1 - make it easier to catch conjugate expressions
2 - make sure there is no unecessary copy (we had NestByValue<Derived> which seems to be very bad)
* update eigensolver wrt recent changes
* move solveTriangular*() to TriangularView::solve*()
* move .llt() to SelfAdjointView
* add a high level wrapper to the efficient selfadjoint * vector product
* improve LLT so that we can specify which triangular part is meaningless
=> there are still many things to do (doc, cleaning, improve the matrix products, etc.)
* Cholesky decs are NOT rank revealing so remove all the rank/isPositiveDefinite etc stuff.
* fix bug in LLT: s/return/continue/
* introduce machine_epsilon constants, they are actually needed for Higman's formula determining
the cutoff in Cholesky. Btw fix the page reference to his book (chat with Keir).
* solve methods always return true, since this isn't a rank revealing dec. Actually... they already did always return true!! Now it's explicit.
* updated dox and unit-test
* in LDLT, support the negative semidefinite case
* fix bad floating-point comparisons, improves greatly the accuracy of methods like
isPositiveDefinite() and rank()
* simplifications
* identify (but not resolve) bug: claim that only triangular part is used, is inaccurate
* expanded unit-tests
MatrixStorage returning a null pointer). For instance this is very
useful to make Tridiagonalization compile for 1x1 matrices
* fix LLT and eigensolver for 1x1 matrix
Derived to MatrixBase.
* the optimization of eval() for Matrix now consists in a partial
specialization of ei_eval, which returns a reference type for Matrix.
No overriding of eval() in Matrix anymore. Consequence: careful,
ei_eval is no longer guaranteed to give a plain matrix type!
For that, use ei_plain_matrix_type, or the PlainMatrixType typedef.
* so lots of changes to adapt to that everywhere. Hope this doesn't
break (too much) MSVC compilation.
* add code examples for the new image() stuff.
* lower a bit the precision for floats in the unit tests as
we were already doing some workarounds in inverse.cpp and we got some
failed tests.
* rename Cholesky to LLT
* rename CholeskyWithoutSquareRoot to LDLT
* rename MatrixBase::cholesky() to llt()
* rename MatrixBase::choleskyNoSqrt() to ldlt()
* make {LLT,LDLT}::solve() API consistent with other modules
Note that we are going to keep a source compatibility untill the next beta release.
E.g., the "old" Cholesky* classes, etc are still available for some time.
To be clear, Eigen beta2 should be (hopefully) source compatible with beta1,
and so beta2 will contain all the deprecated API of beta1. Those features marked
as deprecated will be removed in beta3 (or in the final 2.0 if there is no beta 3 !).
Also includes various updated in sparse Cholesky.
