
plot(x, r, '-');
hold off;
Note that if you want to fit an arbitrary polynomial to your data you can do so by changing the last parameter of polyfit to be the dimensionality of the curvefit. Suppose we call this dimension d, you'll receive back d+1 coefficients in p, which represent a polynomial conforming to an estimate of f(x):
f(x) = p(1) * x^d + p(2) * x^(d-1) + ... + p(d)*x + p(d+1)
Edit, as noted in a comment you can also use polyval to compute r, its syntax would like like this:
r = polyval(p, x);
Infs, NaNs, and imaginaryparts of complex numbers are ignored in the data.
Curve Fitting Tool provides a flexible graphical user interfacewhere you can interactively fit curves and surfaces to data and viewplots. You can:
Create, plot, and compare multiple fits
Use linear or nonlinear regression, interpolation,local smoothing regression, or custom equations
View goodness-of-fit statistics, display confidenceintervals and residuals, remove outliers and assess fits with validationdata
Automatically generate code for fitting and plottingsurfaces, or export fits to workspace for further analysis