[GiNaC-list] matrix::solve()-related problems

[Vitaly Magerya]

On 01/31/2018 12:26 PM, Richard B. Kreckel wrote:
> Could you guys please re-test against current git HEAD? The crashes you
> reported should be fixed and timings should have improved.

The crashes have vanished in my test case. Well done.

> Based on this, it may now make more sense to compare algorithms for
> solving linear equations.

With today's commits, the same toy benchmark gives these timings (with 5
measurements per matrix size):

    matrix  gauss time/bareiss time
    size    average   min     max
    2x2     1.261     1.181   1.313
    3x3     1.569     1.385   1.661
    4x4     1.549     1.490   1.647
    5x5     1.629     1.598   1.692
    6x6     1.409     1.191   1.713
    7x7     1.014     0.742   1.335
    8x8     0.843     0.385   1.542
    9x9     0.414     0.172   0.599
    10x10   0.184     0.061   0.622
    11x11   0.096     0.029   0.210

So, Bareiss performs much better than previously.

Returning to the previous topic of switching to Gauss elimination for
sparse matrices: my goal here was to demonstrate that on dense matrices
Gauss elimination is at least comparable to Bareiss. I think this point
should be uncontroversial now.