如何捕获 scipy.sparse.linalg.spsolve() 的异常（Windows 致命异常：访问冲突）

Question

我正在使用 scipy.sparse.linalg.spsolve() 来求解循环中的一组线性方程，其中方程根据先前的解进行迭代更新。有时，我最终会遇到奇异矩阵问题，在尝试再次求解之前，我会使用 try- except 在对角线上添加项（吉洪诺夫正则化）。这似乎适用于有关奇异矩阵的警告，但现在我遇到了另一个问题，它以我无法用 try- except 捕获的方式崩溃。该消息如下，我用“...”替换了系统上的实际名称和路径：

Windows fatal exception: access violation


Main thread:
Current thread 0x00000270 (most recent call first):
  File "...\lib\site-packages\scipy\sparse\linalg\dsolve\linsolve.py", line 203 in spsolve
  File "...\curvefit.py", line 401 in solve_linear_system_with_regularization
  File "...\curvefit.py", line 320 in smoothing_spline
  File "...\curvefit.py", line 580 in run_curvefit
  File "...\fitSplinesShapeConstraints.py", line 53 in fitSplinesShapeConstraints
  File "...\main.py", line 107 in <module>
  File "C:\Users\...\AppData\Local\anaconda3\envs\...\lib\site-packages\spyder_kernels\py3compat.py", line 356 in compat_exec
  File "C:\Users\...\AppData\Local\anaconda3\envs\...\lib\site-packages\spyder_kernels\customize\spydercustomize.py", line 473 in exec_code
  File "C:\Users\...\AppData\Local\anaconda3\envs\...\lib\site-packages\spyder_kernels\customize\spydercustomize.py", line 615 in _exec_file
  File "C:\Users\...\AppData\Local\anaconda3\envs\...\lib\site-packages\spyder_kernels\customize\spydercustomize.py", line 528 in runfile
  File "C:\Users\...\AppData\Local\Temp\ipykernel_25612\3794581249.py", line 1 in <module>


Restarting kernel...

我的代码如下所示：

import numpy as np
import scipy.sparse as sp
import scipy.sparse.linalg as la
#from scipy.linalg import LinAlgError
from scipy.optimize import minimize_scalar
from scipy.sparse import identity
import scipy.sparse
from scipy.sparse.linalg.dsolve.linsolve import MatrixRankWarning  # Import the custom warning class
import warnings

def solve_linear_system_with_regularization(A, bb):
    regularization_range = np.logspace(-20, 15, 36)  # Regularization parameter range
    best_residual_norm = np.inf
    best_solution = None
    best_reg_param = None
    consecutive_error_increases_regularized_solution = 0
    with warnings.catch_warnings():
        # Convert warnings to exceptions
        warnings.simplefilter("error", MatrixRankWarning)
        try:
            parameters = la.spsolve(A, bb)
            return parameters
        except MatrixRankWarning as e:
            # If the matrix is singular, apply Tikhonov regularization
            if 'singular' in str(e):
                print("Matrix is singular. Applying Tikhonov regularization in an attempt to solve anyways...")
                for reg_param in regularization_range:
                    try:
                        print('trying with regularization parameter: ' + str(reg_param))
                        # Try solving the regularized system
                        
                        # Create a sparse identity matrix with the same shape as A
                        identity_matrix = identity(A.shape[0], format='csr')
                        A_reg = A + reg_param * identity_matrix
                        
                        x_reg = la.spsolve(A_reg, bb)  # Regularized solution
                        
                        # Calculate the dot product result
                        dot_product_result = np.dot(A.toarray(), x_reg)
                        
                        # Calculate the residual norm (error) of the solution
                        residual_norm = np.linalg.norm(dot_product_result - bb)    
                        # Check if the residual norm is increasing
                        if residual_norm > best_residual_norm:
                            consecutive_error_increases_regularized_solution += 1
                        else:
                            consecutive_error_increases_regularized_solution = 0
                        
                        # Update best solution if the residual norm is smaller
                        if residual_norm < best_residual_norm:
                            best_solution = x_reg
                            best_reg_param = reg_param
                            best_residual_norm = residual_norm
    
                    except MatrixRankWarning:
                        # Skip if regularization causes singularity
                        continue
                    # Break out of the loop if residual_norm is increasing three times
                    if consecutive_error_increases_regularized_solution >= 3:
                        print('The error from adding more regularization seems to be increasing for the last 3 increases of the regularization parameter')
                        break
    
                if best_solution is None:
                    raise Warning("Unable to find a suitable regularization parameter.")
    
                print("The system of equations has been solved with a regularization parameter of:", best_reg_param)
                return best_solution
    
            else:
                # If it's another type of error, raise it
                # I never reach this point... 
                raise e

我考虑过添加其他东西来让 except 行捕获像

except (MatrixRankWarning, ??) as e:

这样的东西，但我不知道在“??”处放什么捕获此“Windows 致命异常：访问冲突”

Answer 1

避免错误的解决方案（不捕获它，因为这是不可能的）是：

scipy.sparse.linalg..spsolve(A_reg, bb, permc_spec='NATURAL')

而不是默认值：

permc_spec='COLAMD'. 

我不知道为什么他们在这种情况下表现不同。