python SciPy官方文件: Optimization and root finding
python scipy拟合优化常见方法
局部优化
- optimize.minimize:函数最小值
全局优化
- differential_evolution
- optimize.basinhopping：
最小二乘及拟合
- least_squares：非线性最小二乘法
- curve_fit：拟合
求根
- root
Legacy functions
- The functions below are not recommended for use in new scripts; all of these methods are accessible via a newer, more consistent interfaces.详见官方文件。
- fsolve：非线性方程求解
- leastsq:
fsolve: 非线性方程组求解
-
局部最优，初值x0怼结果影响很大
optimize.minimize：函数最小值
optimize.basinhoppin：全局寻优
最小二乘法
最小二乘法求解方程组
方程组形式
- A*x=b
- A写入excel文件的sheet1，第一行为变量名
- b写入excel文件的sheet2，第一行为因变量名
- x的初值x0写入excel文件的sheet3，第一行为说明
代码
dataAnalysis_v5.py原代码见下，将dataTest_Table3.xlsx作为第一参数传给dataAnalysis_v5.py即可（若将dataAnalysis_v5.py转换成exe文件则可直接将excel文件拖到exe文件上执行）。
import sys
import pandas as pd
import numpy as np
from sklearn.metrics import r2_score
from scipy.optimize import least_squares
def process_excel(file_path):
try:
# Load data from Excel
df_A = pd.read_excel(file_path, sheet_name='Sheet1')
df_b = pd.read_excel(file_path, sheet_name='Sheet2')
df_x0 = pd.read_excel(file_path, sheet_name='Sheet3')
# Convert dataframes to numpy arrays
A = df_A.values # Assuming A is your independent variables matrix
b = df_b.values.flatten() # Assuming b is your dependent variable vector and flatten it to 1D array
x0 = df_x0.values.flatten() # Assuming x0 is your initial guess for the solution and flatten it to 1D array
# Define the objective function for least squares
def objective_function(x, A, b):
return np.dot(A, x) - b
# Set bounds to ensure x >= 0
bounds = (0, np.inf)
# Use least_squares to solve the problem with non-negative constraints
result = least_squares(objective_function, x0, args=(A, b), bounds=bounds)
# Extract the solution (x)
x = result.x
# Calculate the new dependent variable values using the obtained x
b_calculated = np.dot(A, x)
# Calculate R2 value
r2 = r2_score(b, b_calculated)
# Print the original and calculated dependent variable values (for debugging)
print("Original dependent variable values (b):\n", b)
print("\nCalculated dependent variable values (Ax):\n", b_calculated)
# Print the solution (x) and R2 score (for debugging)
print("\nSolution (x):\n", x)
print("\nR2 Score:", r2)
# Save results to an Excel file (for debugging)
results_df = pd.DataFrame({
'Original b': b.flatten(),
'Calculated b': b_calculated.flatten()
})
# Create ExcelWriter object
with pd.ExcelWriter(file_path + '_results.xlsx') as writer:
# Write results_df to Sheet1
results_df.to_excel(writer, sheet_name='Sheet1-Obs-Calc', index=False)
# Create DataFrame for x and save to Sheet2
x_df = pd.DataFrame({'Solution (x)': x.flatten()})
x_df.to_excel(writer, sheet_name='Sheet2-x', index=False)
# Create DataFrame for r2 and save to Sheet3
r2_df = pd.DataFrame({'R2 Score': [r2]})
r2_df.to_excel(writer, sheet_name='Sheet3-R2', index=False)
# Return the result or any useful information
return f"Processed {file_path} successfully. Generated {file_path}_results.xlsx"
except Exception as e:
return f"Error processing {file_path}: {str(e)}"
if __name__ == "__main__":
file_path = sys.argv[1]
result = process_excel(file_path)
print(result)
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