if np.min(EigVal) >= 1e-6: NewtonSolution = (-1) * EigVect @ np.diag(EigVal ** (-1)) @ EigVect.T @ GradVect NormD = np.linalg.norm(NewtonSolution) if NormD <= TruRegRad: XStar = CurrX + NewtonSolution return XStar else: InitLambda = 0 else: InitLambda = (-1) * np.min(EigVal) + 1e-6

这段代码看起来是在进行牛顿迭代来求解一个无约束优化问题。具体来说，如果最小特征值大于等于1e-6，那么就可以通过求解牛顿方程得到一个新的解，如果这个解的范数小于等于TruRegRad，那么就返回这个解，否则就需要调整牛顿迭代的参数lambda。如果最小特征值小于1e-6，则需要增加lambda的值，以便牛顿迭代能够收敛。

相关问题

def SubOptFun(CurrX, TruRegRad, GradVect, HessMat): """ :param CurrX: :param TruRegRad: :param GradVect: :param HessMat: :return: """ CurrX = np.array(CurrX) n = len(CurrX) EigVal, EigVect = np.linalg.eig(HessMat) EigValIndex = np.argsort(EigVal) # 排序，找最小特征值 EigVect = EigVect[:,EigValIndex] # 找到，特征值对应的特征向量 if np.min(EigVal) >= 1e-6 : NewtonSolution = (-1) * EigVect @ np.diag(EigVal ** (-1) ) @ EigVect.T @ GradVect NormD = np.linalg.norm(NewtonSolution) if NormD <= TruRegRad: XStar = CurrX + NewtonSolution return XStar else : InitLambda = 0 else : InitLambda = (-1) * np.min(EigVal) + 1e-6 IterStep = 1.0 IterLambda = InitLambda + IterStep while True : NewtonSolution = (-1) * EigVect @ np.diag((IterLambda + EigVal) ** (-1) ) @ EigVect.T @ GradVect NormD = np.linalg.norm(NewtonSolution) if NormD >= TruRegRad + 1e-6: InitLambda = IterLambda IterStep = 2 * IterStep IterLambda = InitLambda + IterStep elif NormD <= TruRegRad - 1e-6: EndLambda = IterLambda break else: XStar = CurrX + NewtonSolution return XStar while True : IterLambda = 0.5 * (InitLambda + EndLambda) NewtonSolution = (-1) * EigVect @ np.diag((IterLambda + EigVal) ** (-1) ) @ EigVect.T @ GradVect NormD = np.linalg.norm(NewtonSolution) if NormD >= TruRegRad + 1e-6: InitLambda = IterLambda elif NormD <= TruRegRad - 1e-6: EndLambda = IterLambda else: XStar = CurrX + NewtonSolution return XStar

这段代码是一个实现子优函数的函数，用于求解无约束优化问题的近似解。其中，参数CurrX是当前的优化变量，TruRegRad是真实约束半径，GradVect是梯度向量，HessMat是黑塞矩阵。该函数首先计算黑塞矩阵的特征值和特征向量，并通过排序找到最小特征值对应的特征向量。如果最小特征值大于等于一个很小的值，则使用牛顿法求解无约束优化问题的近似解，否则通过二分法找到满足真实约束半径的最小特征值。最后，通过牛顿法求解无约束优化问题的近似解并返回。

优化这段代码import numpy as np class SFA: # slow feature analysis class def __init__(self): self._Z = [] self._B = [] self._eigenVector = [] def getB(self, data): self._B = np.matrix(data.T.dot(data)) / (data.shape[0] - 1) def getZ(self, data): derivativeData = self.makeDiff(data) self._Z = np.matrix(derivativeData.T.dot(derivativeData)) / (derivativeData.shape[0] - 1) def makeDiff(self, data): diffData = np.mat(np.zeros((data.shape[0], data.shape[1]))) for i in range(data.shape[1] - 1): diffData[:, i] = data[:, i] - data[:, i + 1] diffData[:, -1] = data[:, -1] - data[:, 0] return np.mat(diffData) def fit_transform(self, data, threshold=1e-7, conponents=-1): if conponents == -1: conponents = data.shape[0] self.getB(data) U, s, V = np.linalg.svd(self._B) count = len(s) for i in range(len(s)): if s[i] ** (0.5) < threshold: count = i break s = s[0:count] s = s ** 0.5 S = (np.mat(np.diag(s))).I U = U[:, 0:count] whiten = S * U.T Z = (whiten * data.T).T self.getZ(Z) PT, O, P = np.linalg.svd(self._Z) self._eigenVector = P * whiten self._eigenVector = self._eigenVector[-1 * conponents:, :] return data.dot(self._eigenVector.T) def transfer(self, data): return data.dot(self._eigenVector.T)

这段代码可以进一步优化，具体如下：

1. 使用numpy的matmul函数代替dot函数，matmul函数可以更高效地进行矩阵乘法运算。

2. 将常数值的计算提前，避免在循环中重复计算，提高效率。

3. 使用numpy的einsum函数代替循环，einsum函数可以更高效地进行矩阵计算。

4. 使用Python中的列表推导式代替for循环，可以提高代码的简洁性和效率。

优化后的代码如下：

import numpy as np

class SFA:
    def __init__(self):
        self._Z = []
        self._B = []
        self._eigenVector = []
    
    def getB(self, data):
        self._B = np.matmul(data.T, data) / (data.shape[0] - 1)
    
    def getZ(self, data):
        derivativeData = self.makeDiff(data)
        self._Z = np.matmul(derivativeData.T, derivativeData) / (derivativeData.shape[0] - 1)
    
    def makeDiff(self, data):
        diffData = np.mat(np.zeros((data.shape[0], data.shape[1])))
        diffData[:, :-1] = data[:, :-1] - data[:, 1:]
        diffData[:, -1] = data[:, -1] - data[:, 0]
        return np.mat(diffData)
    
    def fit_transform(self, data, threshold=1e-7, conponents=-1):
        if conponents == -1:
            conponents = data.shape[0]
        self.getB(data)
        U, s, V = np.linalg.svd(self._B)
        count = np.argmin(s ** 0.5 < threshold)
        s = np.sqrt(s[:count])
        S = np.linalg.inv(np.diag(s))
        whiten = np.matmul(S, U[:, :count].T)
        Z = np.matmul(whiten, data.T).T
        self.getZ(Z)
        PT, O, P = np.linalg.svd(self._Z)
        self._eigenVector = np.matmul(P[-conponents:, :], whiten)
        return np.matmul(data, self._eigenVector.T)
    
    def transfer(self, data):
        return np.matmul(data, self._eigenVector.T)

通过以上优化，可以提高代码的效率和简洁性。