Solving equations with different ranges

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jack carter 2017-8-30

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/354622-solving-equations-with-different-ranges

评论： Star Strider 2017-8-31

I need to get the values of P by using different equations under different values of S, as shown in the attached image. I have written codings for the equations but could someone please guide me on how can I make the equations work along with the given different range of S?

       sigma0=5; Lf=12; S=0:0.01:600; S0=0.18;      %arbitrary values
       P=sigma0*[2*sqrt(S/S0)-(S/S0)];              %Run this eq. for S=<S0 (S is less than & equal to S0)
       P=sigma0*(1-2*S/Lf)^2;                       %Run this eq. for S0<=S<=Lf/2 
       P=0;                                         %Run this eq. for S>=Lf/2

The value of S0 will be a constant value which I will get by solving another set of equation (not included in this query). All of the values I have taken are arbitrary. Later I will be plotting the resultant values of P and for corresponding values of S.

Thank you

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jack carter 2017-8-30

Please add one more detail to this question that later in my function I will be needed to use values of P, from both equations, separately. Like, using the resultant values of equation one (when delta (S) is less than delta0 (S0)) and multiply or add to other parameters. And also using the resultant values of P for second equation and third equation separately with some other parameters. These values will be like my input values to solve other equations. How could I use them separately later on?

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Answer 1

Star Strider 2017-8-30

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/354622-solving-equations-with-different-ranges#answer_279733

在 MATLAB Online 中打开

Using ‘logical vectors’, ‘P’ is not defined for ‘S’ greater than or equal to ‘Lf/2’, so an explicit condition for that region to be 0 is not necessary in the expression.

This seems to me to do what you want:

sigma0=5; Lf=12; S=0:0.01:600; S0=0.18;      %arbitrary values
P = @(S,S0,Lf,sigma0) sigma0*((2*sqrt(S/S0)-(S/S0)).*(S<=S0) + ((1-2*S/Lf).^2).*((S0<=S) & (S<=Lf/2)));
figure(1)
plot(S, P(S,S0))
grid
xlabel('S')
ylabel('P')
axis([0  10    ylim])

This uses an anonymous function implementation of your conditional expression.

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jack carter 2017-8-31

编辑：jack carter 2017-8-31

checkranges.m

@Star Strider - I am not sure what I am doing wrong. I am a beginner in MATLAB. As per my understanding the variables are already existed in the workspace when I run these codes. I am able to print all of the variables with fprintf command. I have attached the coding file if you could take a look. In the command window is it like I shall type checkranges and it should work? It is working like this for printing the values of all the variables except P.

Star Strider 2017-8-31

在 MATLAB Online 中打开

The way I wrote my function, you have to supply all the input arguments. It does not automatically take any arguments from your workspace.

This works:

sigma0=5; Lf=12; S=0:0.01:600; S0=130;      %arbitrary values
P = @(S,S0,Lf,sigma0) sigma0*((2*sqrt(S/S0)-(S/S0)).*(S<=S0) + ((1-2*S/Lf).^2).*((S0<=S) & (S<=Lf/2)));
figure(1)
plot(S, P(S,S0,Lf,sigma0))
grid
xlabel('S')
ylabel('P')
axis([0  10    ylim])