From 7ef79a6084b656e3c7d9ea854be6c9f581e7b345 Mon Sep 17 00:00:00 2001 From: Jean-Paul Pelteret Date: Thu, 16 Feb 2017 22:42:56 +0100 Subject: [PATCH] Change template arguments in DerivativeApproximation::approximate_derivative_tensor Fixes #3979 --- .../incompatibilities/20170216Pelteret | 7 + .../numerics/derivative_approximation.h | 18 +- source/numerics/derivative_approximation.cc | 22 +- .../numerics/derivative_approximation.inst.in | 12 +- tests/numerics/derivative_approximation_03.cc | 250 ++++ .../derivative_approximation_03.output | 1030 +++++++++++++++++ 6 files changed, 1313 insertions(+), 26 deletions(-) create mode 100644 doc/news/changes/incompatibilities/20170216Pelteret create mode 100644 tests/numerics/derivative_approximation_03.cc create mode 100644 tests/numerics/derivative_approximation_03.output diff --git a/doc/news/changes/incompatibilities/20170216Pelteret b/doc/news/changes/incompatibilities/20170216Pelteret new file mode 100644 index 0000000000..2d6e9ceb2a --- /dev/null +++ b/doc/news/changes/incompatibilities/20170216Pelteret @@ -0,0 +1,7 @@ +Changed: The template arguments to the +DerivativeApproximation::approximate_derivative_tensor() function have +been modified. It is no longer necessary to explicitly specify the +dim<\tt> and spacedim<\tt> arguments as they are determined from +the input DoFHandler. +
+(Jean-Paul Pelteret, 2017/02/16) diff --git a/include/deal.II/numerics/derivative_approximation.h b/include/deal.II/numerics/derivative_approximation.h index d5923e77de..a31070e93f 100644 --- a/include/deal.II/numerics/derivative_approximation.h +++ b/include/deal.II/numerics/derivative_approximation.h @@ -238,24 +238,24 @@ namespace DerivativeApproximation * In a parallel computation the @p solution vector needs to contain the * locally relevant unknowns. */ - template + template void approximate_derivative_tensor - (const Mapping &mapping, - const DoFHandlerType &dof, - const InputVector &solution, + (const Mapping &mapping, + const DoFHandlerType &dof, + const InputVector &solution, #ifndef _MSC_VER - const typename DoFHandlerType::active_cell_iterator &cell, + const typename DoFHandlerType::active_cell_iterator &cell, #else const TriaActiveIterator > &cell, #endif - Tensor &derivative, - const unsigned int component = 0); + Tensor &derivative, + const unsigned int component = 0); /** * Same as above, with mapping=MappingQGeneric@(1). */ - template + template void approximate_derivative_tensor (const DoFHandlerType &dof, @@ -265,7 +265,7 @@ namespace DerivativeApproximation #else const TriaActiveIterator > &cell, #endif - Tensor &derivative, + Tensor &derivative, const unsigned int component = 0); /** diff --git a/source/numerics/derivative_approximation.cc b/source/numerics/derivative_approximation.cc index 13cb24a9d7..8f4b7193d8 100644 --- a/source/numerics/derivative_approximation.cc +++ b/source/numerics/derivative_approximation.cc @@ -1075,19 +1075,19 @@ namespace DerivativeApproximation } - template + template void approximate_derivative_tensor - (const Mapping &mapping, - const DoFHandlerType &dof, - const InputVector &solution, + (const Mapping &mapping, + const DoFHandlerType &dof, + const InputVector &solution, #ifndef _MSC_VER - const typename DoFHandlerType::active_cell_iterator &cell, + const typename DoFHandlerType::active_cell_iterator &cell, #else const TriaActiveIterator < dealii::DoFCellAccessor < DoFHandlerType, false > > &cell, #endif - Tensor &derivative, - const unsigned int component) + Tensor &derivative, + const unsigned int component) { internal::approximate_cell::DerivDescr> (mapping, @@ -1100,7 +1100,7 @@ namespace DerivativeApproximation - template + template void approximate_derivative_tensor (const DoFHandlerType &dof, @@ -1110,12 +1110,12 @@ namespace DerivativeApproximation #else const TriaActiveIterator < dealii::DoFCellAccessor < DoFHandlerType, false > > &cell, #endif - Tensor &derivative, + Tensor &derivative, const unsigned int component) { // just call the respective function with Q1 mapping - approximate_derivative_tensor - (StaticMappingQ1::mapping, + approximate_derivative_tensor + (StaticMappingQ1::mapping, dof, solution, cell, diff --git a/source/numerics/derivative_approximation.inst.in b/source/numerics/derivative_approximation.inst.in index 13856d98aa..09a35e0d87 100644 --- a/source/numerics/derivative_approximation.inst.in +++ b/source/numerics/derivative_approximation.inst.in @@ -54,7 +54,7 @@ for (deal_II_dimension : DIMENSIONS ; VEC : REAL_SERIAL_VECTORS ; DH : DOFHANDLE template void - approximate_derivative_tensor < DH , deal_II_dimension, deal_II_dimension, VEC, 1 > + approximate_derivative_tensor < DH , VEC, 1 > (const Mapping &mapping, const DH &dof_handler, const VEC &solution, @@ -64,7 +64,7 @@ for (deal_II_dimension : DIMENSIONS ; VEC : REAL_SERIAL_VECTORS ; DH : DOFHANDLE template void - approximate_derivative_tensor < DH , deal_II_dimension, deal_II_dimension, VEC, 2 > + approximate_derivative_tensor < DH , VEC, 2 > (const Mapping &mapping, const DH &dof_handler, const VEC &solution, @@ -74,7 +74,7 @@ for (deal_II_dimension : DIMENSIONS ; VEC : REAL_SERIAL_VECTORS ; DH : DOFHANDLE template void - approximate_derivative_tensor < DH , deal_II_dimension, deal_II_dimension, VEC, 3 > + approximate_derivative_tensor < DH , VEC, 3 > (const Mapping &mapping, const DH &dof_handler, const VEC &solution, @@ -85,7 +85,7 @@ for (deal_II_dimension : DIMENSIONS ; VEC : REAL_SERIAL_VECTORS ; DH : DOFHANDLE template void - approximate_derivative_tensor < DH , deal_II_dimension, deal_II_dimension, VEC, 1 > + approximate_derivative_tensor < DH , VEC, 1 > (const DH &dof_handler, const VEC &solution, const DH ::active_cell_iterator &cell, @@ -94,7 +94,7 @@ for (deal_II_dimension : DIMENSIONS ; VEC : REAL_SERIAL_VECTORS ; DH : DOFHANDLE template void - approximate_derivative_tensor < DH , deal_II_dimension, deal_II_dimension, VEC, 2 > + approximate_derivative_tensor < DH , VEC, 2 > (const DH &dof_handler, const VEC &solution, const DH ::active_cell_iterator &cell, @@ -103,7 +103,7 @@ for (deal_II_dimension : DIMENSIONS ; VEC : REAL_SERIAL_VECTORS ; DH : DOFHANDLE template void - approximate_derivative_tensor < DH , deal_II_dimension, deal_II_dimension, VEC, 3 > + approximate_derivative_tensor < DH , VEC, 3 > (const DH &dof_handler, const VEC &solution, const DH ::active_cell_iterator &cell, diff --git a/tests/numerics/derivative_approximation_03.cc b/tests/numerics/derivative_approximation_03.cc new file mode 100644 index 0000000000..449eb0b533 --- /dev/null +++ b/tests/numerics/derivative_approximation_03.cc @@ -0,0 +1,250 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2017 by the deal.II authors +// +// This file is part of the deal.II library. +// +// The deal.II library is free software; you can use it, redistribute +// it, and/or modify it under the terms of the GNU Lesser General +// Public License as published by the Free Software Foundation; either +// version 2.1 of the License, or (at your option) any later version. +// The full text of the license can be found in the file LICENSE at +// the top level of the deal.II distribution. +// +// --------------------------------------------------------------------- + +// Same as derivative_approximation_02, but without the mapping + +#include "../tests.h" +#include +#include +#include +#include + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +const double a=4,b=5; + + +template +class MyFunction : public Function +{ +public: + MyFunction () : Function() {} + + virtual double value (const Point &p, + const unsigned int) const + { + return sin(p[0]*a)*cos(p[1]*b); + } +}; + +template +void exact_gradient(Point &p, Tensor<1,dim> &grad) +{ + double x=p[0],y=p[1]; + + grad[0]=a*cos(a*x)*cos(b*y); + grad[1]=-b*sin(a*x)*sin(b*y); +} + +template +void exact_second(Point &p, Tensor<2,dim> &sec) +{ + double x=p[0],y=p[1]; + + sec[0][0]=-a*a*sin(a*x)*cos(b*y); +// sec[0][1]=-a*b*cos(a*x)*sin(b*y); + sec[1][0]=sec[0][1]=-a*b*cos(a*x)*sin(b*y); + sec[1][1]=-b*b*sin(a*x)*cos(b*y); +} + +template +void exact_third(Point &p, Tensor<3,dim> &third) +{ + double x=p[0],y=p[1]; + // array of function and its derivatives + double dx[4]= + { + sin(a*x), + a*cos(a*x), + -a *a*sin(a*x), + -a *a *a*cos(a*x) + }; + double dy[4]= + { + cos(b*y), + -b*sin(b*y), + -b *b*cos(b*y), + b *b *b*sin(b*y) + }; + + for (int i=0; i +void derivatives() +{ + MyFunction function; + Triangulation tria; + GridGenerator::hyper_cube(tria); + tria.refine_global(5-dim); + FE_DGQ fe(2); + DoFHandler dof_handler(tria); + Vector solution; + QMidpoint q_midpoint; + FEValues fe_values(fe, q_midpoint, update_quadrature_points); + + dof_handler.distribute_dofs (fe); + solution.reinit(dof_handler.n_dofs()); + + VectorTools::interpolate (dof_handler, function, solution); + + typename DoFHandler::active_cell_iterator + cell=dof_handler.begin_active(), + endc=dof_handler.end(); + + for (; cell!=endc; ++cell) + { + // get derivative approximations + Tensor<1,dim> grad, ex_grad; + Tensor<2,dim> second, ex_second; + Tensor<3,dim> third, ex_third; + + DerivativeApproximation::approximate_derivative_tensor + (dof_handler, + solution, + cell, + grad, + 0); + double normgrad=DerivativeApproximation::derivative_norm(grad); + + DerivativeApproximation::approximate_derivative_tensor + (dof_handler, + solution, + cell, + second, + 0); + double normsecond=DerivativeApproximation::derivative_norm(second); + + DerivativeApproximation::approximate_derivative_tensor + (dof_handler, + solution, + cell, + third, + 0); + double normthird=DerivativeApproximation::derivative_norm(third); + + // symmetry of second derivative + Assert(second==transpose(second), + ExcMessage("Second derivative is not symmetric")); + + // symmetry of third derivative note, + // that this is only part of the truth, + // we would have to test more here to be + // really sure, but this should be enough + for (unsigned int i=0; i > q_point; + q_point=fe_values.get_quadrature_points(); + + exact_gradient(q_point[0],ex_grad); + exact_second (q_point[0],ex_second); + exact_third (q_point[0],ex_third); + + double ex_normgrad =DerivativeApproximation::derivative_norm(ex_grad); + double ex_normsecond=DerivativeApproximation::derivative_norm(ex_second); + double ex_normthird =DerivativeApproximation::derivative_norm(ex_third); + + // output of all values for comparison + deallog<<"cell "<(); + deallog<(); +} diff --git a/tests/numerics/derivative_approximation_03.output b/tests/numerics/derivative_approximation_03.output new file mode 100644 index 0000000000..9f0d29fd19 --- /dev/null +++ b/tests/numerics/derivative_approximation_03.output @@ -0,0 +1,1030 @@ + +DEAL::------------ 2D ------------ +DEAL:: +DEAL::cell 3.0 +DEAL::approx. gradient: 3.30563 -0.712054 , norm: 3.38145 +DEAL:: exact gradient: 3.68794 -0.380308 , norm: 3.70750 +DEAL::approx. second derivative (hessian): -7.14849 -8.14611 -8.14611 -4.85472 , norm: 14.2281 +DEAL:: exact second derivative (hessian): -3.76675 -5.95762 -5.95762 -5.88554 , norm: 10.8772 +DEAL::approx. third derivative: -52.6152 11.3518 11.3518 -77.4973 11.3518 -77.4973 -77.4973 17.6570 , norm: 146.575 +DEAL:: exact third derivative: -59.0071 6.08492 6.08492 -92.1986 6.08492 -92.1986 -92.1986 9.50769 , norm: 170.836 +DEAL:: +DEAL::cell 3.1 +DEAL::approx. gradient: 2.67041 -1.96183 , norm: 3.31358 +DEAL:: exact gradient: 2.78501 -1.04781 , norm: 2.97560 +DEAL::approx. second derivative (hessian): -9.84763 -6.29001 -6.29001 -13.3756 , norm: 18.1443 +DEAL:: exact second derivative (hessian): -10.3780 -4.49899 -4.49899 -16.2156 , norm: 18.6597 +DEAL::approx. third derivative: -42.5044 20.8424 20.8424 -59.9624 20.8424 -59.9624 -59.9624 48.6478 , norm: 127.526 +DEAL:: exact third derivative: -44.5601 16.7650 16.7650 -69.6252 16.7650 -69.6252 -69.6252 26.1953 , norm: 134.380 +DEAL:: +DEAL::cell 3.2 +DEAL::approx. gradient: 2.05586 -0.933477 , norm: 2.25786 +DEAL:: exact gradient: 2.29363 -0.997138 , norm: 2.50100 +DEAL::approx. second derivative (hessian): -4.44583 -14.1228 -14.1228 -3.37118 , norm: 18.0416 +DEAL:: exact second derivative (hessian): -2.34264 -15.6204 -15.6204 -3.66037 , norm: 18.6358 +DEAL::approx. third derivative: -32.7228 24.8109 24.8109 -51.8345 24.8109 -51.8345 -51.8345 23.1476 , norm: 107.302 +DEAL:: exact third derivative: -36.6981 15.9542 15.9542 -57.3407 15.9542 -57.3407 -57.3407 24.9285 , norm: 112.230 +DEAL:: +DEAL::cell 3.3 +DEAL::approx. gradient: 1.66080 -2.57188 , norm: 3.06151 +DEAL:: exact gradient: 1.73207 -2.74728 , norm: 3.24771 +DEAL::approx. second derivative (hessian): -6.12450 -11.0278 -11.0278 -9.28815 , norm: 18.8470 +DEAL:: exact second derivative (hessian): -6.45436 -11.7960 -11.7960 -10.0849 , norm: 20.2045 +DEAL::approx. third derivative: -26.4346 41.0017 41.0017 -40.0387 41.0017 -40.0387 -40.0387 63.7755 , norm: 120.908 +DEAL:: exact third derivative: -27.7131 43.9565 43.9565 -43.3017 43.9565 -43.3017 -43.3017 68.6820 , norm: 130.026 +DEAL:: +DEAL::cell 3.4 +DEAL::approx. gradient: 1.15082 -2.73128 , norm: 2.96382 +DEAL:: exact gradient: 1.20020 -1.45877 , norm: 1.88905 +DEAL::approx. second derivative (hessian): -13.7100 -2.71069 -2.71069 -18.6216 , norm: 19.8235 +DEAL:: exact second derivative (hessian): -14.4484 -1.93884 -1.93884 -22.5756 , norm: 23.0144 +DEAL::approx. third derivative: -18.3173 29.0170 29.0170 -25.8409 29.0170 -25.8409 -25.8409 67.7280 , norm: 97.2205 +DEAL:: exact third derivative: -19.2032 23.3404 23.3404 -30.0051 23.3404 -30.0051 -30.0051 36.4693 , norm: 77.6788 +DEAL:: +DEAL::cell 3.5 +DEAL::approx. gradient: -0.650535 -2.83201 , norm: 2.90577 +DEAL:: exact gradient: -0.678453 -1.51258 , norm: 1.65776 +DEAL::approx. second derivative (hessian): -14.2156 1.53230 1.53230 -19.3084 , norm: 19.7339 +DEAL:: exact second derivative (hessian): -14.9813 1.09599 1.09599 -23.4082 , norm: 23.5484 +DEAL::approx. third derivative: 10.3545 30.0872 30.0872 14.6074 30.0872 14.6074 14.6074 70.2260 , norm: 91.6229 +DEAL:: exact third derivative: 10.8552 24.2012 24.2012 16.9613 24.2012 16.9613 16.9613 37.8144 , norm: 64.5594 +DEAL:: +DEAL::cell 3.6 +DEAL::approx. gradient: 0.715722 -3.58060 , norm: 3.65143 +DEAL:: exact gradient: 0.746437 -3.82479 , norm: 3.89695 +DEAL::approx. second derivative (hessian): -8.52660 -4.75246 -4.75246 -12.9311 , norm: 15.9667 +DEAL:: exact second derivative (hessian): -8.98582 -5.08351 -5.08351 -14.0403 , norm: 17.1902 +DEAL::approx. third derivative: -11.3920 57.0831 57.0831 -17.2547 57.0831 -17.2547 -17.2547 88.7889 , norm: 136.682 +DEAL:: exact third derivative: -11.9430 61.1967 61.1967 -18.6609 61.1967 -18.6609 -18.6609 95.6198 , norm: 146.852 +DEAL:: +DEAL::cell 3.7 +DEAL::approx. gradient: -0.404585 -3.71266 , norm: 3.73464 +DEAL:: exact gradient: -0.421948 -3.96586 , norm: 3.98825 +DEAL::approx. second derivative (hessian): -8.84108 2.68648 2.68648 -13.4080 , norm: 14.6504 +DEAL:: exact second derivative (hessian): -9.31725 2.87362 2.87362 -14.5582 , norm: 15.8268 +DEAL::approx. third derivative: 6.43971 59.1884 59.1884 9.75378 59.1884 9.75378 9.75378 92.0637 , norm: 138.969 +DEAL:: exact third derivative: 6.75116 63.4538 63.4538 10.5487 63.4538 10.5487 10.5487 99.1466 , norm: 149.294 +DEAL:: +DEAL::cell 3.8 +DEAL::approx. gradient: 0.0288201 -1.15800 , norm: 1.15836 +DEAL:: exact gradient: 0.0321533 -1.23698 , norm: 1.23740 +DEAL::approx. second derivative (hessian): -0.0623240 -17.5198 -17.5198 -0.0472589 , norm: 17.5746 +DEAL:: exact second derivative (hessian): -0.0328403 -19.3776 -19.3776 -0.0513130 , norm: 19.4197 +DEAL::approx. third derivative: -0.458725 30.7786 30.7786 -0.726643 30.7786 -0.726643 -0.726643 28.7152 , norm: 60.5667 +DEAL:: exact third derivative: -0.514453 19.7916 19.7916 -0.803832 19.7916 -0.803832 -0.803832 30.9244 , norm: 46.1914 +DEAL:: +DEAL::cell 3.9 +DEAL::approx. gradient: 0.0232819 -3.19049 , norm: 3.19057 +DEAL:: exact gradient: 0.0242810 -3.40808 , norm: 3.40816 +DEAL::approx. second derivative (hessian): -0.0858564 -13.6803 -13.6803 -0.130206 , norm: 13.7884 +DEAL:: exact second derivative (hessian): -0.0904805 -14.6333 -14.6333 -0.141376 , norm: 14.7492 +DEAL::approx. third derivative: -0.370574 50.8638 50.8638 -0.561283 50.8638 -0.561283 -0.561283 79.1153 , norm: 118.413 +DEAL:: exact third derivative: -0.388497 54.5292 54.5292 -0.607026 54.5292 -0.607026 -0.607026 85.2019 , norm: 127.204 +DEAL:: +DEAL::cell 3.10 +DEAL::approx. gradient: -2.00911 -0.944719 , norm: 2.22014 +DEAL:: exact gradient: -2.24148 -1.00915 , norm: 2.45817 +DEAL::approx. second derivative (hessian): 4.34475 -14.2929 -14.2929 3.29453 , norm: 18.1222 +DEAL:: exact second derivative (hessian): 2.28937 -15.8086 -15.8086 3.57715 , norm: 18.7549 +DEAL::approx. third derivative: 31.9788 25.1097 25.1097 50.6560 25.1097 50.6560 50.6560 23.4264 , norm: 105.646 +DEAL:: exact third derivative: 35.8637 16.1464 16.1464 56.0370 16.1464 56.0370 56.0370 25.2287 , norm: 110.115 +DEAL:: +DEAL::cell 3.11 +DEAL::approx. gradient: -1.62303 -2.60286 , norm: 3.06743 +DEAL:: exact gradient: -1.69269 -2.78037 , norm: 3.25509 +DEAL::approx. second derivative (hessian): 5.98525 -11.1606 -11.1606 9.07697 , norm: 18.7983 +DEAL:: exact second derivative (hessian): 6.30760 -11.9381 -11.9381 9.85563 , norm: 20.1508 +DEAL::approx. third derivative: 25.8336 41.4956 41.4956 39.1283 41.4956 39.1283 39.1283 64.5436 , norm: 120.797 +DEAL:: exact third derivative: 27.0830 44.4859 44.4859 42.3172 44.4859 42.3172 42.3172 69.5092 , norm: 129.901 +DEAL:: +DEAL::cell 3.12 +DEAL::approx. gradient: 0.0100334 -4.44183 , norm: 4.44184 +DEAL:: exact gradient: 0.0104639 -4.74476 , norm: 4.74477 +DEAL::approx. second derivative (hessian): -0.119530 -5.89555 -5.89555 -0.181274 , norm: 6.04604 +DEAL:: exact second derivative (hessian): -0.125968 -6.30623 -6.30623 -0.196825 , norm: 6.46773 +DEAL::approx. third derivative: -0.159700 70.8131 70.8131 -0.241886 70.8131 -0.241886 -0.241886 110.145 , norm: 164.850 +DEAL:: exact third derivative: -0.167423 75.9162 75.9162 -0.261599 75.9162 -0.261599 -0.261599 118.619 , norm: 177.089 +DEAL:: +DEAL::cell 3.13 +DEAL::approx. gradient: -0.00567168 -4.60566 , norm: 4.60566 +DEAL:: exact gradient: -0.00591508 -4.91976 , norm: 4.91976 +DEAL::approx. second derivative (hessian): -0.123939 3.33265 3.33265 -0.187960 , norm: 3.48875 +DEAL:: exact second derivative (hessian): -0.130614 3.56480 3.56480 -0.204084 , norm: 3.73234 +DEAL::approx. third derivative: 0.0902753 73.4249 73.4249 0.136734 73.4249 0.136734 0.136734 114.208 , norm: 170.930 +DEAL:: exact third derivative: 0.0946413 78.7162 78.7162 0.147877 78.7162 0.147877 0.147877 122.994 , norm: 183.620 +DEAL:: +DEAL::cell 3.14 +DEAL::approx. gradient: -0.699449 -3.62373 , norm: 3.69061 +DEAL:: exact gradient: -0.729466 -3.87086 , norm: 3.93899 +DEAL::approx. second derivative (hessian): 8.33273 -4.80970 -4.80970 12.6370 , norm: 15.7541 +DEAL:: exact second derivative (hessian): 8.78151 -5.14473 -5.14473 13.7211 , norm: 16.9582 +DEAL::approx. third derivative: 11.1330 57.7705 57.7705 16.8624 57.7705 16.8624 16.8624 89.8583 , norm: 138.072 +DEAL:: exact third derivative: 11.6715 61.9337 61.9337 18.2366 61.9337 18.2366 18.2366 96.7714 , norm: 148.344 +DEAL:: +DEAL::cell 3.15 +DEAL::approx. gradient: 0.395386 -3.75738 , norm: 3.77812 +DEAL:: exact gradient: 0.412354 -4.01363 , norm: 4.03475 +DEAL::approx. second derivative (hessian): 8.64006 2.71883 2.71883 13.1031 , norm: 14.3890 +DEAL:: exact second derivative (hessian): 9.10540 2.90822 2.90822 14.2272 , norm: 15.5413 +DEAL::approx. third derivative: -6.29329 59.9013 59.9013 -9.53201 59.9013 -9.53201 -9.53201 93.1725 , norm: 140.562 +DEAL:: exact third derivative: -6.59766 64.2180 64.2180 -10.3088 64.2180 -10.3088 -10.3088 100.341 , norm: 151.005 +DEAL:: +DEAL::cell 3.16 +DEAL::approx. gradient: -2.29261 -2.23937 , norm: 3.20482 +DEAL:: exact gradient: -2.39100 -1.19605 , norm: 2.67346 +DEAL::approx. second derivative (hessian): -11.2408 5.40013 5.40013 -15.2679 , norm: 19.0176 +DEAL:: exact second derivative (hessian): -11.8462 3.86250 3.86250 -18.5097 , norm: 20.2789 +DEAL::approx. third derivative: 36.4911 23.7910 23.7910 51.4793 23.7910 51.4793 51.4793 55.5302 , norm: 118.590 +DEAL:: exact third derivative: 38.2560 19.1368 19.1368 59.7750 19.1368 59.7750 59.7750 29.9012 , norm: 119.060 +DEAL:: +DEAL::cell 3.17 +DEAL::approx. gradient: -3.37338 -1.09846 , norm: 3.54772 +DEAL:: exact gradient: -3.51815 -0.586686 , norm: 3.56673 +DEAL::approx. second derivative (hessian): -5.51386 7.94582 7.94582 -7.48920 , norm: 14.5085 +DEAL:: exact second derivative (hessian): -5.81082 5.68332 5.68332 -9.07941 , norm: 13.3588 +DEAL::approx. third derivative: 53.6935 11.6700 11.6700 75.7472 11.6700 75.7472 75.7472 27.2387 , norm: 145.762 +DEAL:: exact third derivative: 56.2903 9.38698 9.38698 87.9537 9.38698 87.9537 87.9537 14.6672 , norm: 163.877 +DEAL:: +DEAL::cell 3.18 +DEAL::approx. gradient: -1.42584 -2.93574 , norm: 3.26367 +DEAL:: exact gradient: -1.48703 -3.13595 , norm: 3.47065 +DEAL::approx. second derivative (hessian): -6.99096 9.46767 9.46767 -10.6022 , norm: 18.4349 +DEAL:: exact second derivative (hessian): -7.36748 10.1272 10.1272 -11.5117 , norm: 19.7766 +DEAL::approx. third derivative: 22.6948 46.8024 46.8024 34.3742 46.8024 34.3742 34.3742 72.7981 , norm: 126.217 +DEAL:: exact third derivative: 23.7924 50.1752 50.1752 37.1756 50.1752 37.1756 37.1756 78.3988 , norm: 135.688 +DEAL:: +DEAL::cell 3.19 +DEAL::approx. gradient: -2.09799 -1.44004 , norm: 2.54466 +DEAL:: exact gradient: -2.18803 -1.53825 , norm: 2.67464 +DEAL::approx. second derivative (hessian): -3.42921 13.9308 13.9308 -5.20059 , norm: 18.2739 +DEAL:: exact second derivative (hessian): -3.61390 14.9013 14.9013 -5.64672 , norm: 19.5662 +DEAL::approx. third derivative: 33.3934 22.9576 22.9576 50.5787 22.9576 50.5787 50.5787 35.7090 , norm: 107.917 +DEAL:: exact third derivative: 35.0084 24.6120 24.6120 54.7007 24.6120 54.7007 54.7007 38.4562 , norm: 116.182 +DEAL:: +DEAL::cell 3.20 +DEAL::approx. gradient: -3.62822 0.311397 , norm: 3.64156 +DEAL:: exact gradient: -3.78393 0.166317 , norm: 3.78758 +DEAL::approx. second derivative (hessian): 1.56309 8.54610 8.54610 2.12308 , norm: 10.3938 +DEAL:: exact second derivative (hessian): 1.64728 6.11268 6.11268 2.57388 , norm: 8.24079 +DEAL::approx. third derivative: 57.7498 -3.30827 -3.30827 81.4696 -3.30827 81.4696 81.4696 -7.72177 , norm: 152.772 +DEAL:: exact third derivative: 60.5428 -2.66107 -2.66107 94.5982 -2.66107 94.5982 94.5982 -4.15792 , norm: 174.787 +DEAL:: +DEAL::cell 3.21 +DEAL::approx. gradient: -3.52740 1.64501 , norm: 3.89212 +DEAL:: exact gradient: -3.12327 0.878600 , norm: 3.24450 +DEAL::approx. second derivative (hessian): 5.23036 7.47725 7.47725 11.2155 , norm: 16.2768 +DEAL:: exact second derivative (hessian): 8.70207 5.04543 5.04543 13.5970 , norm: 16.7572 +DEAL::approx. third derivative: 56.1450 -14.2694 -14.2694 71.6481 -14.2694 71.6481 71.6481 -40.7917 , norm: 144.317 +DEAL:: exact third derivative: 49.9724 -14.0576 -14.0576 78.0818 -14.0576 78.0818 78.0818 -21.9650 , norm: 147.861 +DEAL:: +DEAL::cell 3.22 +DEAL::approx. gradient: -2.25649 0.408230 , norm: 2.29312 +DEAL:: exact gradient: -2.35332 0.436070 , norm: 2.39338 +DEAL::approx. second derivative (hessian): 0.972130 14.9833 14.9833 1.47429 , norm: 16.2086 +DEAL:: exact second derivative (hessian): 1.02449 16.0270 16.0270 1.60076 , norm: 17.3422 +DEAL::approx. third derivative: 35.9161 -6.50812 -6.50812 54.3997 -6.50812 54.3997 54.3997 -10.1230 , norm: 101.968 +DEAL:: exact third derivative: 37.6532 -6.97712 -6.97712 58.8331 -6.97712 58.8331 58.8331 -10.9018 , norm: 109.848 +DEAL:: +DEAL::cell 3.23 +DEAL::approx. gradient: -2.19378 2.15655 , norm: 3.07626 +DEAL:: exact gradient: -1.94244 2.30362 , norm: 3.01327 +DEAL::approx. second derivative (hessian): 3.25290 13.4770 13.4770 7.78821 , norm: 19.1870 +DEAL:: exact second derivative (hessian): 5.41205 13.2287 13.2287 8.45632 , norm: 20.2502 +DEAL::approx. third derivative: 34.9180 -25.9716 -25.9716 47.6399 -25.9716 47.6399 47.6399 -53.4764 , norm: 113.628 +DEAL:: exact third derivative: 31.0791 -36.8580 -36.8580 48.5611 -36.8580 48.5611 48.5611 -57.5906 , norm: 124.228 +DEAL:: +DEAL::cell 3.24 +DEAL::approx. gradient: -0.0199881 -3.64186 , norm: 3.64192 +DEAL:: exact gradient: -0.0208459 -3.89023 , norm: 3.89029 +DEAL::approx. second derivative (hessian): -0.0980029 11.7449 11.7449 -0.148627 , norm: 11.8682 +DEAL:: exact second derivative (hessian): -0.103281 12.5630 12.5630 -0.161377 , norm: 12.6954 +DEAL::approx. third derivative: 0.318148 58.0597 58.0597 0.481876 58.0597 0.481876 0.481876 90.3080 , norm: 135.163 +DEAL:: exact third derivative: 0.333534 62.2437 62.2437 0.521147 62.2437 0.521147 0.521147 97.2558 , norm: 145.198 +DEAL:: +DEAL::cell 3.25 +DEAL::approx. gradient: -0.0294107 -1.78641 , norm: 1.78665 +DEAL:: exact gradient: -0.0306729 -1.90824 , norm: 1.90849 +DEAL::approx. second derivative (hessian): -0.0480725 17.2816 17.2816 -0.0729046 , norm: 17.3421 +DEAL:: exact second derivative (hessian): -0.0506616 18.4854 18.4854 -0.0791587 , norm: 18.5503 +DEAL::approx. third derivative: 0.468126 28.4795 28.4795 0.709038 28.4795 0.709038 0.709038 44.2980 , norm: 66.3120 +DEAL:: exact third derivative: 0.490767 30.5318 30.5318 0.766823 30.5318 0.766823 0.766823 47.7060 , norm: 71.2351 +DEAL:: +DEAL::cell 3.26 +DEAL::approx. gradient: 1.39342 -2.97109 , norm: 3.28162 +DEAL:: exact gradient: 1.45321 -3.17372 , norm: 3.49061 +DEAL::approx. second derivative (hessian): 6.83201 9.58170 9.58170 10.3611 , norm: 18.3394 +DEAL:: exact second derivative (hessian): 7.19997 10.2491 10.2491 11.2500 , norm: 19.6722 +DEAL::approx. third derivative: -22.1788 47.3661 47.3661 -33.5927 47.3661 -33.5927 -33.5927 73.6749 , norm: 126.633 +DEAL:: exact third derivative: -23.2514 50.7795 50.7795 -36.3304 50.7795 -36.3304 -36.3304 79.3430 , norm: 136.130 +DEAL:: +DEAL::cell 3.27 +DEAL::approx. gradient: 2.05029 -1.45738 , norm: 2.51548 +DEAL:: exact gradient: 2.13828 -1.55677 , norm: 2.64495 +DEAL::approx. second derivative (hessian): 3.35124 14.0986 14.0986 5.08235 , norm: 18.3420 +DEAL:: exact second derivative (hessian): 3.53173 15.0807 15.0807 5.51833 , norm: 19.6384 +DEAL::approx. third derivative: -32.6341 23.2341 23.2341 -49.4286 23.2341 -49.4286 -49.4286 36.1390 , norm: 106.396 +DEAL:: exact third derivative: -34.2125 24.9084 24.9084 -53.4570 24.9084 -53.4570 -53.4570 38.9194 , norm: 114.540 +DEAL:: +DEAL::cell 3.28 +DEAL::approx. gradient: -0.0316326 0.506420 , norm: 0.507407 +DEAL:: exact gradient: -0.0329901 0.540957 , norm: 0.541962 +DEAL::approx. second derivative (hessian): 0.0136278 18.5872 18.5872 0.0206674 , norm: 18.6043 +DEAL:: exact second derivative (hessian): 0.0143618 19.8819 19.8819 0.0224403 , norm: 19.9003 +DEAL::approx. third derivative: 0.503491 -8.07350 -8.07350 0.762603 -8.07350 0.762603 0.762603 -12.5578 , norm: 18.8478 +DEAL:: exact third derivative: 0.527842 -8.65531 -8.65531 0.824753 -8.65531 0.824753 0.824753 -13.5239 , norm: 20.2474 +DEAL:: +DEAL::cell 3.29 +DEAL::approx. gradient: -0.0307535 2.67526 , norm: 2.67544 +DEAL:: exact gradient: -0.0272302 2.85771 , norm: 2.85784 +DEAL::approx. second derivative (hessian): 0.0456009 16.7186 16.7186 0.109179 , norm: 16.7960 +DEAL:: exact second derivative (hessian): 0.0758689 16.4106 16.4106 0.118545 , norm: 16.5078 +DEAL::approx. third derivative: 0.489499 -32.2184 -32.2184 0.667841 -32.2184 0.667841 0.667841 -66.3390 , norm: 86.6979 +DEAL:: exact third derivative: 0.435683 -45.7233 -45.7233 0.680755 -45.7233 0.680755 0.680755 -71.4427 , norm: 106.665 +DEAL:: +DEAL::cell 3.30 +DEAL::approx. gradient: 2.20518 0.413146 , norm: 2.24355 +DEAL:: exact gradient: 2.29982 0.441322 , norm: 2.34178 +DEAL::approx. second derivative (hessian): -0.950026 15.1637 15.1637 -1.44077 , norm: 16.3611 +DEAL:: exact second derivative (hessian): -1.00119 16.2200 16.2200 -1.56436 , norm: 17.5052 +DEAL::approx. third derivative: -35.0995 -6.58650 -6.58650 -53.1628 -6.58650 -53.1628 -53.1628 -10.2449 , norm: 99.7293 +DEAL:: exact third derivative: -36.7971 -7.06115 -7.06115 -57.4954 -7.06115 -57.4954 -57.4954 -11.0331 , norm: 107.436 +DEAL:: +DEAL::cell 3.31 +DEAL::approx. gradient: 2.14390 2.18252 , norm: 3.05936 +DEAL:: exact gradient: 1.89828 2.33137 , norm: 3.00645 +DEAL::approx. second derivative (hessian): -3.17894 13.6393 13.6393 -7.61113 , norm: 19.2132 +DEAL:: exact second derivative (hessian): -5.28899 13.3881 13.3881 -8.26405 , norm: 20.2470 +DEAL::approx. third derivative: -34.1241 -26.2844 -26.2844 -46.5567 -26.2844 -46.5567 -46.5567 -54.1205 , norm: 112.555 +DEAL:: exact third derivative: -30.3725 -37.3019 -37.3019 -47.4570 -37.3019 -47.4570 -47.4570 -58.2842 , norm: 123.492 +DEAL:: +DEAL::cell 3.32 +DEAL::approx. gradient: -3.28746 -0.374262 , norm: 3.30869 +DEAL:: exact gradient: -3.66767 -0.399786 , norm: 3.68939 +DEAL::approx. second derivative (hessian): 7.10918 -5.66231 -5.66231 5.39074 , norm: 11.9771 +DEAL:: exact second derivative (hessian): 3.74604 -6.26275 -6.26275 5.85318 , norm: 11.1504 +DEAL::approx. third derivative: 52.3259 9.94750 9.94750 82.8869 9.94750 82.8869 82.8869 9.28064 , norm: 154.051 +DEAL:: exact third derivative: 58.6827 6.39657 6.39657 91.6917 6.39657 91.6917 91.6917 9.99464 , norm: 169.966 +DEAL:: +DEAL::cell 3.33 +DEAL::approx. gradient: -2.65572 -1.03115 , norm: 2.84888 +DEAL:: exact gradient: -2.76969 -1.10148 , norm: 2.98068 +DEAL::approx. second derivative (hessian): 9.79349 -4.42142 -4.42142 14.8524 , norm: 17.4168 +DEAL:: exact second derivative (hessian): 10.3209 -4.72941 -4.72941 16.1265 , norm: 18.7729 +DEAL::approx. third derivative: 42.2707 16.4390 16.4390 64.0245 16.4390 64.0245 64.0245 25.5697 , norm: 124.695 +DEAL:: exact third derivative: 44.3151 17.6236 17.6236 69.2423 17.6236 69.2423 69.2423 27.5369 , norm: 134.303 +DEAL:: +DEAL::cell 3.34 +DEAL::approx. gradient: -3.32290 0.337694 , norm: 3.34001 +DEAL:: exact gradient: -3.70721 0.360725 , norm: 3.72471 +DEAL::approx. second derivative (hessian): 7.18582 5.10908 5.10908 5.44885 , norm: 11.4997 +DEAL:: exact second derivative (hessian): 3.78642 5.65085 5.65085 5.91628 , norm: 10.6017 +DEAL::approx. third derivative: 52.8900 -8.97558 -8.97558 83.7805 -8.97558 83.7805 83.7805 -8.37388 , norm: 155.456 +DEAL:: exact third derivative: 59.3153 -5.77160 -5.77160 92.6801 -5.77160 92.6801 92.6801 -9.01812 , norm: 171.664 +DEAL:: +DEAL::cell 3.35 +DEAL::approx. gradient: -2.68435 0.930404 , norm: 2.84102 +DEAL:: exact gradient: -2.79955 0.993856 , norm: 2.97073 +DEAL::approx. second derivative (hessian): 9.89907 3.98943 3.98943 15.0125 , norm: 17.1942 +DEAL:: exact second derivative (hessian): 10.4322 4.26732 4.26732 16.3003 , norm: 18.5450 +DEAL::approx. third derivative: 42.7264 -14.8328 -14.8328 64.7147 -14.8328 64.7147 64.7147 -23.0714 , norm: 124.827 +DEAL:: exact third derivative: 44.7928 -15.9017 -15.9017 69.9888 -15.9017 69.9888 69.9888 -24.8464 , norm: 134.453 +DEAL:: +DEAL::cell 3.36 +DEAL::approx. gradient: -1.14449 -1.43558 , norm: 1.83596 +DEAL:: exact gradient: -1.19360 -1.53349 , norm: 1.94326 +DEAL::approx. second derivative (hessian): 13.6346 -1.90542 -1.90542 20.6776 , norm: 21.1601 +DEAL:: exact second derivative (hessian): 14.3689 -2.03815 -2.03815 22.4515 , norm: 22.9363 +DEAL::approx. third derivative: 18.2166 22.8865 22.8865 27.5915 22.8865 27.5915 27.5915 35.5984 , norm: 73.8534 +DEAL:: exact third derivative: 19.0977 24.5358 24.5358 29.8401 24.5358 29.8401 29.8401 38.3371 , norm: 79.4466 +DEAL:: +DEAL::cell 3.37 +DEAL::approx. gradient: 0.646959 -1.48853 , norm: 1.62305 +DEAL:: exact gradient: 0.674723 -1.59005 , norm: 1.72728 +DEAL::approx. second derivative (hessian): 14.1375 1.07710 1.07710 21.4403 , norm: 21.5958 +DEAL:: exact second derivative (hessian): 14.8989 1.15213 1.15213 23.2795 , norm: 23.4350 +DEAL::approx. third derivative: -10.2975 23.7306 23.7306 -15.5970 23.7306 -15.5970 -15.5970 36.9114 , norm: 62.3515 +DEAL:: exact third derivative: -10.7956 25.4407 25.4407 -16.8681 25.4407 -16.8681 -16.8681 39.7511 , norm: 67.0222 +DEAL:: +DEAL::cell 3.38 +DEAL::approx. gradient: -1.15683 1.29532 , norm: 1.73669 +DEAL:: exact gradient: -1.20647 1.38366 , norm: 1.83578 +DEAL::approx. second derivative (hessian): 13.7816 1.71925 1.71925 20.9005 , norm: 21.2940 +DEAL:: exact second derivative (hessian): 14.5238 1.83901 1.83901 22.6935 , norm: 23.0884 +DEAL::approx. third derivative: 18.4130 -20.6504 -20.6504 27.8889 -20.6504 27.8889 27.8889 -32.1203 , norm: 70.5935 +DEAL:: exact third derivative: 19.3035 -22.1385 -22.1385 30.1618 -22.1385 30.1618 30.1618 -34.5914 , norm: 75.9522 +DEAL:: +DEAL::cell 3.39 +DEAL::approx. gradient: 0.653933 1.34309 , norm: 1.49383 +DEAL:: exact gradient: 0.681996 1.43469 , norm: 1.58854 +DEAL::approx. second derivative (hessian): 14.2899 -0.971861 -0.971861 21.6714 , norm: 21.7972 +DEAL:: exact second derivative (hessian): 15.0595 -1.03956 -1.03956 23.5305 , norm: 23.6562 +DEAL::approx. third derivative: -10.4085 -21.4120 -21.4120 -15.7651 -21.4120 -15.7651 -15.7651 -33.3050 , norm: 57.7806 +DEAL:: exact third derivative: -10.9119 -22.9550 -22.9550 -17.0499 -22.9550 -17.0499 -17.0499 -35.8673 , norm: 62.1163 +DEAL:: +DEAL::cell 3.40 +DEAL::approx. gradient: -2.10204 0.921977 , norm: 2.29534 +DEAL:: exact gradient: -2.34515 0.984855 , norm: 2.54355 +DEAL::approx. second derivative (hessian): 4.54569 13.9489 13.9489 3.44690 , norm: 17.9560 +DEAL:: exact second derivative (hessian): 2.39526 15.4280 15.4280 3.74259 , norm: 18.5116 +DEAL::approx. third derivative: 33.4578 -24.5052 -24.5052 52.9988 -24.5052 52.9988 52.9988 -22.8625 , norm: 108.951 +DEAL:: exact third derivative: 37.5224 -15.7577 -15.7577 58.6287 -15.7577 58.6287 58.6287 -24.6214 , norm: 114.329 +DEAL:: +DEAL::cell 3.41 +DEAL::approx. gradient: -1.69810 2.54020 , norm: 3.05551 +DEAL:: exact gradient: -1.77097 2.71344 , norm: 3.24023 +DEAL::approx. second derivative (hessian): 6.26207 10.8920 10.8920 9.49678 , norm: 18.8908 +DEAL:: exact second derivative (hessian): 6.59933 11.6507 11.6507 10.3115 , norm: 20.2530 +DEAL::approx. third derivative: 27.0284 -40.4966 -40.4966 40.9380 -40.4966 40.9380 40.9380 -62.9899 , norm: 121.020 +DEAL:: exact third derivative: 28.3356 -43.4150 -43.4150 44.2743 -43.4150 44.2743 44.2743 -67.8359 , norm: 130.153 +DEAL:: +DEAL::cell 3.42 +DEAL::approx. gradient: -0.0864524 1.14837 , norm: 1.15162 +DEAL:: exact gradient: -0.0964510 1.23664 , norm: 1.24039 +DEAL::approx. second derivative (hessian): 0.186955 17.4428 17.4428 1.98163 , norm: 18.5501 +DEAL:: exact second derivative (hessian): 0.0985119 19.3722 19.3722 0.153925 , norm: 19.4985 +DEAL::approx. third derivative: 1.37605 -30.7207 -30.7207 21.1949 -30.7207 21.1949 21.1949 -28.4765 , norm: 70.6524 +DEAL:: exact third derivative: 1.54322 -19.7862 -19.7862 2.41128 -19.7862 2.41128 2.41128 -30.9159 , norm: 46.3691 +DEAL:: +DEAL::cell 3.43 +DEAL::approx. gradient: -0.0698393 3.16396 , norm: 3.16473 +DEAL:: exact gradient: -0.0728364 3.40714 , norm: 3.40792 +DEAL::approx. second derivative (hessian): 0.257546 13.6221 13.6221 5.45973 , norm: 16.7268 +DEAL:: exact second derivative (hessian): 0.271417 14.6292 14.6292 0.424089 , norm: 14.9772 +DEAL::approx. third derivative: 1.11162 -50.7137 -50.7137 16.0433 -50.7137 16.0433 16.0433 -78.4573 , norm: 121.015 +DEAL:: exact third derivative: 1.16538 -54.5142 -54.5142 1.82091 -54.5142 1.82091 1.82091 -85.1785 , norm: 127.209 +DEAL:: +DEAL::cell 3.44 +DEAL::approx. gradient: -0.731799 3.53649 , norm: 3.61141 +DEAL:: exact gradient: -0.763204 3.77768 , norm: 3.85400 +DEAL::approx. second derivative (hessian): 8.71812 4.69391 4.69391 13.2215 , norm: 16.1759 +DEAL:: exact second derivative (hessian): 9.18766 5.02088 5.02088 14.3557 , norm: 17.4185 +DEAL::approx. third derivative: 11.6479 -56.3798 -56.3798 17.6423 -56.3798 17.6423 17.6423 -87.6951 , norm: 135.262 +DEAL:: exact third derivative: 12.2113 -60.4428 -60.4428 19.0801 -60.4428 19.0801 19.0801 -94.4419 , norm: 145.329 +DEAL:: +DEAL::cell 3.45 +DEAL::approx. gradient: 0.413673 3.66693 , norm: 3.69019 +DEAL:: exact gradient: 0.431425 3.91701 , norm: 3.94069 +DEAL::approx. second derivative (hessian): 9.03967 -2.65338 -2.65338 13.7092 , norm: 14.9087 +DEAL:: exact second derivative (hessian): 9.52653 -2.83822 -2.83822 14.8852 , norm: 16.1090 +DEAL::approx. third derivative: -6.58436 -58.4593 -58.4593 -9.97287 -58.4593 -9.97287 -9.97287 -90.9296 , norm: 137.340 +DEAL:: exact third derivative: -6.90281 -62.6721 -62.6721 -10.7856 -62.6721 -10.7856 -10.7856 -97.9252 , norm: 147.544 +DEAL:: +DEAL::cell 3.46 +DEAL::approx. gradient: -0.0300973 4.40490 , norm: 4.40500 +DEAL:: exact gradient: -0.0313890 4.74345 , norm: 4.74356 +DEAL::approx. second derivative (hessian): 0.358558 5.87044 5.87044 7.60109 , norm: 10.8773 +DEAL:: exact second derivative (hessian): 0.377869 6.30449 6.30449 0.590421 , norm: 6.78953 +DEAL::approx. third derivative: 0.479055 -70.6041 -70.6041 6.91388 -70.6041 6.91388 6.91388 -109.229 , norm: 164.406 +DEAL:: exact third derivative: 0.502223 -75.8953 -75.8953 0.784724 -75.8953 0.784724 0.784724 -118.586 , norm: 177.045 +DEAL:: +DEAL::cell 3.47 +DEAL::approx. gradient: 0.0170135 4.56736 , norm: 4.56739 +DEAL:: exact gradient: 0.0177436 4.91841 , norm: 4.91844 +DEAL::approx. second derivative (hessian): 0.371782 -3.31846 -3.31846 7.88144 , norm: 9.13769 +DEAL:: exact second derivative (hessian): 0.391806 -3.56382 -3.56382 0.612197 , norm: 4.06752 +DEAL::approx. third derivative: -0.270801 -73.2082 -73.2082 -3.90829 -73.2082 -3.90829 -3.90829 -113.258 , norm: 170.152 +DEAL:: exact third derivative: -0.283898 -78.6945 -78.6945 -0.443590 -78.6945 -0.443590 -0.443590 -122.960 , norm: 183.571 +DEAL:: +DEAL::cell 3.48 +DEAL::approx. gradient: 2.28001 -1.17703 , norm: 2.56590 +DEAL:: exact gradient: 2.37785 -1.25731 , norm: 2.68980 +DEAL::approx. second derivative (hessian): 11.1790 3.79590 3.79590 16.9536 , norm: 18.8355 +DEAL:: exact second derivative (hessian): 11.7811 4.06032 4.06032 18.4080 , norm: 20.3352 +DEAL::approx. third derivative: -36.2905 18.7646 18.7646 -54.9667 18.7646 -54.9667 -54.9667 29.1872 , norm: 110.857 +DEAL:: exact third derivative: -38.0457 20.1169 20.1169 -59.4463 20.1169 -59.4463 -59.4463 31.4327 , norm: 119.378 +DEAL:: +DEAL::cell 3.49 +DEAL::approx. gradient: 3.35483 -0.577360 , norm: 3.40415 +DEAL:: exact gradient: 3.49880 -0.616735 , norm: 3.55274 +DEAL::approx. second derivative (hessian): 5.48354 5.58534 5.58534 8.31609 , norm: 12.6619 +DEAL:: exact second derivative (hessian): 5.77887 5.97440 5.97440 9.02949 , norm: 13.5957 +DEAL::approx. third derivative: -53.3983 9.20444 9.20444 -80.8787 9.20444 -80.8787 -80.8787 14.3169 , norm: 151.442 +DEAL:: exact third derivative: -55.9808 9.86775 9.86775 -87.4701 9.86775 -87.4701 -87.4701 15.4184 , norm: 163.146 +DEAL:: +DEAL::cell 3.50 +DEAL::approx. gradient: 2.30459 1.06203 , norm: 2.53752 +DEAL:: exact gradient: 2.40349 1.13446 , norm: 2.65777 +DEAL::approx. second derivative (hessian): 11.2995 -3.42502 -3.42502 17.1364 , norm: 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exact gradient: 3.76312 0.174835 , norm: 3.76718 +DEAL::approx. second derivative (hessian): -1.55450 6.00729 6.00729 -2.35749 , norm: 7.97668 +DEAL:: exact second derivative (hessian): -1.63822 6.42575 6.42575 -2.55972 , norm: 8.54122 +DEAL::approx. third derivative: -57.4323 -2.60932 -2.60932 -86.9887 -2.60932 -86.9887 -86.9887 -4.05863 , norm: 161.358 +DEAL:: exact third derivative: -60.2100 -2.79736 -2.79736 -94.0781 -2.79736 -94.0781 -94.0781 -4.37087 , norm: 173.839 +DEAL:: +DEAL::cell 3.53 +DEAL::approx. gradient: 3.50800 0.864632 , norm: 3.61298 +DEAL:: exact gradient: 3.10610 0.923599 , norm: 3.24051 +DEAL::approx. second derivative (hessian): -5.20161 5.40338 5.40338 -12.4539 , norm: 15.3351 +DEAL:: exact second derivative (hessian): -8.65422 5.30384 5.30384 -13.5222 , norm: 16.9239 +DEAL::approx. third derivative: -55.8363 -10.4129 -10.4129 -76.1794 -10.4129 -76.1794 -76.1794 -21.4405 , norm: 145.988 +DEAL:: exact third derivative: -49.6976 -14.7776 -14.7776 -77.6525 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second derivative (hessian): 3.69508 -14.7177 -14.7177 5.77356 , norm: 19.4886 +DEAL::approx. third derivative: -34.1435 -22.6747 -22.6747 -51.7147 -22.6747 -51.7147 -51.7147 -35.2691 , norm: 109.432 +DEAL:: exact third derivative: -35.7948 -24.3088 -24.3088 -55.9294 -24.3088 -55.9294 -55.9294 -37.9825 , norm: 117.818 +DEAL:: +DEAL::cell 3.58 +DEAL::approx. gradient: 0.0599588 3.61158 , norm: 3.61207 +DEAL:: exact gradient: 0.0625319 3.88916 , norm: 3.88966 +DEAL::approx. second derivative (hessian): 0.293982 -11.6949 -11.6949 6.23214 , norm: 15.3289 +DEAL:: exact second derivative (hessian): 0.309815 -12.5596 -12.5596 0.484086 , norm: 12.9568 +DEAL::approx. third derivative: -0.954355 -57.8883 -57.8883 -13.7736 -57.8883 -13.7736 -13.7736 -89.5570 , norm: 136.542 +DEAL:: exact third derivative: -1.00051 -62.2266 -62.2266 -1.56330 -62.2266 -1.56330 -1.56330 -97.2290 , norm: 145.184 +DEAL:: +DEAL::cell 3.59 +DEAL::approx. gradient: 0.0882242 1.77155 , norm: 1.77375 +DEAL:: exact gradient: 0.0920103 1.90771 , norm: 1.90993 +DEAL::approx. second derivative (hessian): 0.144204 -17.2080 -17.2080 3.05699 , norm: 18.8701 +DEAL:: exact second derivative (hessian): 0.151971 -18.4803 -18.4803 0.237454 , norm: 18.6751 +DEAL::approx. third derivative: -1.40425 -28.3954 -28.3954 -20.2666 -28.3954 -20.2666 -20.2666 -43.9296 , norm: 74.7187 +DEAL:: exact third derivative: -1.47216 -30.5234 -30.5234 -2.30026 -30.5234 -2.30026 -2.30026 -47.6928 , norm: 71.3280 +DEAL:: +DEAL::cell 3.60 +DEAL::approx. gradient: 2.30717 -0.403201 , norm: 2.34214 +DEAL:: exact gradient: 2.40618 -0.430698 , norm: 2.44443 +DEAL::approx. second derivative (hessian): -0.993965 -14.7987 -14.7987 -1.50740 , norm: 16.0516 +DEAL:: exact second derivative (hessian): -1.04750 -15.8295 -15.8295 -1.63672 , norm: 17.1744 +DEAL::approx. third derivative: -36.7229 6.42795 6.42795 -55.6216 6.42795 -55.6216 -55.6216 9.99825 , norm: 104.181 +DEAL:: exact third derivative: -38.4989 6.89117 6.89117 -60.1546 6.89117 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gradient: -0.620717 -1.73631 0.00000 , norm: 1.84393 +DEAL:: exact gradient: -1.05146 -2.28707 0.00000 , norm: 2.51719 +DEAL::approx. second derivative (hessian): 3.70772 -10.7223 0.00000 -10.7223 2.55155 0.00000 0.00000 0.00000 0.00000 , norm: 13.8675 +DEAL:: exact second derivative (hessian): 2.29766 -16.7458 0.00000 -16.7458 3.59010 0.00000 0.00000 0.00000 0.00000 , norm: 19.7021 +DEAL::approx. third derivative: 9.72628 45.9222 4.11639e-10 45.9222 16.9488 -8.82233e-10 4.11639e-10 -8.82233e-10 0.00000 45.9222 16.9488 -8.82233e-10 16.9488 42.0131 3.19990e-10 -8.82233e-10 3.19990e-10 -2.36848e-15 4.11639e-10 -8.82233e-10 0.00000 -8.82233e-10 3.19990e-10 -2.36848e-15 0.00000 -2.36848e-15 0.00000 , norm: 95.1212 +DEAL:: exact third derivative: 16.8234 36.5930 0.00000 36.5930 26.2865 0.00000 0.00000 0.00000 0.00000 36.5930 26.2865 0.00000 26.2865 57.1766 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 , norm: 98.1952 +DEAL:: +DEAL::cell 2.3 +DEAL::approx. gradient: -0.0713169 -3.61258 0.00000 , norm: 3.61328 +DEAL:: exact gradient: -0.0847526 -4.75848 0.00000 , norm: 4.75923 +DEAL::approx. second derivative (hessian): 3.85715 -1.02293 0.00000 -1.02293 5.30876 0.00000 0.00000 0.00000 0.00000 , norm: 5.83722 +DEAL:: exact second derivative (hessian): 4.78053 -1.34979 0.00000 -1.34979 7.46958 0.00000 0.00000 0.00000 0.00000 , norm: 8.03022 +DEAL::approx. third derivative: 1.11750 57.2075 7.77759e-10 57.2075 1.53782 3.77879e-10 7.77759e-10 3.77879e-10 -1.65793e-14 57.2075 1.53782 3.77879e-10 1.53782 87.4126 1.15707e-09 3.77879e-10 1.15707e-09 -9.47390e-15 7.77759e-10 3.77879e-10 -1.65793e-14 3.77879e-10 1.15707e-09 -9.47390e-15 -1.65793e-14 -9.47390e-15 0.00000 , norm: 132.164 +DEAL:: exact third derivative: 1.35604 76.1357 0.00000 76.1357 2.11882 0.00000 0.00000 0.00000 0.00000 76.1357 2.11882 0.00000 2.11882 118.962 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 , norm: 177.643 +DEAL:: +DEAL::cell 2.4 +DEAL::approx. gradient: 1.68054 -2.12960 0.00000 , norm: 2.71283 +DEAL:: exact gradient: 2.84675 -1.40255 0.00000 , norm: 3.17350 +DEAL::approx. second derivative (hessian): -10.0384 -10.3133 0.00000 -10.3133 -3.31217 0.00000 0.00000 0.00000 0.00000 , norm: 17.5230 +DEAL:: exact second derivative (hessian): -6.22074 -10.2694 0.00000 -10.2694 -9.71991 0.00000 0.00000 0.00000 0.00000 , norm: 18.3877 +DEAL::approx. third derivative: -26.3331 33.7236 -1.00947e-09 33.7236 -29.0569 -1.12650e-09 -1.00947e-09 -1.12650e-09 4.73695e-15 33.7236 -29.0569 -1.12650e-09 -29.0569 51.5294 -2.13648e-10 -1.12650e-09 -2.13648e-10 -4.73695e-15 -1.00947e-09 -1.12650e-09 4.73695e-15 -1.12650e-09 -2.13648e-10 -4.73695e-15 4.73695e-15 -4.73695e-15 0.00000 , norm: 96.4027 +DEAL:: exact third derivative: -45.5480 22.4408 0.00000 22.4408 -71.1687 0.00000 0.00000 0.00000 0.00000 22.4408 -71.1687 0.00000 -71.1687 35.0638 0.00000 0.00000 0.00000 0.00000 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