How can I solve a cubic equation in which the coefficients are vector arrays?

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letoppina 2018-7-9

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回答： letoppina 2018-7-11

Hi everyone,

My intention is to find the roots of a cubic function. My only problem is that each coefficient is a vector array (1x30). Also, I want to take only the positive roots (and bigger than 0.1) so that in the end also the resulting roots vector has a dimension of 1x30. How can I do that? I have tried by making a loop but there is still something wrong.

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Stephan 2018-7-9

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Hi,

please share your code by inserting it, mark it and press the {}Code button, so that it looks like this:

A = Your code

Best regards

Stephan

letoppina 2018-7-10

编辑：letoppina 2018-7-10

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   R = linspace(1000,100e4,30); %I create my array 
for ii = 1:length(R)
    %coefficients of my polyonmial equation (they are all in function of R(ii) so that they are all arrays)
    a(ii) = CONSTANTS*R(ii); 
    b(ii) = CONSTANTS*R(ii);
    c(ii) = CONSTANTS*R(ii);
    d(ii) = CONSTANTS*R(ii);
end
%so my polynomial is defined by the coefficients:
p = [a(:) -b(:) -c(:) d(:)];
%i used roots in order to find the roots of my cubic equation
r = roots(p);

the problem is that since p is a matrix, i don't know how to delcare it when declaring the command "roots(p)". Of course, since it's a cubic equation, for each vector I will have 3 different roots. Then i will only select the one bigger than 0.1 by declaring:

V3 = r(r>0.1) %this should give a vecotr of the same length of R(ii) since i take only one root instead of three.

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Answer 1

letoppina 2018-7-11

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So in the end I have figured it was just a way to declare my variables. Here below my working code:

R = linspace(1000,100e4,30); %I create my array 
rts = zeros(3, length(R)); %inizialization of rts (matrix of the roots --> it,s a cubic equation, so three roots for each component of the arrays)
    for ii = 1:length(R)   
        a(ii) = CONSTANTS*R(ii);
        b(ii) = CONSTANTS*R(ii);
        c(ii) = CONSTANTS*R(ii);
        d(ii) = CONSTANTS*R(ii);
        p = [a1(ii) -b1(ii) -c1(ii) d1(ii)];
        rts(:,ii) = roots(p); %find the roots of the polynomial equation
    end
    coeff = rts.*(rts>0.1); %condition that I put in order to exctact only the parameters that I need

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Answer 2

Shantanu Gontia 2018-7-10

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You can find the roots for the polynomial inside the loop itself. I'm assuming that only one root will satisfy the criteria of being positive and greater than 0.1. Here is a sample code implementing this

R = linspace(1000,100e4,30); %I create my array 
% Declare roots array (initialize with zeros)
r = zeros(1, 30); % 30 roots
for ii = 1:length(R)
    %coefficients of my polyonmial equation (they are all in function of R(ii) so that they are all arrays)
    a(ii) = CONSTANT*R(ii); 
    b(ii) = CONSTANT*R(ii);
    c(ii) = CONSTANT*R(ii);
    d(ii) = CONSTANT*R(ii);
      p = [a(ii) -b(ii) -c(ii) d(ii)];
      rts = roots(p); % Get the roots
      rts = rts(rts > 0.1); % Get the roots satisfying the criteria
      r(ii) = rts(1); % Get one of the roots (if more than one)
  end