Computing the determinant of a C array

Question

I have written a program that generates a few N x N matrices for which I would like to compute their determinant. Related to this I have two questions

What library is the best for doing so? I would like the fastest possible library since I have millions of such matrices.
Are there any specifics I should take care of when casting the result to an integer? All matrices that I will generate have integer determinants and I would like to make sure that no rounding error skews the correct value of the determinant.

Edit. If possible provide an example of computing the determinant for the recommended library.

So by "a few" you mean "millions"? Cool. – unwind Jul 05 '12 at 13:34 — unwind, Jul 05 '12 at 13:34

score 4 · Accepted Answer · edited May 23 '17 at 11:44

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As for Matrix Libraries, it looks like that question is answered here:

Recommendations for a small c-based vector and matrix library

As for casting to an integer: if the determinant is not an integer, then you shouldn't be casting it to an integer, you should be using round, floor, or ceil to convert it in an acceptable way. These will probably give you integral values, but you will still need to cast them; however, you will now be able to do so without fear of losing any information.

edited May 23 '17 at 11:44

Community

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answered Jul 05 '12 at 13:36

Dancrumb

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Actually `floor` doesn't return an integer; as for `round`: http://stackoverflow.com/questions/485525/round-for-float-in-c (that's for c++, but applies to c too) – anatolyg Jul 05 '12 at 13:41

score 3 · Answer 2 · answered Jul 05 '12 at 13:37

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You can work wonders with matrices by blas and lapack. They are actually written in fortran and using them from "c" is kind of a tweak. but all in all they can crunch numbers in horrendous speed.

http://www.netlib.org/lapack/lug/node11.html

answered Jul 05 '12 at 13:37

Aftnix

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Are you sure they contain rutines to compute the determinant? LAPACK FAQ (http://www.netlib.org/lapack/faq.html#_are_there_routines_in_lapack_to_compute_determinants) states there is no such routine. – Jernej Jul 05 '12 at 14:30
The FAQ also says LAPACK can solve eigenproblems (http://www.netlib.org/lapack/faq.html#_what_and_where_is_lapack). The determinant of a matrix is the product of its eigenvalues. – andand Jul 05 '12 at 14:45
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Right. But the eigenvalues could be nasty real numbers with a messy product which would make the computation non stable – Jernej Jul 05 '12 at 16:48

score 2 · Answer 3 · answered Jul 05 '12 at 13:45

You have GSL, but the choice really depends on your matrices. Are the matrices dense or sparse? Is N big or small? For small Ns you may find that coding the determinant yourself using Cramer's rule or Gauss elimination is faster, since most hight performance libraries focus on big matrices and their optimisations may introduce overhead on simple problems.

Computing the determinant of a C array

3 Answers3