* Change eigen algebra to support Eigen>=3.3
An internal change in Eigen made odeint incompatible with Eigen
versions >=3.3. This commit changes odeint in such a way that it
does not rely on the changed behvior, so it is now compatible with
old and new Eigen.
Fixes#194
* Remove obsolete Eigen fail compile test
* Remove compile-fail test for C++98 unwrap_reference
* Enable the adaption of the maximal step size of dense output steppers.
For efficient simulation of "hybrid" systems the integrator must approach
the sample points where the discrete variables change their value.
(hybrid systems = systems of ODEs which include discrete variables, beeing
internal variables of the system which only change their value at discrete
sample points)
Approaching sample points can be done by adapting the maximal integrator
step size to min(max_step_size, next_sample_point_time - current_time)
before each do_step.
To achive this in odeint for all dense output steppers the following
changes must be done (which does not change the existing API):
- make private members in bulirsch_stoer_dense_out,
default_step_adjuster, rosenbrock4_controller protected.
- allow std::ref/boost::ref for step_adjuster in controlled_runge_kutta
and controlled_runge_kutta and for stepper in rosenbrock4_dense_output
by unwrapping these before use.
This allows to pass the step adjusters by reference to the dense output
steppers which than allows to change the maximal step size (in the step
adjuster) before each call to do_step.
* Added test for a reference controller in the Rosenbrock4 dense output stepper.
* Make in bulirsch_stoer_dense_out only the required m_max_dt member
protected not all.
Extend the test in rosenbrock4.cpp to test that the controller is a
reference and the maximal step size is applied.
* Fixed build with gcc-4.8
do_step must return the pair (t, t+dt) but (t, dt) is returned.
Note that dense_output_runge_kutta<Stepper, explicit_controlled_stepper_fsal_tag>::do_step(...)
works correctly.
- errors might already occur during the first few steps if the stepsize is chosen too big
- initialize_controlled takes advantage of controlled steppers to initialize the controlled abm stepper
* improves the order selection and modifies the error estimation accordingly
- assumes constant stepsize for the next step to approximate error
- moves the complete order adjustment to the class order_adjustment
- slight changes to adaptive_adams_coefficients
* changed the commit according to the requests and comments
- controlled_adams_bashforth_moulton.hpp, adaptive_adams_coefficients.hpp and pid_step_adjuster.hpp extract absolute values using fabs() without a namespace qualifier
- if the integration value type is not double then this can cause problems, since fabs() is not required to have a long double overload. In such cases it is safer to use std::abs, and also this matches the rest of the odeint-v2 codebase
A bug introduced with the recent max_dt facility prevented the rosenbrock
controller to increase step size in most cases (if max_dt=0). This is fixed
now, and a regression test case has been added.
Becoming suspicious by the difference of the exponents used for computing the
new step size in the BS and BS denseout stepper (see
0f943fbf8b) I checked again the Hairer book and
I'm now convinced there was a mistake in our implementation and both
steppers should use 1/(2*k+1) as exponent. The background is the this exponent
represents the order of the error of the k-th iteration, and this order is
always 2k+1, independent of the interval_sequence. This error is computed from
the difference of the k-th and k-1 - th iteration, which have the orders 2k+2
2k respectively, which means the computed error has order 2k+1.
