mailRe: Optimisation tests in the test suite.


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Posted by Chris MacRaild on October 26, 2006 - 13:07:
I'm still failing on the grid search, both BFGS and the Newton
+backtracking tests (though the reasons for failure are new). 

For the grid search I have:

Parameter values: array([ 1.,  0.,  0.])
Function value:   3.9844117908982244
Iterations:       1331
Function calls:   1331
Gradient calls:   0
Hessian calls:    0
Warning:          None

The chi-squared value of '3.9844117908982244' should be within +/-
9.9999999999999995e-21 of 3.9844117908982288.


For both BFGS tests:

Parameter values: array([  9.70000000e-01,   2.04800000e+03,
1.49000000e-01])
Function value:   4.1720494200991728e-21
Iterations:       157
Function calls:   699
Gradient calls:   164
Hessian calls:    0
Warning:          None

The te value of '2047.9999998929304' should be within +/- 1e-08 of
2048.0.


And for the Newton+backtracking test:

Parameter values: array([  9.70000000e-01,   2.04800000e+03,
1.49000000e-01])
Function value:   7.5138787163096146e-28
Iterations:       18
Function calls:   96
Gradient calls:   23
Hessian calls:    18
Warning:          None

The function count of '96.0' should be greater than 55.0.




My suggestions:

It was quite appropriate to test finite values with a relative tolerance
of 1e-8. This is the test that should be applied for the grid search
chi2 and all finite parameter values. 

It is clearly not appropriate to test finite chi2 values to an absolute
tolerance of 1e-20. Rather, use the relative 1e-8 tolerance for finite
chi2 and a simple chi2 < 1e-20 test for values expected to be (close to)
zero.

Obviously the Newton failure there is a simple typo



Chris


On Thu, 2006-10-26 at 19:32 +1000, Edward d'Auvergne wrote:
I've overhauled the optimisation tests.  This improves the
optimisation tests and makes them a little more lenient to allow for
machine precision and round-off error artifacts on different
architectures, operating systems, etc.  This has been applied to the
1.2 line and also ported to the 1.3 line.  Many of the changes
suggested in this thread have been incorporated.  The full details of
the changes can be seen in the commit message located at
https://mail.gna.org/public/relax-commits/2006-10/msg00106.html
(Message-id: <E1Gd1Cx-0007rj-4Z@xxxxxxxxxxxxxxxxxx>).

If the test suite still fails on certain architectures, please report
the results and the tests will then be loosened.

Edward

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