Using the bisection method, why is f(a) not a real integer or logical?

I am trying to use the bisection method to optimize the cost of the pipeline, but I can't get a value for f(a)? What am I doing wrong with my while loop or if statement?

function [x] = myPipeBuilder(C_ocean, C_land, L, H)
%L=length of x, C_ocean=cost of pipeline in ocean, C_land=cost of pipeline on land, H=some distance in water
a=0;

b=L;

xM = (a + b)/2;

f(xM)= (C_ocean/sqrt(H^2+xM^2))-C_land;
% derivative of function

while abs(f(xM))>1*10^(-6)
% tolerance 

      if sign(f(a))==sign(f(xM))

          a=xM;

      elseif sign(f(b))==sign(f(xM))

          b=xM;

      end

      xM = (a + b)/2; 

end

x=xM;

end

Answer 1

[Walter Roberson]

You have the statement

f(xM)= (C_ocean/sqrt(H^2+xM^2))-C_land;

that does not define a function f(xM), it defines an assignment to the array elment f(xM) where xM would have to be a valid subscript. subscripts can only be non-negative integers. You calculated xM on the line above as xM = (a + b)/2; and we have no reason to expect that the result is going to be an integer. For example if L had been passed in as 19 then since b=L and a=0, then (a+b)/2 would be (0+19)/2 which would be 9.5 which would not be an integer.

Answer 2

[Andrei Bobrov]

x = sqrt((C_ocean/C_land).^2-H^2);

[Christopher]

what do you mean by this?