Squashed 'third_party/boostorg/odeint/' content from commit 6ff2719
Change-Id: If4892e29c1a5e6cf3a7aa51486a2725c251b0c7d
git-subtree-dir: third_party/boostorg/odeint
git-subtree-split: 6ff2719b6907b86596c3d43e88c1bcfdf29df560
diff --git a/doc/controlled_stepper_table.qbk b/doc/controlled_stepper_table.qbk
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+[/============================================================================
+ Boost.odeint
+
+ Copyright 2011-2012 Karsten Ahnert
+ Copyright 2011-2012 Mario Mulansky
+
+ Use, modification and distribution is subject to the Boost Software License,
+ Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================/]
+
+[table Adaptive step size algorithms
+ [ [Stepper] [Tolerance formula] [Norm] [Step size adaption] ]
+ [ [`controlled_runge_kutta`]
+ [
+ ['val = || | err[subl i] | / ( __epsilon[subl abs] + __epsilon[subl rel] * ( a[subl x] | x[subl i] | + a[subl dxdt] | | dxdt[subl i] | )|| ]
+ ]
+ [['||x|| = max( x[subl i] )]]
+ [
+ ['val > 1 : dt[subl new] = dt[subl current] max( 0.9 pow( val , -1 / ( O[subl E] - 1 ) ) , 0.2 )]
+
+ ['val < 0.5 : dt[subl new] = dt[subl current] min( 0.9 pow( val , -1 / O[subl S] ) , 5 )]
+
+ ['else : dt[subl new] = dt[subl current]]
+ ] ]
+ [ [`rosenbrock4_controller`]
+ [
+ ['val = || err[subl i] / ( __epsilon[subl abs] + __epsilon[subl rel] max( | x[subl i] | , | xold[subl i] | ) ) || ]
+ ]
+ [['||x||=(__Sigma[subl i] x[subl i][super 2])[super 1/2]]]
+ [
+ ['fac = max( 1 / 6 , min( 5 , pow( val , 1 / 4 ) / 0.9 ) ]
+
+ ['fac2 = max( 1 / 6 , min( 5 , dt[subl old] / dt[subl current] pow( val[super 2] / val[subl old] , 1 / 4 ) / 0.9 ) ]
+
+ ['val > 1 : dt[subl new] = dt[subl current] / fac ]
+
+ ['val < 1 : dt[subl new] = dt[subl current] / max( fac , fac2 ) ]
+ ]
+ ]
+ [ [bulirsch_stoer] [['tol=1/2]] [-] [['dt[subl new] = dt[subl old][super 1/a]]] ]
+]
+
+[/
+
+safe = 0.9 , fac1 = 5.0 , fac2 = 1.0 / 6.0
+
+value_type fac_pred = ( m_dt_old / dt ) * pow( err * err / m_err_old , 0.25 ) / safe;
+ fac_pred = std::max( fac2 , std::min( fac1 , fac_pred ) );
+ fac = std::max( fac , fac_pred );
+ dt_new = dt / fac;
+
+
+fac = max( fac2 , min( fac1 , pow( err , 0.25 ) / safe ) )
+]
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