echelonize() on RR matrices should not use "classical" algorithm #34724
Description
From sage-devel:
Inverting RR-matrix
sage: m
[-6.12323399573677e-17 -1.72508242466029]
[ 0.579682446302195 6.12323399573677e-17]
sage: m.parent()
Full MatrixSpace of 2 by 2 dense matrices over Real Field with 53 bits of precision
because it uses classical echelonize:
sage: A=m.augment(identity_matrix(RR,2))
sage: A
[-6.12323399573677e-17 -1.72508242466029 1.00000000000000 0.000000000000000]
[ 0.579682446302195 6.12323399573677e-17 0.000000000000000 1.00000000000000]
sage: A.echelonize()
sage: A
[ 1.00000000000000 0.000000000000000 4.00000000000000 1.72508242466029]
[ 0.000000000000000 1.00000000000000 -0.579682446302195 -6.12323399573676e-17]
instead of
sage: A.echelonize(algorithm='scaled_partial_pivoting');A
[ 1.00000000000000 0.000000000000000 6.12323399573677e-17 1.72508242466029]
[ 0.000000000000000 1.00000000000000 -0.579682446302195 -6.12323399573677e-17]
Initial motivation : see this sage-devel thread, which exhibits a serious numerical error on matrix inversion.
CC: @mkoeppe
Component: linear algebra
Author: Dima Pasechnik
Branch/Commit: 605968d
Reviewer: Nils Bruin
Issue created by migration from https://trac.sagemath.org/ticket/34724