From 22a313fdc44ce2acb5fb01435d8bd63185bdc237 Mon Sep 17 00:00:00 2001 From: Maximilian Bergbauer Date: Fri, 28 Apr 2023 14:35:01 +0200 Subject: [PATCH] Implement path for values only --- include/deal.II/fe/mapping_q_internal.h | 73 ++- .../deal.II/matrix_free/fe_point_evaluation.h | 354 ++++++---- .../matrix_free/tensor_product_kernels.h | 479 +++++++++++++- source/fe/mapping_q.cc | 13 +- source/non_matching/quadrature_generator.cc | 13 +- tests/matrix_free/point_evaluation_25.cc | 142 ++++ tests/matrix_free/point_evaluation_25.output | 616 ++++++++++++++++++ 7 files changed, 1516 insertions(+), 174 deletions(-) create mode 100644 tests/matrix_free/point_evaluation_25.cc create mode 100644 tests/matrix_free/point_evaluation_25.output diff --git a/include/deal.II/fe/mapping_q_internal.h b/include/deal.II/fe/mapping_q_internal.h index e39202634c..2b9c03b680 100644 --- a/include/deal.II/fe/mapping_q_internal.h +++ b/include/deal.II/fe/mapping_q_internal.h @@ -1301,6 +1301,15 @@ namespace internal if (update_flags & update_covariant_transformation) inverse_jacobians.resize(n_points); + const bool is_translation = + cell_similarity == CellSimilarity::translation; + + const bool needs_gradient = + !is_translation && + (update_flags & + (update_covariant_transformation | + update_contravariant_transformation | update_volume_elements)); + // Use the more heavy VectorizedArray code path if there is more than // one point left to compute for (unsigned int i = 0; i < n_points; i += n_lanes) @@ -1315,25 +1324,39 @@ namespace internal for (unsigned int d = 0; d < dim; ++d) p_vec[d][j] = unit_points[i][d]; - const auto result = - internal::evaluate_tensor_product_value_and_gradient( + Tensor<1, spacedim, VectorizedArray> value; + DerivativeForm<1, dim, spacedim, VectorizedArray> + derivative; + if (needs_gradient) + { + const auto result = + internal::evaluate_tensor_product_value_and_gradient( + polynomials_1d, + support_points, + p_vec, + polynomials_1d.size() == 2, + renumber_lexicographic_to_hierarchic); + + value = result.first; + + for (unsigned int d = 0; d < spacedim; ++d) + for (unsigned int e = 0; e < dim; ++e) + derivative[d][e] = result.second[e][d]; + } + else + value = internal::evaluate_tensor_product_value( polynomials_1d, support_points, p_vec, polynomials_1d.size() == 2, renumber_lexicographic_to_hierarchic); - DerivativeForm<1, dim, spacedim, VectorizedArray> - derivative; - for (unsigned int d = 0; d < spacedim; ++d) - for (unsigned int e = 0; e < dim; ++e) - derivative[d][e] = result.second[e][d]; if (update_flags & update_quadrature_points) for (unsigned int j = 0; j < n_lanes && i + j < n_points; ++j) for (unsigned int d = 0; d < spacedim; ++d) - quadrature_points[i + j][d] = result.first[d][j]; + quadrature_points[i + j][d] = value[d][j]; - if (cell_similarity == CellSimilarity::translation) + if (is_translation) continue; if (update_flags & update_contravariant_transformation) @@ -1357,8 +1380,26 @@ namespace internal } else { - const auto result = - internal::evaluate_tensor_product_value_and_gradient( + Tensor<1, spacedim, double> value; + DerivativeForm<1, dim, spacedim, double> derivative; + if (needs_gradient) + { + const auto result = + internal::evaluate_tensor_product_value_and_gradient( + polynomials_1d, + support_points, + unit_points[i], + polynomials_1d.size() == 2, + renumber_lexicographic_to_hierarchic); + + value = result.first; + + for (unsigned int d = 0; d < spacedim; ++d) + for (unsigned int e = 0; e < dim; ++e) + derivative[d][e] = result.second[e][d]; + } + else + value = internal::evaluate_tensor_product_value( polynomials_1d, support_points, unit_points[i], @@ -1366,18 +1407,16 @@ namespace internal renumber_lexicographic_to_hierarchic); if (update_flags & update_quadrature_points) - quadrature_points[i] = result.first; + quadrature_points[i] = value; - if (cell_similarity == CellSimilarity::translation) + if (is_translation) continue; if (dim == spacedim && update_flags & update_volume_elements) - data.volume_elements[i] = - DerivativeForm<1, spacedim, dim>(result.second).determinant(); + data.volume_elements[i] = derivative.determinant(); if (update_flags & update_contravariant_transformation) - jacobians[i] = - DerivativeForm<1, spacedim, dim>(result.second).transpose(); + jacobians[i] = derivative; if (update_flags & update_covariant_transformation) inverse_jacobians[i] = jacobians[i].covariant_form().transpose(); diff --git a/include/deal.II/matrix_free/fe_point_evaluation.h b/include/deal.II/matrix_free/fe_point_evaluation.h index b2e5f20b29..db961b8550 100644 --- a/include/deal.II/matrix_free/fe_point_evaluation.h +++ b/include/deal.II/matrix_free/fe_point_evaluation.h @@ -1028,10 +1028,12 @@ private: * batch. */ void - compute_evaluate_fast(const unsigned int n_shapes, - const unsigned int qb, - vectorized_value_type & value, - interface_vectorized_gradient_type &gradient); + compute_evaluate_fast( + const EvaluationFlags::EvaluationFlags &evaluation_flags, + const unsigned int n_shapes, + const unsigned int qb, + vectorized_value_type & value, + interface_vectorized_gradient_type & gradient); /** * Fast path of the evaluate function. @@ -1053,10 +1055,12 @@ private: * cell or face for a given quadrature batch. */ void - compute_integrate_fast(const unsigned int n_shapes, - const unsigned int qb, - const vectorized_value_type & value, - const interface_vectorized_gradient_type &gradient); + compute_integrate_fast( + const EvaluationFlags::EvaluationFlags & integration_flags, + const unsigned int n_shapes, + const unsigned int qb, + const vectorized_value_type & value, + const interface_vectorized_gradient_type &gradient); /** * Addition across the lanes of VectorizedArray as accumulated by the @@ -1653,18 +1657,21 @@ FEPointEvaluation::do_reinit() if (dim > 1) { shapes_faces.resize_fast(n_batches * n_shapes); - internal::compute_values_of_array(shapes_faces.data() + - qb * n_shapes, - poly, - unit_point_faces_ptr[qb]); + internal::compute_values_of_array( + shapes_faces.data() + qb * n_shapes, + poly, + unit_point_faces_ptr[qb], + update_flags & UpdateFlags::update_gradients ? 1 : 0); } } else { shapes.resize_fast(n_batches * n_shapes); - internal::compute_values_of_array(shapes.data() + qb * n_shapes, - poly, - unit_point_ptr[qb]); + internal::compute_values_of_array( + shapes.data() + qb * n_shapes, + poly, + unit_point_ptr[qb], + update_flags & UpdateFlags::update_gradients ? 1 : 0); } } @@ -1748,88 +1755,128 @@ FEPointEvaluation::prepare_evaluate_fast( template inline void FEPointEvaluation::compute_evaluate_fast( - const unsigned int n_shapes, - const unsigned int qb, - vectorized_value_type & value, - interface_vectorized_gradient_type &gradient) + const EvaluationFlags::EvaluationFlags &evaluation_flags, + const unsigned int n_shapes, + const unsigned int qb, + vectorized_value_type & value, + interface_vectorized_gradient_type & gradient) { if (use_face_path) { - const std::array interpolated_value = - polynomials_are_hat_functions ? - internal::evaluate_tensor_product_value_and_gradient_linear< - dim - 1, - scalar_value_type, - VectorizedArrayType, - 2>(n_shapes, solution_renumbered.data(), unit_point_faces_ptr[qb]) : - internal::evaluate_tensor_product_value_and_gradient_shapes< - dim - 1, - scalar_value_type, - VectorizedArrayType, - 2, - false>(shapes_faces.data() + qb * n_shapes, - n_shapes, - solution_renumbered.data()); - - value = interpolated_value[dim - 1]; - // reorder derivative from tangential/normal derivatives into tensor in - // physical coordinates - if (current_face_number / 2 == 0) - { - gradient[0] = interpolated_value[dim]; - if (dim > 1) - gradient[1] = interpolated_value[0]; - if (dim > 2) - gradient[2] = interpolated_value[1]; - } - else if (current_face_number / 2 == 1) + if (evaluation_flags & EvaluationFlags::gradients) { - if (dim > 1) - gradient[1] = interpolated_value[dim]; - if (dim == 3) + const std::array interpolated_value = + polynomials_are_hat_functions ? + internal::evaluate_tensor_product_value_and_gradient_linear< + dim - 1, + scalar_value_type, + VectorizedArrayType, + 2>(n_shapes, + solution_renumbered.data(), + unit_point_faces_ptr[qb]) : + internal::evaluate_tensor_product_value_and_gradient_shapes< + dim - 1, + scalar_value_type, + VectorizedArrayType, + 2, + false>(shapes_faces.data() + qb * n_shapes, + n_shapes, + solution_renumbered.data()); + + value = interpolated_value[dim - 1]; + // reorder derivative from tangential/normal derivatives into tensor + // in physical coordinates + if (current_face_number / 2 == 0) { - gradient[0] = interpolated_value[1]; - gradient[2] = interpolated_value[0]; + gradient[0] = interpolated_value[dim]; + if (dim > 1) + gradient[1] = interpolated_value[0]; + if (dim > 2) + gradient[2] = interpolated_value[1]; } - else if (dim == 2) - gradient[0] = interpolated_value[0]; - else - Assert(false, ExcInternalError()); - } - else if (current_face_number / 2 == 2) - { - if (dim > 2) + else if (current_face_number / 2 == 1) { - gradient[0] = interpolated_value[0]; - gradient[1] = interpolated_value[1]; - gradient[2] = interpolated_value[dim]; + if (dim > 1) + gradient[1] = interpolated_value[dim]; + if (dim == 3) + { + gradient[0] = interpolated_value[1]; + gradient[2] = interpolated_value[0]; + } + else if (dim == 2) + gradient[0] = interpolated_value[0]; + else + Assert(false, ExcInternalError()); + } + else if (current_face_number / 2 == 2) + { + if (dim > 2) + { + gradient[0] = interpolated_value[0]; + gradient[1] = interpolated_value[1]; + gradient[2] = interpolated_value[dim]; + } + else + Assert(false, ExcInternalError()); } else Assert(false, ExcInternalError()); } else - Assert(false, ExcInternalError()); + { + value = polynomials_are_hat_functions ? + internal::evaluate_tensor_product_value_linear< + dim - 1, + scalar_value_type, + VectorizedArrayType>(n_shapes, + solution_renumbered.data(), + unit_point_faces_ptr[qb]) : + internal::evaluate_tensor_product_value_shapes< + dim - 1, + scalar_value_type, + VectorizedArrayType, + false>(shapes_faces.data() + qb * n_shapes, + n_shapes, + solution_renumbered.data()); + } } else { - const std::array result = - polynomials_are_hat_functions ? - internal::evaluate_tensor_product_value_and_gradient_linear( - n_shapes, solution_renumbered.data(), unit_point_ptr[qb]) : - internal::evaluate_tensor_product_value_and_gradient_shapes< - dim, - scalar_value_type, - VectorizedArrayType, - 1, - false>(shapes.data() + qb * n_shapes, - n_shapes, - solution_renumbered.data()); - gradient[0] = result[0]; - if (dim > 1) - gradient[1] = result[1]; - if (dim > 2) - gradient[2] = result[2]; - value = result[dim]; + if (evaluation_flags & EvaluationFlags::gradients) + { + const std::array result = + polynomials_are_hat_functions ? + internal::evaluate_tensor_product_value_and_gradient_linear( + n_shapes, solution_renumbered.data(), unit_point_ptr[qb]) : + internal::evaluate_tensor_product_value_and_gradient_shapes< + dim, + scalar_value_type, + VectorizedArrayType, + 1, + false>(shapes.data() + qb * n_shapes, + n_shapes, + solution_renumbered.data()); + gradient[0] = result[0]; + if (dim > 1) + gradient[1] = result[1]; + if (dim > 2) + gradient[2] = result[2]; + value = result[dim]; + } + else + { + value = + polynomials_are_hat_functions ? + internal::evaluate_tensor_product_value_linear( + n_shapes, solution_renumbered.data(), unit_point_ptr[qb]) : + internal::evaluate_tensor_product_value_shapes< + dim, + scalar_value_type, + VectorizedArrayType, + false>(shapes.data() + qb * n_shapes, + n_shapes, + solution_renumbered.data()); + } } } @@ -1850,7 +1897,7 @@ FEPointEvaluation::evaluate_fast( for (unsigned int qb = 0, q = 0; q < n_q_points_scalar; ++qb, q += n_lanes_internal) { - compute_evaluate_fast(n_shapes, qb, value, gradient); + compute_evaluate_fast(evaluation_flags, n_shapes, qb, value, gradient); if (evaluation_flags & EvaluationFlags::values) { @@ -1993,6 +2040,7 @@ FEPointEvaluation::evaluate( template inline void FEPointEvaluation::compute_integrate_fast( + const EvaluationFlags::EvaluationFlags & integration_flags, const unsigned int n_shapes, const unsigned int qb, const vectorized_value_type & value, @@ -2000,74 +2048,100 @@ FEPointEvaluation::compute_integrate_fast( { if (use_face_path) { - std::array value_face = {}; - Tensor<1, dim - 1, vectorized_value_type> gradient_in_face; - - value_face[0] = value; - // fill derivative in physical coordinates into tangential/normal - // derivatives - if (current_face_number / 2 == 0) - { - value_face[1] = gradient[0]; - if (dim > 1) - gradient_in_face[0] = gradient[1]; - if (dim > 2) - gradient_in_face[1] = gradient[2]; - } - else if (current_face_number / 2 == 1) + if (integration_flags & EvaluationFlags::gradients) { - if (dim > 1) - value_face[1] = gradient[1]; - if (dim == 3) + std::array value_face = {}; + Tensor<1, dim - 1, vectorized_value_type> gradient_in_face; + + value_face[0] = value; + // fill derivative in physical coordinates into tangential/normal + // derivatives + if (current_face_number / 2 == 0) { - gradient_in_face[0] = gradient[2]; - gradient_in_face[1] = gradient[0]; + value_face[1] = gradient[0]; + if (dim > 1) + gradient_in_face[0] = gradient[1]; + if (dim > 2) + gradient_in_face[1] = gradient[2]; } - else if (dim == 2) - gradient_in_face[0] = gradient[0]; - else - Assert(false, ExcInternalError()); - } - else if (current_face_number / 2 == 2) - { - if (dim > 2) + else if (current_face_number / 2 == 1) { - value_face[1] = gradient[2]; - gradient_in_face[0] = gradient[0]; - gradient_in_face[1] = gradient[1]; + if (dim > 1) + value_face[1] = gradient[1]; + if (dim == 3) + { + gradient_in_face[0] = gradient[2]; + gradient_in_face[1] = gradient[0]; + } + else if (dim == 2) + gradient_in_face[0] = gradient[0]; + else + Assert(false, ExcInternalError()); + } + else if (current_face_number / 2 == 2) + { + if (dim > 2) + { + value_face[1] = gradient[2]; + gradient_in_face[0] = gradient[0]; + gradient_in_face[1] = gradient[1]; + } + else + Assert(false, ExcInternalError()); } else Assert(false, ExcInternalError()); + + internal::integrate_tensor_product_value_and_gradient< + dim - 1, + VectorizedArrayType, + vectorized_value_type, + 2>(shapes_faces.data() + qb * n_shapes, + n_shapes, + value_face.data(), + gradient_in_face, + solution_renumbered_vectorized.data(), + unit_point_faces_ptr[qb], + polynomials_are_hat_functions, + qb != 0); } else - Assert(false, ExcInternalError()); - - internal::integrate_tensor_product_value_and_gradient< - dim - 1, - VectorizedArrayType, - vectorized_value_type, - 2>(shapes_faces.data() + qb * n_shapes, - n_shapes, - value_face.data(), - gradient_in_face, - solution_renumbered_vectorized.data(), - unit_point_faces_ptr[qb], - polynomials_are_hat_functions, - qb != 0); + internal::integrate_tensor_product_value( + shapes_faces.data() + qb * n_shapes, + n_shapes, + value, + solution_renumbered_vectorized.data(), + unit_point_faces_ptr[qb], + polynomials_are_hat_functions, + qb != 0); } else { - internal::integrate_tensor_product_value_and_gradient< - dim, - VectorizedArrayType, - vectorized_value_type>(shapes.data() + qb * n_shapes, - n_shapes, - &value, - gradient, - solution_renumbered_vectorized.data(), - unit_point_ptr[qb], - polynomials_are_hat_functions, - qb != 0); + if (integration_flags & EvaluationFlags::gradients) + internal::integrate_tensor_product_value_and_gradient< + dim, + VectorizedArrayType, + vectorized_value_type>(shapes.data() + qb * n_shapes, + n_shapes, + &value, + gradient, + solution_renumbered_vectorized.data(), + unit_point_ptr[qb], + polynomials_are_hat_functions, + qb != 0); + else + internal::integrate_tensor_product_value( + shapes.data() + qb * n_shapes, + n_shapes, + value, + solution_renumbered_vectorized.data(), + unit_point_ptr[qb], + polynomials_are_hat_functions, + qb != 0); } } @@ -2213,7 +2287,7 @@ FEPointEvaluation::integrate_fast( } } - compute_integrate_fast(n_shapes, qb, value, gradient); + compute_integrate_fast(integration_flags, n_shapes, qb, value, gradient); } // add between the lanes and write into the result diff --git a/include/deal.II/matrix_free/tensor_product_kernels.h b/include/deal.II/matrix_free/tensor_product_kernels.h index e4b12fa363..17ce0cf346 100644 --- a/include/deal.II/matrix_free/tensor_product_kernels.h +++ b/include/deal.II/matrix_free/tensor_product_kernels.h @@ -3007,7 +3007,8 @@ namespace internal compute_values_of_array( dealii::ndarray * shapes, const std::vector> &poly, - const Point & p) + const Point & p, + const unsigned int derivative = 1) { const int n_shapes = poly.size(); @@ -3016,7 +3017,7 @@ namespace internal for (unsigned int d = 0; d < dim; ++d) point[d] = p[d]; for (int i = 0; i < n_shapes; ++i) - poly[i].values_of_array(point, 1, shapes[i].data()); + poly[i].values_of_array(point, derivative, shapes[i].data()); } @@ -3028,7 +3029,8 @@ namespace internal inline void compute_values_of_array(dealii::ndarray *, const std::vector> &, - const Point<0, Number> &) + const Point<0, Number> &, + const unsigned int) { Assert(false, ExcInternalError()); } @@ -3391,6 +3393,204 @@ namespace internal + template + inline +#ifndef DEBUG + DEAL_II_ALWAYS_INLINE +#endif + typename ProductTypeNoPoint::type + do_interpolate_xy_value(const Number * values, + const std::vector & renumber, + const dealii::ndarray *shapes, + const int n_shapes_runtime, + int & i) + { + const int n_shapes = length > 0 ? length : n_shapes_runtime; + using Number3 = typename ProductTypeNoPoint::type; + Number3 result = {}; + for (int i1 = 0; i1 < (dim > 1 ? n_shapes : 1); ++i1) + { + // Interpolation x direction + Number3 value = {}; + + // Distinguish the inner loop based on whether we have a + // renumbering or not + if (do_renumber && !renumber.empty()) + for (int i0 = 0; i0 < n_shapes; ++i0, ++i) + value += shapes[i0][0][0] * values[renumber[i]]; + else + for (int i0 = 0; i0 < n_shapes; ++i0, ++i) + value += shapes[i0][0][0] * values[i]; + + if (dim > 1) + result += value * shapes[i1][0][1]; + else + result = value; + } + return result; + } + + + + template + inline typename ProductTypeNoPoint::type + evaluate_tensor_product_value_shapes( + const dealii::ndarray *shapes, + const int n_shapes, + const Number * values, + const std::vector & renumber = {}) + { + static_assert(dim >= 0 && dim <= 3, "Only dim=0,1,2,3 implemented"); + + // we only need the value on faces of a 1d element + if (dim == 0) + { + return values[0]; + } + + using Number3 = typename ProductTypeNoPoint::type; + + // Go through the tensor product of shape functions and interpolate + // with optimal algorithm + Number3 result = {}; + for (int i2 = 0, i = 0; i2 < (dim > 2 ? n_shapes : 1); ++i2) + { + Number3 inner_result; + // Generate separate code with known loop bounds for the most common + // cases + if (n_shapes == 2) + inner_result = + do_interpolate_xy_value( + values, renumber, shapes, n_shapes, i); + else if (n_shapes == 3) + inner_result = + do_interpolate_xy_value( + values, renumber, shapes, n_shapes, i); + else if (n_shapes == 4) + inner_result = + do_interpolate_xy_value( + values, renumber, shapes, n_shapes, i); + else if (n_shapes == 5) + inner_result = + do_interpolate_xy_value( + values, renumber, shapes, n_shapes, i); + else if (n_shapes == 6) + inner_result = + do_interpolate_xy_value( + values, renumber, shapes, n_shapes, i); + else + inner_result = + do_interpolate_xy_value( + values, renumber, shapes, n_shapes, i); + if (dim == 3) + { + // Interpolation + derivative in z direction + result += inner_result * shapes[i2][0][2]; + } + else + { + result = inner_result; + } + } + + return result; + } + + + + template + inline typename ProductTypeNoPoint::type + evaluate_tensor_product_value_linear( + const unsigned int n_shapes, + const Number * values, + const Point & p, + const std::vector &renumber = {}) + { + (void)n_shapes; + static_assert(dim >= 0 && dim <= 3, "Only dim=0,1,2,3 implemented"); + + using Number3 = typename ProductTypeNoPoint::type; + + AssertDimension(n_shapes, 2); + for (unsigned int i = 0; i < renumber.size(); ++i) + AssertDimension(renumber[i], i); + + if (dim == 0) + { + // we only need the value on faces of a 1d element + return values[0]; + } + else if (dim == 1) + { + return (1. - p[0]) * values[0] + p[0] * values[1]; + } + else if (dim == 2) + { + const Number2 x0 = 1. - p[0], x1 = p[0]; + const Number3 tmp0 = x0 * values[0] + x1 * values[1]; + const Number3 tmp1 = x0 * values[2] + x1 * values[3]; + const Number3 mapped = (1. - p[1]) * tmp0 + p[1] * tmp1; + return mapped; + } + else if (dim == 3) + { + const Number2 x0 = 1. - p[0], x1 = p[0], y0 = 1. - p[1], y1 = p[1], + z0 = 1. - p[2], z1 = p[2]; + const Number3 tmp0 = x0 * values[0] + x1 * values[1]; + const Number3 tmp1 = x0 * values[2] + x1 * values[3]; + const Number3 tmpy0 = y0 * tmp0 + y1 * tmp1; + const Number3 tmp2 = x0 * values[4] + x1 * values[5]; + const Number3 tmp3 = x0 * values[6] + x1 * values[7]; + const Number3 tmpy1 = y0 * tmp2 + y1 * tmp3; + const Number3 mapped = z0 * tmpy0 + z1 * tmpy1; + return mapped; + } + + // work around a compile error: missing return statement + return Number3(); + } + + + + template + inline typename ProductTypeNoPoint::type + evaluate_tensor_product_value( + const std::vector> &poly, + const std::vector & values, + const Point & p, + const bool d_linear = false, + const std::vector & renumber = {}) + { + typename ProductTypeNoPoint::type result; + if (d_linear) + { + result = evaluate_tensor_product_value_linear(poly.size(), + values.data(), + p, + renumber); + } + else + { + AssertIndexRange(poly.size(), 200); + std::array, 200> shapes; + const int n_shapes = poly.size(); + std::array point; + for (unsigned int d = 0; d < dim; ++d) + point[d] = p[d]; + for (int i = 0; i < n_shapes; ++i) + poly[i].values_of_array(point, 0, shapes[i].data()); + result = evaluate_tensor_product_value_shapes( + shapes.data(), n_shapes, values.data(), renumber); + } + return result; + } + + + /** * This function computes derivatives of arbitrary orders in 1d, returning a * Tensor with the respective derivative @@ -4005,6 +4205,279 @@ namespace internal + /** + * Test inner dimensions of tensor product shape functions and accumulate. + */ + template + inline +#ifndef DEBUG + DEAL_II_ALWAYS_INLINE +#endif + void + do_apply_test_functions_xy_value( + Number2 * values, + const dealii::ndarray *shapes, + const Number2 & test_value, + const int n_shapes_runtime, + int & i) + { + if (length > 0) + { + constexpr unsigned int array_size = length > 0 ? length : 1; + std::array shape_values_x; + for (unsigned int i1 = 0; i1 < array_size; ++i1) + shape_values_x[i1] = shapes[i1][0][0]; + for (unsigned int i1 = 0; i1 < (dim > 1 ? length : 1); ++i1) + { + const Number2 test_value_y = + dim > 1 ? test_value * shapes[i1][0][1] : test_value; + + Number2 *values_ptr = values + i + i1 * length; + for (unsigned int i0 = 0; i0 < length; ++i0) + { + if (add) + values_ptr[i0] += shape_values_x[i0] * test_value_y; + else + values_ptr[i0] = shape_values_x[i0] * test_value_y; + } + } + i += (dim > 1 ? length * length : length); + } + else + { + for (int i1 = 0; i1 < (dim > 1 ? n_shapes_runtime : 1); ++i1) + { + const Number2 test_value_y = + dim > 1 ? test_value * shapes[i1][0][1] : test_value; + + Number2 *values_ptr = values + i + i1 * n_shapes_runtime; + for (int i0 = 0; i0 < n_shapes_runtime; ++i0) + { + if (add) + values_ptr[i0] += shapes[i0][0][0] * test_value_y; + else + values_ptr[i0] = shapes[i0][0][0] * test_value_y; + } + } + i += (dim > 1 ? n_shapes_runtime * n_shapes_runtime : n_shapes_runtime); + } + } + + + + /** + * Same as evaluate_tensor_product_value_shapes() but for integration. + */ + template + inline void + integrate_add_tensor_product_value_shapes( + const dealii::ndarray *shapes, + const int n_shapes, + const Number2 & value, + Number2 * values) + { + static_assert(dim >= 0 && dim <= 3, "Only dim=0,1,2,3 implemented"); + + // as in evaluate, use `int` type to produce better code in this context + + if (dim == 0) + { + if (add) + values[0] += value; + else + values[0] = value; + return; + } + + // Implement the transpose of the function above + Number2 test_value; + for (int i2 = 0, i = 0; i2 < (dim > 2 ? n_shapes : 1); ++i2) + { + // test value z + test_value = dim > 2 ? value * shapes[i2][0][2] : value; + + // Generate separate code with known loop bounds for the most common + // cases + if (n_shapes == 2) + do_apply_test_functions_xy_value( + values, shapes, test_value, n_shapes, i); + else if (n_shapes == 3) + do_apply_test_functions_xy_value( + values, shapes, test_value, n_shapes, i); + else if (n_shapes == 4) + do_apply_test_functions_xy_value( + values, shapes, test_value, n_shapes, i); + else if (n_shapes == 5) + do_apply_test_functions_xy_value( + values, shapes, test_value, n_shapes, i); + else if (n_shapes == 6) + do_apply_test_functions_xy_value( + values, shapes, test_value, n_shapes, i); + else + do_apply_test_functions_xy_value( + values, shapes, test_value, n_shapes, i); + } + } + + + + /** + * Specializes @p integrate_tensor_product_value_shapes() for linear + * polynomials which massively reduces the necessary instructions. + */ + template + inline void + integrate_add_tensor_product_value_linear(const unsigned int n_shapes, + const Number2 & value, + Number2 * values, + const Point &p) + { + (void)n_shapes; + static_assert(dim >= 0 && dim <= 3, "Only dim=0,1,2,3 implemented"); + + AssertDimension(n_shapes, 2); + + if (dim == 0) + { + if (add) + values[0] += value; + else + values[0] = value; + } + else if (dim == 1) + { + const auto x0 = 1. - p[0], x1 = p[0]; + + if (add) + { + values[0] += value * x0; + values[1] += value * x1; + } + else + { + values[0] = value * x0; + values[1] = value * x1; + } + } + else if (dim == 2) + { + const auto x0 = 1. - p[0], x1 = p[0], y0 = 1. - p[1], y1 = p[1]; + + const auto test_value_y0 = value * y0; + const auto test_value_y1 = value * y1; + + if (add) + { + values[0] += x0 * test_value_y0; + values[1] += x1 * test_value_y0; + values[2] += x0 * test_value_y1; + values[3] += x1 * test_value_y1; + } + else + { + values[0] = x0 * test_value_y0; + values[1] = x1 * test_value_y0; + values[2] = x0 * test_value_y1; + values[3] = x1 * test_value_y1; + } + } + else if (dim == 3) + { + const auto x0 = 1. - p[0], x1 = p[0], y0 = 1. - p[1], y1 = p[1], + z0 = 1. - p[2], z1 = p[2]; + + const auto test_value_z0 = value * z0; + const auto test_value_z1 = value * z1; + + const auto test_value_y00 = test_value_z0 * y0; + const auto test_value_y01 = test_value_z0 * y1; + const auto test_value_y10 = test_value_z1 * y0; + const auto test_value_y11 = test_value_z1 * y1; + + if (add) + { + values[0] += x0 * test_value_y00; + values[1] += x1 * test_value_y00; + values[2] += x0 * test_value_y01; + values[3] += x1 * test_value_y01; + values[4] += x0 * test_value_y10; + values[5] += x1 * test_value_y10; + values[6] += x0 * test_value_y11; + values[7] += x1 * test_value_y11; + } + else + { + values[0] = x0 * test_value_y00; + values[1] = x1 * test_value_y00; + values[2] = x0 * test_value_y01; + values[3] = x1 * test_value_y01; + values[4] = x0 * test_value_y10; + values[5] = x1 * test_value_y10; + values[6] = x0 * test_value_y11; + values[7] = x1 * test_value_y11; + } + } + } + + + + /** + * Calls the correct @p integrate_add_tensor_product_value_...() + * function depending on if values should be added to or set and if + * polynomials are linear. + */ + template + inline void + integrate_tensor_product_value(const dealii::ndarray *shapes, + const unsigned int n_shapes, + const Number2 & value, + Number2 * values, + const Point &p, + const bool is_linear, + const bool do_add) + { + if (do_add) + { + if (is_linear) + internal::integrate_add_tensor_product_value_linear(n_shapes, + value, + values, + p); + else + internal::integrate_add_tensor_product_value_shapes(shapes, + n_shapes, + value, + values); + } + else + { + if (is_linear) + internal::integrate_add_tensor_product_value_linear(n_shapes, + value, + values, + p); + else + internal::integrate_add_tensor_product_value_shapes(shapes, + n_shapes, + value, + values); + } + } + + + template inline void weight_fe_q_dofs_by_entity(const Number * weights, diff --git a/source/fe/mapping_q.cc b/source/fe/mapping_q.cc index bd3d1dcf50..7d0f7472ff 100644 --- a/source/fe/mapping_q.cc +++ b/source/fe/mapping_q.cc @@ -290,13 +290,12 @@ MappingQ::transform_unit_to_real_cell( const typename Triangulation::cell_iterator &cell, const Point & p) const { - return Point(internal::evaluate_tensor_product_value_and_gradient( - polynomials_1d, - this->compute_mapping_support_points(cell), - p, - polynomials_1d.size() == 2, - renumber_lexicographic_to_hierarchic) - .first); + return Point(internal::evaluate_tensor_product_value( + polynomials_1d, + this->compute_mapping_support_points(cell), + p, + polynomials_1d.size() == 2, + renumber_lexicographic_to_hierarchic)); } diff --git a/source/non_matching/quadrature_generator.cc b/source/non_matching/quadrature_generator.cc index 463b7caa53..f8f70355f7 100644 --- a/source/non_matching/quadrature_generator.cc +++ b/source/non_matching/quadrature_generator.cc @@ -1516,13 +1516,12 @@ namespace NonMatching if (!poly.empty() && component == 0) { // TODO: this could be extended to a component that is not zero - return dealii::internal::evaluate_tensor_product_value_and_gradient( - poly, - local_dof_values, - point, - polynomials_are_hat_functions, - renumber) - .first; + return dealii::internal::evaluate_tensor_product_value( + poly, + local_dof_values, + point, + polynomials_are_hat_functions, + renumber); } else { diff --git a/tests/matrix_free/point_evaluation_25.cc b/tests/matrix_free/point_evaluation_25.cc new file mode 100644 index 0000000000..233f52d957 --- /dev/null +++ b/tests/matrix_free/point_evaluation_25.cc @@ -0,0 +1,142 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2020 - 2022 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.md at +// the top level directory of deal.II. +// +// --------------------------------------------------------------------- + + +// check FEPointEvaluation for scalar FE_Q and MappingQ by comparing to +// the output of FEValues with the same settings for values only + +#include + +#include + +#include +#include +#include + +#include +#include + +#include + +#include + +#include + +#include + +#include "../tests.h" + + + +template +void +test(const unsigned int degree) +{ + using namespace dealii; + Triangulation tria; + + if (dim > 1) + GridGenerator::hyper_shell(tria, Point(), 0.5, 1, 6); + else + GridGenerator::subdivided_hyper_cube(tria, 2, 0, 1); + + MappingQ mapping(degree); + deallog << "Mapping of degree " << degree << std::endl; + + std::vector> unit_points; + for (unsigned int i = 0; i < 13; ++i) + { + Point p; + for (unsigned int d = 0; d < dim; ++d) + p[d] = static_cast(i) / 17. + 0.015625 * d; + unit_points.push_back(p); + } + + FE_Q fe(degree); + FEValues fe_values(mapping, + fe, + Quadrature(unit_points), + update_values); + + DoFHandler dof_handler(tria); + dof_handler.distribute_dofs(fe); + Vector vector(dof_handler.n_dofs()); + + FEPointEvaluation<1, dim, dim, Number> evaluator(mapping, fe, update_values); + + Tensor<1, dim, Number> exponents; + exponents[0] = 1.; + VectorTools::interpolate(mapping, + dof_handler, + Functions::Monomial(exponents), + vector); + + std::vector solution_values(fe.dofs_per_cell); + std::vector function_values(unit_points.size()); + + // For float numbers that are sensitive to roundoff in the numdiff + // tolerances (absolute 1e-8), we multiply by 1e-3 to ensure that the test + // remains robust + const double factor_float = std::is_same::value ? 0.001 : 1.; + + for (const auto &cell : dof_handler.active_cell_iterators()) + { + fe_values.reinit(cell); + fe_values.get_function_values(vector, function_values); + + cell->get_dof_values(vector, + solution_values.begin(), + solution_values.end()); + + evaluator.reinit(cell, unit_points); + evaluator.evaluate(solution_values, EvaluationFlags::values); + + deallog << "Cell with center " << cell->center(true) << std::endl; + for (unsigned int i = 0; i < function_values.size(); ++i) + deallog << mapping.transform_unit_to_real_cell(cell, unit_points[i]) + << ": " << factor_float * evaluator.get_value(i) + << " error value " + << factor_float * (function_values[i] - evaluator.get_value(i)) + << std::endl; + deallog << std::endl; + + for (const auto q : evaluator.quadrature_point_indices()) + evaluator.submit_value(evaluator.get_value(q), q); + + evaluator.integrate(solution_values, EvaluationFlags::values); + + for (const auto i : solution_values) + deallog << factor_float * i << ' '; + deallog << std::endl; + } +} + + + +int +main() +{ + initlog(); + deallog << std::setprecision(10); + + test<1>(3); + test<2>(1); + test<2>(2); + test<2>(6); + test<3>(1); + test<3>(5); + + test<3, float>(5); +} diff --git a/tests/matrix_free/point_evaluation_25.output b/tests/matrix_free/point_evaluation_25.output new file mode 100644 index 0000000000..f84cb20208 --- /dev/null +++ b/tests/matrix_free/point_evaluation_25.output @@ -0,0 +1,616 @@ + +DEAL::Mapping of degree 3 +DEAL::Cell with center 0.2500000000 +DEAL::0.000000000: 0.000000000 error value 0.000000000 +DEAL::0.02941176471: 0.02941176471 error value 0.000000000 +DEAL::0.05882352941: 0.05882352941 error value -2.081668171e-17 +DEAL::0.08823529412: 0.08823529412 error value 1.387778781e-17 +DEAL::0.1176470588: 0.1176470588 error value 1.387778781e-17 +DEAL::0.1470588235: 0.1470588235 error value 0.000000000 +DEAL::0.1764705882: 0.1764705882 error value -2.775557562e-17 +DEAL::0.2058823529: 0.2058823529 error value 5.551115123e-17 +DEAL::0.2352941176: 0.2352941176 error value -2.775557562e-17 +DEAL::0.2647058824: 0.2647058824 error value 0.000000000 +DEAL::0.2941176471: 0.2941176471 error value 5.551115123e-17 +DEAL::0.3235294118: 0.3235294118 error value 0.000000000 +DEAL::0.3529411765: 0.3529411765 error value 0.000000000 +DEAL:: +DEAL::-0.07875863555 -0.1540929826 1.229550458 1.297418807 +DEAL::Cell with center 0.7500000000 +DEAL::0.5000000000: 0.5000000000 error value 0.000000000 +DEAL::0.5294117647: 0.5294117647 error value 0.000000000 +DEAL::0.5588235294: 0.5588235294 error value -1.110223025e-16 +DEAL::0.5882352941: 0.5882352941 error value 1.110223025e-16 +DEAL::0.6176470588: 0.6176470588 error value -1.110223025e-16 +DEAL::0.6470588235: 0.6470588235 error value -1.110223025e-16 +DEAL::0.6764705882: 0.6764705882 error value -1.110223025e-16 +DEAL::0.7058823529: 0.7058823529 error value 1.110223025e-16 +DEAL::0.7352941176: 0.7352941176 error value -1.110223025e-16 +DEAL::0.7647058824: 0.7647058824 error value 0.000000000 +DEAL::0.7941176471: 0.7941176471 error value 1.110223025e-16 +DEAL::0.8235294118: 0.8235294118 error value -1.110223025e-16 +DEAL::0.8529411765: 0.8529411765 error value 0.000000000 +DEAL:: +DEAL::0.8063421176 -0.3869446008 5.040935062 3.333785069 +DEAL::Mapping of degree 1 +DEAL::Cell with center 0.6495190528 0.3750000000 +DEAL::0.9921875000 0.000000000: 0.9921875000 error value 0.000000000 +DEAL::0.9344588019 0.04904636735: 0.9344588019 error value -2.220446049e-16 +DEAL::0.8784602076 0.09509610700: 0.8784602076 error value -2.220446049e-16 +DEAL::0.8241917171 0.1381492190: 0.8241917171 error value 0.000000000 +DEAL::0.7716533304 0.1782057032: 0.7716533304 error value 1.110223025e-16 +DEAL::0.7208450476 0.2152655598: 0.7208450476 error value 0.000000000 +DEAL::0.6717668685 0.2493287887: 0.6717668685 error value 0.000000000 +DEAL::0.6244187933 0.2803953898: 0.6244187933 error value 0.000000000 +DEAL::0.5788008218 0.3084653633: 0.5788008218 error value -1.110223025e-16 +DEAL::0.5349129542 0.3335387091: 0.5349129542 error value 0.000000000 +DEAL::0.4927551903 0.3556154272: 0.4927551903 error value 0.000000000 +DEAL::0.4523275303 0.3746955176: 0.4523275303 error value -5.551115123e-17 +DEAL::0.4136299740 0.3907789803: 0.4136299740 error value 0.000000000 +DEAL:: +DEAL::4.728978921 1.400889928 1.539802564 1.220737324 +DEAL::Cell with center 4.592425497e-17 0.7500000000 +DEAL::0.4960937500 0.8592595803: 0.4960937500 error value 0.000000000 +DEAL::0.4247540009 0.8337882449: 0.4247540009 error value 0.000000000 +DEAL::0.3568744593 0.8083169095: 0.3568744593 error value -5.551115123e-17 +DEAL::0.2924551254 0.7828455741: 0.2924551254 error value -5.551115123e-17 +DEAL::0.2314959991 0.7573742387: 0.2314959991 error value 0.000000000 +DEAL::0.1739970804 0.7319029033: 0.1739970804 error value 5.551115123e-17 +DEAL::0.1199583694 0.7064315679: 0.1199583694 error value 1.387778781e-17 +DEAL::0.06937986592 0.6809602325: 0.06937986592 error value 0.000000000 +DEAL::0.02226157007 0.6554888971: 0.02226157007 error value -6.938893904e-18 +DEAL::-0.02139651817 0.6300175617: -0.02139651817 error value 2.081668171e-17 +DEAL::-0.06159439879 0.6045462263: -0.06159439879 error value -1.387778781e-17 +DEAL::-0.09833207180 0.5790748909: -0.09833207180 error value 0.000000000 +DEAL::-0.1316095372 0.5536035555: -0.1316095372 error value 0.000000000 +DEAL:: +DEAL::1.584558981 0.1589710319 0.1882575584 -0.05744987630 +DEAL::Cell with center -0.6495190528 0.3750000000 +DEAL::-0.4960937500 0.8592595803: -0.4960937500 error value 0.000000000 +DEAL::-0.5097048010 0.7847418776: -0.5097048010 error value -1.110223025e-16 +DEAL::-0.5215857483 0.7132208025: -0.5215857483 error value 0.000000000 +DEAL::-0.5317365917 0.6446963551: -0.5317365917 error value 0.000000000 +DEAL::-0.5401573313 0.5791685355: -0.5401573313 error value -1.110223025e-16 +DEAL::-0.5468479671 0.5166373435: -0.5468479671 error value 0.000000000 +DEAL::-0.5518084991 0.4571027792: -0.5518084991 error value -1.110223025e-16 +DEAL::-0.5550389273 0.4005648426: -0.5550389273 error value 1.110223025e-16 +DEAL::-0.5565392517 0.3470235337: -0.5565392517 error value -1.110223025e-16 +DEAL::-0.5563094723 0.2964788525: -0.5563094723 error value 0.000000000 +DEAL::-0.5543495891 0.2489307990: -0.5543495891 error value 0.000000000 +DEAL::-0.5506596021 0.2043793732: -0.5506596021 error value 0.000000000 +DEAL::-0.5452395112 0.1628245751: -0.5452395112 error value 0.000000000 +DEAL:: +DEAL::-3.144419940 -1.241918896 -1.351545006 -1.278187200 +DEAL::Cell with center -0.6495190528 -0.3750000000 +DEAL::-0.9921875000 1.215079246e-16: -0.9921875000 error value 0.000000000 +DEAL::-0.9344588019 -0.04904636735: -0.9344588019 error value 1.110223025e-16 +DEAL::-0.8784602076 -0.09509610700: -0.8784602076 error value 1.110223025e-16 +DEAL::-0.8241917171 -0.1381492190: -0.8241917171 error value 1.110223025e-16 +DEAL::-0.7716533304 -0.1782057032: -0.7716533304 error value 0.000000000 +DEAL::-0.7208450476 -0.2152655598: -0.7208450476 error value 0.000000000 +DEAL::-0.6717668685 -0.2493287887: -0.6717668685 error value 0.000000000 +DEAL::-0.6244187933 -0.2803953898: -0.6244187933 error value 0.000000000 +DEAL::-0.5788008218 -0.3084653633: -0.5788008218 error value -1.110223025e-16 +DEAL::-0.5349129542 -0.3335387091: -0.5349129542 error value 0.000000000 +DEAL::-0.4927551903 -0.3556154272: -0.4927551903 error value 5.551115123e-17 +DEAL::-0.4523275303 -0.3746955176: -0.4523275303 error value 0.000000000 +DEAL::-0.4136299740 -0.3907789803: -0.4136299740 error value 0.000000000 +DEAL:: +DEAL::-4.728978921 -1.400889928 -1.539802564 -1.220737324 +DEAL::Cell with center -1.377727649e-16 -0.7500000000 +DEAL::-0.4960937500 -0.8592595803: -0.4960937500 error value 0.000000000 +DEAL::-0.4247540009 -0.8337882449: -0.4247540009 error value 5.551115123e-17 +DEAL::-0.3568744593 -0.8083169095: -0.3568744593 error value 0.000000000 +DEAL::-0.2924551254 -0.7828455741: -0.2924551254 error value 5.551115123e-17 +DEAL::-0.2314959991 -0.7573742387: -0.2314959991 error value -2.775557562e-17 +DEAL::-0.1739970804 -0.7319029033: -0.1739970804 error value 5.551115123e-17 +DEAL::-0.1199583694 -0.7064315679: -0.1199583694 error value -1.387778781e-17 +DEAL::-0.06937986592 -0.6809602325: -0.06937986592 error value 2.775557562e-17 +DEAL::-0.02226157007 -0.6554888971: -0.02226157007 error value 1.040834086e-17 +DEAL::0.02139651817 -0.6300175617: 0.02139651817 error value -1.040834086e-17 +DEAL::0.06159439879 -0.6045462263: 0.06159439879 error value 1.387778781e-17 +DEAL::0.09833207180 -0.5790748909: 0.09833207180 error value 0.000000000 +DEAL::0.1316095372 -0.5536035555: 0.1316095372 error value 0.000000000 +DEAL:: +DEAL::-1.584558981 -0.1589710319 -0.1882575584 0.05744987630 +DEAL::Cell with center 0.6495190528 -0.3750000000 +DEAL::0.4960937500 -0.8592595803: 0.4960937500 error value 0.000000000 +DEAL::0.5097048010 -0.7847418776: 0.5097048010 error value 1.110223025e-16 +DEAL::0.5215857483 -0.7132208025: 0.5215857483 error value 0.000000000 +DEAL::0.5317365917 -0.6446963551: 0.5317365917 error value -1.110223025e-16 +DEAL::0.5401573313 -0.5791685355: 0.5401573313 error value 0.000000000 +DEAL::0.5468479671 -0.5166373435: 0.5468479671 error value 0.000000000 +DEAL::0.5518084991 -0.4571027792: 0.5518084991 error value 0.000000000 +DEAL::0.5550389273 -0.4005648426: 0.5550389273 error value 0.000000000 +DEAL::0.5565392517 -0.3470235337: 0.5565392517 error value 0.000000000 +DEAL::0.5563094723 -0.2964788525: 0.5563094723 error value -1.110223025e-16 +DEAL::0.5543495891 -0.2489307990: 0.5543495891 error value 0.000000000 +DEAL::0.5506596021 -0.2043793732: 0.5506596021 error value 0.000000000 +DEAL::0.5452395112 -0.1628245751: 0.5452395112 error value 0.000000000 +DEAL:: +DEAL::3.144419940 1.241918896 1.351545006 1.278187200 +DEAL::Mapping of degree 2 +DEAL::Cell with center 0.6495190528 0.3750000000 +DEAL::0.9921875000 0.000000000: 0.9921875000 error value 0.000000000 +DEAL::0.9591965610 0.06332871922: 0.9591965610 error value -1.110223025e-16 +DEAL::0.9234265460 0.1210574346: 0.9234265460 error value 0.000000000 +DEAL::0.8851608469 0.1733497625: 0.8851608469 error value 0.000000000 +DEAL::0.8446828558 0.2203693193: 0.8446828558 error value 0.000000000 +DEAL::0.8022759646 0.2622797217: 0.8022759646 error value 1.110223025e-16 +DEAL::0.7582235654 0.2992445859: 0.7582235654 error value 0.000000000 +DEAL::0.7128090500 0.3314275284: 0.7128090500 error value 0.000000000 +DEAL::0.6663158106 0.3589921657: 0.6663158106 error value 0.000000000 +DEAL::0.6190272391 0.3821021142: 0.6190272391 error value -1.110223025e-16 +DEAL::0.5712267275 0.4009209903: 0.5712267275 error value 0.000000000 +DEAL::0.5231976677 0.4156124105: 0.5231976677 error value 1.110223025e-16 +DEAL::0.4752234518 0.4263399913: 0.4752234518 error value 0.000000000 +DEAL:: +DEAL::2.440840497 -0.2583714273 -0.3074271504 0.1329272017 1.393777186 -0.1435492795 1.078765728 -0.05629448584 5.452285517 +DEAL::Cell with center 4.592425497e-17 0.7500000000 +DEAL::0.4960937500 0.8592595803: 0.4960937500 error value 0.000000000 +DEAL::0.4247540009 0.8623529487: 0.4247540009 error value -1.665334537e-16 +DEAL::0.3568744593 0.8602395646: 0.3568744593 error value 5.551115123e-17 +DEAL::0.2924551254 0.8532466611: 0.2924551254 error value -5.551115123e-17 +DEAL::0.2314959991 0.8417014709: 0.2314959991 error value 0.000000000 +DEAL::0.1739970804 0.8259312270: 0.1739970804 error value -2.775557562e-17 +DEAL::0.1199583694 0.8062631623: 0.1199583694 error value 1.387778781e-17 +DEAL::0.06937986592 0.7830245096: 0.06937986592 error value 0.000000000 +DEAL::0.02226157007 0.7565425018: 0.02226157007 error value 0.000000000 +DEAL::-0.02139651817 0.7271443718: -0.02139651817 error value 0.000000000 +DEAL::-0.06159439879 0.6951573525: -0.06159439879 error value 6.938893904e-18 +DEAL::-0.09833207180 0.6609086767: -0.09833207180 error value 0.000000000 +DEAL::-0.1316095372 0.6247255774: -0.1316095372 error value 0.000000000 +DEAL:: +DEAL::1.030731128 -0.06585461437 -0.08429024741 -0.0009954758098 0.5052610584 -0.1527433541 0.4062261221 -0.1563339714 0.3923370491 +DEAL::Cell with center -0.6495190528 0.3750000000 +DEAL::-0.4960937500 0.8592595803: -0.4960937500 error value 0.000000000 +DEAL::-0.5344425601 0.7990242294: -0.5344425601 error value 0.000000000 +DEAL::-0.5665520866 0.7391821301: -0.5665520866 error value -1.110223025e-16 +DEAL::-0.5927057215 0.6798968986: -0.5927057215 error value 0.000000000 +DEAL::-0.6131868567 0.6213321516: -0.6131868567 error value -1.110223025e-16 +DEAL::-0.6282788842 0.5636515054: -0.6282788842 error value -1.110223025e-16 +DEAL::-0.6382651960 0.5070185764: -0.6382651960 error value 0.000000000 +DEAL::-0.6434291841 0.4515969812: -0.6434291841 error value 0.000000000 +DEAL::-0.6440542406 0.3975503361: -0.6440542406 error value 0.000000000 +DEAL::-0.6404237573 0.3450422576: -0.6404237573 error value 0.000000000 +DEAL::-0.6328211262 0.2942363621: -0.6328211262 error value 0.000000000 +DEAL::-0.6215297395 0.2452962662: -0.6215297395 error value 0.000000000 +DEAL::-0.6068329890 0.1983855861: -0.6068329890 error value 0.000000000 +DEAL:: +DEAL::-1.410109369 0.1925168129 0.2231369030 -0.1339226775 -0.8885161276 -0.009194074657 -0.6725396055 -0.1000394856 -5.059948468 +DEAL::Cell with center -0.6495190528 -0.3750000000 +DEAL::-0.9921875000 1.215079246e-16: -0.9921875000 error value 0.000000000 +DEAL::-0.9591965610 -0.06332871922: -0.9591965610 error value 0.000000000 +DEAL::-0.9234265460 -0.1210574346: -0.9234265460 error value -1.110223025e-16 +DEAL::-0.8851608469 -0.1733497625: -0.8851608469 error value 1.110223025e-16 +DEAL::-0.8446828558 -0.2203693193: -0.8446828558 error value 0.000000000 +DEAL::-0.8022759646 -0.2622797217: -0.8022759646 error value 1.110223025e-16 +DEAL::-0.7582235654 -0.2992445859: -0.7582235654 error value 0.000000000 +DEAL::-0.7128090500 -0.3314275284: -0.7128090500 error value 0.000000000 +DEAL::-0.6663158106 -0.3589921657: -0.6663158106 error value 0.000000000 +DEAL::-0.6190272391 -0.3821021142: -0.6190272391 error value 1.110223025e-16 +DEAL::-0.5712267275 -0.4009209903: -0.5712267275 error value 0.000000000 +DEAL::-0.5231976677 -0.4156124105: -0.5231976677 error value 0.000000000 +DEAL::-0.4752234518 -0.4263399913: -0.4752234518 error value 0.000000000 +DEAL:: +DEAL::-2.440840497 0.2583714273 0.3074271504 -0.1329272017 -1.393777186 0.1435492795 -1.078765728 0.05629448584 -5.452285517 +DEAL::Cell with center -1.377727649e-16 -0.7500000000 +DEAL::-0.4960937500 -0.8592595803: -0.4960937500 error value 0.000000000 +DEAL::-0.4247540009 -0.8623529487: -0.4247540009 error value -5.551115123e-17 +DEAL::-0.3568744593 -0.8602395646: -0.3568744593 error value 0.000000000 +DEAL::-0.2924551254 -0.8532466611: -0.2924551254 error value -5.551115123e-17 +DEAL::-0.2314959991 -0.8417014709: -0.2314959991 error value -2.775557562e-17 +DEAL::-0.1739970804 -0.8259312270: -0.1739970804 error value 0.000000000 +DEAL::-0.1199583694 -0.8062631623: -0.1199583694 error value 2.775557562e-17 +DEAL::-0.06937986592 -0.7830245096: -0.06937986592 error value 1.387778781e-17 +DEAL::-0.02226157007 -0.7565425018: -0.02226157007 error value 0.000000000 +DEAL::0.02139651817 -0.7271443718: 0.02139651817 error value 3.469446952e-18 +DEAL::0.06159439879 -0.6951573525: 0.06159439879 error value 0.000000000 +DEAL::0.09833207180 -0.6609086767: 0.09833207180 error value 0.000000000 +DEAL::0.1316095372 -0.6247255774: 0.1316095372 error value 2.775557562e-17 +DEAL:: +DEAL::-1.030731128 0.06585461437 0.08429024741 0.0009954758098 -0.5052610584 0.1527433541 -0.4062261221 0.1563339714 -0.3923370491 +DEAL::Cell with center 0.6495190528 -0.3750000000 +DEAL::0.4960937500 -0.8592595803: 0.4960937500 error value 0.000000000 +DEAL::0.5344425601 -0.7990242294: 0.5344425601 error value 0.000000000 +DEAL::0.5665520866 -0.7391821301: 0.5665520866 error value 0.000000000 +DEAL::0.5927057215 -0.6798968986: 0.5927057215 error value 0.000000000 +DEAL::0.6131868567 -0.6213321516: 0.6131868567 error value -1.110223025e-16 +DEAL::0.6282788842 -0.5636515054: 0.6282788842 error value 0.000000000 +DEAL::0.6382651960 -0.5070185764: 0.6382651960 error value 0.000000000 +DEAL::0.6434291841 -0.4515969812: 0.6434291841 error value 0.000000000 +DEAL::0.6440542406 -0.3975503361: 0.6440542406 error value 0.000000000 +DEAL::0.6404237573 -0.3450422576: 0.6404237573 error value 0.000000000 +DEAL::0.6328211262 -0.2942363621: 0.6328211262 error value -1.110223025e-16 +DEAL::0.6215297395 -0.2452962662: 0.6215297395 error value 1.110223025e-16 +DEAL::0.6068329890 -0.1983855861: 0.6068329890 error value 0.000000000 +DEAL:: +DEAL::1.410109369 -0.1925168129 -0.2231369030 0.1339226775 0.8885161276 0.009194074657 0.6725396055 0.1000394856 5.059948468 +DEAL::Mapping of degree 6 +DEAL::Cell with center 0.6495190528 0.3750000000 +DEAL::0.9921875000 0.000000000: 0.9921875000 error value 0.000000000 +DEAL::0.9609496573 0.05926936446: 0.9609496573 error value 4.440892099e-16 +DEAL::0.9262895583 0.1146994816: 0.9262895583 error value -2.220446049e-16 +DEAL::0.8885607198 0.1661007475: 0.8885607198 error value 1.110223025e-16 +DEAL::0.8481266485 0.2133123969: 0.8481266485 error value 0.000000000 +DEAL::0.8053586039 0.2562030323: 0.8053586039 error value 2.220446049e-16 +DEAL::0.7606333492 0.2946709691: 0.7606333492 error value -3.330669074e-16 +DEAL::0.7143309018 0.3286444014: 0.7143309018 error value 2.220446049e-16 +DEAL::0.6668322927 0.3580813945: 0.6668322927 error value -1.110223025e-16 +DEAL::0.6185173440 0.3829697098: 0.6185173440 error value 1.110223025e-16 +DEAL::0.5697624746 0.4033264664: 0.5697624746 error value 3.330669074e-16 +DEAL::0.5209385434 0.4191976473: 0.5209385434 error value 1.110223025e-16 +DEAL::0.4724087397 0.4306574530: 0.4724087397 error value -5.551115123e-17 +DEAL:: +DEAL::0.7398642945 -0.01072583123 -0.02292771262 0.007402570776 0.3882582369 -0.2189890995 0.1613403773 -0.1241404853 0.06266231691 0.02927373814 -0.01716410118 -0.01221251692 0.07689074796 -0.02214474692 -0.1318782560 -0.02072685663 0.05679579401 -0.06545253382 0.03015196503 0.04424674378 -0.03800911713 0.01227096513 0.06378579706 -0.02194049097 1.894049141 0.08663285048 -0.1712163042 0.1823933318 -0.08279176509 0.5328859715 2.716961127 0.09763628093 -0.1812686236 0.05480736891 -0.3545757407 0.4811418615 2.431119203 0.1326617218 0.02188684329 0.2699613681 -0.3228470451 0.3929269603 1.027171018 -0.2379690564 -0.1235627493 0.1131635165 -0.05146893104 -0.1973690626 0.06593524875 +DEAL::Cell with center 4.592425497e-17 0.7500000000 +DEAL::0.4960937500 0.8592595803: 0.4960937500 error value 0.000000000 +DEAL::0.4291460533 0.8618414972: 0.4291460533 error value 5.551115123e-17 +DEAL::0.3638121143 0.8595400296: 0.3638121143 error value 0.000000000 +DEAL::0.3004328929 0.8525665299: 0.3004328929 error value 5.551115123e-17 +DEAL::0.2393293696 0.8411554217: 0.2393293696 error value 2.775557562e-17 +DEAL::0.1808009674 0.8255625263: 0.1808009674 error value -2.775557562e-17 +DEAL::0.1251241296 0.8060632879: 0.1251241296 error value -1.110223025e-16 +DEAL::0.07255105048 0.7829509083: 0.07255105048 error value 4.163336342e-17 +DEAL::0.02330856204 0.7565344028: 0.02330856204 error value -2.428612866e-17 +DEAL::-0.02240282557 0.7271365875: -0.02240282557 error value -6.938893904e-18 +DEAL::-0.06440972863 0.6950920104: -0.06440972863 error value 0.000000000 +DEAL::-0.1025665400 0.6607448360: -0.1025665400 error value -8.326672685e-17 +DEAL::-0.1367559248 0.6244466961: -0.1367559248 error value 2.775557562e-17 +DEAL:: +DEAL::0.3630990917 -0.001887905233 -0.007710749179 -3.573351993e-05 0.2116773321 -0.1126759929 0.06508855203 -0.02844439000 0.02030261786 0.003911670862 0.007075242722 -0.01403465852 -0.008573383074 0.0004000958502 -0.03909453760 -0.02695273922 0.02540847059 -0.005864562581 0.004937683641 0.009506747084 0.002514381134 -0.01438418027 -0.005493402465 0.0003753665572 0.7579388554 0.07801932073 -0.06603778755 0.01149782782 -0.01029995528 0.2335331402 0.6747009903 0.01596559510 0.04152693805 -0.01935990133 -0.1121845503 0.07318123610 0.05551516826 -0.1047366574 0.04071077920 0.03145504118 0.02801317788 -0.1311181765 -0.1996626245 0.02919024004 -0.02519518590 -0.007058846468 0.04236244905 0.01934768614 -0.001985907164 +DEAL::Cell with center -0.6495190528 0.3750000000 +DEAL::-0.4960937500 0.8592595803: -0.4960937500 error value -1.110223025e-16 +DEAL::-0.5318036039 0.8025721327: -0.5318036039 error value -2.220446049e-16 +DEAL::-0.5624774440 0.7448405480: -0.5624774440 error value 4.440892099e-16 +DEAL::-0.5881278268 0.6864657824: -0.5881278268 error value -2.220446049e-16 +DEAL::-0.6087972789 0.6278430248: -0.6087972789 error value 2.220446049e-16 +DEAL::-0.6245576365 0.5693594940: -0.6245576365 error value -1.110223025e-16 +DEAL::-0.6355092196 0.5113923188: -0.6355092196 error value 0.000000000 +DEAL::-0.6417798513 0.4543065070: -0.6417798513 error value -2.220446049e-16 +DEAL::-0.6435237306 0.3984530082: -0.6435237306 error value 1.110223025e-16 +DEAL::-0.6409201696 0.3441668777: -0.6409201696 error value -1.110223025e-16 +DEAL::-0.6341722033 0.2917655439: -0.6341722033 error value -3.330669074e-16 +DEAL::-0.6235050834 0.2415471888: -0.6235050834 error value -3.330669074e-16 +DEAL::-0.6091646645 0.1937892431: -0.6091646645 error value 0.000000000 +DEAL:: +DEAL::-0.3767652029 0.008837925993 0.01521696344 -0.007438304296 -0.1765809048 0.1063131066 -0.09625182525 0.09569609534 -0.04235969905 -0.02536206728 0.02423934390 -0.001822141604 -0.08546413103 0.02254484277 0.09278371838 -0.006225882594 -0.03138732342 0.05958797124 -0.02521428139 -0.03473999670 0.04052349827 -0.02665514540 -0.06927919953 0.02231585752 -1.136110285 -0.008613529741 0.1051785167 -0.1708955040 0.07249180980 -0.2993528313 -2.042260137 -0.08167068583 0.2227955617 -0.07416727024 0.2423911904 -0.4079606254 -2.375604034 -0.2373983792 0.01882393591 -0.2385063269 0.3508602230 -0.5240451368 -1.226833642 0.2671592964 0.09836756340 -0.1202223630 0.09383138009 0.2167167488 -0.06792115591 +DEAL::Cell with center -0.6495190528 -0.3750000000 +DEAL::-0.9921875000 1.215079246e-16: -0.9921875000 error value 0.000000000 +DEAL::-0.9609496573 -0.05926936446: -0.9609496573 error value -7.771561172e-16 +DEAL::-0.9262895583 -0.1146994816: -0.9262895583 error value 3.330669074e-16 +DEAL::-0.8885607198 -0.1661007475: -0.8885607198 error value -1.110223025e-16 +DEAL::-0.8481266485 -0.2133123969: -0.8481266485 error value 1.110223025e-16 +DEAL::-0.8053586039 -0.2562030323: -0.8053586039 error value 1.110223025e-16 +DEAL::-0.7606333492 -0.2946709691: -0.7606333492 error value 1.110223025e-16 +DEAL::-0.7143309018 -0.3286444014: -0.7143309018 error value -2.220446049e-16 +DEAL::-0.6668322927 -0.3580813945: -0.6668322927 error value 0.000000000 +DEAL::-0.6185173440 -0.3829697098: -0.6185173440 error value 0.000000000 +DEAL::-0.5697624746 -0.4033264664: -0.5697624746 error value -1.110223025e-16 +DEAL::-0.5209385434 -0.4191976473: -0.5209385434 error value 1.110223025e-16 +DEAL::-0.4724087397 -0.4306574530: -0.4724087397 error value 0.000000000 +DEAL:: +DEAL::-0.7398642945 0.01072583123 0.02292771262 -0.007402570776 -0.3882582369 0.2189890995 -0.1613403773 0.1241404853 -0.06266231691 -0.02927373814 0.01716410118 0.01221251692 -0.07689074796 0.02214474692 0.1318782560 0.02072685663 -0.05679579401 0.06545253382 -0.03015196503 -0.04424674378 0.03800911713 -0.01227096513 -0.06378579706 0.02194049097 -1.894049141 -0.08663285048 0.1712163042 -0.1823933318 0.08279176509 -0.5328859715 -2.716961127 -0.09763628093 0.1812686236 -0.05480736891 0.3545757407 -0.4811418615 -2.431119203 -0.1326617218 -0.02188684329 -0.2699613681 0.3228470451 -0.3929269603 -1.027171018 0.2379690564 0.1235627493 -0.1131635165 0.05146893104 0.1973690626 -0.06593524875 +DEAL::Cell with center -1.377727649e-16 -0.7500000000 +DEAL::-0.4960937500 -0.8592595803: -0.4960937500 error value 0.000000000 +DEAL::-0.4291460533 -0.8618414972: -0.4291460533 error value -1.110223025e-16 +DEAL::-0.3638121143 -0.8595400296: -0.3638121143 error value 1.110223025e-16 +DEAL::-0.3004328929 -0.8525665299: -0.3004328929 error value -1.665334537e-16 +DEAL::-0.2393293696 -0.8411554217: -0.2393293696 error value 5.551115123e-17 +DEAL::-0.1808009674 -0.8255625263: -0.1808009674 error value 8.326672685e-17 +DEAL::-0.1251241296 -0.8060632879: -0.1251241296 error value 5.551115123e-17 +DEAL::-0.07255105048 -0.7829509083: -0.07255105048 error value -2.775557562e-17 +DEAL::-0.02330856204 -0.7565344028: -0.02330856204 error value 1.387778781e-17 +DEAL::0.02240282557 -0.7271365875: 0.02240282557 error value 6.938893904e-18 +DEAL::0.06440972863 -0.6950920104: 0.06440972863 error value 0.000000000 +DEAL::0.1025665400 -0.6607448360: 0.1025665400 error value 6.938893904e-17 +DEAL::0.1367559248 -0.6244466961: 0.1367559248 error value 5.551115123e-17 +DEAL:: +DEAL::-0.3630990917 0.001887905233 0.007710749179 3.573351993e-05 -0.2116773321 0.1126759929 -0.06508855203 0.02844439000 -0.02030261786 -0.003911670862 -0.007075242722 0.01403465852 0.008573383074 -0.0004000958502 0.03909453760 0.02695273922 -0.02540847059 0.005864562581 -0.004937683641 -0.009506747084 -0.002514381134 0.01438418027 0.005493402465 -0.0003753665572 -0.7579388554 -0.07801932073 0.06603778755 -0.01149782782 0.01029995528 -0.2335331402 -0.6747009903 -0.01596559510 -0.04152693805 0.01935990133 0.1121845503 -0.07318123610 -0.05551516826 0.1047366574 -0.04071077920 -0.03145504118 -0.02801317788 0.1311181765 0.1996626245 -0.02919024004 0.02519518590 0.007058846468 -0.04236244905 -0.01934768614 0.001985907164 +DEAL::Cell with center 0.6495190528 -0.3750000000 +DEAL::0.4960937500 -0.8592595803: 0.4960937500 error value 0.000000000 +DEAL::0.5318036039 -0.8025721327: 0.5318036039 error value 4.440892099e-16 +DEAL::0.5624774440 -0.7448405480: 0.5624774440 error value -3.330669074e-16 +DEAL::0.5881278268 -0.6864657824: 0.5881278268 error value 0.000000000 +DEAL::0.6087972789 -0.6278430248: 0.6087972789 error value -2.220446049e-16 +DEAL::0.6245576365 -0.5693594940: 0.6245576365 error value -1.110223025e-16 +DEAL::0.6355092196 -0.5113923188: 0.6355092196 error value -1.110223025e-16 +DEAL::0.6417798513 -0.4543065070: 0.6417798513 error value 4.440892099e-16 +DEAL::0.6435237306 -0.3984530082: 0.6435237306 error value 0.000000000 +DEAL::0.6409201696 -0.3441668777: 0.6409201696 error value 3.330669074e-16 +DEAL::0.6341722033 -0.2917655439: 0.6341722033 error value 3.330669074e-16 +DEAL::0.6235050834 -0.2415471888: 0.6235050834 error value 1.110223025e-16 +DEAL::0.6091646645 -0.1937892431: 0.6091646645 error value 1.110223025e-16 +DEAL:: +DEAL::0.3767652029 -0.008837925993 -0.01521696344 0.007438304296 0.1765809048 -0.1063131066 0.09625182525 -0.09569609534 0.04235969905 0.02536206728 -0.02423934390 0.001822141604 0.08546413103 -0.02254484277 -0.09278371838 0.006225882594 0.03138732342 -0.05958797124 0.02521428139 0.03473999670 -0.04052349827 0.02665514540 0.06927919953 -0.02231585752 1.136110285 0.008613529741 -0.1051785167 0.1708955040 -0.07249180980 0.2993528313 2.042260137 0.08167068583 -0.2227955617 0.07416727024 -0.2423911904 0.4079606254 2.375604034 0.2373983792 -0.01882393591 0.2385063269 -0.3508602230 0.5240451368 1.226833642 -0.2671592964 -0.09836756340 0.1202223630 -0.09383138009 -0.2167167488 0.06792115591 +DEAL::Mapping of degree 1 +DEAL::Cell with center -3.778985438e-18 0.000000000 -0.7500000000 +DEAL::-0.5683291712 -0.5505688846 -0.5683291712: -0.5683291712 error value 0.000000000 +DEAL::-0.4864837773 -0.4692541435 -0.5513482810: -0.4864837773 error value 1.110223025e-16 +DEAL::-0.4086338870 -0.3919349060 -0.5343673907: -0.4086338870 error value -5.551115123e-17 +DEAL::-0.3347795003 -0.3186111721 -0.5173865004: -0.3347795003 error value 0.000000000 +DEAL::-0.2649206171 -0.2492829418 -0.5004056102: -0.2649206171 error value 0.000000000 +DEAL::-0.1990572376 -0.1839502151 -0.4834247199: -0.1990572376 error value -2.775557562e-17 +DEAL::-0.1371893617 -0.1226129920 -0.4664438296: -0.1371893617 error value 0.000000000 +DEAL::-0.07931698930 -0.06527127244 -0.4494629393: -0.07931698930 error value 0.000000000 +DEAL::-0.02544012053 -0.01192505650 -0.4324820491: -0.02544012053 error value -1.734723476e-17 +DEAL::0.02444124464 0.03742565585 -0.4155011588: 0.02444124464 error value -6.938893904e-18 +DEAL::0.07032710621 0.08278086460 -0.3985202685: 0.07032710621 error value 1.387778781e-17 +DEAL::0.1122174642 0.1241405698 -0.3815393783: 0.1122174642 error value 2.775557562e-17 +DEAL::0.1501123186 0.1615047713 -0.3645584880: 0.1501123186 error value 0.000000000 +DEAL:: +DEAL::-1.585409703 -0.1667399467 -0.1974139529 -0.01357279413 -0.2291363246 -0.01539811819 -0.01827180774 0.07889011931 +DEAL::Cell with center 0.7500000000 -2.814297100e-18 -4.163336342e-17 +DEAL::0.5728397202 -0.5728397202 -0.5370372377: 0.5728397202 error value 0.000000000 +DEAL::0.5558588299 -0.4904636735 -0.4557224966: 0.5558588299 error value -1.110223025e-16 +DEAL::0.5388779397 -0.4120831303 -0.3784032591: 0.5388779397 error value 1.110223025e-16 +DEAL::0.5218970494 -0.3376980908 -0.3050795252: 0.5218970494 error value -1.110223025e-16 +DEAL::0.5049161591 -0.2673085548 -0.2357512949: 0.5049161591 error value -1.110223025e-16 +DEAL::0.4879352689 -0.2009145225 -0.1704185682: 0.4879352689 error value 0.000000000 +DEAL::0.4709543786 -0.1385159937 -0.1090813450: 0.4709543786 error value 0.000000000 +DEAL::0.4539734883 -0.08011296853 -0.05173962551: 0.4539734883 error value -5.551115123e-17 +DEAL::0.4369925980 -0.02570544694 0.001606590434: 0.4369925980 error value 0.000000000 +DEAL::0.4200117078 0.02470657105 0.05095730278: 0.4200117078 error value -5.551115123e-17 +DEAL::0.4030308175 0.07112308544 0.09631251154: 0.4030308175 error value 5.551115123e-17 +DEAL::0.3860499272 0.1135440962 0.1376722167: 0.3860499272 error value 0.000000000 +DEAL::0.3690690370 0.1519696035 0.1750364183: 0.3690690370 error value -5.551115123e-17 +DEAL:: +DEAL::2.335379602 0.5686027136 0.6303531451 0.4176921568 0.6950930332 0.4486148769 0.4825270535 0.5441443410 +DEAL::Cell with center -2.814297100e-18 -4.163336342e-17 0.7500000000 +DEAL::-0.5728397202 -0.5370372377 0.5728397202: -0.5728397202 error value 0.000000000 +DEAL::-0.4904636735 -0.4557224966 0.5558588299: -0.4904636735 error value 5.551115123e-17 +DEAL::-0.4120831303 -0.3784032591 0.5388779397: -0.4120831303 error value 0.000000000 +DEAL::-0.3376980908 -0.3050795252 0.5218970494: -0.3376980908 error value 1.110223025e-16 +DEAL::-0.2673085548 -0.2357512949 0.5049161591: -0.2673085548 error value -5.551115123e-17 +DEAL::-0.2009145225 -0.1704185682 0.4879352689: -0.2009145225 error value -2.775557562e-17 +DEAL::-0.1385159937 -0.1090813450 0.4709543786: -0.1385159937 error value 2.775557562e-17 +DEAL::-0.08011296853 -0.05173962551 0.4539734883: -0.08011296853 error value 1.387778781e-17 +DEAL::-0.02570544694 0.001606590434 0.4369925980: -0.02570544694 error value -2.081668171e-17 +DEAL::0.02470657105 0.05095730278 0.4200117078: 0.02470657105 error value -3.469446952e-18 +DEAL::0.07112308544 0.09631251154 0.4030308175: 0.07112308544 error value 0.000000000 +DEAL::0.1135440962 0.1376722167 0.3860499272: 0.1135440962 error value 2.775557562e-17 +DEAL::0.1519696035 0.1750364183 0.3690690370: 0.1519696035 error value 0.000000000 +DEAL:: +DEAL::-1.598616905 -0.1681599827 -0.1990886995 -0.01357228884 -0.2310742028 -0.01540395342 -0.01829240449 0.07990969193 +DEAL::Cell with center -0.7500000000 -1.407148550e-18 0.000000000 +DEAL::-0.5773502692 -0.5593080733 -0.5412658774: -0.5773502692 error value 0.000000000 +DEAL::-0.5603693789 -0.4769320265 -0.4594204835: -0.5603693789 error value 3.330669074e-16 +DEAL::-0.5433884886 -0.3985514834 -0.3815705931: -0.5433884886 error value -1.110223025e-16 +DEAL::-0.5264075984 -0.3241664439 -0.3077162064: -0.5264075984 error value 1.110223025e-16 +DEAL::-0.5094267081 -0.2537769079 -0.2378573233: -0.5094267081 error value 0.000000000 +DEAL::-0.4924458178 -0.1873828755 -0.1719939437: -0.4924458178 error value -5.551115123e-17 +DEAL::-0.4754649276 -0.1249843468 -0.1101260678: -0.4754649276 error value 5.551115123e-17 +DEAL::-0.4584840373 -0.06658132159 -0.05225369543: -0.4584840373 error value 0.000000000 +DEAL::-0.4415031470 -0.01217380001 0.001623173335: -0.4415031470 error value -5.551115123e-17 +DEAL::-0.4245222568 0.03823821798 0.05150453850: -0.4245222568 error value -5.551115123e-17 +DEAL::-0.4075413665 0.08465473238 0.09739040008: -0.4075413665 error value -5.551115123e-17 +DEAL::-0.3905604762 0.1270757432 0.1392807581: -0.3905604762 error value 0.000000000 +DEAL::-0.3735795859 0.1655012504 0.1771756125: -0.3735795859 error value 5.551115123e-17 +DEAL:: +DEAL::-2.355513803 -0.5741096774 -0.6364243162 -0.4220890865 -0.7017570429 -0.4533351732 -0.4875993478 -0.5502156111 +DEAL::Cell with center -1.407148550e-18 -0.7500000000 -4.163336342e-17 +DEAL::-0.5728397202 -0.5728397202 -0.5370372377: -0.5728397202 error value 0.000000000 +DEAL::-0.4904636735 -0.5558588299 -0.4557224966: -0.4904636735 error value 5.551115123e-17 +DEAL::-0.4120831303 -0.5388779397 -0.3784032591: -0.4120831303 error value 0.000000000 +DEAL::-0.3376980908 -0.5218970494 -0.3050795252: -0.3376980908 error value 1.110223025e-16 +DEAL::-0.2673085548 -0.5049161591 -0.2357512949: -0.2673085548 error value -5.551115123e-17 +DEAL::-0.2009145225 -0.4879352689 -0.1704185682: -0.2009145225 error value -2.775557562e-17 +DEAL::-0.1385159937 -0.4709543786 -0.1090813450: -0.1385159937 error value 2.775557562e-17 +DEAL::-0.08011296853 -0.4539734883 -0.05173962551: -0.08011296853 error value 1.387778781e-17 +DEAL::-0.02570544694 -0.4369925980 0.001606590434: -0.02570544694 error value -2.081668171e-17 +DEAL::0.02470657105 -0.4200117078 0.05095730278: 0.02470657105 error value -3.469446952e-18 +DEAL::0.07112308544 -0.4030308175 0.09631251154: 0.07112308544 error value 0.000000000 +DEAL::0.1135440962 -0.3860499272 0.1376722167: 0.1135440962 error value 2.775557562e-17 +DEAL::0.1519696035 -0.3690690370 0.1750364183: 0.1519696035 error value 0.000000000 +DEAL:: +DEAL::-1.598616905 -0.1681599827 -0.1990886995 -0.01357228884 -0.2310742028 -0.01540395342 -0.01829240449 0.07990969193 +DEAL::Cell with center -1.407148550e-18 0.7500000000 0.000000000 +DEAL::-0.5593080733 0.5773502692 -0.5412658774: -0.5593080733 error value 0.000000000 +DEAL::-0.4769320265 0.5603693789 -0.4594204835: -0.4769320265 error value 1.110223025e-16 +DEAL::-0.3985514834 0.5433884886 -0.3815705931: -0.3985514834 error value 0.000000000 +DEAL::-0.3241664439 0.5264075984 -0.3077162064: -0.3241664439 error value -5.551115123e-17 +DEAL::-0.2537769079 0.5094267081 -0.2378573233: -0.2537769079 error value -1.110223025e-16 +DEAL::-0.1873828755 0.4924458178 -0.1719939437: -0.1873828755 error value 0.000000000 +DEAL::-0.1249843468 0.4754649276 -0.1101260678: -0.1249843468 error value 4.163336342e-17 +DEAL::-0.06658132159 0.4584840373 -0.05225369543: -0.06658132159 error value 4.163336342e-17 +DEAL::-0.01217380001 0.4415031470 0.001623173335: -0.01217380001 error value -6.938893904e-18 +DEAL::0.03823821798 0.4245222568 0.05150453850: 0.03823821798 error value 6.938893904e-18 +DEAL::0.08465473238 0.4075413665 0.09739040008: 0.08465473238 error value 1.387778781e-17 +DEAL::0.1270757432 0.3905604762 0.1392807581: 0.1270757432 error value 2.775557562e-17 +DEAL::0.1655012504 0.3735795859 0.1771756125: 0.1655012504 error value -2.775557562e-17 +DEAL:: +DEAL::-1.538214301 -0.1516390913 -0.1808751863 -0.0003814995919 -0.2110821735 -0.001243064482 -0.003075521626 0.09812350239 +DEAL::Mapping of degree 5 +DEAL::Cell with center -3.778985438e-18 0.000000000 -0.7500000000 +DEAL::-0.5759520655 -0.5527659841 -0.5759520655: -0.5759520655 error value 1.110223025e-16 +DEAL::-0.5254898676 -0.5029040719 -0.6187865537: -0.5254898676 error value 2.220446049e-16 +DEAL::-0.4685426073 -0.4464599093 -0.6616551149: -0.4685426073 error value -5.551115123e-17 +DEAL::-0.4051542510 -0.3835292107 -0.7012978956: -0.4051542510 error value 1.110223025e-16 +DEAL::-0.3359932318 -0.3148223149 -0.7343028440: -0.3359932318 error value -1.110223025e-16 +DEAL::-0.2623766962 -0.2416891159 -0.7575161861: -0.2623766962 error value 0.000000000 +DEAL::-0.1861925434 -0.1660412603 -0.7684224851: -0.1861925434 error value -5.551115123e-17 +DEAL::-0.1097387169 -0.09019150189 -0.7654365722: -0.1097387169 error value 0.000000000 +DEAL::-0.03550798632 -0.01663873419 -0.7480737719: -0.03550798632 error value 6.938893904e-18 +DEAL::0.03404970570 0.05216906594 -0.7169856075: 0.03404970570 error value 1.387778781e-17 +DEAL::0.09675558003 0.1140621810 -0.6738655685: 0.09675558003 error value -1.110223025e-16 +DEAL::0.1508930055 0.1673387801 -0.6212435337: 0.1508930055 error value -1.110223025e-16 +DEAL::0.1953394317 0.2108952300 -0.5621980946: 0.1953394317 error value 8.326672685e-17 +DEAL:: +DEAL::-0.2716217707 1.021162528e-05 -0.004300557707 2.287946993e-05 -0.008750400522 2.237087864e-05 -0.0001172111941 -8.801181648e-05 -0.1244676665 0.03222705985 -0.01899374528 0.01163427216 -0.002882737289 -0.001823234711 0.0008179963034 -1.337990857e-05 -0.02123299977 -0.003016994890 0.0005497096772 -3.059621925e-05 -0.003289433497 -0.001745504839 0.0009681954441 -1.882394703e-05 -0.007100021820 -0.0009330249253 0.0003029380191 0.0003737480361 -0.0005026793843 -0.0009840870636 0.001390945864 0.0003934539408 -0.003740939656 -0.001864857707 0.001036484704 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0.01043485885 0.006361099400 -0.002770360038 -0.0002103121493 0.007135060248 0.01557917001 -0.005431519741 0.001571052318 0.01016990569 0.008644741359 -0.001645053918 0.003303945602 -0.004845330906 -0.001089960392 -0.01097629243 -0.007524211237 0.001235261893 0.003216802989 -0.004505133609 -0.001720630378 0.03989601880 0.03944477940 -0.01527523708 0.007910617851 0.04941795174 0.01932783042 -0.008325306312 0.005273091394 -0.01756814018 -0.008456933143 -0.004948414677 -0.002813734293 0.009069134792 0.005112577380 -0.003503197754 -0.0001506800162 0.01533473659 0.01097192513 -0.005125884972 0.001250909787 0.01398222051 0.003268816819 -0.0002978062180 0.003076168824 -0.005551967613 -0.001190184792 -0.01807103342 -0.005307631730 0.001588627520 0.003242883186 -0.007225092655 -0.001638417918 -1.046360176 -0.05181888480 0.003687780204 0.001680373275 -0.1543572782 -0.1226568202 0.05163547877 -0.03035098607 0.04267395240 0.05072260555 0.003634402280 0.01383637177 -0.02012438602 -0.02900069909 0.01573425833 -0.002834031602 -0.2796308062 -0.1823107853 0.06390941954 -0.03662299809 -0.2694924569 -0.6638074804 0.08287741725 -0.03797475697 0.07986629779 0.05022746025 -0.06531638904 0.003073021787 -0.04419482000 -0.02310919364 -0.001125245895 -0.01029458584 0.08461109085 0.05651181428 -0.005631413791 0.01407778819 0.07243474279 0.01585266776 -0.04668487468 0.002475047797 -0.01847026054 -0.02977819580 0.3692387327 0.02151078160 0.01679813973 0.001567722375 0.04724653871 0.01771102492 -0.04285475241 -0.03151869939 0.01709668784 -0.002764165470 -0.03994548941 -0.007307481757 -0.004414313623 -0.01023667385 0.01777057631 -0.0008509825029 0.07762073559 0.02203539174 -0.003619906429 -0.01095192702 0.03019064626 0.007338717008 +DEAL::Cell with center 0.7500000000 -2.814297100e-18 -4.163336342e-17 +DEAL::0.5879922187 -0.5879922187 -0.5412602679: 0.5879922187 error value 1.110223025e-16 +DEAL::0.6317656581 -0.5359927398 -0.4904247681: 0.6317656581 error value 0.000000000 +DEAL::0.6752050943 -0.4774156808 -0.4328300536: 0.6752050943 error value 1.110223025e-16 +DEAL::0.7149693757 -0.4123477836 -0.3686646352: 0.7149693757 error value 7.771561172e-16 +DEAL::0.7476112822 -0.3415220448 -0.2987437738: 0.7476112822 error value 4.440892099e-16 +DEAL::0.7699931685 -0.2663289165 -0.2245218407: 0.7699931685 error value -3.330669074e-16 +DEAL::0.7796633598 -0.1887262238 -0.1480024603: 0.7796633598 error value 2.220446049e-16 +DEAL::0.7751382896 -0.1110685560 -0.07156802410: 0.7751382896 error value -4.440892099e-16 +DEAL::0.7560592058 -0.03588516627 0.002241853775: 0.7560592058 error value 2.220446049e-16 +DEAL::0.7232127397 0.03436118254 0.07097021235: 0.7232127397 error value 0.000000000 +DEAL::0.6784217227 0.09750269006 0.1324691326: 0.6784217227 error value -7.771561172e-16 +DEAL::0.6243263560 0.1518546010 0.1850850191: 0.6243263560 error value -4.440892099e-16 +DEAL::0.5640861853 0.1963417794 0.2277818661: 0.5640861853 error value 1.110223025e-16 +DEAL:: +DEAL::0.2772679012 -7.316870196e-06 0.004394490876 6.062054207e-05 0.008938343363 6.219979547e-05 0.0002058237908 -1.443124993e-05 0.1359319315 -0.02272648114 0.02239336201 -0.01190588592 0.003940907813 0.007155484120 0.004191356674 -0.0001237865745 0.03065297738 0.01292048104 0.002245302236 2.108008556e-06 0.004724035484 0.007656816027 0.004379268245 -0.0001331004886 0.008594140209 0.007030441456 0.005427839393 -0.0005047546939 0.0004364571878 0.004539190323 0.007554888948 0.0003434473659 0.005370902900 0.008186884023 0.004688845545 -0.0001324592768 0.0006515988766 0.005160170664 0.008499531180 0.0003044893141 0.2918990383 -0.06039265214 0.04390545844 -0.02424959334 0.004969750275 0.007833948167 0.004804395636 -0.0001087016083 0.009767195731 0.007192868419 0.005774469562 -0.0004908425700 0.0004005249297 0.004336731694 0.007600407638 0.0003921159628 0.2004474448 -0.1400529612 0.03858572458 -0.02659357598 -0.1462270506 -0.06201840635 0.06327773038 -0.02117635811 0.03215509367 0.07011725491 0.05347769001 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-0.01571655755 0.0001010826285 -0.02627882543 -0.03459894736 -0.01070459627 -0.001292705599 -0.03900009749 0.04581740959 0.05649912292 -0.01299654516 -0.009982756555 0.06478194579 -0.01589706210 -0.02663211523 -0.001939530302 -0.01487388916 -0.03143961984 -0.002159766381 1.510920095 0.2130389183 0.001707280492 0.007975659795 0.3733330354 0.05499394167 -0.2256632793 0.08804140106 -0.05364338967 -0.2501110436 -0.02550908361 0.03440366503 0.03989163980 0.09190235215 0.03806110617 0.003931992276 0.5795867754 0.2324810335 -0.2475997695 0.1007890493 0.4656160480 2.639276316 0.1627013616 -0.003336211277 -0.2913759646 0.3506963927 0.2791408295 -0.1652431454 0.1177981291 -0.07167298619 -0.1692829381 0.03465081542 -0.1096364313 -0.2897969401 -0.08023513876 0.03949892615 -0.3059411316 0.5819131790 0.4424266611 -0.1920982784 -0.1341834103 0.6489342480 2.096484131 -0.1295579048 0.04081772023 -0.2221046729 -0.01906495600 0.09389261274 0.07319212518 0.1010479064 0.04222650155 0.004526649564 0.1129886457 -0.1444668294 -0.1883146118 0.03638963157 0.03933319532 -0.2121865383 0.1091903299 0.1005901577 0.006505812228 0.04180954069 0.1219576180 0.01268222472 +DEAL::Cell with center -2.814297100e-18 -4.163336342e-17 0.7500000000 +DEAL::-0.5879922187 -0.5412602679 0.5879922187: -0.5879922187 error value -1.110223025e-16 +DEAL::-0.5359927398 -0.4904247681 0.6317656581: -0.5359927398 error value 0.000000000 +DEAL::-0.4774156808 -0.4328300536 0.6752050943: -0.4774156808 error value -1.110223025e-16 +DEAL::-0.4123477836 -0.3686646352 0.7149693757: -0.4123477836 error value 0.000000000 +DEAL::-0.3415220448 -0.2987437738 0.7476112822: -0.3415220448 error value 0.000000000 +DEAL::-0.2663289165 -0.2245218407 0.7699931685: -0.2663289165 error value 0.000000000 +DEAL::-0.1887262238 -0.1480024603 0.7796633598: -0.1887262238 error value -8.326672685e-17 +DEAL::-0.1110685560 -0.07156802410 0.7751382896: -0.1110685560 error value 4.163336342e-17 +DEAL::-0.03588516627 0.002241853775 0.7560592058: -0.03588516627 error value -2.081668171e-17 +DEAL::0.03436118254 0.07097021235 0.7232127397: 0.03436118254 error value 1.387778781e-17 +DEAL::0.09750269006 0.1324691326 0.6784217227: 0.09750269006 error value -1.110223025e-16 +DEAL::0.1518546010 0.1850850191 0.6243263560: 0.1518546010 error value -2.775557562e-17 +DEAL::0.1963417794 0.2277818661 0.5640861853: 0.1963417794 error value 1.110223025e-16 +DEAL:: +DEAL::-0.2773002233 9.789374525e-06 -0.004391114574 2.369582029e-05 -0.008933999043 2.320364942e-05 -0.0001192690414 -8.818777987e-05 -0.1270270270 0.03292605427 -0.01939908204 0.01187899779 -0.002936445027 -0.001851063476 0.0008262090469 -1.543109321e-05 -0.02163467356 -0.003057662422 0.0005525201967 -2.972727283e-05 -0.003349959668 -0.001771613307 0.0009771210300 -2.089534470e-05 -0.007240093851 -0.0009405122936 0.0002988904768 0.0003794990089 -0.0005131964739 -0.0009968406775 0.001399788271 0.0003946975576 -0.003809968069 -0.001892641326 0.001045913553 -1.603577079e-05 -0.0006459363904 -0.001023876150 0.001827166706 0.0003776711183 -0.2803710410 0.07193002692 -0.04031730636 0.02422580683 -0.003886004952 -0.002243554416 0.0008287450675 -2.783439006e-06 -0.008467718599 -0.001189836802 0.0002342356193 0.0003882589878 -0.0005049088731 -0.001058708417 0.001205720993 0.0004154329353 -0.2019601424 0.09131000223 -0.04099983892 0.02308021555 0.08910958818 0.03672096331 -0.006582206708 0.003680728883 -0.03597158718 -0.005317578423 -0.001735620205 -0.001301160744 0.01980462662 0.003025045669 -0.001692739790 -0.001309131703 -0.0008098330664 0.01091035809 -0.004509607712 0.001251348288 0.01316797652 0.01400472305 -0.002133281502 0.003302506716 -0.004640757251 -0.001832893447 -0.004555019115 -0.004684403479 0.001249092384 0.003217231378 -0.005751084617 -0.001801064617 -0.02358513433 0.06208181710 -0.02048876266 0.01052688715 0.04796479228 0.03255748692 -0.009508603917 0.005589809628 -0.01988160316 -0.01065306158 -0.001949888832 -0.003913215480 0.01063429521 0.006458163587 -0.002796980848 -0.0002055876475 0.007248132968 0.01583974710 -0.005510848010 0.001606143469 0.01033905477 0.008808532013 -0.001697329330 0.003342348584 -0.004910072130 -0.001143799309 -0.01101969801 -0.007567926864 0.001263422239 0.003258037936 -0.004533714515 -0.001727276219 0.04053681017 0.04014234770 -0.01554618257 0.008058578278 0.05028706981 0.01968075496 -0.008471356041 0.005352514559 -0.01787938526 -0.008599712127 -0.004952803663 -0.002839573385 0.009236725512 0.005187753962 -0.003532482457 -0.0001458538639 0.01560262801 0.01115244752 -0.005192873246 0.001279358824 0.01421550019 0.003355860594 -0.0003421895768 0.003113822672 -0.005630822341 -0.001239677158 -0.01815746547 -0.005339792919 0.001623718202 0.003280873283 -0.007267233613 -0.001644650639 -1.066214258 -0.05244450900 0.003613616900 0.001769820482 -0.1568730450 -0.1248861632 0.05255606231 -0.03085617244 0.04333705156 0.05161012999 0.003452149477 0.01401950199 -0.02044671642 -0.02947761728 0.01592608121 -0.002909155664 -0.2844339433 -0.1854630226 0.06502757834 -0.03722912450 -0.2740485519 -0.6735318615 0.08419076834 -0.03863689498 0.08124703958 0.05109363277 -0.06593469431 0.003228397692 -0.04492893110 -0.02356107574 -0.0009941892973 -0.01041779492 0.08606168162 0.05748642309 -0.005882183660 0.01426752818 0.07368944930 0.01623410680 -0.04716122558 0.002613035768 -0.01885036491 -0.03015014727 0.3716113886 0.02156214217 0.01702826726 0.001700537538 0.04745060019 0.01781808337 -0.04360642248 -0.03203099989 0.01729850917 -0.002839900373 -0.04060574522 -0.007536420705 -0.004314797666 -0.01035183925 0.01800297654 -0.0007309825836 0.07800408964 0.02216297909 -0.003713814241 -0.01106952712 0.03036072457 0.007370219834 +DEAL::Cell with center -0.7500000000 -1.407148550e-18 0.000000000 +DEAL::-0.6012515503 -0.5766780283 -0.5531118850: -0.6012515503 error value 2.220446049e-16 +DEAL::-0.6458946236 -0.5236491363 -0.5006487306: -0.6458946236 error value 4.440892099e-16 +DEAL::-0.6898189280 -0.4638689601 -0.4413495827: -0.6898189280 error value 0.000000000 +DEAL::-0.7296048967 -0.3975220470 -0.3754490693: -0.7296048967 error value -3.330669074e-16 +DEAL::-0.7617762381 -0.3254496235 -0.3038288032: -0.7617762381 error value 5.551115123e-16 +DEAL::-0.7832188522 -0.2491480826 -0.2280163559: -0.7832188522 error value 3.330669074e-16 +DEAL::-0.7915521155 -0.1706669598 -0.1500833118: -0.7915521155 error value -2.220446049e-16 +DEAL::-0.7854001879 -0.09242877894 -0.07246518026: -0.7854001879 error value 1.110223025e-16 +DEAL::-0.7645345314 -0.01700078778 0.002266559507: -0.7645345314 error value 2.220446049e-16 +DEAL::-0.7298790026 0.05314854421 0.07164727507: -0.7298790026 error value -6.661338148e-16 +DEAL::-0.6833856700 0.1158765656 0.1335451305: -0.6833856700 error value 3.330669074e-16 +DEAL::-0.6278029298 0.1695497377 0.1863429372: -0.6278029298 error value 3.330669074e-16 +DEAL::-0.5663675440 0.2131627953 0.2290556314: -0.5663675440 error value -1.110223025e-16 +DEAL:: +DEAL::-0.2835224186 8.766681601e-06 -0.004492274113 -6.068481192e-05 -0.009138560751 -6.226517805e-05 -0.0002090913881 1.303987559e-05 -0.1389688946 0.02332858811 -0.02285253161 0.01217053484 -0.004029939503 -0.007264733516 -0.004218720784 0.0001244048983 -0.03131118593 -0.01312179031 -0.002252663177 -5.941534510e-06 -0.004829135881 -0.007769808353 -0.004405866927 0.0001337182339 -0.008787315660 -0.007129425911 -0.005473457296 0.0005140602007 -0.0004498872475 -0.004604585331 -0.007606858696 -0.0003400302648 -0.005490074149 -0.008307807128 -0.004717262420 0.0001330915570 -0.0006696532182 -0.005232515792 -0.008553519053 -0.0003009755754 -0.2984519477 0.06185235145 -0.04484192233 0.02479257954 -0.005082324293 -0.007957861198 -0.004837751623 0.0001093234054 -0.009987558794 -0.007298569535 -0.005824633712 0.0005001551093 -0.0004131773587 -0.004401254258 -0.007656146035 -0.0003888289978 -0.2050730621 0.1428647253 -0.03957226269 0.02719437195 0.1491217983 0.06343304002 -0.06409581779 0.02148862442 -0.03301647870 -0.07098000576 -0.05402680846 0.01957914019 0.02403228817 0.02123639436 0.01911589759 -0.0009804158118 0.002809897014 0.03111425929 0.009472214603 0.001239780420 0.03578698689 0.001747523964 -0.05270365190 0.01257745942 0.01114918489 -0.06145792785 -0.04739365018 0.02702456902 0.001402950525 0.01321041407 0.02827702641 0.002536758108 0.002599913944 0.1259142731 -0.01825629537 0.01513740413 0.09398983480 0.02668313677 -0.07898506850 0.02457084645 -0.01746779612 -0.06295829183 -0.03102271443 0.01740670553 0.01384771748 0.02304777413 0.01634897026 -1.122303853e-05 0.01460388315 0.04173472666 0.01103012861 0.002035605925 0.03213629095 -0.02163031115 -0.07014771768 0.01510061315 0.009983356119 -0.05245403711 -0.01726538498 0.03263996874 0.001210250250 0.01256123771 0.02643131411 0.002356428775 0.08679010946 0.08626128549 -0.01266313849 0.01099841987 0.1046775496 -0.01604835642 -0.06031943500 0.02115435878 -0.01635775492 -0.06893816066 -0.01202730805 0.01449347158 0.01326437594 0.02286211671 0.01581209942 -0.0001036732708 0.02683403182 0.03515748406 0.01072181792 0.001328269797 0.03965937062 -0.04623308979 -0.05708941979 0.01318839351 0.009984495261 -0.06547408130 0.01573612901 0.02680824126 0.001988009540 0.01508828766 0.03163044541 0.002152882586 -1.543368363 -0.2165400465 -0.001487330486 -0.008125641785 -0.3802187958 -0.05777104278 0.2289294235 -0.08949994578 0.05507330542 0.2536139255 0.02583876204 -0.03450964795 -0.04072624987 -0.09337671372 -0.03817039060 -0.004020947358 -0.5907367776 -0.2382714292 0.2513354513 -0.1025040435 -0.4754847698 -2.679790359 -0.1627724257 0.002630944072 0.2958579228 -0.3533597131 -0.2832135658 0.1670104105 -0.1198285828 0.07197101448 0.1710156654 -0.03520138131 0.1123332124 0.2938262986 0.08094100181 -0.03964808717 0.3104293691 -0.5876488184 -0.4478088065 0.1941261840 0.1351965640 -0.6561058653 -2.110861210 0.1312259458 -0.04093016816 0.2244258961 0.02008441940 -0.09453018158 -0.07474080978 -0.1026699989 -0.04235040071 -0.004622431066 -0.1148887814 0.1458328543 0.1901814903 -0.03695612010 -0.03941415620 0.2143649144 -0.1089152754 -0.1012205462 -0.006637866589 -0.04244538852 -0.1226599732 -0.01268175186 +DEAL::Cell with center -1.407148550e-18 -0.7500000000 -4.163336342e-17 +DEAL::-0.5879922187 -0.5879922187 -0.5412602679: -0.5879922187 error value 0.000000000 +DEAL::-0.5359927398 -0.6317656581 -0.4904247681: -0.5359927398 error value 0.000000000 +DEAL::-0.4774156808 -0.6752050943 -0.4328300536: -0.4774156808 error value -5.551115123e-17 +DEAL::-0.4123477836 -0.7149693757 -0.3686646352: -0.4123477836 error value 5.551115123e-17 +DEAL::-0.3415220448 -0.7476112822 -0.2987437738: -0.3415220448 error value 5.551115123e-17 +DEAL::-0.2663289165 -0.7699931685 -0.2245218407: -0.2663289165 error value -5.551115123e-17 +DEAL::-0.1887262238 -0.7796633598 -0.1480024603: -0.1887262238 error value -8.326672685e-17 +DEAL::-0.1110685560 -0.7751382896 -0.07156802410: -0.1110685560 error value -1.387778781e-17 +DEAL::-0.03588516627 -0.7560592058 0.002241853775: -0.03588516627 error value -2.081668171e-17 +DEAL::0.03436118254 -0.7232127397 0.07097021235: 0.03436118254 error value 2.081668171e-17 +DEAL::0.09750269006 -0.6784217227 0.1324691326: 0.09750269006 error value -1.387778781e-16 +DEAL::0.1518546010 -0.6243263560 0.1850850191: 0.1518546010 error value -5.551115123e-17 +DEAL::0.1963417794 -0.5640861853 0.2277818661: 0.1963417794 error value 2.775557562e-17 +DEAL:: +DEAL::-0.2773002233 9.789374525e-06 -0.004391114574 2.369582029e-05 -0.008933999043 2.320364942e-05 -0.0001192690414 -8.818777987e-05 -0.1270270270 0.03292605427 -0.01939908204 0.01187899779 -0.002936445027 -0.001851063476 0.0008262090469 -1.543109321e-05 -0.02163467356 -0.003057662422 0.0005525201967 -2.972727283e-05 -0.003349959668 -0.001771613307 0.0009771210300 -2.089534470e-05 -0.007240093851 -0.0009405122936 0.0002988904768 0.0003794990089 -0.0005131964739 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-0.009508603917 0.005589809628 -0.01988160316 -0.01065306158 -0.001949888832 -0.003913215480 0.01063429521 0.006458163587 -0.002796980848 -0.0002055876475 0.007248132968 0.01583974710 -0.005510848010 0.001606143469 0.01033905477 0.008808532013 -0.001697329330 0.003342348584 -0.004910072130 -0.001143799309 -0.01101969801 -0.007567926864 0.001263422239 0.003258037936 -0.004533714515 -0.001727276219 0.04053681017 0.04014234770 -0.01554618257 0.008058578278 0.05028706981 0.01968075496 -0.008471356041 0.005352514559 -0.01787938526 -0.008599712127 -0.004952803663 -0.002839573385 0.009236725512 0.005187753962 -0.003532482457 -0.0001458538639 0.01560262801 0.01115244752 -0.005192873246 0.001279358824 0.01421550019 0.003355860594 -0.0003421895768 0.003113822672 -0.005630822341 -0.001239677158 -0.01815746547 -0.005339792919 0.001623718202 0.003280873283 -0.007267233613 -0.001644650639 -1.066214258 -0.05244450900 0.003613616900 0.001769820482 -0.1568730450 -0.1248861632 0.05255606231 -0.03085617244 0.04333705156 0.05161012999 0.003452149477 0.01401950199 -0.02044671642 -0.02947761728 0.01592608121 -0.002909155664 -0.2844339433 -0.1854630226 0.06502757834 -0.03722912450 -0.2740485519 -0.6735318615 0.08419076834 -0.03863689498 0.08124703958 0.05109363277 -0.06593469431 0.003228397692 -0.04492893110 -0.02356107574 -0.0009941892973 -0.01041779492 0.08606168162 0.05748642309 -0.005882183660 0.01426752818 0.07368944930 0.01623410680 -0.04716122558 0.002613035768 -0.01885036491 -0.03015014727 0.3716113886 0.02156214217 0.01702826726 0.001700537538 0.04745060019 0.01781808337 -0.04360642248 -0.03203099989 0.01729850917 -0.002839900373 -0.04060574522 -0.007536420705 -0.004314797666 -0.01035183925 0.01800297654 -0.0007309825836 0.07800408964 0.02216297909 -0.003713814241 -0.01106952712 0.03036072457 0.007370219834 +DEAL::Cell with center -1.407148550e-18 0.7500000000 0.000000000 +DEAL::-0.5766780283 0.6012515503 -0.5531118850: -0.5766780283 error value 1.110223025e-16 +DEAL::-0.5236491363 0.6458946236 -0.5006487306: -0.5236491363 error value 2.220446049e-16 +DEAL::-0.4638689601 0.6898189280 -0.4413495827: -0.4638689601 error value 5.551115123e-17 +DEAL::-0.3975220470 0.7296048967 -0.3754490693: -0.3975220470 error value 0.000000000 +DEAL::-0.3254496235 0.7617762381 -0.3038288032: -0.3254496235 error value 5.551115123e-17 +DEAL::-0.2491480826 0.7832188522 -0.2280163559: -0.2491480826 error value 5.551115123e-17 +DEAL::-0.1706669598 0.7915521155 -0.1500833118: -0.1706669598 error value -2.775557562e-17 +DEAL::-0.09242877894 0.7854001879 -0.07246518026: -0.09242877894 error value -1.387778781e-17 +DEAL::-0.01700078778 0.7645345314 0.002266559507: -0.01700078778 error value -3.122502257e-17 +DEAL::0.05314854421 0.7298790026 0.07164727507: 0.05314854421 error value 6.938893904e-17 +DEAL::0.1158765656 0.6833856700 0.1335451305: 0.1158765656 error value -9.714451465e-17 +DEAL::0.1695497377 0.6278029298 0.1863429372: 0.1695497377 error value -8.326672685e-17 +DEAL::0.2131627953 0.5663675440 0.2290556314: 0.2131627953 error value 0.000000000 +DEAL:: +DEAL::-0.2719660587 1.003680094e-05 -0.004306164427 2.530777595e-05 -0.008761612853 2.484587485e-05 -0.0001148632240 -8.975212231e-05 -0.1243863172 0.03253889936 -0.01894558065 0.01164881672 -0.002858770485 -0.001685682823 0.0009419357345 -1.812773524e-05 -0.02101755151 -0.002759409154 0.0006172894519 -3.080146401e-05 -0.003255971558 -0.001592904371 0.001099535094 -2.390011989e-05 -0.007071982151 -0.0007735376072 0.0004434634573 0.0003696531203 -0.0005057034286 -0.0008910320166 0.001609068587 0.0004086452712 -0.003703011665 -0.001701600854 0.001177030152 -1.895073883e-05 -0.0006340321368 -0.0009026604980 0.002065829039 0.0003904127106 -0.2747249544 0.07082346006 -0.03944606894 0.02375815700 -0.003788566601 -0.002064371908 0.0009600006922 -4.922032643e-06 -0.008277460263 -0.001020939658 0.0003867878178 0.0003788746887 -0.0004982130714 -0.0009584844679 0.001413656467 0.0004308805169 -0.1981508374 0.08840649244 -0.04030678359 0.02256224004 0.08605186345 0.03548722456 -0.005040446966 0.003184657677 -0.03541158377 -0.003590547704 -0.0003885841115 -0.001818565137 0.01934473465 0.002529330843 -0.002203673004 -0.001296593525 -0.0008744358071 0.01022323009 -0.004792352327 0.001228480445 0.01238433648 0.01408597781 -0.0008155063924 0.003019719835 -0.004967011656 -0.0002922978735 -0.003427097751 -0.005424299011 0.001222088804 0.002918311005 -0.006536598540 -0.001889090833 -0.02374790985 0.05944251918 -0.02020229553 0.01023188408 0.04599254204 0.03217922225 -0.007604201082 0.005025213350 -0.01960369428 -0.009161240874 -0.001202042022 -0.004398795603 0.01036900035 0.005939154144 -0.003241229302 -0.0002098235681 0.006950861506 0.01493005015 -0.005842187258 0.001566157389 0.009621548569 0.009428045643 6.396324219e-05 0.002997575702 -0.005211064322 0.0001800907124 -0.01073204246 -0.008486874499 0.001241479058 0.002975119059 -0.005256718619 -0.001809797632 0.03874123512 0.03831065045 -0.01535865528 0.007846773797 0.04808180456 0.02025606317 -0.007025618085 0.004870914090 -0.01761956991 -0.006939592520 -0.004720471623 -0.003237938860 0.008978630236 0.004662085146 -0.003973076442 -0.0001469402663 0.01506407694 0.01036716360 -0.005516041872 0.001254680490 0.01334361974 0.004541969772 0.001107125386 0.002814183308 -0.005937770235 0.0004096540247 -0.01879096128 -0.006082978984 0.001585191339 0.002935649144 -0.008156854655 -0.001720967347 -1.035802520 -0.04759196417 0.003755980255 0.001954491371 -0.1487565772 -0.1244939818 0.04723545456 -0.02887657185 0.04237250609 0.04566449549 0.002916461152 0.01503093427 -0.01961850671 -0.02738970388 0.01705481207 -0.002823834702 -0.2720731685 -0.1810966582 0.05925928571 -0.03498167715 -0.2645209555 -0.6125232278 0.08908556271 -0.03904618352 0.07450432622 0.06046147464 -0.05955130066 -0.0009873975098 -0.04231386676 -0.02556947997 -0.005364593045 -0.009641252158 0.08399868172 0.05058518138 -0.007919902667 0.01541022487 0.06651162171 0.03116345572 -0.03640452396 -0.002289238330 -0.02240035120 -0.01393167812 0.4294104359 0.01855795334 0.01822996943 -0.003977350208 0.04757335533 0.02042580151 -0.04210658208 -0.02973509166 0.01854982221 -0.002738471674 -0.03807700751 -0.01124837704 -0.009206422158 -0.009532796651 0.01918014242 -0.006186871507 0.08176301542 0.02499637837 -0.003568185946 -0.01012173065 0.03384037534 0.007787491127 +DEAL::Mapping of degree 5 +DEAL::Cell with center -3.778985438e-18 0.000000000 -0.7500000000 +DEAL::-0.5759520655 -0.5527659841 -0.5759520655: -0.0005759518743 error value -2.384185791e-10 +DEAL::-0.5254898676 -0.5029040719 -0.6187865537: -0.0005254898667 error value 2.384185791e-10 +DEAL::-0.4685426073 -0.4464599093 -0.6616551149: -0.0004685425162 error value 2.980232239e-11 +DEAL::-0.4051542510 -0.3835292107 -0.7012978956: -0.0004051542580 error value 1.192092896e-10 +DEAL::-0.3359932318 -0.3148223149 -0.7343028440: -0.0003359931707 error value -1.192092896e-10 +DEAL::-0.2623766962 -0.2416891159 -0.7575161861: -0.0002623766065 error value -8.940696716e-11 +DEAL::-0.1861925434 -0.1660412603 -0.7684224851: -0.0001861924827 error value -4.470348358e-11 +DEAL::-0.1097387169 -0.09019150189 -0.7654365722: -0.0001097386777 error value -3.725290298e-11 +DEAL::-0.03550798632 -0.01663873419 -0.7480737719: -3.550796211e-05 error value -2.235174179e-11 +DEAL::0.03404970570 0.05216906594 -0.7169856075: 3.404977545e-05 error value -6.705522537e-11 +DEAL::0.09675558003 0.1140621810 -0.6738655685: 9.675560147e-05 error value -2.235174179e-11 +DEAL::0.1508930055 0.1673387801 -0.6212435337: 0.0001508930176 error value 1.490116119e-11 +DEAL::0.1953394317 0.2108952300 -0.5621980946: 0.0001953394562 error value -1.490116119e-11 +DEAL:: +DEAL::-0.0002716215551 1.021163916e-08 -4.300554283e-06 2.287941606e-08 -8.750393987e-06 2.237081753e-08 -1.172111588e-07 -8.801198419e-08 -0.0001244676039 3.222703934e-05 -1.899373531e-05 1.163426507e-05 -2.882736968e-06 -1.823234139e-06 8.179966826e-07 -1.337967842e-08 -2.123299614e-05 -3.016994335e-06 5.497097736e-07 -3.059615847e-08 -3.289432963e-06 -1.745504793e-06 9.681959637e-07 -1.882372453e-08 -7.100019604e-06 -9.330248577e-07 3.029387735e-07 3.737480729e-07 -5.026791478e-07 -9.840871207e-07 1.390947145e-06 3.934546839e-07 -3.740939079e-06 -1.864857273e-06 1.036485308e-06 -1.393055572e-08 -6.330209435e-07 -1.011226210e-06 1.816124422e-06 3.765122965e-07 -0.0002746849060 7.042680681e-05 -3.948329017e-05 2.372825332e-05 -3.813328920e-06 -2.209479921e-06 8.201912278e-07 -7.292255759e-10 -8.302314207e-06 -1.178317703e-06 2.385213156e-07 3.824593732e-07 -4.944854882e-07 -1.044622273e-06 1.197704580e-06 4.140872625e-07 -0.0001978351474 8.958991617e-05 -4.021380097e-05 2.262882888e-05 8.746610582e-05 3.617062420e-05 -6.495342590e-06 3.643787000e-06 -3.529107571e-05 -5.251230206e-06 -1.713050064e-06 -1.308588544e-06 1.942077279e-05 2.999155782e-06 -1.698494423e-06 -1.292422181e-06 -7.735742256e-07 1.073017903e-05 -4.446385428e-06 1.223181956e-06 1.295211539e-05 1.376772020e-05 -2.073268406e-06 3.260943107e-06 -4.575112835e-06 -1.779407961e-06 -4.550677724e-06 -4.655019846e-06 1.220653648e-06 3.178860527e-06 -5.716765765e-06 -1.794053591e-06 -2.299735695e-05 6.100802869e-05 -2.012984082e-05 1.033529360e-05 4.710833728e-05 3.201280534e-05 -9.352566674e-06 5.509286188e-06 -1.952377521e-05 -1.047246717e-05 -1.965981908e-06 -3.881470533e-06 1.043485850e-05 6.361097097e-06 -2.770361491e-06 -2.103133302e-07 7.135060150e-06 1.557916589e-05 -5.431520753e-06 1.571051194e-06 1.016990468e-05 8.644735441e-06 -1.645049779e-06 3.303946462e-06 -4.845332354e-06 -1.089955098e-06 -1.097630151e-05 -7.524218410e-06 1.235261210e-06 3.216803074e-06 -4.505137913e-06 -1.720633707e-06 3.989600390e-05 3.944477439e-05 -1.527523622e-05 7.910617627e-06 4.941794276e-05 1.932782121e-05 -8.325301111e-06 5.273090675e-06 -1.756813750e-05 -8.456929587e-06 -4.948418587e-06 -2.813736210e-06 9.069133550e-06 5.112576298e-06 -3.503199900e-06 -1.506809494e-07 1.533473190e-05 1.097192429e-05 -5.125886761e-06 1.250909059e-06 1.398221683e-05 3.268814879e-06 -2.978011034e-07 3.076169640e-06 -5.551968701e-06 -1.190180308e-06 -1.807104610e-05 -5.307637155e-06 1.588626299e-06 3.242883831e-06 -7.225099951e-06 -1.638421090e-06 -0.001046360016 -5.181889981e-05 3.687791526e-06 1.680369489e-06 -0.0001543572247 -0.0001226567999 5.163546279e-05 -3.035098314e-05 4.267394543e-05 5.072259903e-05 3.634416498e-06 1.383637730e-05 -2.012437768e-05 -2.900069579e-05 1.573426649e-05 -2.834028797e-06 -0.0002796307206 -0.0001823107004 6.390938908e-05 -3.662298620e-05 -0.0002694923282 -0.0006638070941 8.287737519e-05 -3.797473013e-05 7.986627519e-05 5.022743717e-05 -6.531639397e-05 3.073005937e-06 -4.419480264e-05 -2.310917340e-05 -1.125266310e-06 -1.029458828e-05 8.461106569e-05 5.651179701e-05 -5.631402601e-06 1.407779194e-05 7.243470848e-05 1.585266739e-05 -4.668487608e-05 2.475033049e-06 -1.847024821e-05 -2.977820486e-05 0.0003692387342 2.151081339e-05 1.679814234e-05 1.567704836e-06 4.724658281e-05 1.771104336e-05 -4.285474122e-05 -3.151869401e-05 1.709669642e-05 -2.764161909e-06 -3.994547948e-05 -7.307473104e-06 -4.414333496e-06 -1.023667771e-05 1.777058281e-05 -8.510006592e-07 7.762078196e-05 2.203541622e-05 -3.619901370e-06 -1.095193159e-05 3.019067831e-05 7.338731084e-06 +DEAL::Cell with center 0.7500000000 -2.814297100e-18 -4.163336342e-17 +DEAL::0.5879922187 -0.5879922187 -0.5412602679: 0.0005879920125 error value 2.384185791e-10 +DEAL::0.6317656581 -0.5359927398 -0.4904247681: 0.0006317655444 error value -1.192092896e-10 +DEAL::0.6752050943 -0.4774156808 -0.4328300536: 0.0006752049327 error value 0.000000000 +DEAL::0.7149693757 -0.4123477836 -0.3686646352: 0.0007149694562 error value -1.788139343e-10 +DEAL::0.7476112822 -0.3415220448 -0.2987437738: 0.0007476111650 error value 2.384185791e-10 +DEAL::0.7699931685 -0.2663289165 -0.2245218407: 0.0007699929476 error value 2.384185791e-10 +DEAL::0.7796633598 -0.1887262238 -0.1480024603: 0.0007796633244 error value 0.000000000 +DEAL::0.7751382896 -0.1110685560 -0.07156802410: 0.0007751380801 error value 1.192092896e-10 +DEAL::0.7560592058 -0.03588516627 0.002241853775: 0.0007560591102 error value 0.000000000 +DEAL::0.7232127397 0.03436118254 0.07097021235: 0.0007232125401 error value -5.960464478e-11 +DEAL::0.6784217227 0.09750269006 0.1324691326: 0.0006784215569 error value 5.960464478e-11 +DEAL::0.6243263560 0.1518546010 0.1850850191: 0.0006243262887 error value 0.000000000 +DEAL::0.5640861853 0.1963417794 0.2277818661: 0.0005640861392 error value 1.192092896e-10 +DEAL:: +DEAL::0.0002772676349 -7.317328709e-09 4.394487478e-06 6.062009925e-08 8.938335814e-06 6.219932402e-08 2.058231330e-07 -1.443208021e-08 0.0001359318644 -2.272646315e-05 2.239334583e-05 -1.190587599e-05 3.940908238e-06 7.155479863e-06 4.191354848e-06 -1.237851830e-07 3.065297380e-05 1.292047836e-05 2.245299984e-06 2.109387424e-09 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4.581737891e-05 5.649910122e-05 -1.299653202e-05 -9.982751682e-06 6.478191912e-05 -1.589713246e-05 -2.663211897e-05 -1.939534908e-06 -1.487387158e-05 -3.143962845e-05 -2.159778029e-06 0.001510919690 0.0002130389214 1.707246527e-06 7.975683548e-06 0.0003733329177 5.499400198e-05 -0.0002256632000 8.804136515e-05 -5.364339799e-05 -0.0002501109838 -2.550897188e-05 3.440365568e-05 3.989165276e-05 9.190230817e-05 3.806110471e-05 3.932007123e-06 0.0005795866251 0.0002324809581 -0.0002475996912 0.0001007890031 0.0004656157792 0.002639275074 0.0001627013385 -3.336219117e-06 -0.0002913758755 0.0003506962955 0.0002791405916 -0.0001652431041 0.0001177980751 -7.167294621e-05 -0.0001692828983 3.465077281e-05 -0.0001096364260 -0.0002897967994 -8.023500443e-05 3.949890658e-05 -0.0003059409857 0.0005819128156 0.0004424262941 -0.0001920981854 -0.0001341832727 0.0006489337683 0.002096483707 -0.0001295576692 4.081770405e-05 -0.0002221045494 -1.906472072e-05 9.389261901e-05 7.319212705e-05 0.0001010478586 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-1.035184320e-05 1.800298318e-05 -7.310011424e-07 7.800415158e-05 2.216300368e-05 -3.713809652e-06 -1.106953155e-05 3.036075458e-05 7.370234001e-06 +DEAL::Cell with center -0.7500000000 -1.407148550e-18 0.000000000 +DEAL::-0.6012515503 -0.5766780283 -0.5531118850: -0.0006012513041 error value -2.384185791e-10 +DEAL::-0.6458946236 -0.5236491363 -0.5006487306: -0.0006458944678 error value -2.384185791e-10 +DEAL::-0.6898189280 -0.4638689601 -0.4413495827: -0.0006898187995 error value -5.960464478e-11 +DEAL::-0.7296048967 -0.3975220470 -0.3754490693: -0.0007296048999 error value 2.384185791e-10 +DEAL::-0.7617762381 -0.3254496235 -0.3038288032: -0.0007617759109 error value -4.172325134e-10 +DEAL::-0.7832188522 -0.2491480826 -0.2280163559: -0.0007832186222 error value -2.980232239e-10 +DEAL::-0.7915521155 -0.1706669598 -0.1500833118: -0.0007915520072 error value 0.000000000 +DEAL::-0.7854001879 -0.09242877894 -0.07246518026: -0.0007853998542 error value 0.000000000 +DEAL::-0.7645345314 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