Pythonfiles

Datumsfestlegung.py

@@ -1,4 +1,59 @@
 import sympy as sp
+from typing import List, Iterable, Tuple
+
+def raenderungsmatrix_G(
+    x0: sp.Matrix,
+    idx_X: List[int],
+    idx_Y: List[int],
+    idx_Z: List[int],
+    mit_massstab: bool = True,
+    ) -> sp.Matrix:
+
+    u = x0.rows
+    d = 7 if mit_massstab else 6
+    G = sp.zeros(u, d)
+
+    # --- Translationen ---
+    for i in idx_X:
+        G[i, 0] = 1
+    for i in idx_Y:
+        G[i, 1] = 1
+    for i in idx_Z:
+        G[i, 2] = 1
+
+    # --- Rotationen ---
+    # Rotation um X-Achse
+    for iy, iz in zip(idx_Y, idx_Z):
+        zi = x0[iz, 0]
+        yi = x0[iy, 0]
+        G[iy, 3] = -zi
+        G[iz, 3] = yi
+
+    # Rotation um Y-Achse
+    for ix, iz in zip(idx_X, idx_Z):
+        zi = x0[iz, 0]
+        xi = x0[ix, 0]
+        G[ix, 4] = zi
+        G[iz, 4] = -xi
+
+    # Rotation um Z-Achse
+    for ix, iy in zip(idx_X, idx_Y):
+        yi = x0[iy, 0]
+        xi = x0[ix, 0]
+        G[ix, 5] = -yi
+        G[iy, 5] = xi
+
+    # --- Maßstab ---
+    if mit_massstab:
+        for ix, iy, iz in zip(idx_X, idx_Y, idx_Z):
+            xi = x0[ix, 0]
+            yi = x0[iy, 0]
+            zi = x0[iz, 0]
+            G[ix, 6] = xi
+            G[iy, 6] = yi
+            G[iz, 6] = zi
+    return G
+
 
 def auswahlmatrix_E(u: int, aktive_unbekannte_indices: Iterable[int]) -> sp.Matrix:
     E = sp.zeros(u, u)
@@ -6,9 +61,21 @@ def auswahlmatrix_E(u: int, aktive_unbekannte_indices: Iterable[int]) -> sp.Matr
         E[int(idx), int(idx)] = 1
     return E
 
-def raenderungsmatric_G():
-
 
 def teilspurminimierung_Gi(G: sp.Matrix, E: sp.Matrix) -> sp.Matrix:
     Gi = E * G
     return Gi
+
+
+def berechne_dx_geraendert(N: sp.Matrix, n: sp.Matrix, Gi: sp.Matrix) -> sp.Matrix:
+    u = N.rows
+    d = Gi.shape[1]
+
+    K = N.row_join(Gi)
+    K = K.col_join(Gi.T.row_join(sp.zeros(d, d)))
+
+    rhs = n.col_join(sp.zeros(d, 1))
+
+    sol = K.LUsolve(rhs)
+    dx = sol[:u, :]
+    return dx