AAAAAA

Л2-В6/Программа/requirements.txt

@@ -2,4 +2,4 @@ sympy
 numpy
 matplotlib
 pyqt6
-scipy
+scipy

Л3-В6/Программа/requirements.txt

@@ -1,3 +1,4 @@
 sympy
 numpy
-scipy
+scipy
+pyqt6

Л3-В6/Программа/src/algorithm.py

@@ -0,0 +1,100 @@
+from typing import List, Tuple
+import numpy as np
+
+
+def det(matrix: np.matrix):
+    if matrix.shape[0] != matrix.shape[1]:
+        return None
+    if matrix.shape[0] == 1:
+        return matrix[0, 0]
+
+    return _det(matrix)
+
+
+def _det(matrix: np.matrix):
+    matrix, swaps = triangle(np.copy(matrix))
+    if matrix is None:
+        return 0.0
+
+    n = matrix.shape[0]
+    determinant = (-1) ** swaps
+    for i in range(n):
+        determinant *= matrix[i, i]
+
+    return determinant
+
+
+def triangle(matrix: np.matrix):
+    swaps = 0
+    n = matrix.shape[0]
+
+    for i in range(n):
+        if matrix[i, i] == 0:
+            if not swap_first_non_zero(matrix, i)[0]:
+                return None, swaps
+            swaps += 1
+
+        for j in range(i + 1, n):
+            matrix[j, :] = matrix[j, :] - matrix[i, :] * (matrix[j, i] / matrix[i, i])
+
+    return matrix, swaps
+
+
+def swap_first_non_zero(matrix, i):
+    n = matrix.shape[0]
+    for j in range(i, n):
+        if matrix[j, i] != 0:
+            if i != j:
+                matrix[[i, j], :] = matrix[[j, i], :]
+            return True, j
+    return False, -1
+
+
+def swap_max_row(matrix, i):
+    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], :]
+
+    return max_j
+
+
+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]]
+
+    return max_j
+
+
+def norm(matrix: np.matrix):
+    n = matrix.shape[0]
+    m = matrix.shape[1]
+
+    m_norm = float("-inf")
+    for i in range(n):
+        s = 0.0
+        for j in range(m):
+            s += abs(matrix[i, j])
+
+        if s > m_norm:
+            m_norm = s
+
+    return m_norm
+
+
+def cond(matrix: np.matrix):
+    return norm(matrix) * norm(np.linalg.inv(matrix))

Л3-В6/Программа/src/main.py

@@ -1,68 +1,63 @@
 import numpy as np
 
-
+import solution
-def det(matrix: np.matrix):
-    if matrix.shape[0] != matrix.shape[1]:
-        return None
-    if matrix.shape[0] == 1:
-        return matrix[0, 0]
-
-    return _det(matrix)
-
-
-def _det(matrix: np.matrix):
-    matrix, swaps = triangle(np.copy(matrix))
-    if matrix is None:
-        return 0.0
-
-    n = matrix.shape[0]
-    determinant = (-1) ** swaps
-    for i in range(n):
-        determinant *= matrix[i, i]
-
-    return determinant
-
-
-def triangle(matrix: np.matrix):
-    swaps = 0
-    n = matrix.shape[0]
-
-    for i in range(n):
-        if matrix[i, i] == 0:
-            if not swap_first_non_zero(matrix, i):
-                return None, swaps
-            swaps += 1
-
-        for j in range(i + 1, n):
-            matrix[j, :] = matrix[j, :] - matrix[i, :] * (matrix[j, i] / matrix[i, i])
-
-    return matrix, swaps
-
-
-def swap_first_non_zero(matrix, i):
-    n = matrix.shape[0]
-    for j in range(i + 1, n):
-        if matrix[j, i] != 0:
-            matrix[[i, j], :] = matrix[[j, i], :]
-            return True
-    return False
-
 
 A = np.matrix(
     [
         [4.3, -12.1, 23.2, -14.1],
         [2.4, -4.4, 3.5, 5.5],
-        [5.4, 8.3, -7.4, 12.7],
+        [5.4, 8.3, -7.4, -12.7],
         [6.3, -7.6, 1.34, 3.7],
     ],
     dtype=np.float64,
 )
 
-print(det(A))
+B = np.matrix([[15.5, 2.5, 8.6, 12.1]], dtype=np.float64).T
-print(np.linalg.det(A))
 
-print(A)
+# 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
 
-# X = np.linalg.inv(A) * B
+
+# A = np.matrix(
+#     [
+#         [-1, 11, -1, 3],
+#         [10, -1, 2, 0],
+#         [2, -1, 10, -1],
+#         [0, 3, -1, 8],
+#     ],
+#     dtype=np.float64,
+# )
+
+# B = np.matrix([[25, 6, -11, 15]], dtype=np.float64).T
+
+# print(algorithm.det(A))
+# print(np.linalg.det(A))
+
+# print(algorithm.norm(A))
+# print(np.linalg.norm(A, ord=float("inf")))
+
+# print(algorithm.cond(A))
+# print(np.linalg.cond(A, p=float("inf")))
+
+# koef = np.matrix([[1 / 10000000000000, 1/100000000000, 1, 1]], dtype=np.float64)
+# for i in range(A.shape[0]):
+#     A[i, :] *= koef[0, i]
+#     B[i, :] *= koef[0, i]
+
+# print(A)
+# print(algorithm.cond(A))
+# print(B)
+
+X = np.linalg.inv(A) * B
+
+print(solution.iterative_method(A, B))
+print(X)

Л3-В6/Программа/src/solution.py

@@ -0,0 +1,65 @@
+import algorithm
+import numpy as np
+
+
+def iterative_method(
+    A: np.matrix, B: np.matrix, eps: float = 0.0001, max_iterations: int = 10000
+) -> np.matrix:
+    if A.shape[0] != A.shape[1] or A.shape[0] != B.shape[0] or B.shape[1] != 1:
+        return None
+
+    n = A.shape[0]
+
+    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], :]
+
+    swaps = []
+    for i in range(n):
+        j = algorithm.swap_max_column(alpha, i)
+
+        if alpha[i, i] == 0:
+            return None
+
+        swaps.append((i, j))
+
+    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:
+                continue
+
+            alpha[i, j] = -(alpha[i, j] / alpha[i, i])
+
+        alpha[i, i] = 0
+
+    print(algorithm.cond(alpha))
+
+    if algorithm.cond(alpha) >= 1.0:
+        return None
+
+    i = 0
+    while i < max_iterations:
+        i += 1
+
+        X_old = np.copy(X)
+        X = np.add(np.matmul(alpha, X), beta)
+
+        if np.sum(np.abs(X - X_old)) < eps:
+            break
+
+    for i, j in swaps:
+        X[[i, j], :] = X[[j, i], :]
+
+    return X