I need to compute a matrix that is the product of some other matrices. What happens is that the entries of those intermediate matrices (not of the final one) have an extremely large number of significant digits that must be correctly expressed, and standard 64-bit precision is not enough at all. However, once that the final matrix has been computed, it does not have any issue and can be safely expressed using 64-bit precision.
Until now, the only thing that seems to work is storing all the intermediate matrices as sym variables, and applying double() to the result. However, this is EXTREMELY slow, so I have tried to use vpa, which runs must faster, but, unfortunately, I am completely unable to make vpa work with the number of digits it should. I have set the variable digits manually, and also introduced the amount of digits as the second parameter of vpa, but Matlab seems completely unable to work with more than thirty some digits.
Explaining the whole problem would be difficult, but a very minimal version might be the following one:
vpa(prod(sym(1:100)), 1000)
returns the correct answer:
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000.0
whereas
prod(vpa(1:100,1000))
returns
9.3326215443944152681699238856267e+157
and
vpa(prod(vpa(1:100,1000)),1000)
returns an answer where most digits seem to be random.
93326215443944152681699238856266700490706771753645076823290786995083431421157053646876168787770989280157062278101708191343825014815923981815334275914865311744.0
Any help on this would be greatly appreciated.
