How to improve the calculation accuracy of Matlab?

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祥宇崔 2023-4-11

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1944999-how-to-improve-the-calculation-accuracy-of-matlab

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采纳的回答：祥宇崔

在 MATLAB Online 中打开

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.

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VBBV 2023-4-11

移动：VBBV 2023-4-11

在 MATLAB Online 中打开

you can use, smoothdata on the resulting matrix

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_Tx = 1×8

0 0.7854 1.5708 2.3562 3.1416 3.9270 4.7124 5.4978

phi_Rx = phi_Tx

phi_Rx = 1×8

0 0.7854 1.5708 2.3562 3.1416 3.9270 4.7124 5.4978

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

% smooth data with a suitable distribution Guassian

result1 = smoothdata(result,'gaussian',20);

% try with different values

% smooth data with a suitable distribution SGOLAY

result2 = smoothdata(result,'sgolay');

%% Image

figure(1);

set(0,'defaultfigurecolor','w')

set(gcf,'Position',[100 100 700 600]);

plot(misalignment,abs(result1),misalignment,abs(result2));

grid on;

xlabel('distance/meter');

ylabel('Intensity');

legend('Gaussian','Sgolay filter')

VBBV 2023-4-11

移动：VBBV 2023-4-11

在 MATLAB Online 中打开

Calculation accuracy depends on how you set the variable limits used in the program but not using vpa.

l=4;

l1=l;%Tx Mode

l2=l;%Rx Mode

digits(128);

format long

misalignment = (-1:1e-2:1) % 1e-2 to something in finer step 1e-4 or 1e-6 etc

misalignment = 1×201

-1.000000000000000 -0.990000000000000 -0.980000000000000 -0.970000000000000 -0.960000000000000 -0.950000000000000 -0.940000000000000 -0.930000000000000 -0.920000000000000 -0.910000000000000 -0.900000000000000 -0.890000000000000 -0.880000000000000 -0.870000000000000 -0.860000000000000 -0.850000000000000 -0.840000000000000 -0.830000000000000 -0.820000000000000 -0.810000000000000 -0.800000000000000 -0.790000000000000 -0.780000000000000 -0.770000000000000 -0.760000000000000 -0.750000000000000 -0.740000000000000 -0.730000000000000 -0.720000000000000 -0.710000000000000

misalignment = -1:rand(1)*1e-4:1 % this will increase accuracy of dependent variables

misalignment = 1×76132

-1.000000000000000 -0.999973729598183 -0.999947459196366 -0.999921188794550 -0.999894918392733 -0.999868647990916 -0.999842377589099 -0.999816107187283 -0.999789836785466 -0.999763566383649 -0.999737295981832 -0.999711025580015 -0.999684755178199 -0.999658484776382 -0.999632214374565 -0.999605943972748 -0.999579673570931 -0.999553403169115 -0.999527132767298 -0.999500862365481 -0.999474591963664 -0.999448321561848 -0.999422051160031 -0.999395780758214 -0.999369510356397 -0.999343239954581 -0.999316969552764 -0.999290699150947 -0.999264428749130 -0.999238158347313

misalignment = -1:rand(1)*1e-7:1 % same here

misalignment = 1×28566322

-1.000000000000000 -0.999999929987486 -0.999999859974973 -0.999999789962459 -0.999999719949946 -0.999999649937432 -0.999999579924919 -0.999999509912405 -0.999999439899891 -0.999999369887378 -0.999999299874864 -0.999999229862351 -0.999999159849837 -0.999999089837324 -0.999999019824810 -0.999998949812297 -0.999998879799783 -0.999998809787269 -0.999998739774756 -0.999998669762242 -0.999998599749729 -0.999998529737215 -0.999998459724701 -0.999998389712188 -0.999998319699674 -0.999998249687161 -0.999998179674647 -0.999998109662134 -0.999998039649620 -0.999997969637107

misalignment = vpa(-1:1e-2:1) % but not this ... time consuming and boring sometimes

misalignment =

VBBV 2023-4-11

移动：VBBV 2023-4-11

在 MATLAB Online 中打开

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 2023-4-11

移动：VBBV 2023-4-11

hhhhhh, sure. But I have to take that expense since I need the accurate result.

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Answer 1

祥宇崔 2023-4-11

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1944999-how-to-improve-the-calculation-accuracy-of-matlab#answer_1213364

在 MATLAB Online 中打开

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');