ilaplace confusing - result from command window and from m file gui is not the same

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john 2014-1-20

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编辑： john 2014-2-27

采纳的回答： Mischa Kim

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Hi,

I write in command window:

ilaplace((0.99984898859777815438576453743735*s^2 + 1414.0*s - 414151.01140222184561423546256265)/((s + 1000.0)*(s^2 + 1000000.0)))

And I got : ans =

(199002808534433793169*cos(1000*t))/140737488355328000000 - 58286573144567511919/(140737488355328000000*exp(1000*t)) - (1169*sin(1000*t))/140737488355328000000

I write the same in m file from GUI and I got:

    0.707*exp(1000.0*t*i) - 0.41415101140222184561423546256265/exp(1000.0*t) + 0.707*(1/exp(1000.0*t*i))

WHY I GOT COMPLEX NUMBER? "i"?

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john 2014-1-21

No idea?

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采纳的回答

Mischa Kim 2014-1-21

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https://ww2.mathworks.cn/matlabcentral/answers/113043-ilaplace-confusing-result-from-command-window-and-from-m-file-gui-is-not-the-same#answer_121624

编辑：Mischa Kim 2014-1-21

Hello John, it is actually the same. Try plotting the two results.

The reason you get complex numbers is because of Euler's formula:

exp^(ix) = cos(x) + i*sin(x)

If you analyze the results you'll see that you get (really) small imaginary numbers. That's because the computation is done in floating point arithmetic (see this answer). In case you are not comfortable with the imaginary parts, just plot the real parts.

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john 2014-2-25

编辑：john 2014-2-27

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Sorry, but for relative little number simplify doesn't help.

In command window I it is OK, I get:

>> r=simplify(ilaplace(-((4280819729186186979044460847261*s^2)/51422017416287688817342786954917203280710495801049370729644032 + (994733177774077628149071673933*s)/50216813883093446110686315385661331328818843555712276103168 - 949357667952072971550917252451/1569275433846670190958947355801916604025588861116008628224)/((3*s + 200)*(s^2 + 98596))))
r =
19981467697883435869/(3970734387895709337413208929317684822969348320657408*exp((200*t)/3)) - (694227838351497933185*cos(314*t))/21177250068777116466203780956360985722503191043506176 - (11693735405742169632973*sin(314*t))/831207065199501821298498402537168689608250248457617408

But in guide I get:

r=simplify(ilaplace(-((4280819729186186979044460847261*s^2)/51422017416287688817342786954917203280710495801049370729644032 + (994733177774077628149071673933*s)/50216813883093446110686315385661331328818843555712276103168 - 949357667952072971550917252451/1569275433846670190958947355801916604025588861116008628224)/((3*s + 200)*(s^2 + 98596))))
r =
3.0679013785265445477520983725365*10^(-35)*dirac(t)

Why? It is sooo bad!

john 2014-2-26