Error using symengine in numerical solver

Question

David Keller 2020-3-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/512600-error-using-symengine-in-numerical-solver

评论： Walter Roberson 2020-3-28

Hi guys

Im trying to calculate the Worst Case Expected returns according to Tüntücu and König (2004). In order to derive the robust weights, I need to solve an equation numerically. Below is the code for the calculation of the weights.

syms w_r
S = vpasolve(0==(1-((length(r_dc_s)^(-0.5))*(chi2inv(0.95,length(mu))))... 
    /(1*sqrt(w_r'*V*w_r)+((length(r_dc_s)^(-0.5))*(chi2inv(0.95,length(mu))))))...
    *w1+w2-w_r,w_r);

w_r would be the robust weights in a vector of Nx1. When I run the code, I always get the following error message:

Error using symengine
Invalid operands.
Error in sym/privBinaryOp (line 1032)
            Csym = mupadmex(op,args{1}.s, args{2}.s, varargin{:});
Error in  /  (line 375)
        X = privBinaryOp(A, B, 'symobj::mrdivide');  

If I understand the error message correctly, I would have to use element-wise multiplication or division. I do not see though where this would make sense. It can be seen that only the first line of the equation would result in a 1x1 double object, so would the second. The third line contains only Nx1 vectors (w1 and w2 are the speculative and minimal weights). The only place where I can imagine it could make sense to perform a element-wise multiplication would be .*w1+w2-w_r. This leads to the same error message though..

Do you guys can help me out with this? Would be highly appreciated!

Thanks in advance,

David

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Answer 1

Walter Roberson 2020-3-28

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https://ww2.mathworks.cn/matlabcentral/answers/512600-error-using-symengine-in-numerical-solver#answer_422553

syms w_r
S = vpasolve(0==(1-((length(r_dc_s)^(-0.5))*(chi2inv(0.95,length(mu))))... 
    /(1*sqrt(w_r'*V*w_r)+((length(r_dc_s)^(-0.5))*(chi2inv(0.95,length(mu))))))...
    *w1+w2-w_r,w_r);

w_r would be the robust weights in a vector of Nx1

No, when you syms and give a name, the symbolic solver always treats it as referring to a scalar. With your expression being non-scalar, you would be asking vpasolve() to find the single w_r that solves all of the elements in the vector simultaneously. vpasolve() always treats the input as simultaneous equations, and never as an array of equations to solve individually.

In the case where the desired w_r do not interact with each other, the easiest approach is:

syms w_r
S = arrayfun(@(EXPR) vpasolve(EXPR, w_r), 0==(1-((length(r_dc_s)^(-0.5))*(chi2inv(0.95,length(mu))))... 
    /(1*sqrt(w_r'*V*w_r)+((length(r_dc_s)^(-0.5))*(chi2inv(0.95,length(mu))))))...
    *w1+w2-w_r, 'uniform', 0);

The uniform, 0 option is there because I speculate that there might not be (findable) solutions for some of the values.

In the case where the w_r values do interact with each other, then you need to create a symbolic vector:

w_r = sym('w_r', N, 1);

followed by your existing vpasolve()

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David Keller 2020-3-28

The first option worked, the second option did not. After reading a bit about arrayfun, it is clear what I did wrong with my code at the start.

Walter Roberson 2020-3-28

You might find that you do not need the 'uniform', 0 option. I put it in to cover the case where vpasolve() could not find a solution.

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Answer 2

Devineni Aslesha 2020-3-27

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https://ww2.mathworks.cn/matlabcentral/answers/512600-error-using-symengine-in-numerical-solver#answer_422247

Hi David,

The above issue is replicated by assuming that ‘V’ is also a NX1 vector. The issue can be solved by using ‘./’ instead of ‘/’ in the vpasolve expression.

Here is a similar question for your information.

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Walter Roberson 2020-3-28

vpasolve() simply does not support having more equations than variables for non-polynomial systems. vpasolve() uses modified newton for nonlinear cases, and that method only works for square systems (same number of equations and variables.)

David Keller 2020-3-28

Thank you for your answers, really appreciate it. I understand the error message now, no idea though how to solve it. Seems like my approach won't work as I have hoped.

Anyways, thanks again and all the best,

David

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