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Image Search Results
Journal: BMC Systems Biology
Article Title: A specialized ODE integrator for the efficient computation of parameter sensitivities
doi: 10.1186/1752-0509-6-46
Figure Lengend Snippet: Performance comparison without parameter sensitivities. Performance comparison for integration of ODE-based systems biology models without parameter sensitivities. ( A ) Computation times, ( B ) number of integration steps, ( C ) number of r.h.s. evaluations f ( x ), and ( D ) number of evaluations of the Jacobian J f ( x ) as a function of the relative numerical tolerance. Symbols specify the integrators ode15s (open red squares), radau5 (open green diamonds), odeSD (open black circles), and odeSD mex (filled black circles), respectively. Performance metrics are normalized to the corresponding measures for cvode and averaged (mean ± std.) over all models, which were integrated over the time spans given in Table ; the dashed line indicates performance equal to cvode . ( E ) Computation times and ( F ) number of integration steps as a function of numerical precision (see main text for definition) in analogy to ( A ) and ( B ).
Article Snippet: a We note that it is not possible to execute
Techniques: Comparison
Journal: BMC Systems Biology
Article Title: A specialized ODE integrator for the efficient computation of parameter sensitivities
doi: 10.1186/1752-0509-6-46
Figure Lengend Snippet: Performance comparison with parameter sensitivities. Performance comparison with parameter sensitivities. ( A ) Computation times for the individual models listed in Table with relative tolerance of 10 −6 using odeSD (white bars), odeSD mex (black), ode15s (red), radau5 (green), and cvodes (blue). Due to the explosion in compute time, the three largest steady-state models were not evaluated with ode15s and radau5 . ( B ) CPU times with sensitivity calculation as in ( A ) relative to CPU times without sensitivity calculation. ( C ) Average, normalized (see below) CPU times with sensitivities as a function of the relative numerical tolerance for odeSD (open circles) and odeSD mex (filled circles) relative to cvodes . ( D ) Relative numbers of integration steps (open black circles), of function evaluations f ( x ) (filled black circles), and of evaluations of the Jacobians J · (·) (open red squares) for odeSD mex compared to cvodes , respectively. In all cases, model and sensitivity equations were integrated for the time spans shown in Table . Performance metrics in ( C , D ) are normalized to the corresponding measures for cvodes and averaged (mean ± std.); the dashed line indicates performance equal to cvodes .
Article Snippet: a We note that it is not possible to execute
Techniques: Comparison
Journal: BMC Systems Biology
Article Title: A specialized ODE integrator for the efficient computation of parameter sensitivities
doi: 10.1186/1752-0509-6-46
Figure Lengend Snippet: Precision/work diagrams with parameter sensitivities. Precision-work diagrams for integration with parameter sensitivities. ( A-G ) Computation times for all models for which the systems dynamics were solved with all ODE integrators (see X-axis for model specifications) as a function of precision using odeSD (open black circles), odeSD mex (filled black circles), ode15s (red squares), radau5 (green diamonds), and cvodes (blue squares). The models were integrated for the time spans shown in Table .
Article Snippet: a We note that it is not possible to execute
Techniques: