hell

Л3-В6/Программа/src/algorithm.py

@@ -50,34 +50,54 @@ def swap_first_non_zero(matrix, i):
     return False, -1
 
 
-def swap_max_row(matrix, i):
+def swap_max_row(matrix, j):
     n = matrix.shape[0]
-    col_max = abs(matrix[i, i])
-    max_j = i
-    for j in range(i, n):
-        if abs(matrix[j, i]) > col_max:
-            col_max = abs(matrix[j, i])
-            max_j = j
 
-    if i != max_j:
-        matrix[[i, max_j], :] = matrix[[max_j, i], :]
+    current = float("inf")
+    if matrix[j, j] != 0:
+        current = np.sum(np.abs(matrix[j, :])) / abs(matrix[j, j])
+    max_i = j
+    for i in range(j + 1, n):
+        if matrix[i, j] == 0 or matrix[j, i] == 0:
+            continue
 
-    return max_j
+        target_current = np.sum(np.abs(matrix[i, :])) / abs(matrix[i, i])
+        new = np.sum(np.abs(matrix[i, :])) / abs(matrix[i, j])
+        target_new = np.sum(np.abs(matrix[j, :])) / abs(matrix[j, i])
+
+        if current - new > target_new - target_current:
+            current = new
+            max_i = i
+
+    if j != max_i:
+        matrix[[j, max_i], :] = matrix[[max_i, j], :]
+
+    return max_i
 
 
 def swap_max_column(matrix, i):
     n = matrix.shape[0]
-    row_max = abs(matrix[i, i])
-    max_j = i
-    for j in range(i, n):
-        if abs(matrix[i, j]) > row_max and abs(matrix[i, i]) - abs(matrix[j, j]) > 0.0:
-            row_max = abs(matrix[i, j])
-            max_j = j
 
-    if i != max_j:
-        matrix[:, [i, max_j]] = matrix[:, [max_j, i]]
+    current = float("inf")
+    if matrix[i, i] != 0:
+        current = np.sum(np.abs(matrix[i, :])) / abs(matrix[i, i])
+    best_j = i
+    for j in range(i + 1, n):
+        if matrix[i, j] == 0 or matrix[j, i] == 0:
+            continue
 
-    return max_j
+        target_current = np.sum(np.abs(matrix[j, :])) / abs(matrix[j, j])
+        new = np.sum(np.abs(matrix[i, :])) / abs(matrix[i, j])
+        target_new = np.sum(np.abs(matrix[j, :])) / abs(matrix[j, i])
+
+        if current - new > target_new - target_current:
+            current = new
+            best_j = j
+
+    if i != best_j:
+        matrix[:, [i, best_j]] = matrix[:, [best_j, i]]
+
+    return best_j
 
 
 def norm(matrix: np.matrix):

Л3-В6/Программа/src/main.py

@@ -14,17 +14,17 @@ A = np.matrix(
 
 B = np.matrix([[15.5, 2.5, 8.6, 12.1]], dtype=np.float64).T
 
-# A = np.matrix(
-#     [
-#         [14.4, -5.3, 14.3, -12.7],
-#         [23.4, -14.2, -5.4, 2.1],
-#         [6.3, -13.2, -6.5, 14.3],
-#         [5.6, 8.8, -6.7, -23.8],
-#     ],
-#     dtype=np.float64,
-# )
+A = np.matrix(
+    [
+        [14.4, -5.3, 14.3, -12.7],
+        [23.4, -14.2, -5.4, 2.1],
+        [6.3, -13.2, -6.5, 14.3],
+        [5.6, 8.8, -6.7, -23.8],
+    ],
+    dtype=np.float64,
+)
 
-# B = np.matrix([[-14.4, 6.6, 9.4, 7.3]], dtype=np.float64).T
+B = np.matrix([[-14.4, 6.6, 9.4, 7.3]], dtype=np.float64).T
 
 
 # A = np.matrix(
@@ -48,7 +48,7 @@ B = np.matrix([[15.5, 2.5, 8.6, 12.1]], dtype=np.float64).T
 # print(algorithm.cond(A))
 # print(np.linalg.cond(A, p=float("inf")))
 
-# koef = np.matrix([[1 / 10000000000000, 1/100000000000, 1, 1]], dtype=np.float64)
+# koef = np.matrix([[1, 1, 1, 1]], dtype=np.float64)
 # for i in range(A.shape[0]):
 #     A[i, :] *= koef[0, i]
 #     B[i, :] *= koef[0, i]

Л3-В6/Программа/src/solution.py

@@ -1,3 +1,4 @@
+from typing import List, Tuple
 import algorithm
 import numpy as np
 
@@ -13,28 +14,26 @@ def iterative_method(
     alpha = np.copy(A)
     beta = np.copy(B)
 
-    for i in range(n):
-        j = algorithm.swap_max_row(alpha, i)
-
-        if alpha[i, i] == 0:
-            return None
-
-        beta[[i, j], :] = beta[[j, i], :]
+    print(alpha)
 
     swaps = []
     for i in range(n):
-        j = algorithm.swap_max_column(alpha, i)
-
-        if alpha[i, i] == 0:
+        if not _swap_rows(alpha, beta):
             return None
 
-        swaps.append((i, j))
+        success, swaps_ = _swap_columns(alpha)
+        if not success:
+            return None
+
+        swaps.extend(swaps_)
+
+        print(alpha)
+
+    print(alpha)
 
     for i in range(n):
         beta[i, 0] = beta[i, 0] / alpha[i, i]
 
-    X = np.copy(beta)
-
     for i in range(n):
         for j in range(n):
             if i == j:
@@ -44,12 +43,13 @@ def iterative_method(
 
         alpha[i, i] = 0
 
-    print(algorithm.cond(alpha))
+    print(algorithm.norm(alpha))
 
-    if algorithm.cond(alpha) >= 1.0:
+    if algorithm.norm(alpha) >= 1.0:
         return None
 
     i = 0
+    X = np.copy(beta)
     while i < max_iterations:
         i += 1
 
@@ -63,3 +63,31 @@ def iterative_method(
         X[[i, j], :] = X[[j, i], :]
 
     return X
+
+
+def _swap_rows(a: np.matrix, b: np.matrix) -> bool:
+    n = a.shape[0]
+    for i in range(n):
+        j = algorithm.swap_max_row(a, i)
+
+        if a[i, i] == 0:
+            return False
+
+        b[[i, j], :] = b[[j, i], :]
+
+    return True
+
+
+def _swap_columns(a: np.matrix) -> Tuple[bool, List[Tuple[int, int]] | None]:
+    n = a.shape[0]
+    swaps = []
+    for i in range(n):
+        j = algorithm.swap_max_column(a, i)
+
+        if a[i, i] == 0:
+            return False, None
+
+        if i != j:
+            swaps.append((i, j))
+
+    return True, swaps