This changes the return type of:
* eigenvectors() and eigenvalues() in ComplexEigenSolver
* eigenvalues() in EigenSolver
* eigenvectors() and eigenvalues() in SelfAdjointEigenSolver
This is to avoid dynamic memory allocations in the compute() methods of
ComplexEigenSolver, EigenSolver, and SelfAdjointEigenSolver where possible.
As a result, Tridiagonalization::decomposeInPlace() is no longer used.
Biggest remaining issue is the allocation in HouseholderSequence::evalTo().
* reduce scope of declarations
* use that low = 0 and high = size-1
* rename some variables
* rename hqr2_step2() to computeEigenvectors()
* exploit that ei_isMuchSmallerThan takes absolute value of arguments
- Updated unit tests to check above constructor.
- In the compute() method of decompositions: Made temporary matrices/vectors class members to avoid heap allocations during compute() (when dynamic matrices are used, of course).
These changes can speed up decomposition computation time when a solver instance is used to solve multiple same-sized problems. An added benefit is that the compute() method can now be invoked in contexts were heap allocations are forbidden, such as in real-time control loops.
CAVEAT: Not all of the decompositions in the Eigenvalues module have a heap-allocation-free compute() method. A future patch may address this issue, but some required API changes need to be incorporated first.
* adapt Eigenvalues module to the new rule that the RowMajorBit must have the proper value for vectors
* Fix RowMajorBit in ei_traits<ProductBase>
* Fix vectorizability logic in CoeffBasedProduct
NOTE: The ComplexEigenSolver class currently _does_ allocate (line 135 of Eigenvalues/ComplexEigenSolver.h), but the reason appears to be in the implementation of matrix-matrix products, and not in the decomposition itself.
The nomalloc unit test has been extended to verify that decompositions do not allocate when max sizes are specified. There are currently two workarounds to prevent the test from failing (see comments in test/nomalloc.cpp), both of which are related to matrix products that allocate on the stack.
* add a new Eigen2Support module including Cwise, Flagged, and some other deprecated stuff
* add a few cwiseXxx functions
* adapt a few modules to use cwiseXxx instead of the .cwise() prefix
