In many engineering problems, sparse matrices arise: Electrical engineering, Chemical engineering, Civil engineering (structural calculations), Finite element methods (FEM), etc.
Below is an example of a sparse matrix:
The question is: How to solve this array in Python?
Library to be used: Scipy and numpy.
Both scipy and numpy have linalg (linear algebra). scipy is more complete
Attempt to solve
import numpy as np
from scipy.sparse.linalg import spsolve
from scipy.sparse import csr_matrix
-----INPUT-----
F = 1000
n11 = F / 3
n12 = 2 * F / 3
xa = 0.2
alfa1 = 0.8
alfa2 = 0.9
alfa3 = 0.1
----- EXPRESSIONS -----
Data from the rows (row) and columns (col) of the matrix
row = np.array([0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 10, 10, 11, 15])
col = np.array([0, 9, 2, 10, 2, 11, 0, 3, 0, 1, 4, 2, 5, 3, 6, 6, 9, 4, 7, 10, 5, 8, 11, 3, 9, 4, 10, 5, 15])
data = np.array(
[-1, 1, -1, 1, -1, 1, -(1 - xa), 1, xa, -1, 1, -xa, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, alfa1, -1, alfa2, -1,
alfa3, -1])
Creating the sparse matrix
csr_matrix() = create sparse matrix in row (rows)
A = csr_matrix((data, (row, col)), shape=(29, 29)).toarray()
if you print A generates matrix with zeros - OK
print(A)
1 Question:
How to declare b?
Not is:
b = np.array([-n11, - n12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
=> it’s wrong. Do I only want rows and columns that have values?
2 - How to declare x = A-1 * b ?? THIS IS MY PROBLEM 
3 - The Scipy documentation doesn’t show you how to do this. Shows only simple and straightforward problems.
4 - I want to solve x and print:
m1 = x[0]
m2 = x[1]
m3 = x[3]
print(’ the value of m1 is = ‘. m1)
print(’ the value of m2 is = ‘. m2)
print(’ the value of m2 is = '. m2)
Anyone know how to solve this problem the way row, col, data was assembled?