Optional test method / lambda expression for testing if a FieldElement is zero

[axkr]

For FieldMatrix methods can we have an "extra" method or "lambda function" for the "zero" test of a FieldElement which is not the same as the default "zero" test?

Something similar to:

• https://reference.wolfram.com/language/ref/ZeroTest.html

which will be called in matrix operations like:

• eigen vectors, eigen values, inverse of a matrix, linear solvers, null space, row reduce,...

[maisonobe]

The isZero() method already exists, it was added in version 1.8. I checked were it could be used anbd found only FieldQRDecomposition. Other algorithms like ComplexEigenDecomposition use a user-configurable epsilon to check zero.

[axkr]

Yes you call the FieldElement#isZero() method for FieldQRDecomposition.
In "standard/numeric" calculations this isZero() method often contains a "fast default check" for 0.

But for symbolic matrix "simplification" operations, it often make sense to use a more "expensive" test to check for 0. My proposal means that the zero test should be configurable with a "lambda function" and that the FieldElement#isZero() method should be used as the default operation for this lambda function.

For example you can use different symbolic simplifications to test if an expression is zero:

• https://github.com/axkr/symja_android_library/blob/master/symja_android_library/doc/functions/PossibleZeroQ.md
• https://github.com/axkr/symja_android_library/blob/master/symja_android_library/doc/functions/Simplify.md

[maisonobe]

Could you suggest a list of algorithms where we could put this feature? I guess the lambda function would be an implementation of a new interface in the spirit of:

  public interface ZeroChecker<T extends FieldElement<T>> {
    /** Check if value is semantically zero.
      * @param value value to check
      * @return true if value is semantically zero
      */
  boolean isZero(T value);
  }

[axkr]

In the first moment FieldLUDecomposition and FieldQRDecomposition are the main candidates.

Not sure, but some of these "zero checks" may also be "hidden" in the methods of objects of type AbstractFieldMatrix ?

[maisonobe]

I checked AbstractFieldMatrix but found nothing. This class does not implement any solve operation, i basically just handles the basic operations as well as getter/setters for entries, rows and columns.

I'll do a quick commit, most probably incomplete and let you check of this suit your needs.

[axkr]

Do you provide a 1.9-SNAPSHOT somewhere?

[maisonobe]

I have pushed a basic implementation for testing. You can et the snapshot from the Orekit continuous integration server here: https://packages.orekit.org/#browse/browse:maven-snapshots

It should appear automatically if the tests pass.

[axkr]

For me this implementation seems to work.