Pythonfiles

Stochastisches_Modell.py

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+import sympy as sp
+from dataclasses import dataclass, field
+from typing import Dict, Tuple
+
+@dataclass
+class StochastischesModellApriori:
+
+    sigma_obs: Iterable[float]           # σ_i
+    group_ids: Iterable[int]            # Gruppenzugehörigkeit der i-ten Beobachtung
+    sigma0_sq_groups: Dict[int, float] = field(default_factory=dict)
+
+    def __post_init__(self):
+        # In sympy-Objekte konvertieren
+        self.sigma_obs = sp.Matrix(list(self.sigma_obs))  # Spaltenvektor
+        self.group_ids = sp.Matrix(list(self.group_ids))  # Spaltenvektor
+
+        if self.sigma_obs.rows != self.group_ids.rows:
+            raise ValueError("sigma_obs und group_ids müssen gleich viele Einträge haben.")
+
+        # Fehlende Gruppen mit σ_0j^2 = 1.0 initialisieren
+        unique_groups = sorted({int(g) for g in self.group_ids})
+        for g in unique_groups:
+            if g not in self.sigma0_sq_groups:
+                self.sigma0_sq_groups[g] = 1.0
+
+    @property
+
+    def n_obs(self) -> int:
+        return int(self.sigma_obs.rows)
+
+
+    def build_Qll_P(self) -> Tuple[sp.Matrix, sp.Matrix]:
+
+        n = self.n_obs
+        Q_ll = sp.zeros(n, n)
+        P = sp.zeros(n, n)
+
+        for i in range(n):
+            sigma_i = self.sigma_obs[i, 0]
+            g = int(self.group_ids[i, 0])
+            sigma0_sq = self.sigma0_sq_groups[g]
+
+            q_ii = sigma_i**2
+            Q_ll[i, i] = q_ii
+
+            P[i, i] = 1 / (sigma0_sq * q_ii)
+
+        return Q_ll, P
+
+    @staticmethod
+    def _redundanz_pro_beobachtung(A: sp.Matrix, P: sp.Matrix) -> sp.Matrix:
+
+        n_obs = P.rows
+        n_param = A.cols
+
+        # P^(1/2) aufbauen (diagonal, sqrt der Diagonale)
+        sqrtP = sp.zeros(n_obs, n_obs)
+        for i in range(n_obs):
+            sqrtP[i, i] = sp.sqrt(P[i, i])
+
+        A_tilde = sqrtP * A  # Ã
+
+        # M = (Ãᵀ Ã)^(-1)
+        M = (A_tilde.T * A_tilde).inv()
+
+        r_vec = sp.zeros(n_obs, 1)
+
+        for i in range(n_obs):
+            a_i = A_tilde.row(i)          # 1 × n_param
+            a_i_row = sp.Matrix([a_i])    # explizit 1×n-Matrix
+            r_i = 1 - (a_i_row * M * a_i_row.T)[0, 0]
+            r_vec[i, 0] = r_i
+
+        return r_vec
+
+
+    def varianzkomponenten_schaetzung(
+        self,
+        v: sp.Matrix,   # Residuenvektor (n × 1)
+        A: sp.Matrix,   # Designmatrix
+    ) -> Dict[int, float]:
+
+        if v.rows != self.n_obs:
+            raise ValueError("Länge von v passt nicht zur Anzahl Beobachtungen im Modell.")
+
+        # Aktuelle Gewichte
+        Q_ll, P = self.build_Qll_P()
+
+        # Redundanzzahlen pro Beobachtung
+        r_vec = self._redundanz_pro_beobachtung(A, P)
+
+        new_sigma0_sq: Dict[int, float] = {}
+
+        # Für jede Gruppe j:
+        unique_groups = sorted({int(g) for g in self.group_ids})
+
+        for g in unique_groups:
+            # Indizes der Beobachtungen in dieser Gruppe
+            idx = [i for i in range(self.n_obs) if int(self.group_ids[i, 0]) == g]
+            if not idx:
+                continue
+
+            # v_j, P_j, r_j extrahieren
+            v_j = sp.Matrix([v[i, 0] for i in idx])               # (m_j × 1)
+            P_j = sp.zeros(len(idx), len(idx))
+            r_j = 0
+            for ii, i in enumerate(idx):
+                P_j[ii, ii] = P[i, i]
+                r_j += r_vec[i, 0]
+
+            # σ̂_j^2 = (v_jᵀ P_j v_j) / r_j
+            sigma_hat_j_sq = (v_j.T * P_j * v_j)[0, 0] / r_j
+
+            # als float rausgeben, kann man aber auch symbolisch lassen
+            new_sigma0_sq[g] = float(sigma_hat_j_sq)
+
+        return new_sigma0_sq
+
+    def update_sigma0(self, new_sigma0_sq: Dict[int, float]) -> None:
+
+        for g, val in new_sigma0_sq.items():
+            self.sigma0_sq_groups[int(g)] = float(val)