evalit.m v3 (Jul 2013)

Evaluates a mathematical expression and rounds it accordingly to the error propagation theory.

HAVE YOU EVER WONDERED HOW MANY DIGITS SHOULD YOU USE FROM A CALCULATOR RESULT?

Well, this function will do it for you.

For example, let's calculate Earth's gravity:

>> % Symbolic inputs:
>> syms G M R
>> g = G*M/R^2;
>>
>> % Numerical inputs:
>> Gu=6.67384e-11; eGu=0.00080e-11; % Newton's Gravitational Constant and its error.
>> Me=5.97e24; eMe=-3; % 3 significant figures for Earth's mass.
>> Re=6.371e6; eRe=-4; % 4 significant figures for Earth's radius.
>>
>> % And the calculation:
>> evalit(g,{G M R},[Gu Me Re],[eGu eMe eRe])

So we get:

EVALIT: FUNC(G,M,R) = (G*M)/R^2
--------------------------------------------------
value +/- error (arguments' error contributions)
--------------------------------------------------
9.8160 +/- 0.0085 ( 0.0012 + 0.0082 + 0.0015 )
--------------------------------------------------

That is:
g = (9.8160 ± 0.0085) N/kg
instead of
g = 9.816008178047202... N/kg

As you can see, you'll also get the error contributions of each factor.
In this case, the Earth's mass (2nd one) results with the biggest error: 0.0082 N/kg.
While G contributes with the smallest error.

But most important is that all errors from every factor (G, M and R) have the same order of magnitude.

Besides...
- It works with matrix inputs.
- It andles function_handles (@'s) instead of symbolic expressions.
- It gives numerical and/or printed results.
- It exhaustively checks the inputs so it helps with input mistakes.
- It uses as minumum error the double-precision floating point (since v2).
- Inputs may be arrays of (almost) any kind: cells, matrixes, vectors (v3).
- Empty, zero, INF or NAN errors are changed to double floating point precision errors (v3).
- It uses first order error approx. but checks if they satisfy to be smaller than the second order ones (v3).
- It uses higher order error approx. when the first one is zero (v3).

Enjoy it!
Carlos Vargas