# [SciPy-User] Matrix Exponentials For Very Large Sparse Matrices

Dylan Gorman dgorman@berkeley....
Fri Jan 22 19:24:00 CST 2010

```Dear Chuck and Joshua,

It's a problem in quantum simulation. I'm trying to solve d(rho)/dt =
L*rho for a sparse matrix L. L should be symmetric, and in principle I
just need to compute (e^L*t)*(rho(0)) or something--not e^(L*t)
explicitly.

Regards,
Dylan

On Jan 22, 2010, at 5:16 PM, Joshua Stults wrote:

> On Fri, Jan 22, 2010 at 8:04 PM, Charles R Harris
> <charlesr.harris@gmail.com> wrote:
>>
>>
>> On Fri, Jan 22, 2010 at 5:17 PM, Dylan Gorman
>> <dgorman@berkeley.edu> wrote:
>>>
>>> Hi Folks,
>>>
>>> I'd like to exponentiate very large sparse matrices with scipy,
>>> and I
>>> would be very grateful for any suggestions. Currently, I'm running
>>> into memory errors exponentiating random matrices of order 10^3x10^3
>>> with the standard linalg.expm() routine. However, I suspect that I
>>> may
>>> realistically be able to handle somewhat larger matrices since the
>>> actual matrices I will be using are quite sparse. Ideally, I'd
>>> like to
>>> be able to exponentiate matrices of size 10^5-10^6 x 10^5 - 10^6.
>>> However, there does not seem to be any linalg.sparse.expm()
>>> function--
>>> is this because there is in fact no advantage to exponentiating
>>> sparse
>>> matrices? Or would I need to implement something by hand?
>>>
>>
>> Out of curiosity, do the matrices have any special structure? For
>> instance,
>> are they banded or symmetric? Also, why to you want to exponentiate
>> them?
>>
> Another question: do you need the matrix exponential explicitly, or do
> you just need it's action on a vector?
>
>> Chuck
>>
>>
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>>
>
>
>
> --
> Joshua Stults
> Website: http://j-stults.blogspot.com
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```