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solving equation with if statements

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antoine
antoine on 17 Jan 2020
Commented: antoine on 22 Feb 2020 at 23:32
Hello
I am trying to solve the following equation given input time and values (y) vectors.
I tried the following
syms theta kappa alpha
if time < alpha
eqn = exp(-kappa*time)==y;
else
eqn = exp(-kappa)*exp(-theta*(time-alpha))==y;
end
vars = [theta kappa alpha];
S=solve(eqn);
but it raises an error...
Conversion to logical from sym is not possible.
I tried to convert alpha into double (i.e. double(alpha) ) in the if statement but it did not work...
Any suggestions?
the data look like :
Picture1.png

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Accepted Answer

Walter Roberson
Walter Roberson on 17 Jan 2020
syms theta kappa alpha time y real
eqn = y == piecewise(time < alpha, exp(-kappa*time), exp(-kappa)*exp(-theta*(time-alpha)));
vars = [theta kappa alpha];
S = solve(eqn, kappa, 'returnconditions', true); %solve for which variable ??

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antoine
antoine on 20 Jan 2020
If I run the code above once, I got the following
If 266 is alpha, this is really what I would expect... I am probably missing something (I used alpha guess=150)
best_parameters =
0.0065 0.0060 266.0000
Walter Roberson
Walter Roberson on 20 Jan 2020
Yup, but that gives residue in the range of 62, whereas 5087.59871387777093, 0.00292734523205026836, 803477.437304047635 gives you residue in the range of 39.02 which is significantly better. Given that model, alpha should be large, over 100,000.
antoine
antoine on 20 Jan 2020
ahaha.. I get it. thank you!

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More Answers (2)

antoine
antoine on 18 Jan 2020
time and y are vectors (see plot above for data input). all suggestions are welcome.
I can share the data if it helps
thank you ++

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Walter Roberson
Walter Roberson on 18 Jan 2020
Unless time and y are vectors of length 3 exactly, it seems unlikely that there would be any solutions.
It looks to me as if what you have should be a modeling task to estimate parameters rather than a set of simultaneous equations.

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antoine
antoine on 18 Jan 2020
good not know...Not sure I have the skills to do that.
I really appreciated your input and advices.

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antoine
antoine on 22 Feb 2020 at 23:32
dear Walter
Just realized I forgot to thank you for your help
Problem is fixed! I got my equations working.
(I am know stuck with other timer/loop function : see 'time-dependant iteration through a loop?' if you have time...)

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