Re: Big Loss of Precision

[Thomas D. Dean]

On 07/16/2016 12:05 PM, Montgomery-Smith, Stephen wrote:
> R is of the same order of magnitude as 1e4.  So dot(R,cross(R,V)) is of the 
> same order of magnitude as 1e8.  1e8 times octave eps is about 1e-8.
> ________________________________________
> From: Help-octave address@hidden on behalf of Thomas D. Dean address@hidden
> Sent: Saturday, July 16, 2016 1:35 PM
> To: address@hidden
> Subject: Big Loss of Precision
>
> The cross product of two vectors is orthogonal to both.  The dot product
> of two orthogonal vectors is zero.
>
> This is not an octave problem, just an ill-formed situation.
>
> octave:1405> printf(" %.20f\n",V);
>    3.99120302628332668249
>    -0.91842329903575536942
>    1.29246846883179156151
>
> octave:1406> printf(" %.20f\n",R);
>    -1518.35794621729837672319
>    -4017.17627231122196462820
>    4816.75939627815478161210
>
> octave:1407> dot(cross(R,V),R)
> ans =    1.4901e-08
> octave:1408> dot(cross(R,V),V)
> ans =    3.6380e-12
>
> cross has 6 multiplications and 3 add/subtract
> dot has 3 multiplications and 3 add/subtract
>
> Octave eps is 2.2204e-16
>
> machine eps is 1.11022e-16 (quadmath 1.925930e-34).
>
> This case has a very serious loss of precision!
>
> Tom Dean

A similar problem with similar magnitudes.  Very different outcome.
A = [2 4 8]; norm(A)
B = A.^4; norm(B)
C=cross(A,B)
dot(C,A)
dot(C,B)

tomdean