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cosolver/matlab_scripts/check_basis_transformation.m
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check_basis_transformation.m
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%% Get basis transformation
clear all;
close all;
% directories
T5dir = '/home/bjfrei/Documents/MoliSolver/COSOlver/coeffs/T5src';
file = '00000.csv';
M= readtable(fullfile(T5dir,file));
% Convert to double precision
dims = size(M);
M_dp = zeros(dims(1),dims(2));
% Get indices
M_dp(1:end,1:5) = M{1:end,1:5};
% Convert str to double precisio
for ii=1:dims(1)
M_dp(ii,6) = str2num(strrep(M{ii,6}{1},'M','E'));
end
%% Load basis
[T5coeffs,T5idx] = get_T5([10,10,10,10,10]);
%%
T5 = read_T5([2,3,0,2,3],T5idx,T5coeffs)
%% Define pitch angle basis
PitchBasis = @(s,xi,p,j,m) s^p.*legendrePlm(p,m,xi ).*laguerreL(j,p+1/2,s^2);
HLBasis = @(spar,x,l,k,m) polyval(HermitePoly(l),spar).*polyval(LaguerrePoly(k),x).*x^(m/2);
%% Define velocity grid (normalized to thermal velocity)
Np = 20 ;
% pitch angle
xi = linspace(-1,1,Np);
% speed
s = linspace(0,1,Np);
% parallel velocity
spar = xi.*s;
% v_\perp-squared
xs = s.^2 - spar.^2;
%% Compute Pitch-basis (LHS) on velocity-grid
% Pitch anlge indices
p = 2;
m = 1;
j = 2;
LHS = zeros(Np,Np);
for ixi=1:Np
for is=1:Np
LHS(ixi,is) = PitchBasis(s(is),xi(ixi),p,j,m);
end
end
%% Compute Hermite-Laguerre basis
RHS = zeros(Np,Np);
for ixi=1:Np
for is=1:Np
RHS(ixi,is) =HermiteLaguerre2Pitch(p,j,m,s(is),xi(ixi),T5coeffs,T5idx);
end
end
%% Plot
[X,Y] = meshgrid(xi,s);
figure;
pcolor(X,Y,LHS');
xlabel('$\xi$');
ylabel('$s$');
title(['$(p,j,m) = (',num2str(p),',',num2str(j),',',num2str(m),'$)'])
figure;
pcolor(X,Y,RHS' - LHS');
xlabel('$\xi$');
ylabel('$s$');
title(['$(p,j,m) = (',num2str(p),',',num2str(j),',',num2str(m),'$)'])
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