python sparse gmres 混淆了输入参数

Question

我有一个使用 scipy.sparse.linalg.gmres 求解稀疏线性系统的简单代码

W, S  = load_data()
M = normalize(W.T.astype('float64'),'l1')
S = normalize(S.astype('float64'),'l1')
rhs = S[cat_id,:].T
print M.shape
print rhs.shape 
p = gmres(M, rhs)

函数 load_data 从 matlab 的 .mat 文件中加载两个稀疏矩阵并省略。输出令人惊讶:

(150495, 150495)
(150495, 1)
Traceback (most recent call last):
  File "explain.py", line 54, in <module>
    pr(1)
  File "explain.py", line 42, in pr
    p = gmres(M, rhs)
  File "<string>", line 2, in gmres
  File "/usr/lib/python2.7/dist-packages/scipy/sparse/linalg/isolve/iterative.py", line 85, in non_reentrant
    return func(*a, **kw)
  File "/usr/lib/python2.7/dist-packages/scipy/sparse/linalg/isolve/iterative.py", line 418, in gmres
    A,M,x,b,postprocess = make_system(A,M,x0,b,xtype)
  File "/usr/lib/python2.7/dist-packages/scipy/sparse/linalg/isolve/utils.py", line 78, in make_system
    raise ValueError('A and b have incompatible dimensions')
ValueError: A and b have incompatible dimensions

但是我已经按照文档运行了gmres

A : {sparse matrix, dense matrix, LinearOperator}

The real or complex N-by-N matrix of the linear system.

b : {array, matrix}

Right hand side of the linear system. Has shape (N,) or (N,1).

我只是不明白这段代码有什么问题，希望有任何想法。

Answer 1

gmres 的参数b不能是稀疏矩阵；它可以是一个 numpy 数组或矩阵。尝试

p = gmres(M, rhs.A)