“nan”而不是Python输出中的矩阵元素？

Question

我正在尝试计算这个稀疏矩阵问题 Au=f 的近似解，但我在矩阵的输出中得到“nan”而不是矩阵元素，尽管输入矩阵都包含 np.float64。 我不明白我哪里错了。

这是我的代码：-

import numpy as np
import scipy
from scipy.sparse import coo_matrix
from scipy.sparse import random

#Defining a function that takes N as an input

def our_func (N) :

  #Taking the given values of parameters h and k
  h =  1/N
  k = (29*(np.pi))/2
   
  #Defining initial input matrix with domensions N+1
  I = np.empty([N+1,N+1],  dtype=np.float64) 
  #[REF :- https://www.geeksforgeeks.org/how-to-create-an-empty-matrix-with-numpy-in-python/]
  print("datatype of I is :-")
  print(I.dtype)

  #Generating the matrix A in coo sparse format
  A_coo = coo_matrix(I).reshape((N+1,N+1))
  print("datatype of A_coo is :-")
  print(A_coo.dtype)

  #Converting the matrix A from coo sparse format to CSR sparse format 
  A = A_coo.tocsr().reshape((N+1,N+1))
  print("datatype of A is :-")
  print(A.dtype)
 
  # Creating an empty storage array for the right side of our equation Au=f
  f = np.empty((N+1), dtype=np.float64)

  #The rows of matrix A and f are defined as :-
  A[0,0] = 1    #for i==j==0
  A[N,N] = 1    #for i==j==N
  f[N] = 1      #for i==N
  f[0] = 0      #for i==0
  for i in range (int(N)) :
    for j in range (int(N)) :
        A[i,1] = 2 - ((h**2)*(k**2)) 
        A[i,i+1] = -1
        A[i,i-1] = -1
        A[i,j] = 0      #for i!==j
  
  #Our function Returns matrix A and f, with matrix A in sparse storage format
  return A, f

# Defining a new function using the function scipy.sparse.linalg.spsolve 
# to solve the sparse matrix-vector problem: Au=f

def our_solution(N):
  A,f = our_func(N)
  our_sparse_matrix = scipy.sparse.linalg.spsolve(A,f)
  return our_sparse_matrix

# Using this defined function to compute the approximate solution for our 
# problem, for N=10, N=100, and N=1000.
approx_sol_1 = our_solution(10)
print("approx_sol_1 is :- ")
print(approx_sol_1)

Answer 1

运行较小的函数

N

：

In [4]: A,f = our_func(10)
datatype of I is :-
float64
datatype of A_coo is :-
float64
datatype of A is :-
float64
C:\Users\14256\miniconda3\lib\site-packages\scipy\sparse\_index.py:103: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.
  self._set_intXint(row, col, x.flat[0])

它警告我们，单独设置稀疏

csr

数组的元素效率不高。

In [5]: A
Out[5]: 
<11x11 sparse matrix of type '<class 'numpy.float64'>'
    with 103 stored elements in Compressed Sparse Row format>

请注意，矩阵并不是特别稀疏，121 个可能值中有 103 个非零。

In [6]: A.A
Out[6]: 
array([[  0.        ,  -1.        ,   0.        ,   0.        ,
          0.        ,   0.        ,   0.        ,   0.        ,
          0.        ,   0.        ,  -1.        ],
       [ -1.        , -18.75084325,  -1.        ,   0.        ,
          0.        ,   0.        ,   0.        ,   0.        ,
          0.        ,   0.        ,   0.        ],...

它可以被修剪，去掉很多0。

In [10]: A.eliminate_zeros()
In [11]: A
Out[11]: 
<11x11 sparse matrix of type '<class 'numpy.float64'>'
    with 28 stored elements in Compressed Sparse Row format>