如何在 matlab 中绘制其 x 值取决于另一个函数的分段函数？

Question

我正在尝试绘制一个依赖于 Lambda 的分段函数，但 Lambda 依赖于范围从 -0.9 到 1.0 的 m。我认为我在以不同的 m 和 Lambda 值存储 H 的数据点，然后告诉 matlab 根据条件语句绘制这些存储的值时遇到问题。这在 matlab 中可行吗？

下面可以看到我的代码

% Lambda is the lambda from Thwaites method
% where m is in the range: -0.9 < m <  1.0
m=linspace(-0.9, 1.0, 100)
Lambda = 0.45.*m/((5.*m) +1)

% H needs to be plotted as a piecewise function
% l is also a piecewise function
if (0<Lambda) && (Lambda<0.1)
    H = 2.61 -3.75*Lambda + 5.24*Lambda^2
    l = 0.22 + 1.57*Lambda -1.8*Lambda^2 
elseif (-0.1<Lambda) && (Lambda<0)
    H = 2.088 + (0.0731/(Lambda + 0.14))
    l = 0.22 + 1.402*Lambda + ((0.018*Lambda)/(Lambda+0.107))
else 
    H = 0
    l = 0
end

figure(2)
plot(m,H)
title('H vs m')
xlabel('m')
ylabel('H')

非常欢迎任何帮助！

谢谢:)

Answer 1

% Lambda is the lambda from Thwaites method
% where m is in the range: -0.9 < m <  1.0
m = linspace(-0.9, 1.0, 100);
Lambda = 0.45*m./(5*m+1);

% H needs to be plotted as a piecewise function
H = zeros(size(m));
case1 = (0<Lambda) & (Lambda<0.1);
H1 = 2.61 -3.75*Lambda(case1) + 5.24*Lambda(case1).^2;
H(case1) = H1;

case2 = (-0.1<Lambda) & (Lambda<0);
H2 = 2.088 + (0.0731./(Lambda(case2) + 0.14));
H(case2) = H2;

plot(m, H);
title('H vs m');
xlabel('m');
ylabel('H');

Answer 2

只需使用掩码执行 if-else 部分。

% Lambda is the lambda from Thwaites method
% where m is in the range: -0.9 < m <  1.0
m=linspace(-0.9, 1.0, 100)
Lambda = 0.45.*m/((5.*m) +1)

% allocate space for H & l (also else part in your code)
H = zeros(1, numel(m));
l = zeros(1, numel(m));

% if condition
cond1 = (Lambda > 0) & (Lambda < 0.1);
% attention to the piecewise exponential operator .^, I bet you mean that
H(cond1) = 2.61 - 3.75*Lambda(cond1) + 5.24*Lambda(cond1).^2;
l(cond1) = 0.22 + 1.57*Lambda(cond1) - 1.8*Lambda(cond1).^2;

% elseif condition
cond2 = (Lambda > -0.1) & (Lambda < 0);
H(cond2) = 2.088 + (0.0731 ./ (Lambda(cond2) + 0.14));  % division must be piecewise
l(cond2) = 0.22 + 1.402*Lambda(cond2) + ((0.018*Lambda(cond2)) ./ (Lambda(cond2)+0.107));

figure(2)
plot(m,H)
title('H vs m')
xlabel('m')
ylabel('H')

如何在 matlab 中绘制其 x 值取决于另一个函数的分段函数？

How can I plot a piecewise function in matlab whose x value depends on another function?

matlab

function

plot

piecewise