m.upper() = a+b;
only updates the upper triangular part of m.
Note that:
m = (a+b).upper();
updates all coefficients of m (but half of the additions
will be skiped)
Updated back/forward substitution to better use Eigen's capability.
part of a matrix. Triangular also provide an optimised method for forward
and backward substitution. Further optimizations regarding assignments and
products might come later.
Updated determinant() to take into account triangular matrices.
Started the QR module with a QR decompostion algorithm.
Help needed to build a QR algorithm (eigen solver) based on it.
- support dynamic sizes
- support arbitrary matrix size when the matrix can be seen as a 1D array
(except for fixed size matrices where the size in Bytes must be a factor of 16,
this is to allow compact storage of a vector of matrices)
Note that the explict vectorization is still experimental and far to be completely tested.
are provided to handle not suported types seemlessly.
Added a generic null-ary expression with null-ary functors. They replace
Zero, Ones, Identity and Random.
- let Inverse take template parameter MatrixType instead
of ExpressionType, in order to reduce executable code size
when taking inverses of xpr's.
- introduce ei_corrected_matrix_flags : the flags template
parameter to the Matrix class is only a suggestion. This
is also useful in ei_eval.
(only 30 muls for size 4)
- rework the matrix inversion: now using cofactor technique for size<=3,
so the ugly unrolling is only used for size 4 anymore, and even there
I'm looking to get rid of it.
* Use them to write an unrolled path in echelon.cpp, as an
experiment before I do this LU module.
* For floating-point types, make ei_random() use an amplitude
of 1.
using a macro and _Pragma.
- use OpenMP also in cacheOptimalProduct and in the
vectorized paths as well
- kill the vector assignment unroller. implement in
operator= the logic for assigning a row-vector in
a col-vector.
- CMakeLists support for building tests/examples
with -fopenmp and/or -msse2
- updates in bench/, especially replace identity()
by ones() which prevents underflows from perturbing
bench results.
* add -pedantic to CXXFLAGS
* cleanup intricated expressions with && and ||
which gave warnings because of "missing" parentheses
* fix compile error in NumTraits, apparently discovered
by -pedantic
Currently only the following platform/operations are supported:
- SSE2 compatible architecture
- compiler compatible with intel's SSE2 intrinsics
- float, double and int data types
- fixed size matrices with a storage major dimension multiple of 4 (or 2 for double)
- scalar-matrix product, component wise: +,-,*,min,max
- matrix-matrix product only if the left matrix is vectorizable and column major
or the right matrix is vectorizable and row major, e.g.:
a.transpose() * b is not vectorized with the default column major storage.
To use it you must define EIGEN_VECTORIZE and EIGEN_INTEL_PLATFORM.
- make use of CoeffReadCost to determine when to unroll the loops,
for now only in Product.h and in OperatorEquals.h
performance remains the same: generally still not as good as before the
big changes.
ei_xpr_copy to evaluate args when needed. Had to introduce an ugly
trick with ei_unref as when the XprCopy type is a reference one can't
directly access member typedefs such as Scalar.
in ei_xpr_copy and operator=, respectively.
* added Matrix::lazyAssign() when EvalBeforeAssigningBit must be skipped
(mainly internal use only)
* all expressions are now stored by const reference
* added Temporary xpr: .temporary() must be called on any temporary expression
not directly returned by a function (mainly internal use only)
* moved all functors in the Functors.h header
* added some preliminaries stuff for the explicit vectorization
* added "all" and "any" special redux operators
* added support bool matrices
* added support for cost model of STL functors via ei_functor_traits
(By default ei_functor_traits query the functor member Cost)
useless copies are made when evaluating nested expressions.
Changes:
- kill LazyBit, introduce EvalBeforeNestingBit and EvalBeforeAssigningBit
- product and random don't evaluate immediately anymore
- eval() always evaluates
- change the value of Dynamic to some large positive value,
in preparation of future simplifications
before the Product<> type is constructed. This resets template depth on each
intermediate evaluation, and gives simpler code. Introducing
ei_eval_if_expensive<Derived, n> which evaluates Derived if it's worth it
given that each of its coeffs will be accessed n times. Operator*
uses this with adequate values of n to evaluate args exactly when needed.
when to evaluate arguments and when to meta-unroll.
-use it in Product to determine when to eval args. not yet used
to determine when to unroll. for now, not used anywhere else but
that'll follow.
-fix badness of my last commit
to preserve SVN history). They are made useless by the new
ei_eval_unless_lazy.
- introduce a generic Eval member typedef so one can do e.g.
T t; U u; Product<T, U>::Eval m; m = t*u;
the cacheOptimal is only good for large enough matrices.
When taking a block in a fixed-size (hence small) matrix,
the SizeAtCompileTime is Dynamic hence that's not a good
indicator. This example shows that the good indicator is
MaxSizeAtCompileTime.
Result: +10% speed in echelon.cpp
* macro renaming: EIGEN_NDEBUG becomes EIGEN_NO_DEBUG
as this is much better (and similar to Qt) and
EIGEN_CUSTOM_ASSERT becomes EIGEN_USE_CUSTOM_ASSERT
* protect Core header by a EIGEN_CORE_H
to disable eigen's asserts without disabling one's own program's
asserts. Notice that Eigen code should now use ei_assert()
instead of assert().
* Remove findBiggestCoeff() as it's now almost redundant.
* Improve echelon.cpp: inner for loop replaced by xprs.
* remove useless "(*this)." here and there. I think they were
first introduced by automatic search&replace.
* fix compilation in Visitor.h (issue triggered by echelon.cpp)
* improve comment on swap().
* added cache efficient matrix-matrix product.
- provides a huge speed-up for large matrices.
- currently it is enabled when an explicit unrolling is not possible.
(the global funcs in MathFunctions.h and Fuzzy.h don't count as internal).
* Mainpage.dox. Add a few prospective Eigen users; change the recommended
-finline-limit from 10000 to 1000. The reason is: it could be harmful to have
a too big value here, couldn't it? (e.g. exceedingly large executables, cache
misses). Looking at gcc, a value of 900 would exactly mean "determine the inlining
of all functions as if they were marked with 'inline' keyword". So a value of
1000 seems a reasonable round number. In the benchmark that motivated this
(TestEigenSolvers) a value of 400 is enough on my system.
