I am trying to use the fsolve function to solve a non linear equation .In the function i created all the constants are matrices.and i expect a vector of the unknown.I keep getting error of not enough input argument.Iwould much appreciate your help.

function F = TRIAL3(x, V1,W1 ,W, w, z, Z1,Z, p, p1, q1, q, c1, V, v, j)

a=x(1); r = x(2); s = x(3); b=x(4); g = x(5); d = x(6); h = x(7);

F = [(V1*((c1- W*r - Z*s)+(p*b- W*r*b^2 -Z*s*b.^2 - j*d*b) +(q*g- W*r*g^2- Z*s*g.^2 - j*h*g)))-1*a- a*b^2 - a*g.^2;

   (W1*((c1- V*a - Z*s)+(p*b- V*a*b^2 -Z*s*b.^2 - j*d*b) +(q*g- V*a*g^2 - Z*s*g.^2 - j*h*g)))-1*r- r*b^2 - r*g.^2;

   (Z1*((c1- V*a- W*r)+ (p*b- V*r*b^2 -W*r*b.^2 - j*d*b) +(q*g- V*a*g^2 - W*r*g.^2 - j*h*g)))-1*s- s*b^2 -  s*g.^2;

   (inv(a'*v*V*a + a'*v*W*r +a'*v*Z*s +  r'*w*V*a + r'*w*W*r+ r'*w*Z*s + s'*z*V*a+ s'*z*W*r +s'*z*Z*s)*(p1*V*a+ p1*W*r + p1*Z*s -a'*v*j*d - r'*W'*j*d +s'*Z'*j*d))-b;

   (inv(a'*v*V*a + a'*v*W*r +a'*v*Z*s +  r'*w*V*a + r'*w*W*r+ r'*w*Z*s + s'*z*V*a+ s'*z*W*r +s'*z*Z*s)*(q1*V*a+ q1*W*r + q1*Z*s -a'*v*j*h - r'*W'*j*h +s'*Z'*j*h))-g;

   (0.2*p1*j - 0.2*a'*v*j*b - 0.2*r'*w*j*b - 0.2*s'*z*j*b)- d;

   (0.2*q1*j - 0.2*a'*v*j*b - 0.2*r'*w*j*g - 0.2*s'*z*j*g)- h];

%below is my call function;

fun=@TRIAL3; Xo=[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; X=fsolve(fun,Xo)

%my error message Error using TRIAL3 (line 5) Not enough input arguments.

Error in fsolve (line 217) fuser = feval(funfcn{3},x,varargin{:});

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

Answer 1

[Torsten]

fun = @(x)TRIAL3(x, V1,W1 ,W, w, z, Z1,Z, p, p1, q1, q, c1, V, v, j);
Xo = [1 1 1 1 1 1 1];
X = fsolve(fun,Xo)

[Honey Adams]

i am still getting an error .which i presume is from the x uknowns.These a=x(1); r = x(2); s = x(3); b=x(4); g = x(5); d = x(6); h = x(7); are all supposed to be matrices.How do i define the intialial matrices for solve.I would be glad for your assitance.

%the new error Error using - Matrix dimensions must agree.

Error in TRIAL3 (line 5) F=[(V1*((c1- W*r - Z*s)+(p*b- W*r*b^2 -Z*s*b.^2 - j*d*b) +(q*g- W*r*g^2- Z*s*g.^2 - j*h*g)))-1*a- a*b^2 - a*g.^2;

Error in @(x)TRIAL3(x,V1,W1,W,w,z,Z1,Z,p,p1,q1,q,c1,V,v,j)

Error in fsolve (line 217) fuser = feval(funfcn{3},x,varargin{:});

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

[Torsten]

You must save and concatenate the unknown matrices in one long vector of unknowns.

E.g. if a and r are 3x3 matrices, you can save them in an 18-element x-vector as

x=(a(1,1),a(1,2),a(1,3),a(2,1),a(2,2),a(2,3),a(3,1),a(3,2),a(3,3),r(1,1),r(1,2),r(1,3),r(2,1),r(2,2),r(2,3),r(3,1),r(3,2),r(3,3))

Best wishes

Torsten.

[Honey Adams]

Thank you for your quick response. I am glad. I would like to know whether the unknown vectors need to be defined inside the function or outside the function and how do i also initialize the initial solutions.

[Torsten]

The vector of initial guesses x0 must be created outside the function before calling "fsolve".

Now "fsolve" calls your function with a vector x of the same length as the vector of initial guesses. From this vector, you have to reconstruct your matrices

(e.g. a and r as
a = [x(1) x(2) x(3);x(4) x(5) x(6); x(7) x(8) x(9)];
r = [x(10) x(11) x(12); x(13) x(14) x(15) ; x(16) x(17) x(18)];  
)

and calculate F.

Best wishes

Torsten.

[Honey Adams]

I am finding it difficult to understand.from my code above I have assigned 7 unknown variables to x which all happen to be a matrix. The first problem is where to put the new assigned unknown vector.I tried fixing it both inside the function argument and outside but i keep getting errors. I would be glad if you could also explain the initialization bit further for me My a,r ,s are each 5x1 matrices with b,d ,h,g being a scalar . x=[a(1,1),a(2,1),a(3,1),a(4,1),a(5,1) ,r(1,1),r(2,1),r(3,1),r(4,1),r(5,1), s(1,1),s(2,1),s(3,1),s(4,1),s(5,1),b(1,1),g(1,1),d(1,1),h(1,1)] Undefined function 'a' for input arguments of type 'double'.

[Torsten]

function F= TRIAL3(x,V1,W1,W,w,z,Z1,Z,p,p1,q1,q,c1,V,v,j)
a=[x(1);x(2);x(3);x(4);x(5)];
r=[x(6);x(7);x(8);x(9);x(10)];
s=[x(11);x(12);x(13);x(14);x(15)];
b=x(16);
g=x(17);
d=x(18);
h=x(19);
F = ...

and F must be a 1x19 vector.

Best wishes

Torsten.

[Honey Adams]

fun = @(x)TRIAL3(x, V1,W1 ,W, w, z, Z1,Z, p, p1, q1, q, c1, V, v, j); Xo = [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; X = fsolve(fun,Xo) I am getting error message evertything seems ok too

Error: File: TRIAL3.m Line: 4 Column: 10 Expression or statement is incorrect--possibly unbalanced (, {, or [.

Error in @(x)TRIAL3(x,V1,W1,W,w,z,Z1,Z,p,p1,q1,q,c1,V,v,j)

Error in fsolve (line 217) fuser = feval(funfcn{3},x,varargin{:});

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

[Honey Adams]

I think it worked. Thank you so much. May I have your email address if you don't mind. You saved me after a week of trying to read soo many Matlab previous questions. I am glad for your assistance.

[Honey Adams]

Hello Tornsten,I would like to implement this same nonlinear equation with genetic algorithm.I keep getting not enough input argument,I would be glad if you could assist.Thanks for your time.