numpy Linear algebra with np.linalg Solve linear systems with np.solve
Example
Consider the following three equations:
x0 + 2 * x1 + x2 = 4
x1 + x2 = 3
x0 + x2 = 5
We can express this system as a matrix equation A * x = b with:
A = np.array([[1, 2, 1],
[0, 1, 1],
[1, 0, 1]])
b = np.array([4, 3, 5])
Then, use np.linalg.solve to solve for x:
x = np.linalg.solve(A, b)
# Out: x = array([ 1.5, -0.5, 3.5])
A must be a square and full-rank matrix: All of its rows must be be linearly independent. A should be invertible/non-singular (its determinant is not zero). For example, If one row of A is a multiple of another, calling linalg.solve will raise LinAlgError: Singular matrix:
A = np.array([[1, 2, 1],
[2, 4, 2], # Note that this row 2 * the first row
[1, 0, 1]])
b = np.array([4,8,5])
Such systems can be solved with np.linalg.lstsq.
