There is a function that solve a system of equations with various restrictions?

Question

Santiago Rivera González 2020-2-5

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/503701-there-is-a-function-that-solve-a-system-of-equations-with-various-restrictions

回答： JESUS DAVID ARIZA ROYETH 2020-2-5

clear; clc
v=1.20e-6;
e=4.6e-5;
g=9.80665;
D=[0.3636 0.3636 0.4096 0.289 0.3636 0.3636 0.289 0.317];
L=[25 20 12 20 20 12 25 20];
Q=ones(1,8);
Re=ones(1,8);
f=ones(1,8);
hL=ones(1,8);
p=ones(1,8);

The metod to solve this particular problem needs the asumption of three values for Q and with those calculate the rest of the Qs.

But those Qs needs to satisfy three conditions; all of DQs must be less than 1e-4. (And all of the variables in the code needs to be positive real values).

Q1c=0.3970;
Q4c=0.0934;
Q8c=0.4340;
DQ1=0;
DQ2=0;
DQ3=0;
while abs(Q(1)/Q1c-1)>1e-3
    Q(1)=Q1c-DQ1;
    Q(4)=Q4c-DQ2;
    Q(8)=Q8c-DQ3;
    
    Q(2)=0.6-Q(1);
    Q(3)=1+Q(4)-Q(1);
    Q(5)=Q(2)+0.6-Q(3);
    Q(6)=Q(5)+Q(8);
    Q(7)=0.8-Q(8);
    
    for i=1:8
       Re(i)=4*Q(i)/(pi*D(i)*v); 
    end
 
    for i=1:8
       f(i)=0.25*(log10(e/(3.7*D(i))+5.74/(Re(i)^(0.9))))^(-2); 
    end
 
    for i=1:8
       hL(i)=8*f(i)*L(i)/(g*pi^(2)*D(i)^(5))*Q(i)^(2); 
    end
    
    sum1=hL(3)+hL(2)-hL(1);
    sum2=hL(5)+hL(6)-hL(3)-hL(4);
    sum3=hL(7)-hL(6)-hL(8);
 
    for i=1:8
       p(i)=16*f(i)*L(i)/(g*pi^(2)*D(i)^(5))*Q(i); 
    end
  
    sumk1=sum(p(1:3));
    sumk2=sum(p(3:6));
    sumk3=sum(p(6:8));
    
    DQ1=sum1/sumk1;
    DQ2=sum2/sumk2;
    DQ3=sum3/sumk3;
end
Q(1)=Q1c;
Q(4)=Q4c;
Q(8)=Q8c;

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Answer 1

JESUS DAVID ARIZA ROYETH 2020-2-5

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/503701-there-is-a-function-that-solve-a-system-of-equations-with-various-restrictions#answer_413833

在 MATLAB Online 中打开

debes convertir tu código a función, donde la entrada sean las 3 Q que asumes y la salida el resto de Qs, y luego de eso utilizar el sistema de restricciones de Matlab https://la.mathworks.com/help/optim/ug/nonlinear-systems-with-constraints.html

además de esto tienes for que no son necesarios :

you can convert your code to function, where the input is the 3 Q that you assume and the output the rest of Qs, and after that use the Matlab restriction system https://la.mathworks.com/help/optim/ug /nonlinear-systems-with-constraints.html

furthermore you have unnecessary for loops:

v=1.20e-6;
e=4.6e-5;
g=9.80665;
D=[0.3636 0.3636 0.4096 0.289 0.3636 0.3636 0.289 0.317];
L=[25 20 12 20 20 12 25 20];
Q=ones(1,8);
Re=ones(1,8);
f=ones(1,8);
hL=ones(1,8);
p=ones(1,8);
Q1c=0.3970;
Q4c=0.0934;
Q8c=0.4340;
DQ1=0;
DQ2=0;
DQ3=0;
while abs(Q(1)/Q1c-1)>1e-3
    Q(1)=Q1c-DQ1;
    Q(4)=Q4c-DQ2;
    Q(8)=Q8c-DQ3;
    Q(2)=0.6-Q(1);
    Q(3)=1+Q(4)-Q(1);
    Q(5)=Q(2)+0.6-Q(3);
    Q(6)=Q(5)+Q(8);
    Q(7)=0.8-Q(8);  
    Re=4*Q./(pi.*D.*v);  
    f=0.25*(log10(e./(3.7*D)+5.74./(Re.^(0.9)))).^(-2); 
    hL=8*f.*L./(g*pi.^(2).*D.^(5)).*Q.^2;      
    sum1=hL(3)+hL(2)-hL(1);
    sum2=hL(5)+hL(6)-hL(3)-hL(4);
    sum3=hL(7)-hL(6)-hL(8);
    p=16.*f.*L./(g*pi.^2.*D.^5).*Q;    
    sumk1=sum(p(1:3));
    sumk2=sum(p(3:6));
    sumk3=sum(p(6:8));
    DQ1=sum1/sumk1;
    DQ2=sum2/sumk2;
    DQ3=sum3/sumk3;
end
Q(1)=Q1c;
Q(4)=Q4c;
Q(8)=Q8c;