# How to improve the calculation accuracy of Matlab?

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Moved: VBBV on 11 Apr 2023
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.
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.

Moved: VBBV on 11 Apr 2023
hhhhhh, sure. But I have to take that expense since I need the accurate result.

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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