Warning: convergence tolerance of 1.000000e-06 not reached

时间: 2024-06-05 17:06:45 浏览: 1123
This warning message usually appears in numerical optimization or iterative methods when the desired level of accuracy or convergence has not been achieved. It means that the optimization algorithm or iterative method did not converge to the desired solution within the specified tolerance level. To address this warning, one can try the following: 1. Increase the convergence tolerance level to allow for more iterations and a higher degree of accuracy. 2. Use a different optimization algorithm or iterative method that is better suited for the specific problem. 3. Check the inputs and parameters of the optimization problem to ensure they are correct and appropriate. 4. Use a different initial guess or starting point for the optimization algorithm. 5. Check for any errors or bugs in the code that may be causing the convergence issue. It is important to note that this warning does not necessarily mean that the solution obtained is incorrect or unusable. However, it is always a good practice to investigate the reasons for the warning and ensure that the optimization results are reliable and accurate.
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1. 修改模型参数初始值：可以尝试修改模型参数的初始值，重新运行模型拟合，看是否可以收敛。可以通过多次尝试来找到合适的初始值。 2. 修改模型类型：如果模型无法很好地拟合数据，可以尝试使用其他模型类型进行...

import numpy as np def sigmoid(z): return 1 / (1 + np.exp(-z)) def cost_function(theta, X, y): m = len(y) h = sigmoid(X @ theta) J = -(1/m) * (y.T @ np.log(h) + (1-y).T @ np.log(1-h)) grad = (1/m) * X.T @ (h - y) return J, grad def trust_region_newton_method(X, y, max_iter=100, eta=0.05, delta=0.1): n = X.shape[1] theta = np.zeros((n,1)) J, grad = cost_function(theta, X, y) H = np.eye(n) for i in range(max_iter): # solve trust region subproblem p = np.linalg.solve(H, -grad) if np.linalg.norm(p) <= delta: d = p else: d = delta * p / np.linalg.norm(p) # compute actual reduction and predicted reduction J_new, grad_new = cost_function(theta+d, X, y) actual_reduction = J - J_new predicted_reduction = -grad.T @ d - 0.5 * d.T @ H @ d # update trust region radius rho = actual_reduction / predicted_reduction if rho < 0.25: delta = 0.25 elif rho > 0.75 and np.abs(np.linalg.norm(d) - delta) < 1e-8: delta = min(2delta, eta*np.linalg.norm(theta)) # update parameters if rho > 0: theta += d J, grad = J_new, grad_new H += (grad_new - grad) @ (grad_new - grad).T / ((grad_new - grad).T @ d) # check convergence if np.linalg.norm(grad) < 1e-5: break return theta ——修正代码中的问题，实现信赖域算法求解逻辑回归问题

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% Define the input matrices A_matrix and B A = [0 0 -1 3 -1 0; 0 1/2 0 -1 3 -1; 1/2 0 0 0 -1 3; 3 -1 0 0 0 1.2; -1 3 -1 0 1/2 0; 0 -1 3 -1 0 0]; B = [1; 3/2; 5/2; 5/2; 3/2; 1]; % Define the Gauss-Seidel function function [X] = GaussSeidel(A, b, tol, max_iter) % Get the dimensions of A and initialize the output vector [n, ~] = size(A); X = zeros(n, 1); X_new = X; tolerance = 1e-3; max_iterations = 1000; X1 = GaussSeidel(A_matrix, B, tolerance, max_iterations); disp(X1); % Iterate through the Gauss-Seidel method for iter = 1:max_iter for i = 1:n X_new(i) = (b(i) - A(i, 1:i-1) * X_new(1:i-1) - A(i, i+1:end) * X(i+1:end)) / A(i, i); end % Check for convergence if norm(X_new - X) < tol break; end % Update the approximation X = X_new; tolerance = 1e-3; max_iterations = 1000; X1 = GaussSeidel(A_matrix, B, tolerance, max_iterations); disp(X1); end end % Set the tolerance and maximum number of iterations; % Call the Gauss-Seidel function with the input matrices and parameters % Display the output

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解释这段代码：function [S, Sigma, obj] = graph_minmax(KH, option) num = size(KH, 1); numker = size(KH, 3); %-------------------------------------------------------------------------------- % Options used in subroutines %-------------------------------------------------------------------------------- if ~isfield(option,'goldensearch_deltmax') option.goldensearch_deltmax=5e-2; end if ~isfield(option,'goldensearchmax') optiongoldensearchmax=1e-8; end if ~isfield(option,'firstbasevariable') option.firstbasevariable='first'; end nloop = 1; loop = 1; goldensearch_deltmaxinit = option.goldensearch_deltmax; %% initialization Sigma = ones(numker,1); Sigma = Sigma / sum(Sigma); A_gamma = sumKbeta(KH, Sigma.^2); [S, obj1] = solve_S(A_gamma); [grad] = graphGrad(KH, S, Sigma); obj(nloop) = obj1; Sigmaold = Sigma; %------------------------------------------------------------------------------% % Update Main loop %------------------------------------------------------------------------------% while loop nloop = nloop+1; [Sigma,S,obj(nloop)] = graphupdate(KH,Sigmaold,grad,obj(nloop-1),option); if max(abs(Sigma-Sigmaold))<option.numericalprecision &&... option.goldensearch_deltmax > optiongoldensearchmax option.goldensearch_deltmax=option.goldensearch_deltmax/10; elseif option.goldensearch_deltmax~=goldensearch_deltmaxinit option.goldensearch_deltmax*10; end [grad] = graphGrad(KH, S, Sigma); %---------------------------------------------------- % check variation of Sigma conditions %---------------------------------------------------- if max(abs(Sigma-Sigmaold))<option.seuildiffsigma loop = 0; fprintf(1,'variation convergence criteria reached \n'); end %----------------------------------------------------- % Updating Variables %---------------------------------------------------- Sigmaold = Sigma; end end

1. 初始化Sigma为一个元素均为1的向量，并进行归一化操作。 2. 根据当前的Sigma计算出相应的Kbeta矩阵。 3. 求解二次规划问题，得到划分矩阵S。 4. 计算梯度grad。 5. 迭代更新Sigma和S，直到满足收敛条件。 ...

def gradient_descent(W, eta=0.001, tolerance=0.000001): # Variable to store the W value before update. # This will help to check for convergence. W_prev = 0 # t is an iteration counter to compute the number of steps t = 0 # Save the current weights to a new list and # append the updated weights in each iteration to the same Ws = [W] # Perform the update until convergence # Convergence is said to have taken place if # the absolute difference between the previous and # updated weight is less than the tolerance while ():空格里面应该填啥

while (np.abs(Ws[-1] - W_prev) > tolerance): 这个条件检查前一次更新的权重与当前更新的权重之间的绝对差是否大于给定的容差。如果是，则继续进行更新；如果不是，则认为已经达到了收敛状态，循环结束。

import numpy as npdef sigmoid(z): return 1 / (1 + np.exp(-z))def cost_function(theta, X, y): m = len(y) h = sigmoid(X @ theta) J = -(1/m) * (y.T @ np.log(h) + (1-y).T @ np.log(1-h)) grad = (1/m) * X.T @ (h - y) return J, graddef trust_region_newton_method(X, y, max_iter=100, eta=0.05, delta=0.1): n = X.shape[1] theta = np.zeros((n,1)) J, grad = cost_function(theta, X, y) H = np.eye(n) for i in range(max_iter): # solve trust region subproblem p = np.linalg.solve(H, -grad) if np.linalg.norm(p) <= delta: d = p else: d = delta * p / np.linalg.norm(p) # compute actual reduction and predicted reduction J_new, grad_new = cost_function(theta+d, X, y) actual_reduction = J - J_new predicted_reduction = -grad.T @ d - 0.5 * d.T @ H @ d # update trust region radius rho = actual_reduction / predicted_reduction if rho < 0.25: delta *= 0.25 elif rho > 0.75 and np.abs(np.linalg.norm(d) - delta) < 1e-8: delta = min(2*delta, eta*np.linalg.norm(theta)) # update parameters if rho > 0: theta += d J, grad = J_new, grad_new H += (grad_new - grad) @ (grad_new - grad).T / ((grad_new - grad).T @ d) # check convergence if np.linalg.norm(grad) < 1e-5: break return theta——为什么这个代码运行了没有结果出来

X = np.array([[1, 2], [1, 3], [1, 4], [1, 5]]) y = np.array([[0], [0], [1], [1]]) theta = trust_region_newton_method(X, y) print(theta) 这里的 X 和 y 是输入数据，你需要根据具体问题来设置这些...

Continue to refine the following code and don't add any other packages but numpy: def mean_shift2(xs: np.ndarray, num_iter: int = 50, k_type: str = 'rbf', bandwidth: float = 0.1) -> np.ndarray: """ Implement a variant of mean-shift algorithm, with unchanged kernel matrix :param xs: a set of samples with size (N, D), where N is the number of samples, D is the dimension of features :param num_iter: the number of iterations :param k_type: the type of kernels, including 'rbf', 'gate', 'triangle', 'linear' :param bandwidth: the hyperparameter controlling the width of rbf/gate/triangle kernels :return: the estimated means with size (N, D) """ # TODO: change the code below and implement the modified mean-shift return xs

Here is a possible implementation of the modified mean-shift algorithm: def mean_shift2(xs: np.ndarray, num_iter: int = 50, k_type: str = 'rbf', bandwidth: float = 0.1) -> np.ndarray: ""...

How to prove the cauchy principle of convergence

Proof of 1: Let {an} be a convergent sequence. Then there exists a limit L such that for any ε > 0, there exists an N such that for all n > N, |an - L| ε. Now let ε > 0 be arbitrary. We want to ...

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