当它应该趋向于 0 时，相对差趋向于负无穷大

Question

我编写了以下代码来绘制两个不同模型（蓝色和绿色线）的速度过程以及它们之间的相对差异（橙色线）：

%% ----- Absolulte Carvelocity v[km/h] in carfixed Coordinate system ----
%  Define Plotproperties
figure('Position', [100, 100, 1024, 768]);
hold on; grid on;
title('Absolute Velocity');
xlabel('time t[s]');
ylabel('absolute velocity v[km/h]');
xlim([t_start t_end]);

% Calculate the difference between the models
t = erg_sl.Vehicle.v_ms.Time;
v_ms = reshape(erg_sl.Vehicle.v_ms.Data,1,[],1);
diff=zeros(1,size_cmtime(2));
for ctr=1:size_cmtime(2)
    diff(1,ctr)=-(erg_cm.Car_v.data(ctr)*3.6-v_ms(1,round(ctr*fac))*3.6)/abs(erg_cm.Car_v.data(ctr)*3.6)*100;
end

% From Carmaker
line(erg_cm.Time.data,erg_cm.Car_v.data .* 3.6,'Color','b','LineWidth',2)

% From Simulink
line(erg_sl.Vehicle.v_ms.Time,erg_sl.Vehicle.v_ms.Data .* 3.6,'Color',[0,0.6,0.5],'LineWidth',2)

% Legend
legend('Carmaker','Simulink');

% Change axes
ax1 = gca;
%ax1.XLim = [0 20];
%ax1.YLim = [-15 15];
ax2 = axes('Position',ax1.Position,'YAxisLocation','right', 'Color','none','YColor',[255,127,80]/256);
ax2.YLim = [-30 30];
ax2.YLabel.String = 'Relative difference [%]';
linkaxes([ax1,ax2],'x');

% Plot the difference
line(erg_cm.Time.data,diff,'Parent',ax2,'LineWidth',2,'Color',[255,127,80]/256)

% legend
legend('Relative Abweichung','Location','South')

%  ------------------------------------------------------------------------

实际上它工作得很好，我得到了这个情节：

现在的问题是，开始时差值实际上几乎为零，但橙色线（即相对差值）走向负无穷大。您甚至可以看到从 t=0 到 t~75 绿线甚至在蓝线上方，因此橙色线应该在 0 以上。那么代码有什么问题，所以会发生这种情况？

编辑：这是同一脚本的另一个情节，看起来更像我的预期。橙色线也朝向 -inf，但仅适用于小于我认为合乎逻辑的除数：

Answer 1

相对差异(x-y)./x可以趋向于inf或-inf，即使绝对差异 x-y 趋于 0.

考虑例如：

t = logspace(0,-5,8);        %// tends to zero
x = t;                       %// tends to zero
y = sqrt(t);                 %// tends to zero, but more slowly than x
absDiff = x-y;               %// tends to zero
relDiff = (x-y)./x           %// tends to -inf

这给出了

t =
    1.0000    0.1931    0.0373    0.0072    0.0014    0.0003    0.0001    0.0000

absDiff =
         0   -0.2463   -0.1558   -0.0776   -0.0359   -0.0161   -0.0071   -0.0032

relDiff =
         0   -1.2758   -4.1795  -10.7877  -25.8270  -60.0540 -137.9495 -315.2278

当它应该趋向于 0 时，相对差趋向于负无穷大

The relative difference goes towards negative infinity when it's supposed to go towards 0

matlab

matlab-figure