111

69-5 - 副本.py

@@ -1,92 +0,0 @@
-x = [0,1,2,3]
-y = [0,0,0,0]
-
-def ZGsolve(A,b):
-    n = len(b)
-    beta = [0]*n
-    for i in range(n):
-        if i == 0:
-            beta[i] = A[i][2] / A[i][1]
-        else:
-            beta[i] = A[i][2] / (A[i][1] - A[i][0]*beta[i-1])
-
-    for i in range(n):
-        if i == 0:
-            b[i] = b[i] / A[i][1]
-        else:
-            b[i] = (b[i] - A[i][0]*b[i-1]) / (A[i][1] - A[i][0]*beta[i-1])
-
-    for i in range(n-2,-1,-1):
-        b[i] = b[i] - beta[i]*b[i+1]
-
-    return b
-
-
-def GetDList(list_r):
-    result = []
-    for i in range(1,len(list_r)):
-        result.append(list_r[i] - list_r[i-1])
-    return result
-
-def GetDQList(list_x, list_y):
-    result = []
-    for i in range(1,len(list_y)):
-        result.append((list_y[i] - list_y[i-1]) / (list_x[i] - list_x[i-1]))
-    return result
-
-def CubicSplineInterpolation(list_x,list_y,boundary_type,a1,a2):
-    list_h = GetDList(list_x)
-    list_dqxy = GetDQList(list_x, list_y)
-    list_mu = [list_h[i]/(list_h[i]+list_h[i+1]) for i in range(len(list_h)-1)]
-    list_lamda = [1-i for i in list_mu]
-    list_g = [6*(list_dqxy[i+1]-list_dqxy[i])/(list_h[i+1]+list_h[i]) for i in range(len(list_h)-1)]
-
-    A = []
-    b = []
-    if boundary_type == 0:  # 自然边界条件
-        pass
-    elif boundary_type == 1:  # 一阶导数边界条件
-        A.append([0,2,1])
-        b.append(6/list_h[0]*(list_dqxy[1]-a1))
-        for i in range(len(list_g)):
-            A.append([list_mu[i],2,list_lamda[i]])
-            b.append(list_g[i])
-        A.append([1,2,0])
-        b.append(6/list_h[-1]*(a2-list_dqxy[-1]))
-        M = ZGsolve(A,b)
-
-    elif boundary_type == 2:  # 二阶导数边界条件
-        A.append([0,2,list_lamda[0]])
-        b.append(list_g[0]-list_mu[0]*a1)
-        for i in range(1,len(list_g)-1):
-            A.append([list_mu[i],2,list_lamda[i]])
-            b.append(list_g[i])
-        A.append([list_mu[-1],2,0])
-        b.append(list_g[-1]-list_lamda[-1]*a2)
-        M = ZGsolve(A,b)
-        M = [a1] + M + [a2]
-
-    return M,list_h
-
-
-if __name__ == "__main__":
-    M,list_h = CubicSplineInterpolation(x,y,2,1,0)
-
-    print("list_h:",list_h)
-    print("M:",M)
-    for i in range(3):
-        k1 = (M[i+1]-M[i])/6/list_h[i]
-        k2 = (M[i]*x[i+1]-M[i+1]*x[i])/2/list_h[i]
-        k3 = (3*M[i+1]*x[i]**2-3*M[i]*x[i+1]**2-6*y[i]+M[i]*list_h[i]**2+6*y[i+1]-M[i+1]*list_h[i]**2)/6/list_h[i]
-        k4 = (M[i]*x[i+1]**3-M[i+1]*x[i]**3+6*y[i]*x[i+1]-M[i]*list_h[i]**2*x[i+1]-6*y[i+1]*x[i]+M[i+1]*list_h[i]**2*x[i])/6/list_h[i]
-        # print(k1,k2,k3,k4)
-        print("S(x)=%.10f*x^3+%.10f*x^2+%.10f*x+%.10f"%(k1,k2,k3,k4))
-
-
-
-
-
-    
-
-
-

89-1 - 副本.py

@@ -1,116 +0,0 @@
-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))
-    

89-2 - 副本.py

@@ -1,76 +0,0 @@
-import math
-
-x = [1,2,4,8,16,32,64]
-y = [4.22,4.02,3.85,3.59,3.44,3.02,2.59]
-
-
-# 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)
-
-if __name__ == "__main__":
-    # 取对数 ln(W) = ln(C)+lamda*ln(t)
-    ln_W = [math.log(i) for i in y]
-    ln_t = [math.log(i) for i in x]
-    coeff = LeastSquares(ln_t,ln_W,1)
-    C = math.exp(coeff[0])
-    lamda = coeff[1]
-    print("C:", C)
-    print("lamda:", lamda)

89-3 - 副本.py

@@ -1,69 +0,0 @@
-
-x = [19,25,31,38,44]
-y = [19.0,32.3,49.0,73.3,97.8]
-
-# 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)
-
-if __name__ == "__main__":
-    x_square = [i**2 for i in x]
-    coeff = LeastSquares(x_square, y, 1)
-    print("拟合方程: y = %.6f + %.6f*x^2" % (coeff[0], coeff[1]))