release

a_adoptation.py

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+from typing import List
+
+# A draft for the future realization of a adoptation according:
+# [Everhart2] Everhart, E. 1985, An Efficient Integrator that uses Gauss-Radau Spacings,
+#             The Dynamics of Comets: Their Origin and Evolution
+
+
+def binomial_coeffs(order: int) -> List[int]:
+    """
+    Return binomial coefficients of the defined order
+    :param order: order
+    :type order: int
+    :return: binomial coefficients
+    :rtype: List[int]
+    """
+    def binc(bcs, n, k):
+        if k > n:
+            return 0
+        if k > n // 2:
+            k = n - k
+        if k == 0:
+            return 1
+        if k == 1:
+            return n
+        while len(bcs) < n - 3:
+            for i in range(len(bcs), n - 3):
+                r = []
+                for j in range(2, i // 2 + 3):
+                    r.append(binc(bcs, i + 3, j - 1) + binc(bcs, i + 3, j))
+                bcs.append(r)
+        r = bcs[n - 4]
+        if len(r) < k - 1:
+            for i in range(len(r), k - 1):
+                r.append(binc(bcs, n - 1, k - 1) + binc(bcs, n - 1, k))
+        return bcs[n - 4][k - 2]
+
+    result = []
+    temp = []
+    for m in range(order + 1):
+        result.append(binc(temp, order, m))
+
+    return result
+
+
+if __name__ == '__main__':
+    a_old = [1, 1, 1, 1]
+    a_new = [1, 1, 1, 1]
+    dt_old = 5
+    dt_new = 5
+    q = dt_new / dt_old
+
+    b_c = []
+    for i in range(1, len(a_old) + 1):
+        row = []
+        for j in range(1, len(a_old) + 1):
+            if j >= i:
+                row.append(binomial_coeffs(j)[i])
+            else:
+                row.append(0)
+
+        b_c.append(row)
+
+    for i in range(len(a_old)):
+        a_new[i] = 0
+        for j in range(len(a_old)):
+            a_new[i] += b_c[i][j] * a_old[j]
+        a_new[i] *= q ** (i + 1)
+
+    print(a_old)
+    print(a_new)