20250604

2025-06-04 21:39:19 +08:00
parent 3badad06a0
commit 94c7e886bf
5 changed files with 333 additions and 0 deletions
--- a/228-12.py
+++ b/228-12.py
@@ -0,0 +1,88 @@
+def MullerSolve(fx,x0,x1,x2,err1,err2,N):
+    count = 0
+    f0 = fx(x0)
+    f1 = fx(x1)
+    f2 = fx(x2)
+    q = (x2 - x1) / (x1 - x0)
+    p = 0
+    a = 0
+    b = 0
+    c = 0
+    while True:
+        p = (x2 - x0) / (x1 - x0)
+
+        a = q**2 * f0 - q*p*f1 + q*f2
+        b = q**2 *f0 - p**2 *f1 + (p + q)*f2
+        c = p*f2
+        h1 = 0
+        
+        if  b.real < 0:
+            h1 = -2 * c / (b - (b**2 - 4*a*c)**0.5)
+        else:
+            h1 = -2 * c / (b + (b**2 - 4*a*c)**0.5)
+        x3 = x2 + h1 * (x2 - x1)
+        f3 = fx(x3)
+        k = err1 + 1
+        if abs(f3) < 1:
+            k = abs(x3 - x2)
+        else:
+            k = abs(x3 - x2) / abs(f3)
+
+        if abs(f3) < err2 or k < err1:
+            return x3, 1
+        count += 1
+        if count > N:
+            return None, 0
+        x0 = x1
+        x1 = x2
+        x2 = x3
+        f0 = f1
+        f1 = f2
+        f2 = f3
+        q = h1
+
+def Det(A):
+    if len(A) == 2:
+        return A[0][0] * A[1][1] - A[0][1] * A[1][0]
+    det = 0
+    for c in range(len(A)):
+        sub_matrix = [row[:c] + row[c+1:] for row in A[1:]]
+        det += ((-1) ** c) * A[0][c] * Det(sub_matrix)
+    return det
+
+if __name__ == "__main__":
+    A =[
+        [1,0,1],
+        [2,2,1],
+        [-1,0,0]
+    ]
+    
+    lam = []
+
+    count = 0
+    k = -100
+    fx = lambda x: Det([[A[i][j] - x * (1 if i == j else 0) for j in range(len(A))] for i in range(len(A))])
+    k = 10
+    while len(lam) < len(A):
+        for i in range(-k,k):
+            re,sta = MullerSolve(fx, i, i + 1, i + 2, 1e-10, 1e-10, 100)
+            if sta == 1:
+                a = round(re.real, 9)
+                b = round(re.imag, 9)
+                re_t = complex(a, b)
+                if re_t not in lam:
+                    if re_t.imag != 0:
+                        lam.append(re_t)
+                        lam.append(re_t.conjugate())
+                    else:
+                        lam.append(a)
+                if len(lam) == len(A):
+                    break
+        k *= 10
+    p = abs(lam[0])
+    for i in range(len(lam)):
+        print(f"λ{i+1} = {lam[i]}")
+        if abs(lam[i]) > p:
+            p = abs(lam[i])
+    
+    print(f"谱半径 = {p:.3f}")