reconnect moved files to git repo

venv/lib/python3.11/site-packages/statsmodels/distributions/copula/_special.py

@@ -0,0 +1,110 @@
+"""
+
+Special functions for copulas not available in scipy
+
+Created on Jan. 27, 2023
+"""
+
+import numpy as np
+from scipy.special import factorial
+
+
+class Sterling1():
+    """Stirling numbers of the first kind
+    """
+    # based on
+    # https://rosettacode.org/wiki/Stirling_numbers_of_the_first_kind#Python
+
+    def __init__(self):
+        self._cache = {}
+
+    def __call__(self, n, k):
+        key = str(n) + "," + str(k)
+
+        if key in self._cache.keys():
+            return self._cache[key]
+        if n == k == 0:
+            return 1
+        if n > 0 and k == 0:
+            return 0
+        if k > n:
+            return 0
+        result = sterling1(n - 1, k - 1) + (n - 1) * sterling1(n - 1, k)
+        self._cache[key] = result
+        return result
+
+    def clear_cache(self):
+        """clear cache of Sterling numbers
+        """
+        self._cache = {}
+
+
+sterling1 = Sterling1()
+
+
+class Sterling2():
+    """Stirling numbers of the second kind
+    """
+    # based on
+    # https://rosettacode.org/wiki/Stirling_numbers_of_the_second_kind#Python
+
+    def __init__(self):
+        self._cache = {}
+
+    def __call__(self, n, k):
+        key = str(n) + "," + str(k)
+
+        if key in self._cache.keys():
+            return self._cache[key]
+        if n == k == 0:
+            return 1
+        if (n > 0 and k == 0) or (n == 0 and k > 0):
+            return 0
+        if n == k:
+            return 1
+        if k > n:
+            return 0
+        result = k * sterling2(n - 1, k) + sterling2(n - 1, k - 1)
+        self._cache[key] = result
+        return result
+
+    def clear_cache(self):
+        """clear cache of Sterling numbers
+        """
+        self._cache = {}
+
+
+sterling2 = Sterling2()
+
+
+def li3(z):
+    """Polylogarithm for negative integer order -3
+
+    Li(-3, z)
+    """
+    return z * (1 + 4 * z + z**2) / (1 - z)**4
+
+
+def li4(z):
+    """Polylogarithm for negative integer order -4
+
+    Li(-4, z)
+    """
+    return z * (1 + z) * (1 + 10 * z + z**2) / (1 - z)**5
+
+
+def lin(n, z):
+    """Polylogarithm for negative integer order -n
+
+    Li(-n, z)
+
+    https://en.wikipedia.org/wiki/Polylogarithm#Particular_values
+    """
+    if np.size(z) > 1:
+        z = np.array(z)[..., None]
+
+    k = np.arange(n+1)
+    st2 = np.array([sterling2(n + 1, ki + 1) for ki in k])
+    res = (-1)**(n+1) * np.sum(factorial(k) * st2 * (-1 / (1 - z))**(k+1),
+                               axis=-1)
+    return res