def get_finite_difference_coefficients(derivative_order, accuracy_order,
grid_type):
if derivative_order < 1:
raise ValueError("Wrong derivative order")
if odd(accuracy_order) or accuracy_order < 2:
raise ValueError("Wrong accuracy order")
if grid_type == 'centred':
window_size = accuracy_order / 2
grid = list(range(-window_size, window_size + 1))
elif grid_type == 'forward':
grid = list(range(derivative_order + accuracy_order))
elif grid_type == 'backward':
grid = list(range(-(derivative_order + accuracy_order) + 1, 1))
grid = list(reversed(grid)) # Fixme: why ?
else:
raise ValueError("Wrong grid type")
key = '{}-{}'.format(derivative_order, accuracy_order)
coefficients = _coefficient_cache[grid_type].get(key, None)
if coefficients is None:
coefficients = compute_finite_difference_coefficients(
derivative_order, grid)
_coefficient_cache[grid_type][key] = coefficients
return grid, coefficients
def get_finite_difference_coefficients(derivative_order, accuracy_order, grid_type):
if derivative_order < 1:
raise ValueError("Wrong derivative order")
if odd(accuracy_order) or accuracy_order < 2:
raise ValueError("Wrong accuracy order")
if grid_type == 'centred':
window_size = accuracy_order / 2
grid = list(range(-window_size, window_size +1))
elif grid_type == 'forward':
grid = list(range(derivative_order + accuracy_order))
elif grid_type == 'backward':
grid = list(range(-(derivative_order + accuracy_order) +1, 1))
grid = list(reversed(grid)) # Fixme: why ?
else:
raise ValueError("Wrong grid type")
key = '{}-{}'.format(derivative_order, accuracy_order)
coefficients = _coefficient_cache[grid_type].get(key, None)
if coefficients is None:
coefficients = compute_finite_difference_coefficients(derivative_order, grid)
_coefficient_cache[grid_type][key] = coefficients
return grid, coefficients
8: [1/280., -4/105., 1/5., -4/5., 0],
},
2: {
2: [1, -2],
4: [-1/12., 4/3., -5/2.],
6: [1/90., -3/20., 3/2., -49/18.],
8: [-1/560., 8/315., -1/5., 8/5., -205/72.],
},
}
# complete right coefficients
for derivative_order, derivative_order_dict in centred_coefficients.items():
for coefficients in derivative_order_dict.values():
if len(coefficients) > 1:
for i in range(len(coefficients) -2, -1, -1):
coefficient = coefficients[i]
if odd(derivative_order):
coefficient *= -1
coefficients.append(coefficient)
forward_coefficients = {
# on a grid 0...8
# [order of derivative][order of accuracy] = (coefficients)
0: { None:(1,) },
1: {
1: (-1, 1),
2: (-3/2., 2, -1/2.),
3: (-11/6., 3, -3/2., 1/3.),
4: (-25/12., 4, -3, 4/3., -1/4.),
5: (-137/60., 5, -5, 10/3., -5/4., 1/5.),
6: (-49/20., 6, -15/2., 20/3., -15/4., 6/5., -1/6.),
7: (-363/140., 7, -21/2., 35/3., -35/4., 21/5., -7/6., 1/7.),
8: [1/280., -4/105., 1/5., -4/5., 0],
},
2: {
2: [1, -2],
4: [-1/12., 4/3., -5/2.],
6: [1/90., -3/20., 3/2., -49/18.],
8: [-1/560., 8/315., -1/5., 8/5., -205/72.],
},
}
# complete right coefficients
for derivative_order, derivative_order_dict in centred_coefficients.items():
for coefficients in derivative_order_dict.values():
if len(coefficients) > 1:
for i in range(len(coefficients) -2, -1, -1):
coefficient = coefficients[i]
if odd(derivative_order):
coefficient *= -1
coefficients.append(coefficient)
forward_coefficients = {
# on a grid 0...8
# [order of derivative][order of accuracy] = (coefficients)
0: { None:(1,) },
1: {
1: (-1, 1),
2: (-3/2., 2, -1/2.),
3: (-11/6., 3, -3/2., 1/3.),
4: (-25/12., 4, -3, 4/3., -1/4.),
5: (-137/60., 5, -5, 10/3., -5/4., 1/5.),
6: (-49/20., 6, -15/2., 20/3., -15/4., 6/5., -1/6.),
7: (-363/140., 7, -21/2., 35/3., -35/4., 21/5., -7/6., 1/7.),