Using fzero function to solve a nonlinear equation with one input

Question

Egle 2017-2-13

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https://ww2.mathworks.cn/matlabcentral/answers/324808-using-fzero-function-to-solve-a-nonlinear-equation-with-one-input

评论： Egle 2017-3-23

Hi,

I am trying to solve this non-linear equation for alpha using a range of values of X (0-100) [so that I can plot alpha vs X].

function y=equations(alpha)
[D, A, R] = geom();
[n, m] = setglbl();
[X] = setX();
              Ag            = (R.^2)*(pi-alpha+0.5*sin(2*alpha))             ; 
              Sgw           = 2*R*(pi-alpha)                                 ; 
              Si            = 2*R*sin(alpha)                                 ; 
              Dg            = 4*Ag/(Sgw+Si)                                  ; 
              Al            = (R.^2)*(alpha-0.5*sin(2*alpha))                ; 
              Slw           = 2*R*alpha                                      ; 
              Dl            = 4*Al/Slw                                       ; 
              ag            = Ag/A                                           ; 
y=((X.^2).*(1-ag).^(n-2)*(D/Dl).^(n+1))-(ag.^(m-2)*(D/Dg).^(m+1)*(1+(Dg*Si/Al)));
end

WHERE

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

AND

function [Cg, Cl, n, m] = setglbl
global Cg Cl n m
n=1;
m=1;
end

AND

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

I KEEP GETTING ERRORS:

Error using fzero (line 301)
FZERO cannot continue because user-supplied function_handle ==> equations failed with the error below.
   *Matrix dimensions must agree.*
  >> equations
*Not enough input arguments.*
Error in equations (line 7)
            Ag            = (R.^2)*(pi-alpha+0.5*sin(2*alpha))             ; % [m^2] Cross-sectional area of gas phase in pipe

Does anyone have some advice on what the problem could be?

Should the X interval be defined differently? Or should X be used as a second input to the function?

Any help appreciated!

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Answer 1

Walter Roberson 2017-2-14

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/324808-using-fzero-function-to-solve-a-nonlinear-equation-with-one-input#answer_254654

在 MATLAB Online 中打开

You need to change

function [n, m] = setglbl
global n m
n=1;
m=1;
end

However, you have

X=linspace(0,100,101) ;

so X is a vector of length 101, and you have

y=((X.^2).*(1-ag).^(n-2)*(D/Dl).^(n+1))-(ag.^(m-2)*(D/Dg).^(m+1)*(1+(Dg*Si/Al)));

so y is going to be a vector the same length as X. You cannot fzero an entire vector.

Your formula has some numeric problems that need to be worked around. Revised source is:

function alphaVsX
    [D, A, R] = geom();
    [n, m] = setglbl();
    X = setX();
      alpha = arrayfun( @(x) fzero( @(alpha) equations(alpha, x, D, A, R, m, n), [1E-4, pi-1E-4]), X );
      plot(X, alpha);
      xlabel('X')
      ylabel('alpha')
  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 [n, m] = setglbl
    n=1;
    m=1;
end
function [X] = setX
    X=linspace(0,100,101) ;
end
function y = equations(alpha, X, D, A, R, m, n)
    Ag            = (R.^2)*(pi-alpha+0.5*sin(2*alpha))             ;
    Sgw           = 2*R*(pi-alpha)                                 ;
    Si            = 2*R*sin(alpha)                                 ;
    Dg            = 4*Ag/(Sgw+Si)                                  ;
    Al            = (R.^2)*(alpha-0.5*sin(2*alpha))                ;
    Slw           = 2*R*alpha                                      ;
    Dl            = 4*Al/Slw                                       ;
    ag            = Ag/A                                           ;
      if X == 0
          y = 0;
      else
          y=((X.^2).*(1-ag).^(n-2)*(D/Dl).^(n+1)) - (ag.^(m-2)*(D/Dg).^(m+1)*(1+(Dg*Si/Al)));
      end
end

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Egle 2017-3-16

在 MATLAB Online 中打开

Hello again Walter,

I am trying to adjust previous code to solve a slightly different problem (with two inputs this time). But it does not seem to work.

Could you please give me some advice on this?

My aim is to solve a non-linear equation for alpha with given values of X and al (both ranges of values). 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
function [alpha] = getalphach
[A] = geom();
[n, m, Z] = setglblch();
X = setX();
al = setal();
    alpha = arrayfun( @(x) fzero( @(alpha) equationsch(alpha, X, D, A, R, m, n, Z, al), [1E-4, pi-1E-4]), X, al );
  end

I GET ERROR Too many input arguments.

Can this be fixed? Is it okay to use arrayfun in this case?

Thanks in advance!

Egle

Egle 2017-3-17

Hello again,

Thank you for your reply. Sorry, I didn't need D or R in the function, but it still does not work after deleting it. (Error: too many inputs)

Both my inputs X and al are vectors. Could this be causing the issue?

Thanks in advance! Egle

Walter Roberson 2017-3-17

在 MATLAB Online 中打开

You have

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

which has three arguments for arrayfun: the function handle, X, and al . arrayfun() takes a function handle and passes each of the remaining arguments to it, so because you are providing two arguments after the function handle, the function handle has to take two arguments. But it does not: the function handle takes only one argument, lower-case x. If each X entry is to be paired with each al entry, then you need to have your function handle

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

take two arguments instead.

After that, notice that your function handle has a formal parameter lower-case x as an argument, but it does nothing with that argument. Instead, it passes upper-case X to the function, which is the entire vector of X values.

Perhaps you want

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

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Answer 2

Torsten 2017-3-17

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/324808-using-fzero-function-to-solve-a-nonlinear-equation-with-one-input#answer_259156

在 MATLAB Online 中打开

Does this work ?

function [alpha] = getalphach
[A] = geom();
[n, m, Z] = setglblch();
X = setX();
al = setal();
for i=1:numel(X)
  Xloc = X(i);
  for j = 1:numel(al)
    alloc = al(j);
    alpha(i,j) = fzero(@(x)equationsch(x,Xloc,A,m,n,Z,alloc),[1e-4, pi-1e-4]);
  end 
end

Best wishes

Torsten.

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Torsten 2017-3-17

编辑：Torsten 2017-3-17

在 MATLAB Online 中打开

Try to call fzero with a single starting value, e.g.

alpha(i,j) = fzero(@(x)equationsch(x,Xloc,A,m,n,Z,alloc),pi-1e-4);

If fzero cannot find a solution, you should first plot your function to see whether a zero really exists.

By the way: Your call to fzero must be with a small x:

Not:

alpha(i,j) = fzero(@(x)equationsch(X,Xloc,m,n,Z,alloc),[1e-4, pi-1e-4]);

But:

alpha(i,j) = fzero(@(x)equationsch(x,Xloc,m,n,Z,alloc),[1e-4, pi-1e-4]);

Best wishes

Torsten.

Egle 2017-3-17

编辑：Egle 2017-3-21

在 MATLAB Online 中打开

Dear Torsten,

Thank you for your help! And apologies for disturbing you again.

I finally managed to get your suggested double loop working! The problem was that my al range was defined as: al=linspace(0,1,101) ; and the 0 was putting the code off, once changed to: al=linspace(0.01,1,101) ; it's working fine.

However, I now realised that I cannot use any combinations of X and al ranges. I have a set of experimental (coupled) values instead.

If al and X were defined as such,

function [X, al] = setmartvar
    datalockmart = [0.01 1 1.05 ; 0.02 1 1.07 ; 0.04 1 1.12 ; 0.07 0.96 1.19 ; 0.10 0.96 1.24 ; 0.2 0.91 1.4 ; 0.4 0.86 1.7 ; 0.7 0.81 2.16 ; 1.0 0.77 2.61 ; 2.0 0.69 4.12 ; 4.0 0.60 7 ; 7 0.52 11.2 ; 10 0.47 15 ; 20 0.34 27.3 ; 40 0.24 50 ; 70 0.16 82 ; 100 0.1 111] ;
    X = datalockmart(:,1) ;
    aglm = datalockmart(:,2) ;
    al=1-aglm ;
  end

Can this be incorporated in the loops instead?

function [alpha] = getalphach
[A] = geom();
[n, m, Z] = setglblch();
X = setX();
al = setal();
for i=1:numel(X)
Xloc = X(i);
  for j = 1:numel(al)
    alloc = al(j);
    alpha(i,j) = fzero(@(x)equationsch(x,Xloc,A,m,n,Z,alloc),[1e-4, pi-1e-4]);
  end 
end

Thanks in advance!

Egle

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Answer 3

Torsten 2017-3-22

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/324808-using-fzero-function-to-solve-a-nonlinear-equation-with-one-input#answer_259795

在 MATLAB Online 中打开

Sure.

function [alpha] = getalphach
[A] = geom();
[n, m, Z] = setglblch();
[X,al] = setmartvar();
for i=1:numel(X)
  Xloc = X(i);
  alloc = al(i);
  alpha(i) = fzero(@(x)equationsch(x,Xloc,A,m,n,Z,alloc),[1e-4, pi-1e-4]);
end

Best wishes

Torsten.

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Egle 2017-3-23

This helps, thank you! The code is finally working as expected

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