@@ -1,15 +0,0 @@
|
||||
def trapezoidal_discrete(x, y):
|
||||
"""
|
||||
离散数据点的梯形积分法
|
||||
参数：
|
||||
x: 自变量数组（需单调递增）
|
||||
y: 函数值数组
|
||||
返回：积分近似值
|
||||
"""
|
||||
if len(x) != len(y):
|
||||
raise ValueError("x和y数组长度必须相同")
|
||||
integral = 0.0
|
||||
for i in range(1, len(x)):
|
||||
dx = x[i] - x[i-1]
|
||||
integral += 0.5 * (y[i] + y[i-1]) * dx
|
||||
return integral
|
||||
@@ -1,6 +0,0 @@
|
||||
#对数据做微分操作
|
||||
import torch
|
||||
x = torch.tensor(2.0, requires_grad=True)
|
||||
y = x**2 + 3*x + 1
|
||||
y.backward() # 自动计算梯度
|
||||
print(x.grad) # 输出导数结果
|
||||
@@ -1,29 +0,0 @@
|
||||
import torch
|
||||
import torch.fft
|
||||
#滤波算法
|
||||
|
||||
def fft_filter(input, threshold=0.1):
|
||||
fft_data = torch.fft.fft2(input) # 二维傅里叶变换
|
||||
fft_shift = torch.fft.fftshift(fft_data) # 频谱中心化
|
||||
mask = torch.abs(fft_shift) > threshold # 高频阈值过滤
|
||||
fft_shift *= mask.float()
|
||||
return torch.fft.ifft2(torch.fft.ifftshift(fft_shift)).real
|
||||
|
||||
def gaussian_kernel(size=3, sigma=1.0):
|
||||
kernel = torch.exp(-(torch.arange(size).float()-size//2))
|
||||
kernel = kernel.outer(kernel) # 生成二维核
|
||||
return kernel / kernel.sum()
|
||||
|
||||
def spatial_gaussian_filter(input, kernel_size=3):
|
||||
kernel = gaussian_kernel(kernel_size).to(input.device)
|
||||
return torch.nn.functional.conv2d(
|
||||
input,
|
||||
kernel.view(1, 1, kernel_size, kernel_size),
|
||||
padding=kernel_size//2
|
||||
)
|
||||
|
||||
def median_filter(input, kernel_size=3):
|
||||
pad = kernel_size // 2
|
||||
padded = torch.nn.functional.pad(input, (pad, pad, pad, pad), mode='reflect')
|
||||
unfolded = padded.unfold(2, kernel_size, 1).unfold(3, kernel_size, 1)
|
||||
return unfolded.contiguous().view(*input.shape[:2], -1, kernel_size**2).median(dim=-1)[0]
|
||||
@@ -1,47 +0,0 @@
|
||||
import torch
|
||||
import torch.nn.functional as F
|
||||
import matplotlib.pyplot as plt
|
||||
import numpy as np
|
||||
|
||||
# 1. 一维线性插值示例
|
||||
x_original = torch.linspace(0, 10, 5)
|
||||
y_original = torch.sin(x_original)
|
||||
x_new = torch.linspace(0, 10, 50)
|
||||
y_interp = F.interpolate(
|
||||
y_original.view(1, 1, -1),
|
||||
size=x_new.numel(),
|
||||
mode='linear',
|
||||
align_corners=True
|
||||
).squeeze()
|
||||
|
||||
# 2. 二维双线性插值示例
|
||||
grid_original = torch.rand(1, 1, 5, 5) # 5x5随机矩阵
|
||||
grid_interp = F.interpolate(
|
||||
grid_original,
|
||||
size=(20, 20),
|
||||
mode='bilinear',
|
||||
align_corners=True
|
||||
).squeeze()
|
||||
|
||||
# 可视化
|
||||
plt.figure(figsize=(12, 6))
|
||||
|
||||
# 一维插值对比
|
||||
plt.subplot(1, 2, 1)
|
||||
plt.plot(x_original.numpy(), y_original.numpy(), 'ro-', label='Original')
|
||||
plt.plot(x_new.numpy(), y_interp.numpy(), 'b-', alpha=0.7, label='Interpolated')
|
||||
plt.title('1D Linear Interpolation')
|
||||
plt.legend()
|
||||
|
||||
# 二维插值对比
|
||||
plt.subplot(1, 2, 2)
|
||||
plt.imshow(grid_original.squeeze(), cmap='viridis', extent=[0, 1, 0, 1], interpolation='none')
|
||||
plt.title('Original 5x5')
|
||||
plt.colorbar()
|
||||
plt.tight_layout()
|
||||
|
||||
plt.figure()
|
||||
plt.imshow(grid_interp.numpy(), cmap='viridis', extent=[0, 1, 0, 1])
|
||||
plt.title('Interpolated 20x20')
|
||||
plt.colorbar()
|
||||
plt.show()
|
||||
@@ -1,66 +0,0 @@
|
||||
import torch
|
||||
import torch.nn as nn
|
||||
|
||||
#数据归一化工具类
|
||||
class Normalizer:
|
||||
def __init__(self, method='minmax'):
|
||||
self.method = method
|
||||
self.params = {}
|
||||
|
||||
def fit(self, data):
|
||||
"""计算归一化参数"""
|
||||
if self.method == 'minmax':#Min-Max等区间缩放法
|
||||
self.params['min'] = data.min(dim=0)[0]
|
||||
self.params['max'] = data.max(dim=0)[0]
|
||||
self.params['mean'] = data.mean(dim=0)
|
||||
elif self.method == 'zscore': #Z-score等方差缩放法，用于数据标准化，数据特征：数据分布未知、存在异常值、模型依赖梯度下降
|
||||
self.params['mean'] = data.mean(dim=0)
|
||||
self.params['std'] = data.std(dim=0)
|
||||
elif self.method == 'decimal':#小数定标标准化，与min-max比，保持原始数据分布形态，区间≈[-1,1]
|
||||
self.params['max_abs'] = data.abs().max(dim=0)[0]
|
||||
return self
|
||||
|
||||
def load_params(self,method = "minmax",min_in = 0,max_in = 0,mean_in =0,std=0,max_abs=0):
|
||||
self.method = method
|
||||
self.params['min'] = min_in
|
||||
self.params['max'] = max_in
|
||||
self.params['mean'] = mean_in
|
||||
self.params['std'] = std
|
||||
self.params['max_abs'] = max_abs
|
||||
|
||||
def transform(self, data):
|
||||
"""应用归一化"""
|
||||
if self.method == 'minmax':
|
||||
return (data - self.params['min']) / (self.params['max'] - self.params['min'] + 1e-8)
|
||||
elif self.method == 'zscore':
|
||||
return (data - self.params['mean']) / (self.params['std'] + 1e-8)
|
||||
elif self.method == 'decimal':
|
||||
return data / (10 ** torch.ceil(torch.log10(self.params['max_abs'])))
|
||||
return data
|
||||
|
||||
def inverse_transform(self, data):
|
||||
"""逆归一化"""
|
||||
if self.method == 'minmax':
|
||||
return data * (self.params['max'] - self.params['min']) + self.params['min']
|
||||
elif self.method == 'zscore':
|
||||
return data * self.params['std'] + self.params['mean']
|
||||
elif self.method == 'decimal':
|
||||
return data * (10 ** torch.ceil(torch.log10(self.params['max_abs'])))
|
||||
return data
|
||||
|
||||
|
||||
# 示例用法
|
||||
if __name__ == '__main__':
|
||||
data = torch.randn(100, 3) * 5 + 2 # 模拟数据
|
||||
|
||||
# 初始化归一化器
|
||||
normalizer = Normalizer(method='zscore')
|
||||
normalizer.fit(data)
|
||||
|
||||
# 归一化转换
|
||||
normalized_data = normalizer.transform(data)
|
||||
print(f"归一化后数据范围: {normalized_data.min():.2f} ~ {normalized_data.max():.2f}")
|
||||
|
||||
# 逆归一化
|
||||
original_data = normalizer.inverse_transform(normalized_data)
|
||||
print(f"数据还原误差: {torch.abs(data - original_data).max():.4f}")
|
||||
@@ -1,20 +0,0 @@
|
||||
import numpy as np
|
||||
import torch
|
||||
from scipy.interpolate import RBFInterpolator
|
||||
|
||||
#径向基函数法RBF插值算法
|
||||
X_train = torch.rand(100, 2) # 100个2D训练点
|
||||
y_train = torch.sin(X_train[:,0] * 2 * np.pi) # 目标函数
|
||||
X_test = torch.rand(50, 2) # 50个测试点
|
||||
|
||||
# 初始化插值器
|
||||
rbf = RBFInterpolator(kernel='gaussian', epsilon=0.1)
|
||||
|
||||
# GPU加速（可选）
|
||||
if torch.cuda.is_available():
|
||||
X_train, y_train, X_test = X_train.cuda(), y_train.cuda(), X_test.cuda()
|
||||
rbf = rbf.cuda()
|
||||
|
||||
# 执行插值
|
||||
preds = rbf(X_train, y_train, X_test)
|
||||
print(preds.shape) # 应输出torch.Size([50])
|
||||
@@ -1,28 +0,0 @@
|
||||
import torch
|
||||
#前提
|
||||
#系数选择：L1/L2系数通常取0.001-0.1，需通过验证集调整
|
||||
#L1正则化
|
||||
def l1_regularization(model, lambda_l1):
|
||||
l1_loss = 0.
|
||||
for param in model.parameters():
|
||||
l1_loss += torch.norm(param, p=1)
|
||||
return lambda_l1 * l1_loss
|
||||
# 训练循环示例
|
||||
# for epoch in range(epochs):
|
||||
# loss = criterion(outputs, labels) + l1_regularization(model, 0.001)
|
||||
|
||||
#L2正则化使用样例，pytorch内置L2正则化
|
||||
# import torch.optim as optim
|
||||
#
|
||||
# # 定义模型
|
||||
# model = YourModel()
|
||||
# # 设置weight_decay即为L2正则化系数（推荐0.01-0.001）
|
||||
# optimizer = optim.Adam(model.parameters(), lr=0.001, weight_decay=0.01)
|
||||
|
||||
#混合L1+L2正则化
|
||||
def elastic_regularization(model, lambda_l1, lambda_l2):
|
||||
l1, l2 = 0., 0.
|
||||
for param in model.parameters():
|
||||
l1 += torch.norm(param, p=1)
|
||||
l2 += torch.norm(param, p=2)
|
||||
return lambda_l1*l1 + lambda_l2*l2
|
||||
Reference in New Issue
Block a user