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How to improve the calculation accuracy of Matlab?

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Sometimes when it comes to very small value calculation, the calculation accuracy of Matlab would not be enough.
There would be fluctuation in the result.
For instance:
l=4;
l1=l;%Tx Mode
l2=l;%Rx Mode
misalignment = -1:1e-3:1;
result = zeros(1,length(misalignment));
channel_func = @(d) 1./d.*exp(-1j.*2*pi./3e-3.*d);
phi_Tx = (0:8-1).*2.*pi./8;
phi_Rx = phi_Tx;
F_Tx = exp(1j.*l1.*phi_Tx).';
F_Rx = exp(-1j.*l2.*phi_Rx).';
%% For different misalignment, it output different result.
for i=1:length(misalignment)
distance_fun= @(x,y) sqrt(1e4-2*misalignment(i)/1e2.*cos(x)+2*misalignment(i)/1e2*cos(y)-2e-4*cos(x-y));
H = channel_func(distance_fun(phi_Tx,phi_Rx.'));
result(i) = abs(F_Rx.'*H*F_Tx);% The key calculation. How can I improve the accuracy of this matrix multiplication?
end
%% Image
figure(1);
set(0,'defaultfigurecolor','w')
set(gcf,'Position',[100 100 700 600]);
plot(misalignment,abs(result));
grid on;
xlabel('distance/meter');
ylabel('Intensity');
And in theory, this curve should be smooth. I think the fluctuation is caused by accuracy limit of Matlab.
Is there any suggestion? If it's possible, you can modify the code directly.
Any help is appreciated.
  6 Comments
VBBV
VBBV on 11 Apr 2023
Moved: VBBV on 11 Apr 2023
ok, Here is the program execution speed if you use vpa with 8 digits
clearvars, clc
l=4;
l1=l;%Tx Mode
l2=l;%Rx Mode
digits(8); % using 8 digits
tic
misalignment = vpa(-1:1e-2:1);
and it seems you are using 128 digits !! which probably take even much more time.
祥宇 崔
祥宇 崔 on 11 Apr 2023
Moved: VBBV on 11 Apr 2023
hhhhhh, sure. But I have to take that expense since I need the accurate result.

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Accepted Answer

祥宇 崔
祥宇 崔 on 11 Apr 2023
By using vpa, I improve the accuracy
l=4;
l1=l;%Tx Mode
l2=l;%Rx Mode
digits(128);
misalignment = vpa(-1:1e-2:1);
result = zeros(1,length(misalignment));
channel_func = @(d) 1./d.*exp(-1j.*2*pi./3e-3.*d);
phi_Tx = (0:8-1).*2.*pi./8;
phi_Rx = phi_Tx;
F_Tx = exp(1j.*l1.*phi_Tx).';
F_Rx = exp(-1j.*l2.*phi_Rx).';
%% For different misalignment, it output different result.
for i=1:length(misalignment)
distance_fun= @(x,y) sqrt(1e4-2*misalignment(i)/1e2.*cos(x)+2*misalignment(i)/1e2*cos(y)-2e-4*cos(x-y));
H = channel_func(distance_fun(phi_Tx,phi_Rx.'));
result(i) = abs(F_Rx.'*H*F_Tx);% The key calculation. How can I improve the accuracy of this matrix multiplication?
end
%% Image
figure(1);
set(0,'defaultfigurecolor','w')
set(gcf,'Position',[100 100 700 600]);
plot(misalignment,abs(result));
grid on;
xlabel('distance/meter');
ylabel('Intensity');

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