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- # The fundamental theorem of calculus, in discrete version!
- import numpy as np
- np.set_printoptions(linewidth=200, precision=2)
- print('This Python snippet shows how the sum of many differences is one difference of endpoinds!')
- print('You can consider this the "discrete fundamental theorem of calculus"!')
- # ----------------------------------------------------------------------
- N_VALUES = 16
- vec_a = 10 * np.random.rand(N_VALUES)
- diff_vec_a = np.diff(vec_a) # This is the "discrete derivative"
- endpoints_vec_a = np.array([vec_a[0], vec_a[-1]])
- sum_diff_vec_a = np.sum(diff_vec_a) # This is the "discrete (definite) integral"
- endpoints_diff_vec_a = endpoints_vec_a[1] - endpoints_vec_a[0] # This is like taking a difference of the antiderivative!
- TEMPLATE_STR = '{:24} {}'
- print(TEMPLATE_STR.format('vec_a', vec_a))
- print(TEMPLATE_STR.format('diff_vec_a', diff_vec_a))
- print(TEMPLATE_STR.format('endpoints_vec_a', endpoints_vec_a))
- print(TEMPLATE_STR.format('sum_diff_vec_a', sum_diff_vec_a))
- print(TEMPLATE_STR.format('endpoints_diff_vec_a', endpoints_diff_vec_a))
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