Question

我查看过去关于tridiagonals的问题，但似乎没有人遇到过我遇到的问题。我试图使用scipy.sparse.spdiags为非均匀Poisson方程形成三对角刚度矩阵，但结果似乎没有接收矩阵。

def Poisson_Stiffness(x0):

N = len(x0) - 1 #THE AMOUNT OF ELEMENTS (NOT THE AMOUNT OF POINTS) x0, x1, ... , x_N

h = np.zeros(N)
a = np.zeros(N+1)
b = np.zeros(N)

for i in range(N):
    h[i] = x0[i+1] - x0[i] #Length of each nonuniform element

a[0] = 1/h[0]
for i in range(1,N):
    a[i] = 1/h[i] + 1/h[i-1] #Main Diagonal of stiffness matrix
a[N] = 1/h[N-1]

for i in range(N):
    b[i] = -1/h[i] #Upper and lower diagonal of stiffness matrix.


Tridiagonal_Data = np.array([[a],[b],[b]])
Positions = [0, 1, -1]

Stiffness_Matrix = scipy.sparse.spdiags(Tridiagonal_Data,Positions,N+1,N+1)

print Stiffness_Matrix

因此，x0 = [0,0.3,0.4,0.7,1];我得到刚度矩阵：

Jamess-MBP:Poisson jamesmalone$ python Poisson1d.py
(0, 0)  [  3.33333333  13.33333333  13.33333333   6.66666667   3.33333333]
(1, 0)  [-3.33333333 -10.         -3.33333333 -3.33333333]

我的问题是为什么它会像这样出来而不是以矩阵形式出现？

我尝试更改数据类型以查看是否存在问题，但我会收到错误，例如（for .toarray（））：

Jamess-MBP:Poisson jamesmalone$ python Poisson1d.py
Traceback (most recent call last):
  File "Poisson1d.py", line 33, in <module>
    Poisson_Stiffness([0,0.3,0.4,0.7,1])
  File "Poisson1d.py", line 29, in Poisson_Stiffness
    Stiffness_Matrix = scipy.sparse.spdiags(Tridiagonal_Data,Positions,N+1,N+1).toarray()
  File "/Users/jamesmalone/anaconda/lib/python2.7/site-packages/scipy/sparse/base.py", line 637, in toarray
return self.tocoo().toarray(order=order, out=out)
  File "/Users/jamesmalone/anaconda/lib/python2.7/site-packages/scipy/sparse/coo.py", line 275, in toarray
B.ravel('A'), fortran)

RuntimeError: internal error: failed to resolve data types

提前致谢。

Answer 1

尝试使用scipy.sparse.diags。我还清理了你的代码，因为你没有利用numpy的优势（广播）与for循环。还根据PEP8清理了一些格式：

from scipy.sparse import diags

x0 = np.array(x0)
N = len(x0) - 1

h = x0[1:] - x0[:-1]

a = np.zeros(N+1)
a[0] = 1/h[0]
a[1:-1] = 1/h[1:] + 1/h[:-1]
a[-1] = 1/h[-1]

b = -1/h

data = [a.tolist(), b.tolist(), b.tolist()]
positions = [0, 1, -1]

stiffness_matrix = diags(data, positions, (N+1, N+1))

print stiffness_matrix.toarray()

使用x0 = [0, 0.3, 0.4, 0.7, 1]，这会产生

[[  3.33333333  -3.33333333   0.           0.           0.        ]
 [ -3.33333333  13.33333333 -10.           0.           0.        ]
 [  0.         -10.          13.33333333  -3.33333333   0.        ]
 [  0.           0.          -3.33333333   6.66666667  -3.33333333]
 [  0.           0.           0.          -3.33333333   3.33333333]]

使用Python的三对角矩阵

1 个答案: