ATAN2_SAFE 1.0

This will perform the same function as Matlab built-in function ATAN2 butsafely guarded against erroneous results when the inputs are very small (near to a machine zero).Due to the round off errors in the numerical calculations, the twoinputs to ATAN2, Y and X, had better be thought as x=x_exact + (or -) rand*eps; y=y_exact + (or -) rand*eps;When the theoretically expected values x_exact and y_exact arefar above the machine accuracy, ATAN2 will give you a goodanswer, insensitive to the small unpredictable round off errors.On the other hand, when one or both of the theoretical values iszero, ATAN2 becomes very sensitive to the round off errors andwill give an erroneous result. Consider the case whereboth x_exact and y_exact are zero, then the call to ATAN2 isequivalent to the following random experiment x=(rand-0.5)/0.5*eps; y=(rand-0.5)/0.5*eps; theta=atan2(y, x); Now theta becomes a random number ranging all over between-pi and pi. (This should apply to ATAN as well).Since ATAN2(0,0) will give an exact zero, and since the round-offerrors due to the machine accuracy cannot be meaningfullydistinguished from the true zero, we had better clear off (zero out)the small round off errors before we call ATAN2. To relieve youfrom the cleaning burden every time when you need to call ATAN2,ATAN2_safe automates the cleaning and the calling two stepsfor you.

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Apply,  Drand Eps,  Number,  Ranging,  Theta,  Theta Datan
Users rating:	0/10