如何在 Python 的 SciPy 中更改稀疏矩阵中的元素？

Question

I have built a small code that I want to use for solving eigenvalue problems involving large sparse matrices. It's working fine, all I want to do now is to set some elements in the sparse matrix to zero, ie the ones in the very top row (which corresponds to implementing boundary conditions). I can just adjust the column vectors (C0, C1, and C2) below to achieve that. However, I wondered if there is a more direct way. Evidently, NumPy indexing does not work with SciPy's sparse package.

import scipy.sparse as sp
import scipy.sparse.linalg  as la
import numpy as np
import matplotlib.pyplot as plt

#discretize x-axis
N = 11
x = np.linspace(-5,5,N)
print(x)
V = x * x / 2
h = len(x)/(N)
hi2 = 1./(h**2)
#discretize Schroedinger Equation, i.e. build 
#banded matrix from difference equation
C0 = np.ones(N)*30. + V
C1 = np.ones(N) * -16.
C2 = np.ones(N) * 1.
diagonals = np.array([-2,-1,0,1,2])
H = sp.spdiags([C2, C1, C0,C1,C2],[-2,-1,0,1,2], N, N)
H *= hi2 * (- 1./12.) * (- 1. / 2.)
#solve for eigenvalues
EV = la.eigsh(H,return_eigenvectors = False)

#check structure of H
plt.figure()
plt.spy(H)
plt.show()

This is a visualisation of the matrix that is build by the code above. I want so set the elements in the first row zero.

Answer 1

As suggested in the comments, I'll post the answer that I found to my own question. There are several matrix classes in in SciPy's sparse package, they are listed here . One can convert sparse matrices from one class to another. So for what I need to do, I choose to convert my sparse matrix to the class csr_matrix, simply by

H = sp.csr_matrix(H)

Then I can set the elements in the first row to 0 by using the regular NumPy notation:

H[0,0] = 0
H[0,1] = 0
H[0,2] = 0

For completeness, I post the full modified code snippet below.

#SciPy Sparse linear algebra takes care of sparse matrix computations
#http://docs.scipy.org/doc/scipy/reference/sparse.linalg.html
import scipy.sparse as sp
import scipy.sparse.linalg  as la

import numpy as np
import matplotlib.pyplot as plt

#discretize x-axis
N = 1100
x = np.linspace(-100,100,N)
V = x * x / 2.
h = len(x)/(N)
hi2 = 1./(h**2)

#discretize Schroedinger Equation, i.e. build 
#banded matrix from difference equation
C0 = np.ones(N)*30. + V
C1 = np.ones(N) * -16.
C2 = np.ones(N) * 1.

H = sp.spdiags([C2, C1, C0, C1, C2],[-2,-1,0,1,2], N, N)
H *= hi2 * (- 1./12.) * (- 1. / 2.)
H = sp.csr_matrix(H)
H[0,0] = 0
H[0,1] = 0
H[0,2] = 0

#check structure of H
plt.figure()
plt.spy(H)
plt.show()

EV = la.eigsh(H,return_eigenvectors = False)

Answer 2

Using lil_matrix is much more efficient in scipy to change elements than simple numpy method.

H = sp.csr_matrix(H)
HL = H.tolil()
HL[1,1] = 5  # same as the numpy indexing notation
print HL
print HL.todense() # if numpy style matrix is required
H = HL.tocsr()    # if csr is required