I think this line https://github.com/chebfun/examples/blob/master/sphere/SolidHarmonics.m#L112 was supposed to be the definition of alm. Also, blm has an n, presumably supposed to be l.

Also, the stated complexity https://github.com/chebfun/examples/blob/master/sphere/SolidHarmonics.m#L89, O(l log l), of constructing a regular solid harmonic Rlm as a ballfun should be O(l^2) as determined by the loop https://github.com/chebfun/chebfun/blob/master/%40ballfun/solharm.m#L112 over the O(l) evaluation points https://github.com/chebfun/chebfun/blob/master/%40ballfun/solharm.m#L89, dominating over the additional cost of the FFT.

Actually, this is one application where the algorithm sketched out in chebfun/chebfun#2320 is not only more accurate, being backward stable, but also carries a lower complexity since it would cost only O(lm + l log^2 l): the first part comes from the nested loop of Givens rotations and the second part from the cost of Chebfun's fast polynomial transforms, such as leg2cheb. When m = o(l), this approach should be faster for you.

Alex, would you take a look at this example? It runs, but no longer gives output that matches the text. Hrothgar, this isn't ready for the new web site until Alex gives the all-clear.

Looking at http://chebfun.github.io/examples/ode-eig/SolarQDA.html, I found a couple of issues:

1. Poor Schrödinger is missing the ö from his name again. Is there some encoding issue going on?
2. The math at the start of the example is not on the nice new MathJax format, rather, it is ascii based. There are other mathematical quantities that appear in the example that have not had the MathJax treatment either.

The intent of the ode/PiecewiseDemo example is to give the user a peak at what's going on under the "cheb-hood". As v5 is an entirely new model, this example needs to be re-written to illustrate the v5 "cheb-hood" features.

The plots in roots/WhiteCurves and ode/FourBugs require some tweaks to axis limits to make them look right.

Looking at the ODE-EIG examples, I found many of them had very illegible legends. In particular, http://chebfun.github.io/examples/ode-eig/WaveDecay.html , looks bad, and there are some other around.

As a quick fix, I'd suggest the sizes of the plots to be increased, or at least the font size.

More generally, I don't think that the font shown on the plots in the examples is the most beautiful one. It is easy to get nice looking fonts on Matlab plots via adding (..., 'interpreter', 'latex') to the title() and x/ylabel() commands, and it can be done for legends as well, although a big more involved,

hl = legend('My line')
hl = set(hl, 'interpreter', 'latex')

To keep tickets focused, I didn't want to include this in the previous issue.

Another thing that strikes me when going through the examples is that the font has started to look very nicely for text and math equations, however, the plots leave something to be desired. In particular, their not scalable, which would be a nice feature to have, so that one could zoom into them while keeping the resolution.

A way for dealing with this might be to use the FileExchange package found at http://www.mathworks.co.uk/matlabcentral/fileexchange/7401-scalable-vector-graphics--svg--export-of-figures .

There's a problem related to inpolygon that keeps opt/ConstrainedOptimization from running. @ajt60gaibb , can you check it out? Thanks.

@kuanxu , would you figure out what's wrong with Example complex/ConformalSquare please? The problem appears related to singfun. If there's something I need to know, please teach me. Thanks.

Currenlty, to generate figures for the Examples and Guide, ı am using a command like

export_fig('-painters', '-transparent', figureName)

where export_fig is the popular function from File Exchange (also now on Github!). Most of the figures look great this way, but surface plots are rendered with a strange texture. For example, here’s a figure from Chapter 12 of the Guide:

I would like to reference an Example in a paper, but the URLs are not stable enough for this. (For example, which recently split ode into ode-linear and ode-nonlinear.)

Does anyone have any suggestions as to how we could improve this? Presumably it's something we would like people to do?

I notice in some examples (e.g. http://chebfun.github.io/examples/ode/Carrier.html), that we specify the linewidth to be 1.6. Does this actually have any effect? To my eyes, the lines below prove that's not the case:

>> subplot(1,3,1), plot(sin(4*pi*x),'linewidth', 1), title('LW = 1')
>> subplot(1,3,2), plot(sin(4*pi*x),'linewidth', 1.6), title('LW = 1.6')
>> subplot(1,3,3), plot(sin(4*pi*x),'linewidth', 2), title('LW = 2'), shg

I'm attaching the output with this issue. I suggest that we move from 1.6 to 2.

The ode/ChebfunAD example fails when doing:

x = chebfun('x');
u = sin(x);
ujac = u.jacobian

The .jacobian field does not appear to be supported in v5. I believe there is a different way to do this in v5 after a brief discussion with @asgeirbirkis.

I'm not sure if this is a Chebfun2 problem or an ode45 problem. @ajt60gaibb or @asgeirbirkis, could you check it out? Thanks.

As far as I can tell there are no examples which show how pde15s() and/or pde23t() can be used.

Even if it's just copying one of the exported chebgui demos and adding some more text, that would be useful.

@ajt60gaibb , I notice veccalc/CheckingVectorCalculus doesn't have a figure, which is a shame at http://chebfun.github.io/examples/veccalc/index.html. Any chance you'd like to add a figure?

@ajt60gaibb , would you figure out what it takes to get AverageDegreeReduction1D.m to run? If you commit appropriate changes, then I'll do my polishing thing. Thanks.

The figures in the Spherefun examples on the web are quite blurry. Can this be easily fixed?

More specifically:

1. One can barely make out that the arrows in the quiver plots in http://www.chebfun.org/examples/sphere/HelmholtzDecomposition.html
2. The images in
   http://www.chebfun.org/examples/sphere/SphereHeatConduction.html
   seem very low quality.

If this could be fixed somehow, then @gradywright and I would be very pleased. I assume there is a parameter in an internal PHP script somewhere that is drastically compressing these images before uploading them to the Chebfun web folder. These figures appear fine when I do my own MATLAB publish and view in a web browser.

Something is wrong with geometrical commands in calc/SurfaceRevolution.

@tobydriscoll , I'd be grateful if you would take a look at stats/MercerKarhunenLoeve and fix it up. One issue concerns chebmatrices, and another concerns cov and mesh. Thanks.

@tobydriscoll , I've polished up integro/WikiIntegroDiff a bit but not converted it from linop to chebop form since I'm not so expert at integral operators. Would you be willing to do this? Thanks.

The example ode-nonlin gives an syntactical error message; @asgeirbirkis, could you fix this? Even once it's fixed, the example probably doesn't work, since chebfun/chebfun#829 and chebfun/chebfun#830 were closed without a clear resolution. @asgeirbirkis, can you find a way to make this work? Thanks.

I made several changes to the ODE examples to update the syntax for chebop in v5. I now want to push these changes to the examples repository. When I type
git push origin master
I get the error:
hint: Updates were rejected because the remote contains work that you do
hint: not have locally. This is usually caused by another repository pushing
hint: to the same ref. You may want to first integrate the remote changes
hint: (e.g., 'git pull ...') before pushing again.
hint: See the 'Note about fast-forwards' in 'git push --help' for details.
Can someone help me figure out what this means and how to fix it?

In particular, the line

g = chebfun2(@(z) sum(z.^(0:9)),[-1 1 -1 1]*pi/2,'vectorise');

gives the error

Error using .^
Matrix dimensions must agree.
Error in @(z)sum(z.^(0:9))

Error in chebfun2/constructor>@(x,y)op(x+1i*y) (line 97)
    op = @(x, y) op( x + 1i*y );
Error in chebfun2/sampleTest (line 22)
vOp = feval(op, xeval, yeval);
Error in chebfun2/constructor (line 307)
        pass = g.sampleTest(op, tol);
Error in chebfun2 (line 57)
            f = constructor(f, varargin{:});

I've tried tweaking the line with no luck. Insight, @ajt60gaibb ?

i got

Undefined function or variable 'chebfun'. Error Message.

line 26
dom = [-1 1 -1 1]; x = chebfun('x',dom(1:2)); tspan = [0 3500];

it seems he defined a function named chebfun somewhere but having read through your code, i can't find the function chebfun.
am i missing anything?

My apologies if issues with how examples are displayed on the new website don't belong on this tracker, but in any case, I wanted to mention that there are issues with the LaTeX rendering of:
http://chebfun.github.io/examples/opt/ConstrainedOptimization.html ,

both in the first section and in the second sections.

Also, that example makes use of the method inPolygon(), stating that it may be added to a future version of Chebfun. Is the plan to do so for v5?

@asgeirbirkis, would you take a look at ode-eig/ThermoelasticRod and see if you can get it running? Probably something small is needed. When it's working, please let me know and I will polish it further. Thanks.

Some examples still use the legacy pseudorandom number generator, which can cause problems if several examples are run in succession.

>> rand('seed', 1)
>> rng(1)
Error using rng (line 96)
The current random number generator is the legacy generator.  This is because
you have executed a command such as rand('state',0), which activates MATLAB's
legacy random number behavior.  You may not use RNG to reseed the legacy random
number generator.

Use rng('default') to reinitialize the random number generator to its startup
configuration, or call RNG using a specific generator type, such as
rng(seed,'twister').

ı propose that all examples use rng.

Quasimatrix support in chebop is no longer an option. This means that the second part of the BVPSystem example (Section 3) is obsolete. There is a ticket on the chebfun tracker (277) to add support in chebop for chebmatrices. If this is implemented then the second part of BVPSystem should be updated with this new syntax.

I suspect solutions are returned as chebmatrices now rather than chebfuns? Or something like that.

ode-eig/DoubleWell:

Undefined function 'mrdivide' for input arguments of type 'chebmatrix'.
Error in DoubleWell (line 47)
  v = EV(:,j)/15; d = D(j,j);

ode-eig/Drum:

Error using subsref
Subscript indices must either be real positive integers or logicals.
Error in chebmatrix/subsref (line 20)
        varargout{1} = chebmatrix(subsref(A.blocks, sr1));
Error in Drum (line 42)
V = V*diag(sign(V(0,:)));  % ensure V(0,k) > 0

ode-eig/Eigenstates:

Undefined function 'cheb2cell' for input arguments of type 'chebmatrix'.
Error in chebfun/quantumstates (line 113)
W = cheb2cell(W);
Error in Eigenstates (line 40)
quantumstates(V)

ode-eig/SolarQDA:

Error using semilogy
Conversion to double from chebmatrix is not possible.
Error in SolarQDA (line 75)
semilogy(Psi.^2,LW,lw), ylabel('probability'),

ode-eig/WaveDecay:

Undefined function 'mrdivide' for input arguments of type 'chebmatrix'.
Error in WaveDecay (line 22)
  v = v/norm(v,inf);          % normalize to have amplitude 1

I couldn’t figure out how to fix it. @tobydriscoll, you’ve taken a look at this one recently?

I tried running the code from http://www.chebfun.org/examples/ode-nonlin/TwoElectrons.html but it gets stuck:

LW = 'linewidth'; MS = 'markersize'; lw = 1.2;
chebfunpref.setDefaults('splitting',true)
N = chebop(0,40);
N.op = @(t,z) diff(z,2) + 2*z./abs(z).^3 - 0.25i*imag(z)./imag(z).^3;
V = 1; N.lbc = [1i; V];
tic, z = N\0; x = real(z); y = imag(z);
plot(0,0,'.k',MS,8), hold on
plot(x,y,x,-y,LW,lw), axis(1.2*[-1 1 -1 1]), axis square, hold off
set(gca,'xtick',-1:1,'ytick',-1:1)

Throws an error when it gets to z = N\0:

Undefined function 'imag' for input arguments of type 'treeVar'.

Error in chebop.vectorizeOp/@(t,z)diff(z,2)+2.*z./abs(z).^3-0.25i.*imag(z)./imag(z).^3

Error in treeVar.toFirstOrder (line 58)
    fevalResult = funIn(t, args{:});

Error in chebop/solveivp (line 124)
    [anonFun, varIndex, problemDom, coeffs, diffOrders] = ...

Error in  \  (line 49)
    [varargout{1:nargout}] = solveivp(N, rhs, pref, varargin{:});

Running on Matlab 2014a on a Mac. Chebfun v5.4.0.

I think references [1] and [7] are mixed up in lines 53 and 70 of the file Krylov.m.

Equations are not rendering in at least one Example:
https://www.chebfun.org/examples/ode-eig/RayleighQuotient.html

@mhsnjvd and @Hrothgar , I'm not sure how calc/DeltaDerivs got up on the web site; I think I never declared it "polished". There's no need to take it down I think, but the final plot does reveal a bug I think that I hope @mhsnjvd can correct. That plot is supposed to agree with an earlier plot in the same example, but it doesn't.

@asgeirbirkis, would you take a look at examples/ode/JumpConditions and fix it up, or tell me what to do? Thanks.

Alex, the final computation of roots/MarchingSquares produces a plot that I think is wrong. Can you fix and update this example and push the result? Then I will do one further editing pass before asking @Hrothgar to install it at the new web site.

While using quantumstates along with the potential V=dirac(x), it seems that the energies eigenstates computed by quantumstates are exactly the same as that of V=0. This remains the same for several delta functions, located at different positions. It seems that the delta function potential is 'invisible' to quantumstates. Any ideas on how to fix this? (assuming I want to use the dirac(x) function MATLAB offers, and not write an ad hoc delta potential myself)

Example ode-nonlin/BVPSystem gives the error message

Warning: Rank deficient, rank = 0, tol =  0.000000e+00. 
> In chebop.solvebvpNonlinear at 100
  In chebop.solvebvp at 177
  In BVPSystem at 29 
Warning: Rank deficient, rank = 0, tol =  0.000000e+00. 
> In chebop.solvebvpNonlinear at 100
  In chebop.solvebvp at 177
  In BVPSystem at 65 

@asgeirbirkis, can you sort this out?

The example ode-nonlin/ModellingDiseases has been excluded from the nightly tests until the IVP branch is merged into Chebfun’s development branch. This issue is a reminder to test that example again once the IVP branch is merged.

@ajt60gaibb , would you see if you can get veccalc/EventHandling to work? Thanks.

See chebfun/chebfun#1750 for an example plot and explanation.

Something is wrong in examples/cheb/FastChebyshevLegendreTransform.m. The errors that are supposed to be near-zero are actually equal to about 1/sqrt(2).

The following examples have recently-introduced graphics issues due to the various v5 plotting bugs. In theory the examples do not need to be changed — they just need to be rerun once the bugs in Chebfun are fixed.

• approx/WeierstrassFunction — ylim issue possible related to 'interval' flag
• calc/DeltaDerivs — ylim issue pertaining to deltafuns
• geom/Lissajous — flag 'color' doesn’t work on final plot
• geom/Ellipses — ellipse has a kink in it for some reason
• linalg/LevelRepulsion — ylim issues
• ode/LorenzAttractor — ylim issues
• ode-eig/SolarQDA — ylim issues
• approx/OrthPolys — ylim issues