交叉MATLAB，多根

Question

我在确定这个基本逻辑时遇到了问题。给出2个函数：y1和y2，在MATLAB中绘制在x上。如何使用简单的for循环和if else语句确定交叉点。这些y1和y2有一个以上的交叉点。我很确定我在循环中遗漏了一些东西

clc
clear
x = linspace(0,2);
y1 = 2.*x + 1;
y2 = exp(x);
tol = 0.05;
x_intercept = zeros(size(x));
y_intersect = zeros(size(x));
for i = 1:100
    if abs(y1(i) - y2(i)) == tol
        y_intersect = y2(x(i));
        x_intercept = x(i);
    end

end

plot(x,y1)
hold on
plot(x,y2)
plot(x_intercept, y_intersect,'xr');

你能提供帮助吗？我很抱歉，如果这似乎是一个非常简单的问题，但我搜索过，没有找到答案。我发现只是使用polyval / polyfit等等，但那些只显示1个交集。

Answer 1

尝试将for循环更改为：

ctr=1;
for i = 1:100
    if abs(y1(i) - y2(i)) <= tol
        y_intersect(ctr) = y2(i);
        x_intercept(ctr) = x(i);
        ctr=ctr+1;
    end

end

Answer 2

您可以使用函数solve查找两条曲线的交点：

clc
clear

% Define the symbolic variables
syms x y
vars=[x y]
% Define the two eqautions
equations=([2*x+1-y == 0,exp(x)-y == 0])
% Call SOLVE to find the intersection point
[sol_x,sol_y]=solve(equations,vars,'Real', true)
% Get the values of the x and y coordinates of the intersectiin points
x_inters=double(sol_x)
y_inters=double(sol_y)


% Evaluate the two functions (only to plot them) 
x = linspace(0,2);
y1 = 2.*x + 1;
y2 = exp(x);
plot(x,y1)
hold on
plot(x,y2)
% Add the intersection points
plot(x_inters,y_inters,'or','markerfacecolor','r')

如果您需要/需要使用for和if-else语句，首先需要修改代码中的if条件：

if abs(y1(i) - y2(i)) <= tol

然后你必须增加样本数x以减少它们之间的距离。

此外，您还必须为阈值tol测试不同的值。

这种方法可以识别几种解决方案，因此您可以识别出y1和y2之间的差异较小的那些解决方案。

可能的实施可能是：

clc
clear

% x = linspace(0,2);
% Define the x samaples
x=0:.001:2
y1 = 2.*x + 1;
y2 = exp(x);
% tol = 0.05;
tol = 0.001;
x_intercept = zeros(size(x));
% y_intersect = zeros(size(x));
y1_intersect = zeros(size(x));
y2_intersect = zeros(size(x));
% Initialize the counters 
cnt=0;
once=0;
% Initialize the minimun_difference
min_diff=999;
% for i = 1:100
% Loop over the xsamples
for i = 1:length(x)
   %     if abs(y1(i) - y2(i)) == tol
   y1_y2_diff=abs(y1(i) - y2(i));
   if(y1_y2_diff <= tol)
      % If the difference is lower than the threshold, set the flag to
      % increment the number of solutions
      if(~once)
         cnt=cnt+1;
         once=1;
      end
      % Store the values for the minimum difference
      if(y1_y2_diff <= min_diff)
         min_diff=y1_y2_diff;
         y1_intersect(cnt) = y1(i);
         y2_intersect(cnt) = y2(i);
         x_intercept(cnt) = x(i);
      end
   else
      % Rese the flag
      min_diff=999;
      once=0;
   end
end

plot(x,y1)
hold on
plot(x,y2)
% plot(x_intercept, y_intersect,'xr');
plot(x_intercept(1:cnt), y1_intersect(1:cnt),'xr');
plot(x_intercept(1:cnt), y2_intersect(1:cnt),'dr');

希望这有帮助，

Qapla'