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Adapter for interpolated extrapolation with global grids #11

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28fdf00
Add BSpline Extrapolation.
pascalresch Oct 16, 2020
df6615d
Merge branch 'master' of https://github.com/obersteiner/sparseSpACE i…
pascalresch Oct 16, 2020
8214a27
Add hierarchical lagrange interpolated extrapolation. Generalized ada…
pascalresch Oct 16, 2020
9708bf3
Fix interpolation adapter for extrapolation
pascalresch Oct 27, 2020
a47abfa
Remove comments
pascalresch Oct 27, 2020
4b0feea
Merge branch 'master' of https://github.com/obersteiner/sparseSpACE i…
pascalresch Dec 13, 2020
16fc5e1
Fix import bug
pascalresch Dec 27, 2020
d9b9aa9
Update Extrapolation grid: Differentiate between no/subgrid/full inte…
pascalresch Jan 3, 2021
8f8c1aa
Add possibility to plot basis functions for GlobalBasisGrids
pascalresch Mar 17, 2021
6647702
Fix plots of basis functions
pascalresch Mar 17, 2021
a858b8f
Optimize plots of basis functions
pascalresch Mar 17, 2021
591de88
Add GlobalLagrangeGrid without hierarchical construction
pascalresch Mar 25, 2021
5ee818c
Update class names for global Lagrange grids
pascalresch Mar 25, 2021
42f749b
Setup error plots for interpolation adapter comparison
pascalresch Mar 25, 2021
f7b0397
Merge branch 'master' of https://github.com/obersteiner/sparseSpACE i…
pascalresch Apr 6, 2021
c0ea48c
Remove test file
pascalresch Apr 6, 2021
5182586
Fix some Grid type hints
pascalresch Apr 25, 2021
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2 changes: 1 addition & 1 deletion ipynb/Diss/Figures_Diss.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -1684,4 +1684,4 @@
},
"nbformat": 4,
"nbformat_minor": 1
}
}
54 changes: 43 additions & 11 deletions ipynb/Extrapolation/Extrapolation_Test.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -31,11 +31,10 @@
"# shortcut for romberg SASD\n",
"def get_single_dim_romberg(a, b, f, reference_solution, sasd_version,\n",
" slice_grouping, slice_version, container_version,\n",
" force_balanced_refinement_tree):\n",
" force_balanced_refinement_tree, grid_version = GridVersion.DEFAULT):\n",
" grid_romberg = GlobalRombergGrid(a=a, b=b, modified_basis=False, boundary=True,\n",
" slice_grouping=slice_grouping,\n",
" slice_version=slice_version,\n",
" container_version=container_version)\n",
" slice_version=slice_version)\n",
"\n",
" operation_romberg = Integration(f=f, grid=grid_romberg, dim=dim, reference_solution=reference_solution)\n",
"\n",
Expand Down Expand Up @@ -90,11 +89,11 @@
"\n",
"# Manually override functions array:\n",
"functions = [\n",
" # f_genz_corner,\n",
" f_genz_corner,\n",
" # f_genz_product,\n",
" # f_genz_cont,\n",
" # f_genz_gaussian,\n",
" f_exp_var,\n",
" # f_exp_var,\n",
" # f_genz_osz,\n",
" # f_genz_disc\n",
"]\n",
Expand Down Expand Up @@ -189,19 +188,47 @@
" force_balanced_refinement_tree=True)\n",
" \n",
" # Interpolating Romberg\n",
" r_interpolating_old = get_single_dim_romberg(a, b, f, reference_solution,\n",
" sasd_version=sasd_version,\n",
" slice_grouping=SliceGrouping.GROUPED_OPTIMIZED,\n",
" slice_version=SliceVersion.ROMBERG_DEFAULT, # Makes no difference\n",
" container_version=SliceContainerVersion.LAGRANGE_ROMBERG_OLD,\n",
" force_balanced_refinement_tree=False,\n",
" grid_version=GridVersion.INTERPOLATE_SUB_GRIDS) # Interpolating Romberg\n",
"\n",
" r_interpolating = get_single_dim_romberg(a, b, f, reference_solution,\n",
" sasd_version=sasd_version,\n",
" slice_grouping=SliceGrouping.GROUPED_OPTIMIZED,\n",
" slice_version=SliceVersion.ROMBERG_DEFAULT, # Makes no difference\n",
" container_version=SliceContainerVersion.LAGRANGE_ROMBERG,\n",
" force_balanced_refinement_tree=False)\n",
" force_balanced_refinement_tree=False,\n",
" grid_version=GridVersion.INTERPOLATE_SUB_GRIDS)\n",
" # Interpolating Full grid\n",
" r_interpolating_full_grid = get_single_dim_romberg(a, b, f, reference_solution,\n",
" sasd_version=sasd_version,\n",
" slice_grouping=SliceGrouping.GROUPED_OPTIMIZED,\n",
" slice_version=SliceVersion.ROMBERG_DEFAULT, # Makes no difference\n",
" container_version=SliceContainerVersion.LAGRANGE_FULL_GRID_ROMBERG,\n",
" force_balanced_refinement_tree=False)\n",
" container_version=SliceContainerVersion.LAGRANGE_ROMBERG,\n",
" force_balanced_refinement_tree=False,\n",
" grid_version=GridVersion.INTERPOLATE_FULL_GRID)\n",
" \n",
" # Interpolating Bspline\n",
" r_interpolating_bspline = get_single_dim_romberg(a, b, f, reference_solution,\n",
" sasd_version=sasd_version,\n",
" slice_grouping=SliceGrouping.GROUPED_OPTIMIZED,\n",
" slice_version=SliceVersion.ROMBERG_DEFAULT, # Makes no difference\n",
" container_version=SliceContainerVersion.BSPLINE_ROMBERG,\n",
" force_balanced_refinement_tree=False,\n",
" grid_version=GridVersion.INTERPOLATE_SUB_GRIDS)\n",
" \n",
" # Interpolating Hierarchical Langrange\n",
" r_interpolating_hierarchical_lagrange = get_single_dim_romberg(a, b, f, reference_solution,\n",
" sasd_version=sasd_version,\n",
" slice_grouping=SliceGrouping.GROUPED_OPTIMIZED,\n",
" slice_version=SliceVersion.ROMBERG_DEFAULT, # Makes no difference\n",
" container_version=SliceContainerVersion.HIERARCHICAL_LAGRANGE_ROMBERG,\n",
" force_balanced_refinement_tree=False,\n",
" grid_version=GridVersion.INTERPOLATE_SUB_GRIDS)\n",
" \n",
" # Romberg Constant Subtraction\n",
" r_constant_subtraction = get_single_dim_romberg(a, b, f, reference_solution,\n",
Expand Down Expand Up @@ -259,21 +286,26 @@
" # (r_grouped_optimized, 1, 2, errorOperator, 'Extrapolation Grid (Grouped Optimized, Romberg, Default Romberg)'),\n",
" # (r_full_grouped_optimized, 1, 2, errorOperator, 'Extrapolation Grid (Grouped Optimized, Romberg, Default Romberg, Balanced)'),\n",
" # \n",
" # (r_interpolating, 1, 2, errorOperator, 'Extrapolation Grid (Grouped Optimized, Romberg, Lagrange Romberg)'),\n",
" (r_interpolating_old, 1, 2, errorOperator, 'Extrapolation Grid (Grouped Optimized, Romberg, Lagrange Romberg Old)'),\n",
" # (r_interpolating_full_grid, 1, 2, errorOperator, 'Extrapolation Grid (Grouped Optimized, Romberg, Lagrange Full Romberg)'),\n",
"\n",
" (r_interpolating, 1, 2, errorOperator, 'Extrapolation Grid (Grouped Optimized, Romberg, Lagrange Romberg)'),\n",
" (r_interpolating_bspline, 1, 2, errorOperator, 'Extrapolation Grid (Grouped Optimized, Romberg, Bspline Romberg)'),\n",
" (r_interpolating_hierarchical_lagrange, 1, 2, errorOperator, 'Extrapolation Grid (Grouped Optimized, Romberg, Hierarchical Lagrange Romberg)'),\n",
"\n",
" # \n",
" # (r_simson_full_grouped_optimized, 1, 2, errorOperator, 'Extrapolation Grid (Grouped Optimized, Romberg, Simpson Romberg, Balanced)'),\n",
"\n",
" # (r_constant_subtraction, 1, 2, errorOperator, 'Extrapolation Grid (Unit, DefaultConstantSubtraction)'), \n",
" \n",
" (r_balanced, 1, 2, errorOperator, 'Balanced Extrapolation Grid'),\n",
" # (r_balanced, 1, 2, errorOperator, 'Balanced Extrapolation Grid'),\n",
" ]\n",
" \n",
" function_name = f.__class__.__name__\n",
" filename = \"error_comparison_{}_{}d\".format(function_name, dim)\n",
"\n",
" performTestcaseArbitraryDim(f, a, b, algorithmArray,\n",
" max_tol, dim, 6, grids=standard_combi_grids, evaluation_points=evaluation_points,\n",
" max_tol, dim, 6, grids=standard_combi_grids, evaluation_points=None,\n",
" max_evaluations=max_evaluations,\n",
" calc_standard_schemes=True, # enable for standard schemes\n",
" minLmin=1,\n",
Expand Down
10 changes: 9 additions & 1 deletion sparseSpACE/BasisFunctions.py
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Original file line number Diff line number Diff line change
Expand Up @@ -94,12 +94,15 @@ def get_integral(self, a: float, b: float, coordsD: np.array, weightsD: np.array
return result


# Data structure for one lagrange basis
class LagrangeBasis(BasisFunction):
def __init__(self, p: int, index: int, knots: np.array):
self.p = p
self.knots = knots
#assert p == len(knots) - 1
self.index = index

# Construct factor of lagrange polynomial for this basis point
self.factor = 1
for i, knot in enumerate(self.knots):
assert not isinf(self.knots[i])
Expand All @@ -109,10 +112,15 @@ def __init__(self, p: int, index: int, knots: np.array):

def __call__(self, x: float) -> float:
result = 1

# Evaluate basis function at point x
for i, knot in enumerate(self.knots):
if self.index != i:
result *= (x - self.knots[i])
return result * self.factor

# Complete construction of lagrange polynomial for this basis point evaluated at x
evaluated_basis = result * self.factor
return evaluated_basis

def get_first_derivative(self, x: float) -> float:
return self.derivative_for_index(x, [self.index])
Expand Down
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