I cannot get the real part of the function

Hi

I want to get the real part of this long function, but Matlab does not give me the solution, using "real" command. Here is the function which contains two positive symbols which have been defined as "syms e1 e2 positive". Furthermore, I do no know why it does not collect the numbers. I tried "rewrite" command as well but it does not help me in converting "abs" to square way. (sorry about this long function), I did not know how to compact it.

(17592186044416*abs((114122597371621^(1/2)*16204597220848377856^(1/2)*e1^(1/2)*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/766247770432944429179173513575154591809369561091801088)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/766247770432944429179173513575154591809369561091801088)*(4871707714029958889180730753024 - 4871707714029958326230777331712i))/(74069800477562839527407864990178895673762765033*e1^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) - 74069800477562839527407864990178895673762765033*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) - 74069800477562836847602839116461989558801661952*e1*e2^(1/2) - 74069800477562836847602839116461989558801661952*e1^(1/2)*e2 - 74069800477562839527407864990178895673762765033*e1^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 74069800477562839527407864990178895673762765033*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) - 74069800477562839527407864990178895673762765033*e1^(1/2) - 74069800477562839527407864990178895673762765033*e2^(1/2) + 74069800477562836847602839116461989558801661952*e1*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) - 74069800477562836847602839116461989558801661952*e1^(1/2)*e2*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) - 74069800477562836847602839116461989558801661952*e1*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) + 74069800477562836847602839116461989558801661952*e1^(1/2)*e2*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) + 74069800477562839527407864990178895673762765033*e1^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 74069800477562839527407864990178895673762765033*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e1 + 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e2 + 74069800477562836847602839116461989558801661952*e1*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 74069800477562836847602839116461989558801661952*e1^(1/2)*e2*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) - 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e1*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) - 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e2*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) - 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e1*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) - 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e2*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) + 3444817560549397682511369207808*114122597371621^(1/2)*16204597220848377856^(1/2)*e1^(1/2)*e2^(1/2) + 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e1*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e2*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 3444817560549397682511369207808*114122597371621^(1/2)*16204597220848377856^(1/2)*e1^(1/2)*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 3444817560549397682511369207808*114122597371621^(1/2)*16204597220848377856^(1/2)*e1^(1/2)*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) + 3444817560549397682511369207808*114122597371621^(1/2)*16204597220848377856^(1/2)*e1^(1/2)*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544)) + (2^(1/2)*114122597371621^(1/2)*16204597220848377856^(1/2)*e1^(1/2)*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/766247770432944429179173513575154591809369561091801088)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/766247770432944429179173513575154591809369561091801088)*(3444817560549397682511369207808 - 3444817560549397682511369207808i))/(74069800477562839527407864990178895673762765033*e1^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) - 74069800477562839527407864990178895673762765033*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) - 74069800477562836847602839116461989558801661952*e1*e2^(1/2) - 74069800477562836847602839116461989558801661952*e1^(1/2)*e2 - 74069800477562839527407864990178895673762765033*e1^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 74069800477562839527407864990178895673762765033*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) - 74069800477562839527407864990178895673762765033*e1^(1/2) - 74069800477562839527407864990178895673762765033*e2^(1/2) + 74069800477562836847602839116461989558801661952*e1*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) - 74069800477562836847602839116461989558801661952*e1^(1/2)*e2*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) - 74069800477562836847602839116461989558801661952*e1*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) + 74069800477562836847602839116461989558801661952*e1^(1/2)*e2*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) + 74069800477562839527407864990178895673762765033*e1^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 74069800477562839527407864990178895673762765033*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e1 + 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e2 + 74069800477562836847602839116461989558801661952*e1*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 74069800477562836847602839116461989558801661952*e1^(1/2)*e2*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) - 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e1*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) - 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e2*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) - 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e1*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) - 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e2*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) + 3444817560549397682511369207808*114122597371621^(1/2)*16204597220848377856^(1/2)*e1^(1/2)*e2^(1/2) + 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e1*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 1722408780274698841255684603904*114122597371621^(1/2)*16204597220848377856^(1/2)*e2*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 3444817560549397682511369207808*114122597371621^(1/2)*16204597220848377856^(1/2)*e1^(1/2)*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544) + 3444817560549397682511369207808*114122597371621^(1/2)*16204597220848377856^(1/2)*e1^(1/2)*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544) + 3444817560549397682511369207808*114122597371621^(1/2)*16204597220848377856^(1/2)*e1^(1/2)*e2^(1/2)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e2^(1/2)*2371823033998011i)/383123885216472214589586756787577295904684780545900544)*exp((2031713442118836966767109806277^(1/2)*182687704666362864775460604089535377456991567872^(1/2)*e1^(1/2)*790607677999337i)/383123885216472214589586756787577295904684780545900544)))^2)/6629077645451087

Answer 1

[Star Strider]

That’s a bit long to copy and paste, so I won’t.

The Symbolic Math Toolbox doesn’t ‘know’ what the real and imaginary parts of your function are because you only told it that:

syms e1 e2 positive

meaning that the real parts of those variables are positive, but that they could be complex. I would use the syms declaration to be:

syms e1 e2 real

to remove that ambiguity, if you want to define those symbolic variables to be real.

With respect to simplifying it, I would use:

x = simplify(x, 'steps',20)
x = vpa(x, 8)

You can of course combine them into one assignment, but keeping them as two statements will let you see the results of each operation.

[Hossein]

Many thanks for your answer. But the point is that I used 'syms e1 e2 real', but the problems remained. And also I used "simplify" but it gave me the similar function.

[Hossein]

It does not give me the real part. I think it is because of the abs function which is in the equation. I tried 'rewrite' but did not help me get the real part.

[Star Strider]

My pleasure.

Your expression is to difficult to read. If you used abs on the entire expression or significant parts of it, it will by definition be real because the result of abs is a real non-negative value.

If you declared:

syms x
y = real(x)

yields:

y =
real(x)

however if you declared:

syms x real
y = real(x)

yields:

y =
x

[Hossein]

You are right about the abs, but I need the real part of this to go solve a nonlinear equation using fsolve. If I am not mistaken, fsolve cannot hit this complex function including imaginary part in it (even in the abs part). I used fsolve, but it could not solve it.

[Hossein]

let me explain the actual problem. I want to solve tow nonlinear equations which are complex. I used fsolve, but when I put the initial guess, it gives me that guess not the answer which I expect!! So, I tried to find why, I figured out that fsolve just works with real number, therefore I though the real part of the function should be used for that. even if I use 'real' for the function, there is no difference between that and the equation without 'real' function. many thanks

[Hossein]

here is the file. many thanks

[Star Strider]

The fsolve function will return real and complex results if you want it to. You have to tell it where to look.

For example:

f = @(x,c) c(1).*x.^2 + c(2)*x + c(3);

c = poly([1 + 3*1i; 2 - 4*1i]);                             % Create Function With Complex Roots

B  = fsolve(@(x) f(x,c), [1i; -1i])

B =
            1 +          3i
            2 -          4i

Note the initial parameter estimates: ‘[1i; -1i]’.

Try that, and see if it works with your functions.

[Hossein]

Many thanks for all of your answers which were helpful. I checked this way, but still did not get the right root for my function. To make it easy, I decreased it to one nonlinear complex equation with just one variable. It is attached here (and much more easier to be read), you may be able to help me get out this problem. Thanks

[Hossein]

Hi friend. could you please help me with this problem? I send the function to you.

[Hossein]

I found the best way to do it. fzero is the function which can solve the complex equation of mine (or probably other equations). try fminsearch and fminunc as well.

[Star Strider]

I have no idea what equation you want to solve.

I am happy that you managed to get the result you want, because all my attempts at solving it did not work.

[Walter Roberson]

The code in complex_equation.m has multiple solutions, including an infinite number of positive real solutions that appear in pairs.

The expression has fairly bad numeric properties, involving ratios of values that are in the range of 10^200, so you should expect that any results you get out of a double-precision calculation to be highly suspect.

[Hossein]

Thanks for responding me. How can I avoid these bad numbers? Before reaching these equations, I put some practical numbers which are in order of 10^(-12), but matlab gives me this huge numbers. I guess it does not simplify them.

[Hossein]

even when I reduced the size of number, it could not solve it :(. Unfortunately, fzero is just for 1 equation. I have attached the reduced function with lower numbers here.

[Hossein]

I even reduced much more:

(0.0424403183*exp(-2.51446*imag(e1^(1/2))))/(abs(exp(e1^(1/2)*2.51446i) + 2.0*(1/e1)^(1/2) + 2.0*exp(e1^(1/2)*2.51446i)*(1/e1)^(1/2) - 1.0/e1 + exp(e1^(1/2)*2.51446i)/e1 - 1.0)^2*abs(e1))

_____________

e1 is unknown.

[Hossein]

even when I want to get the real part, it just gives an equation with abs which includes imaginary parts. I guess fsolve faces problems with equations which include "i", even when they are in general real.

Can I reach a pure real function with no "i" in it?

[Walter Roberson]

for (0.0424403183*exp(-2.51446*imag(e1^(1/2))))/(abs(exp(e1^(1/2)*2.51446i) + 2.0*(1/e1)^(1/2) + 2.0*exp(e1^(1/2)*2.51446i)*(1/e1)^(1/2) - 1.0/e1 + exp(e1^(1/2)*2.51446i)/e1 - 1.0)^2*abs(e1))

there are no real roots.

[Walter Roberson]

The function in your Equation_1segment.m has an infinite number of real roots in pairs that are about 5 apart from each other, with the pairs at increasing intervals.

[Walter Roberson]

Your function in Equation_1segment.m can be rewritten as

-(764536806725461/36028797018963968) * e1 / ((e1-1)^2*cos((5662050115671473/2251799813685248)*sqrt(e1))-e1^2-6*e1-1) - 8635647223004599/4611686018427387904

or roughly the form -A * f(e1) - B . With those particular constants it comes out as requiring that f(e1) be roughly -0.088244, which happens infinitely often because of the cos but not evenly spaced because of the linear terms. There is no closed form solution for this expression equalling 0.