CODEWITHSUNDEEP
matlabwolfram-mathematicaprecision
llxxee
llxxee

Reputation: 69

matlab double precision confusion

Matlab sets inputs to double precision by default, so if I input a=1/3 then the variable will be converted with double precision 

>> a=1/3
    a =0.3333

>> whos('a')
    a         1x1                 8  double

However, when I input vpa(a,100) afterwards, I get:

ans=0.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333

My question is that

since a is at double precision and has only 8 Bytes to store its data, why can it have a precision of 100 digits when it comes to vpa(a,100)? In a word, how does Matlab enhance the precision of a from 'double' to 100 digits?

Upvotes: 2

Views: 114

Answers (1)

Thomas
Thomas

Reputation: 1205

This is explained in the doc page of vpa, here is the link.

vpa Restores Precision of Common Double-Precision Inputs

Unlike exact symbolic values, double-precision values inherently contain round-off errors. When you call vpa on a double-precision input, vpa cannot restore the lost precision, even though it returns more digits than the double-precision value. However, vpa can recognize and restore the precision of expressions of the form p/q, pπ/q, (p/q)1/2, 2q, and 10q, where p and q are modest-sized integers.

First, demonstrate that vpa cannot restore precision for a double-precision input. Call vpa on a double-precision result and the same symbolic result.

So the answer is, that Matlab is smart enough to recover your expression, as it is of the form p/q.

Upvotes: 2

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