as described on the wiki (one map per N column)
Here's some bench results for the 4 currently supported map impl:
std::map => 18.3385 (581 MB)
gnu::hash_map => 6.52574 (555 MB)
google::dense => 2.87982 (315 MB)
google::sparse => 15.7441 (165 MB)
This is the time is second (and memory consumption) to insert/lookup
10 million of coeffs with random coords inside a 10000^2 matrix,
with one map per packet of 64 columns => google::dense really rocks !
Note I use for the key value the index of the column in the packet (between 0 and 63)
times the number of rows and I used the default hash function.... so maybe there is
room for improvement here....
solver from suitesparse (as cholmod). It seems to be even faster
than SuperLU and it was much simpler to interface ! Well,
the factorization is faster, but for the solve part, SuperLU is
quite faster. On the other hand the solve part represents only a
fraction of the whole procedure. Moreover, I bench random matrices
that does not represents real cases, and I'm not sure at all
I use both libraries with their best settings !
It is only a first draft and I think it should be reorganized a bit in 2 parts:
1 - a compact table summarizing the main API and its use
(this is what would expect an "expert" user)
2 - a discussion about the various algorithm in Eigen to guide the newbies in linear algebra
Currently I mixed the discussion with the API, but it is still better than nothing !
* 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.
* several fixes (transpose, matrix product, etc...)
* Added a basic cholesky factorization
* Added a low level hybrid dense/sparse vector class
to help writing code involving intensive read/write
in a fixed vector. It is currently used to implement
the matrix product itself as well as in the Cholesky
factorization.
However, for matrices larger than 5, it seems there is constantly a quite large error for a very
few coefficients. I don't what's going on, but that's certainely not due to numerical issues only.
(also note that the test with the pseudo eigenvectors fails the same way)
* eigenvectors => pseudoEigenvectors
* added pseudoEigenvalueMatrix
* clear the documentation
* added respective unit test
Still missing: a proper eigenvectors() function.
based on the former.
* opengl_demo: makes IcoSphere better (vertices are instanciated only once) and
removed the generation of a big geometry for the fancy spheres...
- quaternion vs euler angles interpolation (though the Euler angle version looks a bit too bad)
- navigation using either a mapping from 2D screen coordinates to 3D points on a sphere
or the standard approach mapping mouse displacements as rotations around camera's axes.
