all

89-1.py

@@ -0,0 +1,116 @@
+x = [2,4,6,8]
+y = [2,11,28,40]
+
+
+# 列主元高斯消元法
+def SovleRowMain(A,b):
+    ks = 0.00000001
+    n = len(A)
+    if len(A[0]) != n:
+        raise ValueError("A要为方阵")
+    if len(b) != n:
+        raise ValueError("b与A的行数不匹配")
+    p = list(range(n))
+    for i in range(n):
+        row_max = abs(A[i][i])
+        row_max_index = i
+        for j in range(i + 1, n):
+            if abs(A[j][i]) > row_max:
+                row_max = abs(A[j][i])
+                row_max_index = j
+        A[i], A[row_max_index] = A[row_max_index], A[i]
+        b[i], b[row_max_index] = b[row_max_index], b[i]
+        p[i], p[row_max_index] = p[row_max_index], p[i]
+
+        if abs(A[i][i]) < ks:
+            raise ValueError("A矩阵奇异，无法进行高斯消元")
+        for j in range(i + 1, n):
+            m = A[j][i] / A[i][i]
+            A[j][i] = m
+            for k in range(i + 1, n):
+                A[j][k] -= m * A[i][k]
+            b[j] -= m * b[i]
+
+    if abs(A[n - 1][n - 1]) < ks:
+        raise ValueError("A矩阵奇异，无法进行高斯消元")
+    
+    # 回代求解
+    b[n - 1] /= A[n - 1][n - 1]
+    for i in range(n - 2, -1, -1):
+        for j in range(i + 1, n):
+            b[i] -= A[i][j] * b[j]
+        b[i] /= A[i][i]
+    return b
+
+
+
+def LeastSquares(list_x,list_y,n):
+    m = len(list_x)
+    x_n = []
+    b = []
+    for i in range(2*n+1):
+        x_n.append(0)
+        b.append(0)
+        for j in range(m):
+            x_n[i]+=(list_x[j]**i)
+            b[i]+=(list_y[j]*list_x[j]**i)
+    b = b[:n+1]
+    A = []
+    for i in range(n+1):
+        tmp = []
+        for j in range(n+1):
+            tmp.append(x_n[i+j])
+        A.append(tmp)
+    return SovleRowMain(A,b)
+
+def CalculateY(list_x, coeff):
+    re = []
+    for i in range(len(list_x)):
+        re.append(0)
+        for j in range(len(coeff)):
+            re[i] += coeff[j]*list_x[i]**j
+    return re
+
+def MeanSquareErr(list_y,list_y_approx):
+    m = len(list_y)
+    err = 0
+    for i in range(m):
+        err += (list_y[i] - list_y_approx[i])**2
+    return err**0.5
+
+def MaxErr(list_y,list_y_approx):
+    m = len(list_y)
+    err = 0
+    for i in range(m):
+        if abs(list_y[i] - list_y_approx[i]) > err:
+            err = abs(list_y[i] - list_y_approx[i])
+    return err
+
+def PrintEquation(coeff):
+    n = len(coeff)
+    str_ = str(coeff[0]) + "+"
+    for i in range(0,n-1):
+        str_ += str(coeff[i+1])
+        str_ += "*x^"+str(i+1)+"+"
+    str_ = str_[0:len(str_)-1]
+    print(str_)
+
+if __name__ == "__main__":
+    print("一次拟合")
+    coeff = LeastSquares(x,y,1)
+    PrintEquation(coeff)
+    y_approx = CalculateY(x, coeff)
+    print("MeanSquareErr:")
+    print(MeanSquareErr(y,y_approx))
+    print("MaxErr:")
+    print(MaxErr(y,y_approx))
+
+    print("二次拟合")
+    coeff = LeastSquares(x,y,2)
+    PrintEquation(coeff)
+    y_approx = CalculateY(x, coeff)
+    print("MeanSquareErr:")
+    print(MeanSquareErr(y,y_approx))
+    print("MaxErr:")
+    print(MaxErr(y,y_approx))
+