Solve a linear matrix equation, or system of linear scalar equations.
Computes the “exact” solution, x, of the well-determined, i.e., full rank, linear matrix equation ax = b.
a : array_like, shape (M, M)
b : array_like, shape (M,) or (M, N)
x : ndarray, shape (M,) or (M, N) depending on b
solve is a wrapper for the LAPACK routines dgesv and zgesv, the former being used if a is real-valued, the latter if it is complex-valued. The solution to the system of linear equations is computed using an LU decomposition [R50] with partial pivoting and row interchanges.
a must be square and of full-rank, i.e., all rows (or, equivalently, columns) must be linearly independent; if either is not true, use lstsq for the least-squares best “solution” of the system/equation.
|[R50]||(1, 2) G. Strang, Linear Algebra and Its Applications, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, pg. 22.|
Solve the system of equations 3 * x0 + x1 = 9 and x0 + 2 * x1 = 8:
>>> a = np.array([[3,1], [1,2]]) >>> b = np.array([9,8]) >>> x = np.linalg.solve(a, b) >>> x array([ 2., 3.])
Check that the solution is correct:
>>> (np.dot(a, x) == b).all() True