Class ode_control_gsl (o2scl)¶
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template<class
vec_y_t
= boost::numeric::ublas::vector<double>, classvec_dydx_t
= vec_y_t, classvec_yerr_t
= vec_y_t>
classo2scl
::
ode_control_gsl
¶ Control structure for astep_gsl.
This class implements both the “standard” and “scaled” step control methods from GSL. The standard control method is the default. To use the scaled control, set standard to
false
and set the scale for each component using set_scale().The control object is a four parameter heuristic based on absolute and relative errors eps_abs and eps_rel, and scaling factors a_y and a_dydt for the system state \( y(t) \) and derivatives \( y^{\prime}(t) \) respectively.
The step-size adjustment procedure for this method begins by computing the desired error level \( D_i \) for each component. In the unscaled version,
\[ D_i = \mathrm{eps\_abs}+\mathrm{eps\_rel} \times \left( \mathrm{a\_y} | y_i| + \mathrm{a\_dydt}~h | y_i^{\prime}| \right) \]while in the scaled version the user specifies the scale for each component, \( s_i \),\[ D_i = \mathrm{eps\_abs}~s_i+\mathrm{eps\_rel} \times \left( \mathrm{a\_y} | y_i| + \mathrm{a\_dydt}~h | y_i^{\prime}| \right) \]The desired error level \( D_i \) is compared to then observed error \( E_i = |\mathrm{yerr}_i| \). If the observed error \( E \) exceeds the desired error level \( D \) by more than 10 percent for any component then the method reduces the step-size by an appropriate factor,
\[ h_{\mathrm{new}} = S~h_{\mathrm{old}} \left(\frac{E}{D}\right)^{-1/q} \]where \( q \) is the consistency order of the method (e.g. \( q=4 \) for 4(5) embedded RK), and \( S \) is a safety factor of 0.9. The ratio \( E/D \) is taken to be the maximum of the ratios \( E_i/D_i \).If the observed error E is less than 50 percent of the desired error level \( D \) for the maximum ratio \( E_i/D_i \) then the algorithm takes the opportunity to increase the step-size to bring the error in line with the desired level,
\[ h_{\mathrm{new}} = S~h_{\mathrm{old}} \left(\frac{E}{D}\right)^{-1/(q+1)} \]This encompasses all the standard error scaling methods. To avoid uncontrolled changes in the stepsize, the overall scaling factor is limited to the range 1/5 to 5.If the user specified fewer scaling parameters than the number of ODEs, then the scaling parameters are reused as follows. If there are \( N \) ODEs and \( M \) scaling parameters, then for \( i>M \), the ith scaling parameter \( s_i \) is set to be \( s_{i\%M} \) . If the user selects the scaled control by setting standard to
false
and no scale parameters are specified, this class reverts to the standard control.- Todo:
Double check that the improvements in the ode-initval2 routines are available here
Adjustment specification
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const size_t
hadj_nil
= 0¶ No adjustment required.
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const size_t
hadj_dec
= 1¶ Recommend step decrease.
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const size_t
hadj_inc
= 2¶ Recommend step increase.
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double
eps_abs
¶ Absolute precision (default \( 10^{-6} \))
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double
eps_rel
¶ Relative precision (default 0)
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double
a_y
¶ Function scaling factor (default 1)
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double
a_dydt
¶ Derivative scaling factor (default 0)
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bool
standard
¶ Use standard or scaled algorithm (default true)
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ode_control_gsl
()¶
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~ode_control_gsl
()¶
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template<class
svec_t
>
intset_scale
(size_t nscal, const svec_t &scale)¶ Set the scaling for each differential equation.
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int
hadjust
(size_t dim, unsigned int ord, const vec_y_t &y, vec_yerr_t &yerr, vec_dydx_t &yp, double &h)¶
Public Types
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typedef boost::numeric::ublas::vector<double>
ubvector
¶