Failure in initial objective function evaluation. FSOLVE cannot continue. Please help:(

I have a system of 5 equations to solve which are originally in symbolic form

eqnA = m_s - ((A_sy*P_e)/sqrt(T_e))*sqrt(gamma/R)*M_sy*((1 + ((gamma-1)/2)*M_sy^2)^(-(gamma+1)/(2*(gamma-1))))*eta_s == 0;
eqnB = m_p - ((A_py*P_g)/sqrt(T_g))*sqrt(gamma/R)*M_py*((1 + ((gamma-1)/2)*M_py^2)^(-(gamma+1)/(2*(gamma-1))))*eta_s - m_p == 0;
eqnC = A_py + A_sy - A_3 == 0;
eqnD = P_g/P_c - (1 + (gamma-1)/2*M_py^2)^(gamma/(gamma-1)) == 0;
eqnE = P_e/P_c - (1 + (gamma-1)/2*M_sy^2)^(gamma/(gamma-1))== 0;

I also have known values

val_m_p = 0.3745, val_m_s = 0.1175, val_T_g = 298.0124, val_T_e = 298.0001, val_A_3 = 1.767*10^-4, val_P_e = 4.0000e+06, val_P_g = 5.1e+06

I substituted these values into the equations above, converted the equations into a function handle and proceeded to solve for the remaining 5 unknown variables

 %flow expansion
    eqnAx = subs(eqnA, {P_e, T_e, m_s}, {val_P_e, val_T_e, val_m_s})
    eqnBx = subs(eqnB, {P_g, T_g, m_p}, {val_P_g, val_T_g, val_m_p})
    eqnCx = subs(eqnC, A_3, val_A_3)
    eqnDx = subs(eqnD, P_g, val_P_g)
    eqnEx = subs(eqnE, P_e, val_P_e)
    
    g = matlabFunction([eqnAx; eqnBx; eqnCx; eqnDx; eqnEx])
    options = optimset('Display','off');
 x = fsolve(g, [0 0 0 0 0], options)

With g being

 g =

  function_handle with value:

    @(A_py,A_sy,M_py,M_sy,P_c)[sqrt(7.0).*7.576938695805846e+1.*2.965820800757861e+6.*5.119801572077356e+7.*A_sy.*M_sy.*1.0./(M_sy.^2./5.0+1.0).^3.*(-4.518723221790994e-13)+1.174896374819055e-1==0.0;sqrt(7.0).*7.576938695805846e+1.*2.965820800757861e+6.*5.119907258219913e+7.*A_py.*M_py.*1.0./(M_py.^2./5.0+1.0).^3.*(-5.761966781546089e-13)==0.0;A_py+A_sy-1.767e-4==0.0;5.100744432356854e+6./P_c-(M_py.^2./5.0+1.0).^(7.0./2.0)==0.0;4.000005838383844e+6./P_c-(M_sy.^2./5.0+1.0).^(7.0./2.0)==0.0]

However, I had error message

Not enough input arguments.

Error in
symengine>@(A_py,A_sy,M_py,M_sy,P_c)[sqrt(7.0).*7.576938695805846e+1.*2.965820800757861e+6.*5.119801572077356e+7.*A_sy.*M_sy.*1.0./(M_sy.^2./5.0+1.0).^3.*(-4.518723221790994e-13)+1.174896374819055e-1==0.0;sqrt(7.0).*7.576938695805846e+1.*2.965820800757861e+6.*5.119907258219913e+7.*A_py.*M_py.*1.0./(M_py.^2./5.0+1.0).^3.*(-5.761966781546089e-13)==0.0;A_py+A_sy-1.767e-4==0.0;5.100744432356854e+6./P_c-(M_py.^2./5.0+1.0).^(7.0./2.0)==0.0;4.000005838383844e+6./P_c-(M_sy.^2./5.0+1.0).^(7.0./2.0)==0.0]

Error in fsolve (line 248)
            fuser = feval(funfcn{3},x,varargin{:});

Error in Untitled10 (line 158)
    x = fsolve(g, [0 0 0 0 0], options)

Caused by:
    Failure in initial objective function evaluation. FSOLVE cannot continue.
    

I'm not too sure where it went wrong since the number of initialization parameters is the same as the number of unknowns. Please help:(

Answer 1

[Alan Weiss]

The error is that fsolve expects just one input argument, and you have many (I count 5 arguments, A_py,A_sy,M_py,M_sy,P_c) :

 g =

  function_handle with value:

    @(A_py,A_sy,M_py,M_sy,P_c)[sqrt(7.0).*7.576938695805846e+1.*2.965820800757861e+6.*5.119801572077356e+7.*A_sy.*M_sy.*1.0./(M_sy.^2./5.0+1.0).^3.*(-4.518723221790994e-13)+1.174896374819055e-1==0.0;sqrt(7.0).*7.576938695805846e+1.*2.965820800757861e+6.*5.119907258219913e+7.*A_py.*M_py.*1.0./(M_py.^2./5.0+1.0).^3.*(-5.761966781546089e-13)==0.0;A_py+A_sy-1.767e-4==0.0;5.100744432356854e+6./P_c-(M_py.^2./5.0+1.0).^(7.0./2.0)==0.0;4.000005838383844e+6./P_c-(M_sy.^2./5.0+1.0).^(7.0./2.0)==0.0]

To fix this issue, use the vars argument in matlabFunction:

g = matlabFunction([eqnAx; eqnBx; eqnCx; eqnDx; eqnEx],'vars',{A_py,A_sy,M_py,M_sy,P_c})

For another example using matlabFunction for optimization, see Calculate Gradients and Hessians Using Symbolic Math Toolbox™.

Alan Weiss

MATLAB mathematical toolbox documentation

[Aloysius Phneah]

Hey Alan, thank you for the reply! I've tried your suggestion and I understand that vars converts the 5 arguments into a single vector.

g = matlabFunction([eqnAx; eqnBx; eqnCx; eqnDx; eqnEx], 'Vars', [A_py,A_sy,M_py,M_sy,P_c])

However, I am still getting the same "Failure in initial objective function evaluation. FSOLVE cannot continue" error since g still remains as:

@(A_py,A_sy,M_py,M_sy,P_c)[sqrt(7.0).*7.576938695805846e+1.*2.965820800757861e+6.*5.119801572077356e+7.*A_sy.*M_sy.*1.0./(M_sy.^2./5.0+1.0).^3.*(-4.518723221790994e-13)+1.174896374819055e-1==0.0;sqrt(7.0).*7.576938695805846e+1.*2.965820800757861e+6.*5.119907258219913e+7.*A_py.*M_py.*1.0./(M_py.^2./5.0+1.0).^3.*(-5.761966781546089e-13)==0.0;A_py+A_sy-1.767e-4==0.0;5.100744432356854e+6./P_c-(M_py.^2./5.0+1.0).^(7.0./2.0)==0.0;4.000005838383844e+6./P_c-(M_sy.^2./5.0+1.0).^(7.0./2.0)==0.0]

with the @(A_py, A_sy, M_py, M_sy ,P_c) as 5 separate arguments instead of a single vector.

Is this an error on my part?

[Alan Weiss]

More an error on my part. Sorry. You need to set

g = matlabFunction([eqnAx; eqnBx; eqnCx; eqnDx; eqnEx], 'Vars', {[A_py,A_sy,M_py,M_sy,P_c]})

I forgot the curly braces around the Vars argument before.

Alan Weiss

MATLAB mathematical toolbox documentation

[Aloysius Phneah]

Hi Alan,

Thank you for the suggestion. I've tried the abovementioned suggestion and got the following function handle:

g =

  function_handle with value:

    @(in1)[sqrt(7.0).*7.576938695805846e+1.*2.965820800757861e+6.*5.119801572077356e+7.*in1(:,2).*in1(:,4).*1.0./(in1(:,4).^2./5.0+1.0).^3.*(-4.518723221790994e-13)+1.174896374819055e-1==0.0;sqrt(7.0).*7.576938695805846e+1.*2.965820800757861e+6.*5.119907258219913e+7.*in1(:,1).*in1(:,3).*1.0./(in1(:,3).^2./5.0+1.0).^3.*(-5.761966781546089e-13)==0.0;in1(:,1)+in1(:,2)-1.767e-4==0.0;5.100744432356854e+6./in1(:,5)-(in1(:,3).^2./5.0+1.0).^(7.0./2.0)==0.0;4.000005838383844e+6./in1(:,5)-(in1(:,4).^2./5.0+1.0).^(7.0./2.0)==0.0]

with the following error message:

    Error using fsolve (line 287)
FSOLVE requires all values returned by functions to be of data type double.

Error in Untitled10 (line 126)
    x = fsolve(g, [0 0 0 0 0], options)

Is this a case of fsolve not being able to find the solution to the (5 equations and 5 unknowns)? I've tried the same problem with vpasolve in symbolic form and it got stuck solving. Otherwise, would it be more convenient if I send my script over?

[Walter Roberson]

remove the == 0 in defining eqn variables. If they must be expressed as equations then take lhs(X)-rhs(X) where X is your vector of equations.