Let's say I have a function, f, that maps R^3 to R^3, and I want to find its multivariable roots numerically, using fsolve.
What's a good way to use the counting index, i, in the loops?
For instance, if f(x,y,z) = ( f_1(x,y,z), f_2(x,y,z), f_3(x,y,z) ), and I want to solve f = (0,0,0), then I could write nested for-loops that do something like this:
for x_guess = linspace(-10,10,10)
for y_guess = linspace(-10,10,10)
for z_guess = linspace(-10,10,10)
i = ...
[ multivariable_roots, FVAL, EXITFLAG, OUTPUT, JACOB ] = fsolve( f, [x_guess, y_guess, z_guess] )
Where's a good place to put the counting index? At the innermost loop? Could I do so at the outermost loop?
My mentor showed me a code that uses the counting index in the innermost loop (the code structure that I provided above), but I currently don't understand it, so I'd like to write my own nested for-loops in order to understand what it does.
Also, would using more than one counting index be helpful? I'm thinking of using counting indices i, j, k, if it makes the nested for-loops easier to understand. For instance, in a double summation, we would typically fix i and sum through j -- and then fix another i and sum through j again, etc. Could I do something analogous in nested for-loops? I think I might actually prefer using a different counting index for each loop, since things might look more explicit that way.