Using fzero function to solve a nonlinear function with two inputs

Hi,

My aim is to solve a non-linear equation for alpha with given values of X and al (both ranges of values). But I keep getting errors. Here is the code,

INPUTS:

function [n, m, Z] = setglblch
  n=1   ;
  m=1   ;
  Z=14;
end

function [D, A, R] = geom()
  D = 0.3; %Pipe Diameter (m)
  R = D/2; %Pipe Radius (m)
  A = pi*(R^2); %Cross-sectional Area (m^2)
end

function [X] = setX
  X=linspace(0,100,101) ;
end

function [al] = setal
  al=linspace(0,1,101) ;
end

SOLVING:

function y = equationsch(alpha, X, A, m, n, Z, al)

   beta1 = (1-al).^(-1) ;
   beta2 = al/((1/A)-al) ;
   beta3 = 1/alpha ;
   beta4 = beta1-beta2.*beta3 ;
   beta = beta4.^(-1) ;

      if X == 0
          y = 0;
      else
          y1 = al.^(1-0.5) ; 
          y2 = (1-al).^(0.5*m-1) ;
          y3 = X/Z ;
          y4 = beta.^(1+m) ;
          y5 = alpha.^(1+n) ; 
          y6 = (y4/y5).*y3 ;
          y = y1.*y2-y6 ;         
      end
end

WITH ONE INPUT X:

function [alpha] = getalphach
  [A] = geom();
  [n, m, Z] = setglblch();
  X = setX();
  al = setal();

    alpha = arrayfun( @(x) fzero( @(alpha) equationsch(angle, X, D, A, R, m, n, Z, al), [1E-4, pi-1E-4]), X );

end

I GET ERROR Not enough input arguments.

AND WITH TWO INPUTS X AND al:

function [alpha] = getalphach
  [A] = geom();
  [n, m, Z] = setglblch();
  X = setX();
  al = setal();

    alpha = arrayfun( @(x) fzero( @(alpha) equationsch(angle, X, D, A, R, m, n, Z, al), [1E-4, pi-1E-4]), X, al );

end

I GET ERROR Too many input arguments.

How can this be fixed?

Any help truly appreciated!

Answer 1

[Star Strider]

You need to change the argument from ‘alpha’ to ‘angle’ in the argument list for ‘equationch’.

With that change, it becomes:

alpha = arrayfun( @(x) fzero( @(angle) equationsch(angle, X, D, A, R, m, n, Z, al), [1E-4, pi-1E-4]), X, al );

I did not run your code, but that should resolve at least that problem.

[Egle]

Hello,

Well spotted, this is actually a typo, I am only using alpha argument in this model (angle was from a previous model).

However, after fixing that, the code still does not run and gives the same error.

Thanks!

[Star Strider]

My pleasure!

Note that in your function definition:

function y = equationsch(alpha, X, A, m, n, Z, al)

‘equationsch’ has 7 arguments.

In this line:

alpha = arrayfun( @(x) fzero( @(angle) equationsch(angle, X, D, A, R, m, n, Z, al), [1E-4, pi-1E-4]), X, al );

you are passing it 9 arguments. That is likely what is throwing the error.

[Egle]

Hi again,

Thank for your reply! I fixed them both to have 7 arguments, but it did not help. I keep getting error "Too many input arguments" if I try two inputs X and al.

Answer 2

[Egle]

REVISED CODE:

INPUTS

function [n, m, Z] = setglblch
  n=1   ;
  m=1   ;
  Z=14;
end

function [X] = setX
  X=linspace(0,100,101) ;
end

function [al] = setal
  al=linspace(0,1,101) ;
end

SOLVING:

function y = equationsch(alpha, X, al, m, n, Z)

    beta1 = alpha.*(1-al) ;
    beta2 = alpha-al ;
    beta = beta1./beta2 ;

      if X == 0
          y = 0;
      else
          y1 = al.^(1-0.5) ; 
          y2 = (1-al).^(0.5*m-1) ;
          y3 = X/Z ;
          y4 = beta.^(1+m) ;
          y5 = alpha.^(1+n) ; 
          y6 = (y4/y5).*y3 ;
          y = y1.*y2-y6 ;         
      end
  end

function [alpha] = getalphach
[n, m, Z] = setglblch();
X = setX();
al = setal();

alpha = arrayfun( @(x) fzero( @(alpha) equationsch(alpha, X, al, m, n, Z), [1E-4, pi-1E-4]), X, al );

end

I GET ERROR:

>> getalphach
Error using getalphach>@(x)fzero(@(alpha)equationsch(alpha,X,al,m,n,Z),[1E-4,pi-1E-4])
Too many input arguments.

[Star Strider]

The ‘x’ argument here:

@(x)fzero(@(alpha)equationsch(alpha,X,al,m,n,Z),[1E-4,pi-1E-4])

has to be present in the argument list for ‘equationsch’. It may need to be ‘alpha’ or ‘X’ instead.

(I am having a very difficult time understanding what you are doing, and have not yet succeeded.)

[Torsten]

Egle wants to avoid a double loop and call "fzero" for all possible combinations of the array elements from X and al.

Best wishes

Torsten.

[Egle]

Star Strider,

Thank you for the reply. I understand now that a "small x" should be used instead of capital X in the argument list for equationsch.

What I am trying to do: The equation y is a function of X, al and alpha. (y=0) I want to feed a range of values of X and a range of values of al to solve for alpha.

Does this help?

Egle

[Star Strider]

My pleasure.

It does help. The arrayfun function may not be able to do that.

I noticed that Torsten posted workable code that will do what you want (with a double loop) in your other related question. Torsten’s is probably the only workable solution.