线性共轭梯度法python_python中的预条件共轭梯度与线性化器
[作业]我要用预处理的共轭梯度法求解线性方程组Ax=b，我使用scipy.sparse.linalg先决条件。A是稀疏对称162×162矩阵。因为spilu给出了A的逆的近似值，比如M近似A，所以spilu(A)给出了M^-1，这是预处理条件。我发现我们可以在python共轭梯度函数中直接给出预处理条件，但是我下面的代码不起作用。在M_inverse=scipy.sparse.linalg.spilu(A)
M2=scipy.sparse.linalg.LinearOperator((162,162),M_inverse.solve)
x3=scipy.sparse.linalg.cg(A,b,M2)
TypeError Traceback (most recent call last)
in ()
----> 1 x3=scipy.sparse.linalg.cg(A,b,M2)
/Users/ruobinghan/anaconda/lib/python3.4/site-packages/scipy/sparse/linalg/isolve/iterative.py in cg(A, b, x0, tol, maxiter, xtype, M, callback)
/Users/ruobinghan/anaconda/lib/python3.4/site-packages/scipy/sparse/linalg/isolve/iterative.py in non_reentrant(func, *a, **kw)
83 try:
84 d['__entered'] = True
---> 85 return func(*a, **kw)
86 finally:
87 d['__entered'] = False
/Users/ruobinghan/anaconda/lib/python3.4/site-packages/scipy/sparse/linalg/isolve/iterative.py in cg(A, b, x0, tol, maxiter, xtype, M, callback)
219 @non_reentrant
220 def cg(A, b, x0=None, tol=1e-5, maxiter=None, xtype=None, M=None, callback=None):
--> 221 A,M,x,b,postprocess = make_system(A,M,x0,b,xtype)
222
223 n = len(b)
/Users/ruobinghan/anaconda/lib/python3.4/site-packages/scipy/sparse/linalg/isolve/utils.py in make_system(A, M, x0, b, xtype)
108 x = zeros(N, dtype=xtype)
109 else:
--> 110 x = array(x0, dtype=xtype)
111 if not (x.shape == (N,1) or x.shape == (N,)):
112 raise ValueError('A and x have incompatible dimensions')
TypeError: float() argument must be a string or a number, not 'LinearOperator'
另外，这个问题提示我需要使用linearerator接口，我不明白linearerator到底在做什么，为什么我们需要它。在
任何建议都将不胜感激！
提前谢谢！在