Unrecognized "spharm" for spherical harmonics plot?

Hi, I get the following error when trying to plot

Unrecognized function or variable 'spharm'.

Error in FTyD (line 35)

Ylm = spharm(l, m, Y, X); % Evaluate spherical harmonic Y_lm(x,y)

% Define the function f(t)
f = @(t) 139.85 + (15.8404 + 4.76022i) * exp(-1i * t) + (15.8404 - 4.76022i) * exp(1i * t) + ...
    (4.64917 - 3.3024i) * exp(-2i * t) + (4.64917 + 3.3024i) * exp(2i * t) + ...
    (7.42191 - 0.300123i) * exp(-3i * t) + (7.42191 + 0.300123i) * exp(3i * t) + ...
    (0.340877 - 2.54665i) * exp(-4i * t) + (0.340877 + 2.54665i) * exp(4i * t) + ...
    (7.72422 + 6.71332i) * exp(-5i * t) + (7.72422 - 6.71332i) * exp(5i * t) + ...
    (3.16511 - 9.14479i) * exp(-6i * t) + (3.16511 + 9.14479i) * exp(6i * t) + ...
    (3.31502 + 2.18874i) * exp(-7i * t) + (3.31502 - 2.18874i) * exp(7i * t) + ...
    (9.31827 + 6.94538i) * exp(-8i * t) + (9.31827 - 6.94538i) * exp(8i * t) + ...
    (5.87173 + 18.8341i) * exp(-9i * t) + (5.87173 - 18.8341i) * exp(9i * t) + ...
    (8.75949 + 14.7107i) * exp(-10i * t) + (8.75949 - 14.7107i) * exp(10i * t) + ...
    (19.2903 + 7.78329i) * exp(-11i * t) + (19.2903 - 7.78329i) * exp(11i * t) + ...
    (-3.39063 - 18.5502i) * exp(-12i * t) + (-3.39063 + 18.5502i) * exp(12i * t) + ...
    (3.58427 + 18.7438i) * exp(-13i * t) + (3.58427 - 18.7438i) * exp(13i * t) + ...
    (2.66129 + 20.0781i) * exp(-14i * t) + (2.66129 - 20.0781i) * exp(14i * t) + ...
    (-8.46335 - 9.96867i) * exp(-15i * t) + (-8.46335 + 9.96867i) * exp(15i * t) + ...
    (-8.50037 - 1.20377i) * exp(-16i * t) + (-8.50037 + 1.20377i) * exp(16i * t) + ...
    (-1.36102 - 16.9315i) * exp(-17i * t) + (-1.36102 + 16.9315i) * exp(17i * t) + ...
    (-5.78964 - 2.96094i) * exp(-18i * t) + (-5.78964 + 2.96094i) * exp(18i * t) + ...
    (2.14681 + 8.29635i) * exp(-19i * t) + (2.14681 - 8.29635i) * exp(19i * t) + ...
    (-3.91145 - 10.7712i) * exp(-20i * t) + (-3.91145 + 10.7712i) * exp(20i * t);

% Parameters
lmax = 10; % Maximum degree for spherical harmonics expansion

% Create grid in x and y
x = linspace(-10, 10, 100);
y = linspace(-10, 10, 100);
[X, Y] = meshgrid(x, y);

% Compute f(x,y)
Fxy = zeros(size(X));
for l = 0:lmax
    for m = -l:l
        Ylm = spharm(l, m, Y, X); % Evaluate spherical harmonic Y_lm(x,y)
        integral_value = integral(@(t) f(t) .* conj(Ylm), -pi, pi); % Compute integral
        Fxy = Fxy + integral_value * Ylm; % Accumulate to f(x,y)
    end
end

% Plot
figure;
surf(X, Y, real(Fxy), 'EdgeColor', 'none');
xlabel('x');
ylabel('y');
zlabel('Re(f(x,y))');
title('Method 3: Expansion in Spherical Harmonics');
colorbar;

Cant figure out why...

[Torsten]

Do you have

function  y = spharm( ltab, mtab, theta, phi )
% SPHARM - Spherical harmonics.
%
%  Usage : 
%    y = spharm( ltab, mtab, theta, phi )
%  Input
%    ltab   :  table of spherical harmonic degrees
%    mtab   :  table of spherical harmonic orders
%    theta  :  polar angle
%    phi    :  azimuthal angle
%  Output
%    y      :  spherical harmonic
%  convert to column and row vectors
[ ltab, mtab ] = deal( reshape( ltab,  [], 1 ), reshape( mtab, [], 1 ) );
[ theta, phi ] = deal( reshape( theta, 1, [] ), reshape( phi,  1, [] ) );
%  table of factorials
ftab = factorial( 0 : ( 2 * max( ltab ) + 1 ) );
%  dimension output
y  = zeros( length( ltab ), length( theta ) );
%  loop over unique ltab values
for l = reshape( unique( ltab ), 1, [] )
    
  %  full table of Legendre functions
  ptab = legendre( l, cos( theta ) );
  
  %  index to entries with degree L and 
  %                   with angular order smaller than angular order
  ind = find( ltab == l );
  ind = ind( abs( mtab( ind ) ) <= l );
  
  for i = reshape( ind, 1, [] )
    %  corresponding spherical order (only absolute value considered first)
    m = mtab( i );
    %  prefactor for spherical harmonics
    c = sqrt( ( 2 * l + 1 ) / ( 4 * pi ) *  ...
        ftab( l - abs( m ) + 1 ) / ftab( l + abs( m ) + 1 ) );
    %  spherical harmonics
    y( i, : ) = c * ptab( abs( m ) + 1, : ) .* exp( 1i * abs( m ) * phi );
    %  correct for negative orders
    if ( m < 0 ),  y( i, : ) = ( - 1 ) ^ m * conj( y( i, : ) );  end
  end    
end
end

on your MATLAB path ?

And conj(Ylm) in your integral is just a constant vector that won't depend on t and the length of which is incompatible with the t-vector supplied by the "integral"-function.

[Sergio]

Hmm...where did this code of yours come from?

[Torsten]

https://viewer.mathworks.com/?viewer=plain_code&url=https%3A%2F%2Fde.mathworks.com%2Fmatlabcentral%2Fmlc-downloads%2Fdownloads%2F6ed58da4-9dfb-4c54-b784-6d4ddf22c5f9%2F02228398-8fa2-401b-96aa-b82b7af28bb1%2Ffiles%2FMie%2Fspharm.m&embed=web

[Sergio]

How would the total code look like? Can I just copy that in?

[Umar]

Hi Sergio,

Try this

% Add the sphharm function to your existing code % Code from: https://viewer.mathworks.com/?viewer=plain_code&url=https%3A%2F%2Fjp.mathworks.com%2Fmatlabcentral%2Fmlc-downloads%2Fdownloads%2Fe5abb292-4a80-11e4-9553-005056977bd0%2Fd3323a9d-1c0f-f373-1ffc-69bab360c2c3%2Ffiles%2F%40spherefun%2Fsphharm.m&embed=web

% Paste the code from the provided link here

% This code adds the sphharm function to your Matlab environment

[Torsten]

How would the total code look like? Can I just copy that in?

It depends on your MATLAB release. Usually you can just copy it underneath your script. For earlier MATLAB releases, you should save it as "spharm.m" in your working directory.

Answer 1

[Umar]

Hi Sergio,

To help resolve your problem, you need to define the spharm function or find an alternative way to evaluate the spherical harmonics.One possible solution is to use the sphharm function from the MATLAB File Exchange. This function provides a way to evaluate spherical harmonics. You can download the sphharm function from the MATLAB File Exchange website and add it to your MATLAB path.

For more information regarding this function, please refer to

https://viewer.mathworks.com/?viewer=plain_code&url=https%3A%2F%2Fjp.mathworks.com%2Fmatlabcentral%2Fmlc-downloads%2Fdownloads%2Fe5abb292-4a80-11e4-9553-005056977bd0%2Fd3323a9d-1c0f-f373-1ffc-69bab360c2c3%2Ffiles%2F%40spherefun%2Fsphharm.m&embed=web

Hope this will help resolve your problem.