Warning: Explicit solution could not be found.

Hallo,

I have been trying to to generate a 100x100 table that includes the solution of a certain equation for 10000 different inputs.

My m.file has a double counter i and j and loops as follows

clear
clc

W=zeros(100,100);

for i=1:100
    for j=1:100
        W(i,j)=double(cost_factor(i/100,j/100,2));
    end
end

The function cost factor is called at every iteration and its source code is provided bellow:

function [w] = cost_factor(b,b_plus,x )
%This function is a subroutine that computes the cost factor w as a function of b,b_dash,x

% Inputs

% b        previous day's portfolio 
% b_plus   this day's portfolio
% x        previous day's stock price relative (x=2 or x=0.5)

% Outputs

% w        present cost relative 

c_p=0.01;
r=0;
syms w
assume(1/(1+c_p)<=w<=1)

w=solve(w+0.5*c_p*(abs(b_plus*w-b*x/(b*x+(1-b)*exp(r)))+(b_plus*w-b*x/(b*x+(1-b)*exp(r))))+...
    0.5*c_p*abs((1-b_plus)*w-(1-b)*exp(r)/(b*x+(1-b)*exp(r))+(1-b_plus)*w-(1-b)*exp(r)/(b*x+(1-b)*exp(r)))==1,w);

end

Everything seems to work fine when the first argument cost factor's inputs is larger than the second but in some of the cases where the converse is true I get the message 'Warning: Explicit solution could not be found. '. More specifically, I get this message when the difference b_plus-b>=0.48. So, my loop stops at W(1,52). Finally, note that b and b_plus are assigned values in [0,1] by the counters. Anyone that could enlighten me on the issue?

Thanks in advance,

Konstantinos

At the command prompt, please command

dbstop if warning

and then run your code. When it stops in the debugger, please use dbstep until you get back to the cost_factor routine. Then, please show us the expression

w+0.5*c_p*(abs(b_plus*w-b*x/(b*x+(1-b)*exp(r)))+(b_plus*w-b*x/(b*x+(1-b)*exp(r))))+...
  0.5*c_p*abs((1-b_plus)*w-(1-b)*exp(r)/(b*x+(1-b)*exp(r))+(1-b_plus)*w-(1-b)*exp(r)/(b*x+(1-b)*exp(r)))

Caution: it is safer to write out that compound assumption in full,

assume(1/(1+c_p)<=w & w <= 1)